#115 Revisiting the proof of the Riemann Hypothesis for it is false as there are counterexamples; new textbook: "Mathematical-Physics (p-adic primer) for students of age 6 onwards"
a_plutonium
January of 2007 about
the Riemann Hypothesis. But I expect a bright 6 year old to understand
at the bottom of this
post what I summarize as the Riemann Hypothesis.
#5# book "Correcting Present Day Mathematics...."; chapter (4) proving
Riemann Hypothesis
1
From: a_plutonium
Date: Sat, Jan 20 2007 2:29 pm
Email: "a_plutonium" <a_pluton...@hotmail.com>
Groups: sci.math, sci.physics
I did the below two alleged proofs of Riemann Hypothesis under the old
delusion of Natural Numbers were Finite Integers and the assumption
that the Peano Axioms was a consistent set. But that is false for the
Peano Axioms are self contradictory and must be trashcanned.
This is what I said.
------
TWO PROOFS OF THE RIEMANN HYPOTHESIS
PROOFS: Two proofs of the Riemann Hypothesis follows as A
and B.
Proof (A) is a geometrical proof. It was proved that the Riemann
Hypothesis is equivalent to the following-- the Moebius function mu of
x, m(x), and adding-up the values of m(x) for all n less than or equal
to N giving M(N). Then M(N) grows no faster than a constant multiple k
of (N^1/2)(N^E) as N goes to infinity (E is arbitrary but greater than
0). Figure1, by setting-up a logarithmic spiral in a rectangle of
whirling squares where the squares are the sequences:
1,1,2,3,5,8,13,21,34,55,89, . . . 2,2,4,6,10,16,26, . . .
3,3,6,9,15,24,39, . . . then every number appears in at least one of
these sequences because every number will start a sequence. Since all
numbers are represented uniquely by prime factors (the unique prime
factorization theorem or called the fundamental theorem of arithmetic)
and The Prime Number Theorem: the distribution of prime numbers is
governed by a logarithmic function, where (An/n)/(1/Ln of n) tends to
1
as n increases, where An denotes the number of primes below the
positive integer n, and where An/n is called the density of the primes
in the first n positive integers. The density of the primes, An/n, is
approximated by 1/(Ln of n), and as n increases, the approximation
gets
better. The distribution of prime numbers is governed by a
logarithmic function where these two math concepts-- one of prime
numbers, and the other, logarithms seem unconnected at first
appearance, but in reality they are totally connected. Geometrically,
the logarithmic spiral exhausts every positive integer, see figure 1.
The area of the rectangles containing the logarithmic spiral is always
greater, since the spiral is always inside the rectangles. Thus the
Moebius function k (N^1/2)(N^E) is satisfied since the area of the
logarithmic spiral is less than the rectangle whose area represents
the
number N, and whose sides represent its factors. The area of a
logarithmic spiral is represented by A=(r)(e^(Hj)) , and so depending
on where the point of origin for the spiral is taken rsubO determines
k, and depending on the value of H, H determines the E value for N,
when H=0 then the curve is a circle. The logarithmic spiral inside
rectangles of whirling squares implies that for any number N then
N^1/2
is the limit of the factors for N, for example, given the number 28,
then 28^1/2 = 5.2915. . and so looking for the factors of 28, it is
useless to try beyond 5 because the factors repeat, 4x7 then repeats
as
7x4. But if the Moebius function was false then there must exist a
number M such that M^1/2 is not the limit of the factors for M and the
spiral is outside of the square, which is impossible, hence the
Moebius
function is true. Therefore the Riemann Hypothesis is proved. Q.E.D.
My second proof (B) of the Riemann Hypothesis uses a reductio
ad absurdum argument. Euler proved that a formula encoding the
multiplication of primes was equal to the zeta function. Euler's
formula in complex variable form is as follows:
(1/(1-(1/(2^c))))x(1/(1-(1/(3^c))))x(1/(1-(1/(5^c))))x(1/(1-(1/
(7^c))))x
(1/(1-(1/(11^c))))x . . . , where c is a complex variable, c=u+iv. The
Riemann zeta function is as follows. Re(c) =
1+(1/(2^c))+(1/(3^c))+(1/(4^c))+. . . , where c is a complex variable,
c=u+iv. Euler's formula involves multiplication of terms and the
Riemann zeta function involves addition of terms of a sequence. Taking
Re(c) > 0, suppose the Riemann Hypothesis is false then there is a 0
such that Re(c)=0 and c not equal 1/2 +iy, which implies there is
another 0 which is not on the 1/2 real line. Which means another real
number other than 1/2 works as an exponent resulting in a zero for the
Riemann zeta function, and a zero in the Euler formula. Thus, Riemann
zeta function subtract Euler formula must equal zero. This implies
for
any other real number exponent, either rational or irrational numbers,
such as for example the rational exponents: 1/3,1/4,1/5, . . . (Note:
any other exponent y/x , where y and x are Real numbers and where the
Real number of A^(y/x) such that y not equal 1, immediately transforms
to a number A^y(1/x), so that exponents with a 1 in the numerator
entail all of the Real exponents). To make clear of the above, for
example, 2^2/3 is 4^1/3. So then back to the proof. Then for exponent
1/3 there has to exist a number M not equal 0 where (M+M+M)^1/M =
(MXMXM)^1/M = M. Then for exponent 1/4 there has to exist a number M
not equal 0 where (M+M+M+M)^1/M = (MXMXMXM)^1/M = M, and so on.
Including the infinite number of cases where the x denominator is
irrational are impossible. Only the real number 1/2 works since 2 does
not equal 0, and (2+2)^1/2 = (2X2)^1/2 = 2, and so (2+2)^1/2
- (2X2)^1/2 = 0. In all of Reals and the Complex numbers, 2 is the
only number N which has the encoding ((N+N)^1/N) = ((NxN)^1/N) = N.
Unlike 0, the number 2, its sum equals its product and where the sum
and product is a new number 4. If RH were false, then another number
other than 2 would satisfy a generalized encoding formula ((N+N)^1/N)
= ((NxN)^1/N) = N. False, hence the proof. QED
--------
I think the above was a valiant attempt. But armed with my new
knowledge that the Natural-Numbers are this very larger set that
stretches up to Infinite Integers and ends with the number ....
9999999.
--- end of old January post ---
The Riemann Hypothesis explained to a 6 year old is the idea that
the Prime Numbers of the Counting Numbers are located on the 1/2
Real Line. This problem was considered the most important mathematical
problem because so many other "proofs" depended on the Riemann
Hypothesis. Bernhard Riemann gave his Hypothesis in the 1850s.
But here again the trouble with this conjecture and why noone could
prove
it was that they did not have a clear understanding of what the
Natural Numbers
and Primes and Counting Numbers were. When you have a foggy notion of
what you are working with, it is impossible to prove much about them.
If Riemann and his followers knew that the Natural Numbers were P-
adics
and formed a semicircle on a sphere and not a straight line in
Euclidean
geometry. And if they knew that the Natural Numbers start with 0 then
1
and go all the way to ....9999999999 and if they knew that the last
prime
number in the entire world was ....999999997.
Then they would have known that the Riemann Hypothesis was false.
And one counterexample is the number .....99999997 which is the
world's
largest prime number. And it does not lie on a straight-line of
Euclidean
Geometry but lies in a curved line of Elliptic Geometry.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
a_plutonium
Now when I posted my Riemann Hypothesis proof in 1993 to the sci.math
newsgroup
there was a math student at Princeton University who complained that
my proof did not
work for the negative integers. At that time I really did have a
waterproof answer for him
and at that time I did not have P-adic counterexamples.
But I bring up that past history because the negative integers
question on the Riemann Hypothesis
has become clearer.
You see, the Riemann Hypothesis is Elliptic Geometry mathematics and
that means Positive
P-adics and no negative numbers. In other words, the old Riemann
Hypothesis by Bernhard
Riemann who I have immense respect of his genius, is a Hypothesis that
is grounded solely
in Elliptic Geometry and Positive P-adics. It does not exist or have
any relevancy in negative
integers which would be the Negative P-adics and Hyperbolic Geometry.
And that makes sense and commonsense for a prime number is never the
multiplication of
two negative numbers for that is a positive number. So the idea that
Riemann Hypothesis covered
not only positive realm but negative realm was a bogus and erroneous
conception. The Riemann
Hypothesis lives only in a positive realm which is Elliptic Geometry
and thus the positive
P-adics.
Now I doubt any bright 6 year old will understand what I said above,
but some parts of this
book cannot be accessible to everyone such as 6 year olds. For parents
trying to tutor their
6 year old, it is sufficient to tell them that Bernhard Riemann' s
Hypothesis was extended into
the negative integers, but they had no real justification for doing
that other than that they were
in the wrong geometry of Euclid from the start, whereas they should
have been in Elliptic geometry
where there are no negative numbers.
David R Tribble
>> The Riemann Hypothesis explained to a 6 year old is the idea that
>> the Prime Numbers of the Counting Numbers are located on the 1/2
>> Real Line. This problem was considered the most important mathematical
>> problem because so many other "proofs" depended on the Riemann
>> Hypothesis. Bernhard Riemann gave his Hypothesis in the 1850s.
>> But here again the trouble with this conjecture and why noone could
>> prove it was that they did not have a clear understanding of what the
>> Natural Numbers and Primes and Counting Numbers were.
>> When you have a foggy notion of what you are working with, it is
>> impossible to prove much about them.
>
Can I give the eulogy at your funeral? I'd especially like to
quote that last sentence of yours.
Dik T. Winter
> Archimedes Plutonium wrote:
..
> > The Riemann Hypothesis explained to a 6 year old is the idea that
> > the Prime Numbers of the Counting Numbers are located on the 1/2
> > Real Line.
Do you *know* what the Riemann Hypothesis is?
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
a_plutonium
Good to see you back Dik!
Go ahead and give me a lesson on the Riemann Hypothesis, especially in
geometrical
format, not so much the zeta-function. I need more geometry clarity on
RH.
Major Quaternion Dirt Quantum
seriously, new thought on the same old problem
is *always* appreciated;
the more naieve it is, the better.
Archimedes Plutonium
a_plutonium wrote:
> a_plutonium wrote:
>
>>Dik T. Winter wrote:
>>
>>>In article <1192421170....@v29g2000prd.googlegroups.com> a_plutonium <a_plu...@hotmail.com> writes:
>>> > Archimedes Plutonium wrote:
>>>..
>>> > > The Riemann Hypothesis explained to a 6 year old is the idea that
>>> > > the Prime Numbers of the Counting Numbers are located on the 1/2
>>> > > Real Line.
>>>
>>>Do you *know* what the Riemann Hypothesis is?
>>>--
>>>dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
>>>home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
>>
>>Good to see you back Dik!
>>
>>Go ahead and give me a lesson on the Riemann Hypothesis, especially in
>>geometrical
>>format, not so much the zeta-function. I need more geometry clarity on
>>RH.
>>
>
>
> The reason Dik is concerned is because the standard answer (even a 6
> year old)
> is that the nontrivial zeroes line on the 1/2 straight line, not the
> primes.
>
> But, when the Primes are part of the set that is 1,2,3,......,
> 999999.....9999999
>
> where 9999.....99999 is the last and largest integer and
> 99999....99997 is the
> last and largest Prime number.
>
> Then, is not the proper interpretation of the Riemann Hypothesis that
> the Primes are
> on the 1/2 Real line.
>
> That is why I want a geometrical interpretation. I want the sharpest
> counterexamples
> to the Riemann Hypothesis.
>
> The whole notion that the zeta function makes any sense was under the
> old picture
> that Finite Integers made sense.
>
> There are an infinite number of primes in the Counting Numbers that
> look like these
> 3,5,7
>
> So is the Zeta Function even meaningful and worse yet when Riemann
> attached the complex
> plane.
>
> The essence of the Riemann Hypothesis is the primes. But the primes
> are this set
> 2,3,5,7,....... , 99999.....9999997
>
> And the Riemann Hypothesis with its Zeta Function was never built to
> handle that set.
>
> When you run an exponent on numbers like 999999......999997 you end up
> with a number
> smaller.
>
> And there is no zero number in the P-adics as Counting Numbers for it
> is imaginary.
>
> So what I am saying is that unlike the proof that Fermat's Last
> Theorem is false with
> counterexamples of the idempotents. Where much of FLT is retained in
> offering the counterexamples.
> Unlike FLT, in the Riemann Hypothesis the situation degenerates to the
> point where we
> do not even have a function to work with. In other words we cannot
> even use the function
> to offer up a counterexample.
>
> Now there is a P-adic Zeta Function and the function becomes
> continuous. So that the P-adic
> Zeta Function makes more sense than the Real Zeta Function.
>
> RH is false, just as FLT is false because the Natural Numbers are the
> set 1,2,3,..... , 9999...999
>
> And because the Natural Numbers are that set-- call them the Decimal P-
> adics, that the old
> Riemann Hypothesis with its Zeta Function and its nontrivial zeroes on
> the 1/2 Real line
> no longer make any sense.
>
> When you multiply in the Zeta Function for the Decimal P-adics, you
> get no zeroes.
>
> So I have more thinking to do on this to make it clearer in my mind.
>
> But for a 6 year old, I would rather say that the Riemann Hypothesis
> was an attempt to
> see the distribution of the Primes on the 1/2 Real line.
>
> So do we toss out the entire Zeta Function as the counterexample? I do
> not know. In FLT
> we just enter the idempotents as counterexample. In RH, it becomes
> rough because
> the function no longer even fits the numbers we are to work with.
>
> And the huge problem of a Hypothesis that wants to work in both kinds
> of numbers of the
> Reals and the primes which do not exist in the Reals, for the primes
> exist in those leftward
> infinite strings called P-adics.
>
> So unlike FLT where we retain most of the Conjecture and offer up a
> counterexample, here
> with the Riemann Hypothesis we have to chuck and toss out the function
> we are asked to
> work with.
>
> Note to Dik Winter: you told me in the mid 1990s that if I get the
> operations defined on
> "my P-adics" that you would then tell me what its algebra was such as
> field or ring. Well I
> have those operations defined for the Decimal P-adics, so could you
> kindly tell what the
> algebra is over my p-adics? I am guessing it is either a no-algebra or
> a completed-field
> matching the Reals.
Dik T. Winter
...
> Note to Dik Winter: you told me in the mid 1990s that if I get the
> operations defined on "my P-adics" that you would then tell me what
> its algebra was such as field or ring. Well I have those operations
> defined for the Decimal P-adics, so could you kindly tell what the
> algebra is over my p-adics? I am guessing it is either a no-algebra or
> a completed-field matching the Reals.
It has also been shown to you in the mid 1990s that the 10-adics are the
cartesian product of the 2-adics and the 5-adics. They are not a field
because there are zero-divisors. You already know that in the 10-adics
there are two idem-potents not equal to either 0 or 1. Call them a and
b, it is easy to show that (a - 1) * a = (b - 1) * b = 0.
In general, each 10-adic can be written as a pair (p, q) where p is a
2-adic and q a 5-adic. One of the idempotents a and b corresponds to
the pair (1, 0) and the other to the pair (0, 1).
a_plutonium
Would you care to comment not on the 10-adics.
Would you care to comment on "All Possible Digit Arrangements" for
......000001 to ....99999999999
Where the operations of these numbers are not P-adics.
Where the operations are borrowed from Reals between 0 and 1 in Reals
and
the final answer of any operation is what digits do not change such
as
square root of ....9999999 has two final answer so 99999....99999 and
316.....
Where every operation on Reals between 0 and 1 is transfered to every
operation
of these Decimal P-adics.
So I have something vastly different from the 10-adics for which you
cite above.
So I am asking you, whether these Decimal P-adics also transfer all
the Field
Algebra properties for which the Reals possess? Keep in mind that
these
Decimal P-adics do not end with ....999999 but continue with (pi) as
South Pole
and come back around a circle to the North Pole of 2(pi).
Yes, I agree to your above for the "dressed up Reals pretending to be
P-adics"
Mine are totally different in that they are not Reals but having the
same operations
as Reals.
Care to comment on that Dik.
P.S. someone has found a way of blocking my posts from ever reaching
the newsgroup
so that once I send this post, the thread increases by one more
number, but this post
never actually shows up in the thread for anyone to read. As the above
#135
never appeared and #133 appeared almost 12 hours later and only after
I reposted #133
from a different ISP. So I am afraid some clowns have utilized some
method where a post
never shows up on sci.math. It maybe that Google is fixing something,
but why would
another ISP not have the trouble?
a_plutonium
Would you care to comment not on the 10-adics.
Archimedes Plutonium
Archimedes Plutonium
Jesse F. Hughes
> Either Google is down or we have a censor in our midst
You're paranoid. All of your posts are appearing downstream of Google
just fine.
Honestly, don't you think that it's a little silly to suppose someone
is messing with your posts?
--
Jesse F. Hughes
"I thought it relevant to inform that I notified the FBI a couple of
months ago about some of the math issues I've brought up here."
-- James S. Harris gives Special Agent Fox a new assignment.
Archimedes Plutonium
as a^3 + b^3 = c^3 and where we are dealing only with P-adics
as the Natural Numbers as All Possible Digit Arrangements.
We are not dealing with Reals mixed with P-adics in one equation.
So that the a, b, c, and 3 are all P-adics of infinite leftward
strings, different and distinct from Reals.
So that FLT is false because the above equation is satisfied by
a= ...9977392256259918212890625 b= ...0022607743740081787109376
c = .....000001 and exponent is ....000003
But the situation breaks down and dissolves when you look at the
Riemann Hypothesis with its Zeta Function and its various equivalent
statements. We no longer have "intelligible mathematics". What we have
is a function that uses both infinite rightward strings with infinite
leftward strings.
It is like trying to graft a elm tree with cells from a human to give
an analogy.
What we have in the Riemann Zeta Function is the multiplication
of infinite rightward strings Reals with infinite leftward strings
of P-adics where the last prime in the world is ....9999997.
So what the Zeta Function manages to spit out or produce are numbers
which are infinite in both directions such as
......99999999999decimalpoint55555555.......
These are meaningless numbers
We cannot do mathematics in a function or equation where we intertwine
P-adics with Reals and pretend to have a meaningful result.
It is easy for me to find counterexamples for FLT because I am working
with only P-adics, but with the Riemann Zeta Function I have P-adics
multiplied by Reals and what I end up with such as the nontrivial zeroes
are not 0.00000....... but rather ....0000000decimalpoint000000......
or ....11111decimalpoint77777.......
It is no wonder FLT was never able to be proven ever since Fermat penned
it in the corner of his book in the 17th century because the numbers
of Natural Numbers are nothing what Fermat envisioned. Likewise it is
impossible to prove the Riemann Hypothesis because the Zeta Function
itself is not a mathematical entity for it has a mix of Reals, Complex
and P-adics.
Ever since the mid 1990s I have tried to find the optimal counterexample
for RH, thinking that the number ....999999 or idempotents were the
answer as counterexamples. But only in this month of October 2007 have
I come to the sobering prospect that the disease of RH is deeper than
simply a counterexample. That the Zeta Function itself is bogus.
But this has huge implications in that many other Functions of
mathematics are a fakery mix of P-adics with Reals. Every function that
purports to operate on "all the primes" is probably a fake function
for the Primes are this set 2,3,5,..... , 9999....99997
Oh well, a late realization is better than keeping with a falsehood.
Archimedes Plutonium
Alright, since no algebra can exist where an equation or function has
a mixture of P-adics and Reals. Because such a mix yields Doubly
Infinites which are nonsense. So the Riemann Zeta Function has Reals and
P-adics so when you multiply with Reals on P-adics the entire function
is nonsense. In Fermat's Last Theorem, all the numbers in any equation
are all P-adics where there are no Reals.
Now let us examine the Euler Identity of (e)^2(pi)(i) = 1
Prior to these posts, every mathematician including myself thought
the above was in Reals or to sneak in a P-adic for (i).
We know better now because you cannot have a mix in any equation or
function. So what is the above Euler Identity? Is it P-adics or is it
Reals?
The answer is surprizing and it hinges on the realization that (pi) and
(e) are transcendental meaning that they are not numbers of mathematics
for some spot in their digit arrangement place-value they cease to have
a digit there and beyond. They are not algebraic for algebraic numbers
have no missing digits in any place value. Transcendental is a fancy
name for a number that is growing and changing as the physical cosmic
clock ticks on. That means (pi) and (e) are surrounded by Reals in the
interval between 3 and 4 and we can always approximate pi by a digit
arrangement that is a close approximation such as 3.14159......xxxx
but at some place value we put an "x" mark meaning it has holes from
there on out to infinity. The same thing for (e).
So the Reals do not possess either (pi) or (e) since the Reals are all
possible digit arrangement of infinite strings rightward with finite
portion leftward. And since (pi) and (e) have holes they are not Real
Numbers. The same holds true for (e). And is (pi) and (e) in the
P-adics? Well the value of a pi in Elliptic Geometry varies from
2 to 3.14159...... where it can never reach the upper limit of
3.14159...... As to what (e) value is within Elliptic Geometry I leave
to the reader. But the North and South Pole of Elliptic geometry are
imaginary points in that geometry and (pi) is the South Pole and
2(pi) is the North Pole as either 0 degrees or 360 degrees.
So apparently the Euler Identity exists only in the P-adics as
Elliptic Geometry where the value of (e) is a range of P-adic values
and the value of 2(pi) is 0 for 0 and 360 degrees and (i) is either
(pi) or 2(pi) as one of the Poles.
So the Euler Identity comes packaged wholly from Elliptic Geometry
on the sphere surface as P-adic numbers or P-adic imaginary numbers
(e)^2(pi)(i) = 1
(e)^0 x 0 = 1
(e)^0 = 1
And apparently there are alot of equations and functions existing
in mathematics as I speak, that have a garbled and confused mixture
of Reals with P-adics. Most of trigonometry is Elliptic geometry
and whose equations and functions are really in the P-adics.
The Euler Identity survives and is true. But the Riemann Zeta-Function
is a mixed up mess of both Reals and P-adics.
It is of no wonder at all, that noone would ever prove it.
And the importance of the Riemann Hypothesis was very much overhyped
and inflated because most of the conjectures that depended upon the
truth of the Riemann Hypothesis were a dependence on the picture that
the primes were those old ghost numbers we called "finite integers"
when the true integers were all "infinite integers."
Archimedes Plutonium
such as these
...............9999999999999999999999999
...............9977392256259918212890625
...............0022607743740081787109376
into the (a + bi) in the Riemann Zeta Function
as to whether a nontrivial Zero occurs that is not on the 1/2 Real line
As I stated previously, the Riemann Zeta Function is all about P-adics
with nothing to do with Reals or Complex. But even so, I wonder
if a counterexample can be engineered even though the Function is bogus
since it mixes up Reals with P-adics.
So I am looking to engineer a nontrivial zero that does not exist on
the 1/2 Real Line.
Archimedes Plutonium
Archimedes Plutonium
Infinitude of Primes would be.
Now that we are enlightened that the Natural Numbers or Counting Numbers
is this set
.....000001
......0000002
.......0000003
.
.
.
.......999999999
Since the last number is the world's largest integer but it is still
composite since 9 divides
it and 3 divides it
But we look at the two preceding numbers and particularly .....9999997 and
it is the world's largest prime number, since no number prior divides
into it evenly.
So with these few basic observations we easily generate what would be
the modern
day Euclid Infinitude of Primes Proof. And these are to be emulated as
the best
way to make proofs in mathematics is be simple observation and the
observations are the
steps of the proof itself.
Modern Day Proof of Euclid's Infinitude of Primes:
Construct number ............37312923191713117532 which is the sequence of
all the primes and if finite they end in 0s digits. If infinite they end
in some other digit except
0. So if set of all primes is finite then this string would look like
this 0.....7532 But the world's
largest prime is 99999.....999999997
Archimedes Plutonium
any counterexamples.
All one needs to know is that the n in the Euler sequences of addition
or the p for the primes in multiplication of the Zeta Function, when
those are replaced with Infinite Integers such as .....9999997 as the
world's largest prime number or either one of these idempotents in the
Euler addition:
idempotents
...............9977392256259918212890625
...............0022607743740081787109376
That the Zeta Function ceases to converge and goes to infinity.
In the case of S(1) = 1 + 1/2 + 1/3 + ..... goes to infinity
In the case of S(2) and larger it converges
But when the Zeta Function fills in with those Infinite Integers or
Infinite Integer Primes for multiplication, well, the Functions no
longer converge for S(2) and larger.
Archimedes Plutonium
The above gives an easy proof of the Infinitude of Twin Primes and other
primes separated by a distance metric such as quad primes 3 and 7 or hex
primes 5 and 11 etc etc
What we do is Construct for Twin Primes a list of them as such
3,5 and 5,7 and 11,13 and 17,19 etc etc and then construct the Infinite
Integer:
...........191713117553
Now if that list of Twin Primes is Finite then the number above would be
0............191713117553 If not finite then it would have a digit other
than 0 in frontview.
Now we go to the endview of all the Infinite Integers to the world's
largest prime which is 9999.....99997 and we look for the Worlds last
two Twin Primes and they are if my computations are correct:
9999999....999991 and 9999999......99999989
And so we reason that if the set of all Twin Primes is finite then
there cannot exist two Twin Primes as shown above.
Likewise we do the same for proving the infinity of any type of prime
numbers. Works for the Mersenne Primes or the 2^n +1 primes or any
specific type of primes wanting a proof of whether infinite or finite.
We simply look for that type of prime near the so called end tail and
if we find it there then there are an infinite supply in between.
a_plutonium
are ...00001 to
999....999999 then what happens to the Prime Distribution Theorem x/
logx
Well it no longer holds true. But can I give some reasonable
explanation. Surely that is easy.
When you have infinite integers then you can have what are called
irrational or semi-irrational
infinite integers which do not repeat in blocks such as this number
constructed from
merely counting in a sequence:
..........13121110987654321.
And it is prime. And now the fascinating thing of constructing Triplet
primes such as 3,5,7
onto the above where we have
..........131211109876543217
..........131211109876543219
..........1312111098765432111
There there is the construction of these types of primes
where given a number such as
3333..........3333333 which is merely .......333333 in frontview
loaded.
Now with that number it is not prime as is but what if I sneak in a 1
digit in
successive specific place value and thus making the entire number a
prime
333333333..........33333313
then this one
333333333..........333331313
So by changing one specific place value digit I can construct an
infinite number
of primes in a string. Which would be another proof of the Infinitude
of Primes,
and maybe even shorter than my earlier version tonight.
And the Infinitude of Twin Primes would also be constructable from one
given string
by successive changing of a place value digit.
So what the message I am conveying is that as we get further into the
body of the
Infinite Integers we have increasing means of generating dense numbers
of primes.
So as we approach the world's largest prime
9999999.........9999999997
One can see that we can generate a dense pocket of primes by changing
one digit in
place value so that this one is prime:
9999999.....999999991997
then this one
999999.....99999919971997
So the Prime numbers become more dense the further away one goes from
....0000001.
a_plutonium
this 0.....7532 But the world's
largest prime is 99999.....999999997
tommy1729
you are a funny guy.
trying to disprove RH.
proving RH would be funny...
but disproving it is just hilarious !!
besides your no superhero
only soupman can save the day and prove RH
soupman , we need you , where are you ?
a soupman fan
Proginoskes
wrote:
> [...]
> The above gives an easy proof of the Infinitude of Twin Primes and other
> primes separated by a distance metric such as quad primes 3 and 7 or hex
> primes 5 and 11 etc etc
>
> What we do is Construct for Twin Primes a list of them as such
> 3,5 and 5,7 and 11,13 and 17,19 etc etc and then construct the Infinite
> Integer:
>
> ...........191713117553
>
> Now if that list of Twin Primes is Finite then the number above would be
>
> 0............191713117553
Nope. What if 3, 5, ....1117, and ....1119 were the only primes? You
would have a finite number of primes, yet when you "glue them
together" you get
...1119....111753,
which does not start with a 0. (There are no 0's in there, at all, at
all.)
--- Christopher Heckman
Archimedes Plutonium
Alright, I should count the last 100 Counting Numbers and see what the
density of primes are for that last 100
These are the numbers from
99999.....99999999
to that of 999999.....99999900
So I have 999999.....999999901 then 99999....9999902 etc etc
The maximum density of primes in any group of 100 Counting Numbers
would be a situation where all the odd numbers except those ending in
"5" are prime. So that every number ending in 1 or 3 or 7 or 9 is prime
and that means 40 out of 100 numbers is prime. Now I believe from memory
that the first 100 Counting Numbers there are 25 which are prime.
So if there are some series of Counting Numbers and I define series as
there are ten series where the endpoint or point at infinity is the
0 series of Counting Numbers and the 1 series and so to the 9 series
so that ....00000231 is a 0 series number and ....9999997 is a 9 series
numbers.
So, the most dense packing of primes is 40 primes per 100 Counting Numbers.
Now let me see if the last 100 primes is anywhere near the 40 density.
P.S. I guess I have achieved a world mathematical fame record, in that I
have found the world's largest prime number ....999997 for which noone
else in the world will ever find one larger so that the record book name
will not change from year to year. Bravo
David R Tribble
> [...] of P-adics where the last prime in the world is ....9999997.
>
> [...] Every function that
> purports to operate on "all the primes" is probably a fake function
> for the Primes are this set 2,3,5,..... , 9999....99997
How do you know that that ...9997 is prime?
Most numbers that end in 9997 are not prime.
97: prime
997: prime
9997: composite
99997: composite
999997: composite
9999997: composite
99999997: composite
999999997: composite
9999999997: composite
99999999997: composite
999999999997: composite
9999999999997: composite
99999999999997: composite
999999999999997: composite
9999999999999997: composite
99999999999999997: prime
999999999999999997: composite
etc.
Archimedes Plutonium
I anticipated this type of problem but sought not to make the post long.
Suppose the only primes were 3,5, and ....9999997 and .....9999991
So we string them together as per the above demand:
........9999999997...99999999153
And with our other demand that if finite set then the above becomes
this number
......0000000.....9999999997......9999999999153
The nice thing about infinity is that there are no barriers to stringing
one infinite to another infinite and their final end result is infinite.
The analogy is best seen as infinitely circuiting a sphere so if you add
1 infinity to 2 infinity to 55 infinity the end result is still 1 infinity.
So the way this method of proving Infinitude of Twin Primes or Primes of
some algebraic form such as 2^k +1 or 2^k -1 or Mersenne Primes is
simply find a few endview primes of that form and if you can find just
one of those primes in the ......9999999999 series then you have proven
infinitude of that form
The second method is to construct an infinitude of Twin Primes
........9999999999989
.........9999999999991 are Twin Primes
Now construct an infinitude of Twin Primes
......999999999999997989
......999999999999997991
then
......999999999999797989
......999999999999797991
One method is look to see if All Counting Numbers have an infinitude of
primes that you desire. The second method is do not even bother to look
, for, just build yourself an infinite set of primes that you desire of
some special custom form.
Archimedes Plutonium
Your first and perhaps only decent post and you should be ashamed of all
your past posts.
Anyway, a good question for which I have thus far spent no time on the
definition of Prime Number in the set of all Counting Numbers for this
textbook. And I should spend an entire chapter just on that alone.
In the old maths the definition of prime is clearly defined and in the
new maths which has sight of all the Counting Numbers not just 9% of the
set of all Counting Numbers that the old maths looked at.
Anyway, in this new math we keep the very same definition of prime that
the old math had. When a Revolution comes to science or math, you must
keep some elements of the past that carries forward into the new.
Definition of Prime remains the same.
So how do I know that .....999999997 or frontview-loaded
999999......999999999997 is prime
How do I know it is prime?
Recall that the operations in Decimal P-adics is the very same as in
Reals only where the final answer is what digits remain the same in
specific place-values and thus a Cauchy sequence for the final answer.
So what is 99999....9999999 X 99999....9999998
and the answer is
We do
99
X98
-----
9702
then we do
999
X998
------
997002
then we do
9999
X9998
-------
99970002
and we sequence further and further until we are satisfied with enough
place values which do not change their digits
So the answer to 9999....99999 X 9999....9999998
is the number 9997.........02
So the number 99999.....99999997 has only really two numbers to worry
about if they divide into 9999....999997 evenly and those two are
....999999 and .....9999998
Obviously the way multiplication is set up is that the product of two
infinite integers is less than either of the multipliers
So the number ....999997 has only to worry about ....99998 and
.....99999 and no permutation of them gives ....9999997
Now ....9999997 has to worry about the smallest primes such as 3, 7
and we divide into ....999997 by 3 and then by 7 to see if it leaves a
remainder.
Remainder by the way, as in division is taken care of in Decimal P-adics
as that finite portion rightwards. So the finite portion in Decimal
P-adics is like the fraction between two whole Real numbers where 1.5 is
halfway in between 1 and 2. So with remainders in Decimal P-adics is
taken care of by the finite portion of the radix point.
So neither 3 or 7 divide evenly in ....999997 which then eliminates them
and eliminates 33 or 333 or 77777 or any other variants
We also test for 97 and it is eliminated.
So clearly I have a easy chore to see what the largest Primes in all of
mathematics are in the range of .....99999900 and ......9999999
Jesse F. Hughes
> So we string them together as per the above demand:
>
> ........9999999997...99999999153
>
> And with our other demand that if finite set then the above becomes
> this number
>
> ......0000000.....9999999997......9999999999153
>
> The nice thing about infinity is that there are no barriers to stringing
> one infinite to another infinite and their final end result is
> infinite.
Isn't ....888888....999999 longer than ....99999? After all, the
former has the same number of 9s as the latter, but it has an infinite
number of 8s, too.
But if ....888888....999999 is longer than ....999999, then it must be
a larger number than ....999999.
Where did I go wrong?
--
Jesse F. Hughes
"My baby don't allow me in the kitchen
and I've come to love her decision."
-- Bad Livers
Proginoskes
wrote:
> Proginoskes wrote:
> > On Oct 18, 12:35 am, Archimedes Plutonium <a_pluton...@hotmail.com>
> > wrote:
>
> >>[...]
> >>The above gives an easy proof of the Infinitude of Twin Primes and other
> >> primes separated by a distance metric such as quad primes 3 and 7 or hex
> >>primes 5 and 11 etc etc
>
> >>What we do is Construct for Twin Primes a list of them as such
> >>3,5 and 5,7 and 11,13 and 17,19 etc etc and then construct the Infinite
> >>Integer:
>
> >>...........191713117553
>
> >>Now if that list of Twin Primes is Finite then the number above would be
>
> >>0............191713117553
>
> > Nope. What if 3, 5, ....1117, and ....1119 were the only primes? You
> > would have a finite number of primes, yet when you "glue them
> > together" you get
>
> > ...1119....111753,
>
> > which does not start with a 0. (There are no 0's in there, at all, at
> > all.)
>
>
> Suppose the only primes were 3,5, and ....9999997 and .....9999991
>
> So we string them together as per the above demand:
>
> ........9999999997...99999999153
>
> And with our other demand that if finite set then the above becomes
> this number
>
This is artificial, and the only reason for it seems to be that the
number of primes is known ahead of time to be infinite. It's like
fudging data to fit the theory (except in this case, the theory is
fudged to fit the fact about the number of primes).
I could just as easily prove that the set of primes is *FINITE* by
saying: "Suppose the set of primes is infinite; then string them
together and put a 0 on the left end. Therefore the last prime ...
99997, isn't at the farthest left; contradiction, so the set of primes
is finite."
--- Christopher Heckman
a_plutonium
Proginoskes wrote:
>
> This is artificial, and the only reason for it seems to be that the
> number of primes is known ahead of time to be infinite. It's like
> fudging data to fit the theory (except in this case, the theory is
> fudged to fit the fact about the number of primes).
>
> I could just as easily prove that the set of primes is *FINITE* by
> saying: "Suppose the set of primes is infinite; then string them
> together and put a 0 on the left end. Therefore the last prime ...
> 99997, isn't at the farthest left; contradiction, so the set of primes
> is finite."
>
> --- Christopher Heckman
*** lift-quoted from a popular encyc ***
It is not known whether or not there are an infinite number of prime
Euclid numbers.
Strong Goldbach conjecture: Every even integer greater than 2 can be
written as a
sum of two primes.
Twin prime conjecture: There are infinitely many twin primes, pairs of
primes with difference 2.
Polignac's conjecture: For every positive integer n, there are
infinitely many pairs of
consecutive primes which differ by 2n. When n = 1 this is the twin
prime conjecture.
It is widely believed there are infinitely many Mersenne primes, but
not Fermat primes.
It is conjectured there are infinitely many primes of the form n² + 1.
It is conjectured that there are infinitely many Fibonacci primes.
Legendre's conjecture: There is a prime number between n² and (n + 1)²
for every positive
integer n.
*** end lift-quoted from a popular encyc***
Well, you did not know whether the Twin Primes are infinite before you
read my post.
But after reading my post, and using the Method where we construct an
infinite number
of Twin Primes, then the question is closed:
The second method is to construct an infinitude of Twin Primes
........9999999999989
.........9999999999991 are Twin Primes
Now construct an infinitude of Twin Primes
......999999999999997989
......999999999999997991
then
......999999999999797989
......999999999999797991
ad infinitum
Granted the first method is not as good as the constructive method
since the first method
requires us to find a prime number in the .....9999999 string. And as
the above list
from an encyclopedia shows, there are alot of conjectures that require
a algebraic form
such as 2^n + 1 or 2^n - 1 and it is difficult to find a prime in 9-
series or 8-series or 7-series
etc that has that form. So the method is not a easy cinch in proving
and requires alot of work.
Such as how to exponentiate with say ....55555 or ......11111
But the first method is logically sound. In that if you can find one
example of a prime of
form 2^n -1 in ....9999999 series then you have an infinite supply of
those primes. The difficulty
is finding one such example.
But I have an example of a counterexample for the Goldbach Conjecture
in next post.
Archimedes Plutonium
(snipped in parts)
>
> *** lift-quoted from a popular encyc ***
> It is not known whether or not there are an infinite number of prime
> Euclid numbers.
> Strong Goldbach conjecture: Every even integer greater than 2 can be
> written as a
> sum of two primes.
> Twin prime conjecture: There are infinitely many twin primes, pairs of
> primes with difference 2.
> Polignac's conjecture: For every positive integer n, there are
> infinitely many pairs of
> consecutive primes which differ by 2n. When n = 1 this is the twin
> prime conjecture.
> It is widely believed there are infinitely many Mersenne primes, but
> not Fermat primes.
> It is conjectured there are infinitely many primes of the form n² + 1.
> It is conjectured that there are infinitely many Fibonacci primes.
> Legendre's conjecture: There is a prime number between n² and (n + 1)²
> for every positive
> integer n.
> *** end lift-quoted from a popular encyc***
>
Before I give the counterexample let me comment on the above list. I
think there is a easy proof for the Polignac conjecture following my
proof of the Twin Prime conjecture.
I believe the opposite of the above on Fermat primes and that there are
an infinite supply of Fermat primes.
The rule is in general that if you can find one prime of a special
algebraic feature then you can construct an infinite supply of those
primes. This makes sense in that the density of primes increases as it
goes through all the Counting Numbers.
Here is what I suspect is a counterexample to Goldbach Conjecture in
the Counting Numbers.
0.....1312111098765432106
Now that number is less than 9% on the road to reach the largest Integer
which is 99999......9999999 as a perspective.
The predecessor of the above number is 0....1312111098765432105
and the successor is 0....1312111098765432107
Now someone may ask how does one count past the number
such as 0....1312111098765432106 where we no longer see a "0"
at the *point of infinity* in the frontview. And I can explain
that easier with this number
099999.....9999990 and the answer is that as we count from
09999......99999991 to (...99992 to ....99993 then 4 then 5 then 6 then
7 then 8 then 9 and then add one more and we go to
1000000......000000 and proceed to 100000.....000001
I just wanted to show you how we counted past a "0" as the
point of infinity digit.
So that number 0....1312111098765432106 is even since the backend is
"06"
So, does it obey Goldbach Conjecture?
Well, you see the problem? The problem is that the number is irrational
in old math so finding two numbers to add up to that irrational string
is perhaps impossible and even if you did then you have to negotiate
with a "3" as the last digit for 3+3 = 6 and you cannot do it with
1 + 5 = 6 since all numbers ending in 5 are composite.
That is my best attempt so far, but not fully checked out.
And there is alot of irony to the Goldbach Conjecture in these Infinite
Integers is that the primes are much denser of a set then previously
thought and so one would erroneously think that would boost the chances
of Goldbach being true, but because of Infinite Integers increases the
likelihood that there are very strange even numbers for which
mathematicians never in their wildest dreams could imagine existed.
So the above, I believe is a counterexample to the Goldbach Conjecture.
Another two would be the idempotents with a 06 attached at the endview.
Proginoskes
> Proginoskes wrote:
>
> > This is artificial, and the only reason for it seems to be that the
> > number of primes is known ahead of time to be infinite. It's like
> > fudging data to fit the theory (except in this case, the theory is
> > fudged to fit the fact about the number of primes).
>
> > I could just as easily prove that the set of primes is *FINITE* by
> > saying: "Suppose the set of primes is infinite; then string them
> > together and put a 0 on the left end. Therefore the last prime ...
> > 99997, isn't at the farthest left; contradiction, so the set of primes
> > is finite."
> Well, you did not know whether the Twin Primes are infinite before you
And I still don't. You have a track record of false proofs, which look
as solid as walls, but when you lean against them, they turn out to be
spider webs, and you wave your hands like crazy to get them out of
your hair.
So I would ask for what any real scientist would look for: independent
proof. Ideally, it would be a fact about the P-adics that I know, of
which you are unaware, and I would ask you to prove it one way or
another. Unfortunately I cannot think of such a result right off.
--- Christopher Heckman
a_plutonium
Archimedes Plutonium wrote:
(snipped)
The above does not work because of this:
0....1312111098765432106 = 0....1312111098765432101 + ....000005
So busy trying to wipe out any large primes I failed to check for the
small primes.
So let me try a different even number.
......222222 or frontview loaded is 222222......22222222
I do not have to worry about 1111.....111111 for it is not prime but
what about 202020.....202011 + 020202....020211
No, it is looking bad for counterexamples, maybe the Conjecture is
true afterall?
But let me try one more counterexample tonight with that of
00100000.......000000
Maybe this one is undefeatable.
Its successor is 00100000.....00001
and its predecessor was 0009999999......9999
But it looks like 000999999......999997 + ......0000003
So it is looking like Goldbach does not have counterexamples
and thus is true. So looking the other direction now.
hagman
> It occurred to me tonight of what the world's most simple proof of the
> Infinitude of Primes would be.
> Now that we are enlightened that the Natural Numbers or Counting
> Numbers is this set
> .....000001
> ......0000002
> .......0000003
> .
> .
> .
> .......999999999
>
> Since the last number is the world's largest integer but it is still
> composite since 9 divides
> it and 3 divides it
>
> But we look at the two preceding numbers and particularly .....9999997
> and
> it is the world's largest prime number, since no number prior divides
> into it evenly.
What is 9 * 333...333 ?
>
> So with these few basic observations we easily generate what would be
> the modern
> day Euclid Infinitude of Primes Proof. And these are to be emulated as
> the best
> way to make proofs in mathematics is be simple observation and the
> observations are the
> steps of the proof itself.
>
> Modern Day Proof of Euclid's Infinitude of Primes:
> Construct number ............37312923191713117532 which is the
> sequence of
> all the primes and if finite they end in 0s digits. If infinite they
> end in some other digit except
> 0. So if set of all primes is finite then this string would look like
> this 0.....7532 But the world's
> largest prime is 99999.....999999997
>
> Archimedes Plutoniumwww.iw.net/~a_plutonium
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies
And isn't 99999.....999991 possibly the second-largest prime?
Thus the number constructed looks like
99999....999979999....99991....37312923191713117532
^
Uhm, at which position please was that 7 again?
Archimedes Plutonium
Just a few minutes ago I wrote:
>
>
> The above does not work because of this:
>
>
> 0....1312111098765432106 = 0....1312111098765432101 + ....000005
>
> So busy trying to wipe out any large primes I failed to check for the
> small primes.
>
> So let me try a different even number.
>
> ......222222 or frontview loaded is 222222......22222222
>
> I do not have to worry about 1111.....111111 for it is not prime but
>
> what about 202020.....202011 + 020202....020211
>
> No, it is looking bad for counterexamples, maybe the Conjecture is
> true afterall?
>
> But let me try one more counterexample tonight with that of
>
> 00100000.......000000
>
> Maybe this one is undefeatable.
>
> Its successor is 00100000.....00001
> and its predecessor was 0009999999......9999
>
> But it looks like 000999999......999997 + ......0000003
>
> So it is looking like Goldbach does not have counterexamples
> and thus is true. So looking the other direction now.
>
Directly after sending off the above it dawned on me as to what makes
the mechanism for Goldbach Conjecture to work-- that all even integers
are the sum of two primes.
IT IS A DIGIT ARRANGEMENT MECHANISM. What I mean by that is if the
Goldbach Conjecture works for numbers from 0 to 10 , or better yet as an
example, if Goldbach's conjecture works for numbers from 20 to 30, then
the Conjecture works for all even integers.
So let me explain the case of 20 to 30 because any other ten numbers
because of say Decimal notation or because of Decimal Reals or because
of Decimal P-adics, that if it works for any one single decimal place
value then no matter how large the number is to infinity, it will always
work
So all that anyone needs to prove the Goldbach conjecture is to see if
it works from 20 to 30 So does 20 have a sum of two primes, yes, 7+13,
next is 22 and yes, 19+3, next is 24 then 26 then 28 then 30 and all of
them have a two prime sum
Proof is essentially over with. Because no matter how large the number
you want to test, it all hinges on the fact that the last place value
can always be a sum of two primes since no matter what even digit is in
that last place value, whether it is a 0 or 2, or 4 or 6 or 8 that they
are taken care of by two odd digits and jiggering or manipulating the
other place values in the number in question.
So the proof of Goldbach is the simple fact that no matter what Even
Number you have, that the last place value is taken care of.
Sometimes our most difficult proofs are because their sheer simplicity
was never noticeable. That we carry an army into battle to swat a fly.
Denis Feldmann
show he has a proof of some result without disclosing any hint towards
the proof (typical examples were like showing some graph is having some
property (connectedness, say, except I cant remember the actual result)
by answering questions on the graph which couldn't be answered (except
by luck) if one had no explicit proof of the property ...)
Does anyone know more about it?
Archimedes Plutonium
hagman wrote:
>
> What is 9 * 333...333 ?
Some may think it is 9999....99997
But I get 299999.....999997 as per definition of multiplication
as set forth in this book.
By the way, thanks for asking because I realized I made a mistake
in a previous post where I said the product of infinite integers
is always less than its multipliers. For here is a obvious
counterexample
3 X 3333....33333 = 99999....999999
>
> And isn't 99999.....999991 possibly the second-largest prime?
That is what I get.
> Thus the number constructed looks like
>
> 99999....999979999....99991....37312923191713117532
> ^
> Uhm, at which position please was that 7 again?
>
Well I was giving a proof of the infinitude of primes by two methods.
One method says, if there is a prime in the 9999series then the primes
are infinite because these strings are simply infinite compared to
primes that have 00000series. It is like a water garden hose. If there
is water at one end and you look at the other end of the point of
infinity and see water then the water is infinite.
But I do not like that method as much as a constructive Method, where
we just say-- let us prove infinitude of primes and build them. So we
take the prime 999999......99999997 and build another prime from it.
As 999999.....999999999797. Then we build another new prime
as 9999999.....999999979797 ad infinitum. Proving the Infinitude of
Primes never got so easy as this. Like proving a house. We just go
outside and build one.
Archimedes Plutonium
a_plutonium
I doubt the above explanation is enough for a formal written proof.
A similar proof of something in mathematics would be to say
In a given PLACE-VALUE of a number, that place value can have
only one of ten digits. So how does one write a formal proof of such a
assertion? It was part of the definition of decimal place value.
But the Goldbach Proof is only a few degrees more complex than
the above place-value assertion.
The Proof of Goldbach Conjecture:
Given any Even Number it always has the
lowest place-value and let us call it the Ones-place value where one
of ten
possible digits can fit into that Ones-Place-Value. For example the
number
.......1111111118 has an "8" in its Ones-Place-Value.
Now the proof rests completely on that Ones Place Value as the only
important
issue in the proof. For that Ones Place Value can have only one of
these digits of
0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 . The Ones Place Value
cannot have
any other digit except for one of those ten. Now in the Goldbach
Conjecture we are
interested in only the numbers which have either a 0 or 2 or 4 or 6 or
8 in its
Ones Place Value. Now the crux of the proof is that if the numbers
from 10 to 20
obey the Goldbach Conjecture that all numbers, no matter how large
obey the
Goldbach Conjecture. Now I would have liked to use 0 to 10 instead of
10 to 20
but we must realize that 0 is not a sum of two primes and neither is 2
so we cannot
use 0 to 10 and I must use 10 to 20.
So here is the heart or crux of the proof of Goldbach Conjecture, for
if I can show that
even numbers from 10 to 20 obey Goldbach, then it never matters any
more how large
the number is because the only area in which Goldbach can fail is the
Ones Place Value.
That we can engineer and manipulate and force other Place Values to
make the Ones Place
Value obey Goldbach. So all we need to show is that 10 and 12 and 14
and 16 and 18 obey
Goldbach, and they most certainly do. And what is the Goldbach prime
sum for 18? It is
11 +7
Now remember the above example of ......1111111118 and so does it
matter what digits
exist beyond the 18 in that number? Of course not and it matters not
in any even number.
Because all we need to do to satisfy Goldbach for .....11111118 is
......11111111107 + ......0000000011
So the proof of Goldbach is essentially the element that if the Ones
Place Value is satisfied
for Goldbach that the 0 and 2 and 4 and 6 and 8 digit are satisfied,
then the entire rest of the
place values are engineered to satisfy Goldbach Conjecture.
Another way of saying this is that if Goldbach were false then one of
10 or 12 or 14 or 16 or 18
disobeys Goldbach. But none disobey Goldbach.
So maybe there is a more fancier way of writing this up, but the proof
is sheer simplicity. Sometimes
because something is so simple that it looks like the most difficult
in the world.
Archimedes Plutonium
I suppose the formal write up of the proof would be Math Induction or
Fermat's Infinite Descent which is a form of Math Induction.
The key feature of the above discovery is that faced with Goldbach's
Conjecture I go to look for a counterexample first which would be
natural for anyone doing math to look first for a counterexample. But
what was new and novel above is that upon realizing there is no
counterexample, then to capitalize on that by saying "what mechanism
is preventing there to construct a counterexample?" And after locating
the mechanism then using it as the crux of a proof.
So the formal write up is a Math Induction where you have 0 to 10
satisfied. Then you have 10 to 20 satisfied. Now going to the 20 to 30
where we see that 20 has the 10 as analog and where 10 = 7 + 3 we can
expect a "7" and "3" for 20 where we have 20 = 17 +3 and we go to 22
where its analog was 12 and where 12 = 7 + 5 we can expect a 7 and 5
for the answer to 22 and were 22 = 17 + 5 So you can see and spot the
pattern that is developing. That as we establish the truth of Goldbach
for 0 to 10 and for 10 to 20 and we collect all the primes as we move
next into the 20 to 30 and then move into the 30 to 40. That it hinged
and depended upon the truth of Goldbach for 0 to 10 and 10 to 20. So
that if Goldbach were false for say 888888888888 or even the
infinite integer of .......8888888888888 that Goldbach is false for 0 to
10 and 10 to 20, contradiction and hence true.
David R Tribble
>>[...] of P-adics where the last prime in the world is ....9999997.
>
David R Tribble wrote:
>> How do you know that that ...9997 is prime?
>> Most numbers that end in 9997 are not prime.
>
Archimedes Plutonium wrote:
> Your first and perhaps only decent post and you should be ashamed of all
> your past posts.
I'm not.
But at least you responded to one of my questions instead of
ignoring it like you usually do.
Archimedes Plutonium wrote:
> How do I know it is prime?
> [...]
>
> So the number ....999997 has only to worry about ....99998 and
> .....99999 and no permutation of them gives ....9999997 [...]
>
> So neither 3 or 7 divide evenly in ....999997 which then eliminates them
> and eliminates 33 or 333 or 77777 or any other variants
> We also test for 97 and it is eliminated. [...]
>
> So clearly I have a easy chore to see what the largest Primes in all of
> mathematics are in the range of .....99999900 and ......9999999
Yes, you have only ...9990003 more possible divisors to check
to prove that ...997 is prime.
David R Tribble
> I do not have to worry about 1111.....111111 for it is not prime
How do you know it's not prime? What are its prime factors?
David R Tribble
>> So I would ask for what any real scientist would look for: independent
>> proof. Ideally, it would be a fact about the P-adics that I know, of
>> which you are unaware, and I would ask you to prove it one way or
>> another. Unfortunately I cannot think of such a result right off.
>
Denis Feldmann wrote:
> Actually, I remember now having read about situations where one can
> show he has a proof of some result without disclosing any hint towards
> the proof (typical examples were like showing some graph is having some
> property (connectedness, say, except I cant remember the actual result)
> by answering questions on the graph which couldn't be answered (except
> by luck) if one had no explicit proof of the property ...)
>
> Does anyone know more about it?
I believe it's a variation of "secret sharing".
See http://en.wikipedia.org/wiki/Secret_sharing
David R Tribble
> The Proof of Goldbach Conjecture
>
> satisfied. Then you have 10 to 20 satisfied. Now going to the 20 to 30
> where we see that 20 has the 10 as analog and where 10 = 7 + 3 we can
> expect a "7" and "3" for 20 where we have 20 = 17 +3 and we go to 22
> where its analog was 12 and where 12 = 7 + 5 we can expect a 7 and 5
> for the answer to 22 and were 22 = 17 + 5 So you can see and spot the
> pattern that is developing. That as we establish the truth of Goldbach
> for 0 to 10 and for 10 to 20 and we collect all the primes as we move
> next into the 20 to 30 and then move into the 30 to 40. That it hinged
> and depended upon the truth of Goldbach for 0 to 10 and 10 to 20. So
> that if Goldbach were false for say 888888888888 or even the
> infinite integer of .......8888888888888 that Goldbach is false for 0 to
> 10 and 10 to 20, contradiction and hence true.
Since you claimed that every even number is the sum of
two primes because all the evens between 10 and 20 are,
it follows that all the evens from 8888888888880 to
8888888888888 are also sums of two primes. Finding
them is then a trivial task, since they should resemble
the solutions you found for 10 to 18.
So what are the two primes that sum to 8888888888888?
Archimedes Plutonium
Focus on the Ones and Tens Place Value of 80 to 90 for 88.
Because 8 = 5 + 3 we look first to an arrangement of the 3 and 5 digit,
if that does not work then we look to some other primes in existence
before we reach 88. However, in this case 83 + 5 work.
So the Goldbach solution to ......8888888 = .....8888883 + .....00005
David R Tribble
>> The Proof of Goldbach Conjecture
>
David R Tribble wrote:
>> Since you claimed that every even number is the sum of
>> two primes because all the evens between 10 and 20 are,
>> it follows that all the evens from 8888888888880 to
>> 8888888888888 are also sums of two primes. Finding
>> them is then a trivial task, since they should resemble
>> the solutions you found for 10 to 18.
>>
>> So what are the two primes that sum to 8888888888888?
>
Archimedes Plutonium wrote:
> Focus on the Ones and Tens Place Value of 80 to 90 for 88.
>
> Because 8 = 5 + 3 we look first to an arrangement of the 3 and 5 digit,
> if that does not work then we look to some other primes in existence
> before we reach 88. However, in this case 83 + 5 work.
>
> So the Goldbach solution to ......8888888 = .....8888883 + .....00005
You might try reading the question more closely.
I asked for the two primes that sum to 8888888888888.
And how do you know that ...8888883 is prime?
What is ...2962962961 x 3?
Archimedes Plutonium
No harm to the argument, as I said you first look to the Induction of 80
to 90 with the 1st induction as 0 to 10 and the 2nd of 10 to 20 and if
those primes are not the answer then you look at the primes below 88
and they are 71 and 17.
Goldbach Conjecture proof is going to have to tie into what the primes
are. So the Math Induction part of the proof is not going to say "you
are stuck with only the 8 and 18 whenever you test a large even number.
The Math Induction requires you to use all the primes up to that even
number. So I can use all the primes up to ....8888888888
And so you have shown that .......8888883 is not prime. Okay, then
......88888888 = ......88888871 + .....00000017
So I dare you to find out whether ......888888871 is prime or not
And if not prime, then I have to dig deeper back to find a pair that works.
But all of that is no harm to the proof, because if ....888888 does
not obey Goldbach then numbers between 0 and 20 do not obey Goldbach.
The proof of Goldbach is essentially a very long connected chain wherein
if you insist that some yet uninspected huge even number such as say
.........1615141312111098765432 does not obey Goldbach then the numbers
between 0 and 20 disobey Goldbach.
Archimedes Plutonium
Goldbach Conjecture that all even Integers are the sum of two
Prime Integers. This proof needs some sandpapering or filing to
smooth out, but the essential ingredients are contained. I
derived this alternative proof from having to try to find
a counterexample of Goldbach in the Infinite Integers and when
none were forthcoming, went the opposite direction in that
Goldbach conjecture is true.
So this proof may be a historic first in that the proof method
is to prove that no counterexamples are possible.
Outline of proof of Goldbach Conjecture: We know (pi) is transposed
as a P-adic Infinite Integer as such 314159........r where r is the
radix. We know (pi) is transcendental. We do not know what the digit
of pi is before the radix. However, we know that (pi) is even number
since it is able to form enclosed polygons in a circle such as a
square or 6-sided polygon or 8-sided polygon etc. So we know the digit
before r is even. So according to Goldbach (pi) is the sum of
two other primes.
Now can those two requirements coexist? Can you have a number that
is transcendental, regardless of transposed or not transposed for those
properties of irrational Reals when transposed become irrational
P-adics. Since (pi) is even and since (pi) is transcendental then
it cannot be the sum of two primes for that destroys its characteristic
of transcendental. So here we have a Integer, although we only know
its digit before the radix is even, and which is not the sum of two
primes.
So is Goldbach Conjecture false? No, because a Transcendental Number
is a number that has holes in its digit arrangement so it is not a
P-adic but that (pi) is imaginary for the P-adics as the number that
is one unit distance greater than ....9999999999.
So the Goldbach Conjecture is proven true because if any even Counting
Number disobeys the Goldbach Conjecture is a transcendental number as is
(pi). So the only number that can disobey the Goldbach Conjecture is a
transcendental number. QED
I need to file down the roughness in the above.
Proginoskes
There are also so-called "Zero Knowledge Proofs". See
http://en.wikipedia.org/wiki/Zero-knowledge_proof , for instance. This
is what David Tribble is trying to do. ((Pause)) What you are trying
to do.
AP can be hard of hearing at times. This is the good part; when you
bug him enough, he starts yelling at you and lets loose with non
sequiturs about the legality of your parents' marriage, and any ad
hominems he can dig up. Believe me, I know.
BTW, ANY P-adic (written in base 10) is divisible by 3, by a method
similar to the one you used (and which I call "reverse division"). And
any P-adic in base 3, which ends in 1 or 2, is not divisible by 3. But
try telling AP that; his P-adics are "base free".
--- Christopher Heckman
Proginoskes
wrote:
> [...]
> So I dare you to find out whether ......888888871 is prime or not
Nope. Every 10-adic is divisible by 3 with no remainder, the idea
being what I call "reverse division" (which works, in base 10, if the
divisor ends in a 1, 3, 7, or 9).
It starts off with putting a digit above the 1 at the far right of ...
8888871. The only digit which, when multiplied by 3 is 1, is 7. So our
P-adic ends in 7. Subtract 7*3=21 from the far right and drop the
final 0.
7
___________
3 |...8888871
-21
==========
...888885
Now, which digit when multiplied by 3, yields 5? The answer is 5, so
we put a 5 next to the 7, subtract 5*3=15 from the right end of ...
88885, drop the final 0, and continue.
57
___________
3 |...8888871
-21
==========
...888885
-15
=========
...88887
Continue.
...62962957
___________
3 |...8888871
-21
==========
...888885
-15
=========
...88887
-27
========
...8886
-6
=======
...888
-18
======
...87
You can verify that ...62962957 * 3 = ...88888871 by computing 7*3,
57*3, 957*3, etc.
...888871 wasn't special here; any number will work, even ...00001!
Thus, the only P-adic which can be prime is 3, since all others are
multiples of 3. However ...
... If we do the same trick for 7, we find out that 7 is the only
possible prime as well. Which means that either 3=7, or that we don't
have ANY primes at all in the P-adics! And the Goldbach Conjecture
dies!
(BTW, changing bases won't work, either. And you were told this years
ago.)
--- Christopher Heckman
a_plutonium
Proginoskes wrote:
> On Oct 19, 11:26 am, Archimedes Plutonium <a_plu...@hotmail.com>
> wrote:
> > [...]
> > So I dare you to find out whether ......888888871 is prime or not
> > And if not prime, then I have to dig deeper back to find a pair that works. [...]
>
> Nope. Every 10-adic is divisible by 3 with no remainder, the idea
> being what I call "reverse division" (which works, in base 10, if the
> divisor ends in a 1, 3, 7, or 9).
This book defines P-adics far differently than yours and the old way.
The old
way was a costumed-acting-Reals where they had ....99999 = (-1)
The P-adics as defined in this book are infinite leftward strings of
all possible
digit arrangement and whose operations are the same as for Reals as
a Cauchy sequence to the final answer.
The old math created P-adics to satisfy algebra. These new P-adics
satisfy geometry and symmetry to the Reals.
A waste of time.
Dividing 3 into 88888......88888871 in the new P-adics which I call
Decimal P-adics not 10-adics is this:
3 into 8 is 2 with 2 remainder. Carry the 2 and we have 28.
Then 3 into 28 is 9 with 1 remainder. Carry the 1 and we have 18.
Then 3 into 18 is 6 and we repeat the block of 296 where we have
296296296 and 3 does not divide 71 evenly so the entire
number is prime.
By the way these are the primes in the last 100 numbers before
we reach the last and largest integer in the world 99999.....9999999
.....999997
......999991
.......9999989
......9999983
.......99999979
.....9999973
......99999971
.......99999967
......999999961
.......99999959
.....9999953
......9999949
.......9999947
......99999943
.......99999941
.....99999937
......99999929
.......99999923
......999999913
.......999999911
........9999999907
.........9999999901
So there are 22 Primes in the last interval of one hundred Integers
and there are 24
primes in the first one hundred Integers.
Is there any explanation for the break in symmetry? Yes, because in
the first
one hundred there is the Triplet primes of 2,3,5 and if not for that,
then the last
100 integers would have the same quantity of primes as the first 100
integers.
Proginoskes
> This book defines P-adics far differently than yours and the old way.
And changes definitions every week or so.
> [...]
> Dividing 3 into 88888......88888871 in the new P-adics which I call
> Decimal P-adics not 10-adics is this:
>
> 3 into 8 is 2 with 2 remainder. Carry the 2 and we have 28.
> Then 3 into 28 is 9 with 1 remainder. Carry the 1 and we have 18.
> Then 3 into 18 is 6 and we repeat the block of 296 where we have
> 296296296 and 3 does not divide 71 evenly so the entire
> number is prime. [...]
But 3 does divide evenly into 8871. Hence
...2962962962957 * 3 = ...88888871 as well.
Or has the definition of multiplication changed?
--- Christopher Heckman
Archimedes Plutonium
Here is a good example for the chapter in this textbook on the division.
And the above is all wet and wrong, since he cannot seem to follow what
the definition of division as outlined in this book.
We defined division and the other operations as exactly the same as on
Reals and the final answer is what digits stay the same in the place value.
So we divide
3 into 8871 is 2957
then
3 into 88871 is 29623.6
then
3 into 888871 is 296290.3
then
3 into 8888871 is 29622957
now we go out further which my hand held calculator will not display
but for every even division there are two which end up as "fractional"
So the final answer is that what digits remain the same in place value
and that answer is this
2962........r&&&&&
The "r" is the radix and the & represents digits in the radix.
Now let us try another example of division to illustrate the above in
that of
7 divided into .......99999917
So we divide
7 into 917 is 131
then
7 into 9917 is 1416.7
then
7 into 99917 is 14273.8
then
7 into 999917 is 142845.2
And we see again where the final number will look like this
142......r&&&&&
Now having done that and looking at my previous posts I realize I made a
mistake with .....99999931 and .....999999919 and ......999999917
that those three are also Primes so that the list of largest primes in
the last interval of 100 Counting Numbers is not 22 but 25, the same
number of primes as in the starting first 100 Counting Numbers.
Jesse F. Hughes
> Now having done that and looking at my previous posts I realize I made a
> mistake with .....99999931 and .....999999919 and ......999999917
> that those three are also Primes so that the list of largest primes in
> the last interval of 100 Counting Numbers is not 22 but 25, the same
> number of primes as in the starting first 100 Counting Numbers.
Is ....99997 still on that list of primes? Because I was thinking
about this number and it seems to me that
....999999
x 3
----------
27
27
27
27
.
.
.
----------
....999997
Did I do the multiplication wrong? Also, isn't it strange that we
can multiply a number by three and get a smaller number?
Oh, wait. I know. You're going to try to change the subject to
9...9997, which has a 9 as a first digit. Well, never mind that
number, since I'm asking about ...99997. Is that number prime? And
what does 3 * ...9999 mean anyway? Does it mean adding ...9999 to
itself three times? If so, shouldn't that be a larger number than
...9999?
Very confused.
--
Jesse F. Hughes
"Love songs suck and losing you ain't worth a damn."
-- The poetry of Bad Livers
David R Tribble
>>The Proof of Goldbach Conjecture
>
David R Tribble wrote:
>> You might try reading the question more closely.
>> I asked for the two primes that sum to 8888888888888.
>>
>> And how do you know that ...8888883 is prime?
>> What is ...2962962961 x 3?
>
Archimedes Plutonium wrote:
> No harm to the argument, as I said you first look to the Induction of 80
> to 90 with the 1st induction as 0 to 10 and the 2nd of 10 to 20 and if
> those primes are not the answer then you look at the primes below 88
> and they are 71 and 17.
You still have not answered my question:
What are the two primes that sum to 8888888888888?
David R Tribble
> the last and largest integer in the world 99999.....9999999
You could call this number Lp, the largest AP-adic.
So then we ask, what is Lp x 10 + 9? Why, Lp, of course,
which only makes sense because it's the largest AP-adic:
Lp x 10 + 9
= ...999 x 10 + 9
= ...990 + 9
= ...999
= Lp
So now you have the identity (I):
Lp = Lp x 10 + 9
Again, this makes sense since there can't be an AP-adic greater
than Lp, by definition.
Then, using a little simple arithmetic,
Lp = Lp (identity)
Lp < Lp x 10 (since 10 is positive)
so, adding 9 to both sides:
Lp + 9 < Lp x 10 + 9
and since x+9 < y+9 implies that x < y+9:
Lp < Lp x 10 + 9
so then substituting from the identity (I) above gives:
Lp < Lp
So the largest AP-adic Lp (...999) is not only equal to
itself, it is also less than itself. It is obviously a special
number.
David R Tribble
>> So I dare you to find out whether ......888888871 is prime or not
>> And if not prime, then I have to dig deeper back to find a pair that works. [...]
>
Proginoskes wrote:
>> Nope. Every 10-adic is divisible by 3 with no remainder, the idea
>> being what I call "reverse division" (which works, in base 10, if the
>> divisor ends in a 1, 3, 7, or 9).
>> ...62962957 x 3 = ...88888871.
>
Archimedes Plutonium wrote:
> A waste of time.
>
> Dividing 3 into 88888......88888871 in the new P-adics which I call
> Decimal P-adics not 10-adics is this:
>
> 3 into 8 is 2 with 2 remainder. Carry the 2 and we have 28.
> Then 3 into 28 is 9 with 1 remainder. Carry the 1 and we have 18.
> Then 3 into 18 is 6 and we repeat the block of 296 where we have
> 296296296 and 3 does not divide 71 evenly so the entire
> number is prime.
So you're saying that ...62962957 x 3 does not equal ...88888871?
So what does this product equal, when using your new Decimal
AP-adic arithmetic?
Archimedes Plutonium
One of the prime motivations in writing this textbook was to make
P-adic arithmetic accessible to a young 6 year old. The other prime
motivation is to mapp the Elliptic and Hyperbolic Geometries of their
native and intrinsic Coordinate System. The Reals cannot be placed on
a sphere as the coordinates because there is a continuum from 1 to 2
without any holes, gaps, cuts, tears. But on the surface of a sphere
the numbers between 1 and 2 are filled with holes in order to allow
for the curvature. So when one is given the responsibility of mapping a
Euclidean square such as a piece of sheet steel onto a sphere, there is
going to have to be alot of cutting of the sheet metal to ever have it
fit onto the sphere. So the points between 1 and 2 or between 1 and 5 or
between 8 and 999996 on the sphere have alot of holes as we walk those
Counting Numbers. The holes are represented by the Radix point and it is
finite portion rightwards whereas in Reals it is represented by
decimal-point and the finite portion is leftwards. So in Infinite
Integers the finite portion is hole-ridden whereas in Reals it is a
continuum.
So now we reach the world's largest integer .....999999 and we add 1
to it. This sum is the South Pole which is the imaginary number (pi)
So you add .....9999999 + 1 and your answer is (pi)
So you add .....9999999 + 10 and your answer is (pi) + 9
You see, .....99999999 is one unit distance shy of the angle 180
degrees. It is so shy of 180 degrees that we can in practicality say
it is 180 degrees but in precision know it is short of it.
So that when we have the addition of .....9999999 + 50000....000000
what do we have? Well, we know ......9999999 is almost 180 degrees
and that 500000.....000000 is exactly 90 degrees so that
180 + 90 is 270 degrees and thus we have as the final answer
.....99999999 + 50000....0000000 = (pi) + 4999999....999999
What is .....9999999 + .....999999?
That is almost 180 degrees + 180 degrees and so the final answer
is (pi) + .....9999998. This is where the Old-Mathematics falsely
assumed ....999998 was (-2) and where they assumed ....999999 was (-1).
So what is .....999999X10 + 9?
It is .....9999999 X 10 is .....99999990 which was ten circuits around
the sphere or globe having gone past both Poles ten times and landed
ending up at the tenth circuit at the point of ....9999990. Now we add
9 more units to that we end up with .....9999999 having gone around the
globe ten times.
When you are on a sphere surface there are many ways of ending up in
London as an old Marlowe-Shakespeare play says.
Archimedes Plutonium
I answered that in another post, but since there is so much confusion
I shall answer again and it appears that division may be the worst
operation to set straight in people's mind, although I would have
thought addition and especially subtraction would be the worst
because you run into the imaginaries of pi and the "other half of the
globe".
The operation of division is exactly the same as in Reals only the final
answer is a Cauchy sequence of what digits remain the same in place-values.
So we divide 3 into .....88888871
We first divide 3 into 871 which is 290.3 with a radix fraction
Next we divide 3 into 8871 which is 2957 evenly
Next we divide 3 into 88871 which is 29623.6 with a radix fraction
Next we divide 3 into 888871 which is 296290.3 with another radix fraction
Next we divide 3 into 8888871 which is 2962957 evenly
Next we divide 3 into 88888871 which is another even number and my
calculator does not go any further but the next ones are radix fractions
So the final answer as to 3 divided into .....8888888871 is a Cauchy
sequence and the number is this
2962.......r&&&&&&
where the r is radix and the finite portion as a fraction is represented
by the &.
So that the number .....888888871 is prime, unless, however I am wrong
about the resumption of radix fractions after 8888871 which my
hand calculator does not go beyond. So if the radix fraction ceases with
8888871 then the number .......8888888871 is not prime.
Archimedes Plutonium
....88888871 and ......888888817 are primes as both generate radix
fractions in their Cauchy sequence
a_plutonium
Jesse F. Hughes wrote:
>
> ....999999
> x 3
> ----------
> 27
> 27
> 27
> 27
> .
> .
> .
> ----------
> ....999997
take 99 x 3 is 297
then 999 x 3 is 2997
then 9999 x 3 is 29997
so the Cauchy sequence for final answer is 299.........999997
The above is in my killfile and I no longer answer
Not worth saving since the answer was given previously
Archimedes Plutonium
a_plutonium wrote:
Some dullard wrote:
Against my first judgement, another said that since these so called
"Plutonium Integers" as appearing in Wikipedia under "Archimedes
Plutonium" are so new to the world at large,that alot of people will
repeat a question and so I should not react so fast in the manner I do.
That there are alot of dullards that need walking through more than
once. And I should archive the above since I want a 6 year old to
understand and they often need a second walk through.
Archimedes Plutonium
I answered the above about ....999999 X 10 + 9 in a separate post
earlier, but the question lingers because I never really addressed the
Algebra of these Plutonium Numbers as what Wikipedia is listing them
in a article under "Archimedes Plutonium".
I did ask Dik Winter what the algebra was but he seems to only care
about what mainstream math is, not anything new.
So let me ask David Tribble what he thinks the Algebra of these
Plutonium Numbers from 1 to ....9999999 are.
Picture the Unit Circle only here the numbers from 0 to (pi) are 1 to
.....999999 where 0 is imaginary and let me call it the North Pole for
easy reference and the number (pi) radians or 180 degrees is also
imaginary and let me call it the South Pole. (Hope everyone is with me
so far). So I have a huge circle with the North Pole as 0 or 2(pi)
and the South Pole as (pi) radians or 180 degrees and between 0 and
(pi) are the numbers 1, 2, 3, ..... on up to ....9999999 Now 90 degrees
or pi/2 is represented by the number 50000.....000000 just one unit
larger than 4999....999999. And in this framework the last and largest
integer is .....9999999 or frontviewed as 999999.....999999 and it is
just one unit distance shy of (pi).
Now if you add say 2 to ....9999999 the answer is (pi) + 1. If you
add 1 to ....9999 the answer is (pi). If you add 50000.....00000 to
999999.....9999999 the answer is (pi) + 49999....9999999.
So add and subtract will usually land you in the other half of the
circle where you deal with a (pi).
But multiply and divide these Infinite Integers will keep you on the
same Semicircle where there is no (pi) to deal with.
So the question I ask of either Dik or David, is what kind of Algebra
are we dealing with in this Model. Where add and subtract can land you
in the Semicirle where there is a (pi) prefax or if the numbers are
small enough such as ......222222 + .....333333 is ......555555 and
keeps you still on the same Semicircle side without trespassing into
the (pi) side. But where the multiplication and division of these
numbers always lands you in the same semicircle that has no (pi) prefix.
So I am wondering and questioning what sort of Algebra is this? Is it
similar to the Algebra on the Unit Circle when we deal with radians?
You see, in my Model, all of multiply and divide remain in the same
numbers of P-adics, but add or subtract can land you on the imaginary
semicircle where there is a (pi) prefix. So is anyone familar with an
Algebra where add and subtract stray over into the imaginary side
and where multiply and divide are well behaved and remain with the same
type of numbers?
So is this Algebra of my Model even an Algebra? I would guess it is not
because it does not obey transitivity, but I never expected or wanted
them to obey transitivity since they are the numbers on the surface of a
sphere. But given they are intransitive, do they obey any sort of Algebra?
a_plutonium
Archimedes Plutonium wrote:
(snipped)
>
> I answered the above about ....999999 X 10 + 9 in a separate post
> earlier, but the question lingers because I never really addressed the
> Algebra of these Plutonium Numbers as what Wikipedia is listing them
> in a article under "Archimedes Plutonium".
Wikipedia has a nasty habit of involving alot of people on some
article all to
see it evaporate and down the drain by another editor. So I learned
that if
you do anything with Wikipedia to have it posted to a newsgroup where
the
survival of that work will outlive Wikipedia, at least Archimedes
Plutonium's
work will long survive when there is no Wikipedia Encyclopedia. So
here, Wikipedia
should thank me, not the reverse.
Here is what Wikipedia has an article of Archimedes Plutonium.
*** quoting Wikipedia ***
Archimedes Plutonium
>From Wikipedia, the free encyclopedia
· Find out more about navigating Wikipedia and finding information ·
Jump to: navigation, search
This article is being considered for deletion in accordance with
Wikipedia's deletion policy.
Please share your thoughts on the matter at this article's entry on
the Articles for deletion page.
Feel free to edit the article, but the article must not be blanked,
and this notice must not be removed, until the discussion is closed.
For more information, particularly on merging or moving the article
during the discussion, read the guide to deletion.
Steps to list an article for deletion: 1. {{subst:afd}} 2.
{{subst:afd2|pg=Archimedes Plutonium|cat=|text=}} ~~~~ (categories)
3. {{subst:afd3|pg=Archimedes Plutonium (4th nomination)}} (add to top
of list) 4. Please consider notifying the author(s) by placing
{{subst:adw|Archimedes Plutonium|Archimedes Plutonium (4th
nomination)}} ~~~~ on their talk page(s).
For a list of other Usenet personae, see Notable Usenet personalities.
Archimedes Plutonium (born July 5, 1950), also known as Ludwig
Plutonium, wrote extensively about science and mathematics on Usenet.
In 1990 he became convinced that the universe could be thought of as
an atom of plutonium, and changed his name to Ludwig Plutonium to
reflect this idea. He is notable for his offbeat ideas about physical
constants, human evolution, and nonstandard models of infinite
arithmetic [1][2].
Archimedes Plutonium, in his Usenet posts, was the first to describe
the process of biasing search-engine results by planting references,
and coined the phrase search-engine bombing to describe it. This later
became well-known as google bombing[3][4].
Contents
[hide]
* 1 Biographical Sketch
* 2 Plutonium Atom Totality
* 3 Plutonian Integers
* 4 Other Notable Writing
* 5 Quotes
* 6 References
[edit] Biographical Sketch
Plutonium was born under the name Ludwig Poehlmann in Arzberg,
Germany. His family moved to the United States and settled near
Cincinnati, Ohio, where Plutonium was adopted into the Hansen family
and brought up under the name Ludwig Hansen. After changing his name
to Ludwig Plutonium, he began posting to Usenet in 1993. His prolific
posts quickly made him an internet celebrity.
[edit] Plutonium Atom Totality
Plutonium Atom totality is a metaphysical idea that the universe
should somehow be thought of as a gigantic atom of the element
plutonium, Pu 231. It is not believed by most scientists that the
universe considered as a whole is any type of atom, let alone an atom
of plutonium. The cosmic atom, often written ATOM, is a manifestation
of god, or the totality of all things. It is attributed with some
divine properties, although the physical universe in Plutonium
philosophy only obeys natural laws and does not include supernatural
phenomenon [5]
[edit] Plutonian Integers
An integer in Plutonium's philosophical view includes objects which
have a decimal expansion which never ends. Just as the real number 1/3
can be represented as
\frac{1}{3} = .33333...
the infinite integer whose decimal expansion consists solely of 3s is
a valid Plutonian integer
x = ....33333.\,
This type of number resembles the p-adic integers, but it is very
different because it is not considered as a convergent sequence, but
as a philosophically primitive element of the mathematical universe,
an integer. This type of object has no counterpart in standard
mathematics, and all of the results that Plutonium claims for them are
not accepted as part of mainstream mathematics.
The addition and multiplication of Plutonian integers is defined by a
digit-wise procedure. Any product or sum which produces integers with
equal digits are equal. So for example, in Plutonian arithmetic
.....99999999 + 1 is equal to the South Pole point which is imaginary
and is (pi)
So the Plutonium Integers from 1 to the world's largest number .....
9999999 are points on the sphere that stretch from the North Pole to
the South Pole
In general, arithmetic on the Plutonium Integers is the very same
arithmetic on Reals except the final answer is a sequence of
unchanging digits in a place-value For example
3 X ......9999999
first we take 3 x 9 is 27 then we take 3 x 99 is 297 then we take 3 x
999 is 2997 then we take 3 x 9999 is 29997 and so on.
So the final answer of what is 3 X 99999.....999999 (the frontview
of ....99999)
is this number 299999.....99999997
So the Plutonian integers have no continuity structure analogous to
that on the real numbers or p-adics. Since the Plutonium Integers are
the native coordinate system of the
sphere or Elliptic Geometry and when you put a negative sign on all
the Plutonium Integers you have the coordinate points of Hyperbolic
Geometry.
AP writes about a Model of Elliptic and Hyperbolic that is novel
because it joins both of these geometries into one single model. Prior
to this, mathematics saw Elliptic geometry as a sphere model and
Hyperbolic as a saddle surface model, but AP combines both into the
sphere where the inside surface of a hollow sphere is the Hyperbolic
geometry and thus the Plutonium Integers on the outside surface are
positive Plutonium Integers and the inside points are Negative
Plutonium Integers.
It is a theorem of Peano Arithmetic that
\forall x \, (3x \ne -1),
but this is not a property of the Plutonian integers. So the Plutonian
integers violate some of the usual laws of arithmetic.
Plutonium uses this to find counterexamples to many problems in number
theory. For example, he finds Plutonian integers which have the
property that:
a^3 + b^3 = c^3,\,
the counterpart in Plutonian arithmetic to the well known p-adic
statement that there are counterexamples to Fermat's Last Theorem in
any p-adic base. Accepting the Plutonian integers as the true integers
leads to a philosophical idea of counting which is explicitly
infinitary. In this philosophy, Fermat's Last Theorem, which was
proved to be true of the standard integers by Andrew Wiles, is false.
Plutonium often states that the set of all integers is Countable since
All Possible Digit Arrangements forces the Infinite Integers to be
Countable and thus the Reals also are Countable as seen in AP's post
of Newsgroups: sci.math, sci.physics, sci.edu From: a_plutonium
<a_pluton...@hotmail.com> Date: Mon, 15 Oct 2007 22:56:37 -0700 Local:
Tues, Oct 16 2007 12:56 am Subject: #130 Probability definition of
Reals as All Possible Digit Arrangements clears out much of the mess
in Calculus ; new textbook: "Mathematical-Physics (p-adic primer) for
students of age 6 onwards" He also shows that Cantor diagonal method
fails on the Reals as well as fails for the Plutonium Integers since
All Possible Digit Arrangements cannot construct a new Real Number by
any diagonal. AP shows this for the group
00 01 10 11
IF the above group is the universe of Reals or the universe of
Plutonium Integers then no Cantor diagonal can fetch a new combination
of 0 and 1 that is not already existing and that is true no matter if
the group is finite or infinite as AP posted in October 2007 in the
same newsgroups under the same book title.
Plutonium often refers to the integers as Adic Integers. The name
derives from the loose analogy with p-adics. In later writing, he
extends such infinite integers to sometimes include arbitrary ordinal-
like sequences of digits, with some difficult-to-follow and admittedly
inconclusive results [6].
[edit] Other Notable Writing
Plutonium has supported some well known scholarly positions in his
writing. He has questioned the accuracy of narratives about the
historical Jesus, a popular non-mainstream view in early Christian
scholarship[7]. He also formulated a theory of group selection, caused
by warfare, as the source of human intelligence[8]. He is the author
of countless other ideas and speculations, most of which claim to
displace currently accepted mathematical and scientific theories.
[edit] Quotes
* "The whole entire Universe is just one big atom where dots of
the electron-dot-cloud are galaxies."
* "God is Science, and Science is god."
* "God is this one big atom that comprises all the Universe, much
like what Spinoza discovered some centuries past, called pantheism.
Where we are a tiny part of God itself. And where there is a heaven
and hell in part of the atom structure. And where we will be judged by
God when we die and our photon and neutrino souls will reincarnate
once again in a future life somewhere in the Cosmos."
* "The world's finest Bibles are current physics textbooks or
biology or chemistry textbooks such as the Feynman Lectures on
Physics."
* "When you have a foggy notion of what you are working with, it
is impossible to prove much about them."
[edit] References
1. ^ Joseph C. Scott. "Sometime-scientist Plutonium says science is
'gobbledygook'", The Dartmouth, September 25, 1997.
2. ^ Jennifer Kahn. "Notes from Another Universe", Discover, April
2002.
3. ^ http://www.ifergan.org/google-bombing.html
4. ^ Law and Order on Net and Web (September 17, 1997).
5. ^ http://www.iw.net/~a_plutonium/
6. ^ http://www.iw.net/~a_plutonium/, for further information, see
http://mathforum.org/kb/forum.jspa?forumID=13 , Archimedes Plutonium ,
article: 10/16/07 11 #104 In fact the definition of Reals as *all
possible digit arrangements* bars or precludes Cantor ever applying a
diagonal method ; new textbook: "Mathematical-Physics (p-adic primer)
for students of age 6 onwards"
7. ^ http://www.iw.net/~a_plutonium/
8. ^ http://www.iw.net/~a_plutonium/ , see also
http://forum.lowcarber.org/archive/index.php/t-80681.html
Retrieved from "http://en.wikipedia.org/wiki/Archimedes_Plutonium"
Categories: Articles for deletion | 1950 births | American writers |
Living people | Usenet people
*** end quoting Wikipedia ***
a_plutonium
where I had
some editing on the article. But another editor changed much of what I
had written.
For those in the future who are unaware of what this encyclopedia is,
it is a "anyone
can edit this encyclopedia. So that if you make changes, the
likelihood of it staying
there are slim because the next guy that comes along will change what
you have
done or remove it altogether.
So the below is what Wikipedia has written about Archimedes Plutonium
and
in connection with Plutonium Numbers is there a large swell of
interest.
I am archiving these tidbits because I am sure that my writings will
survive
far longer than Wikipedia, and that deep into the future, about the
only human
that people will want to know alot about is Archimedes Plutonium. At
some point
in the future history of humanity, AP will eclipse even Jesus.
*** quoting what Wikipedia article on Archimedes Plutonium ***
Archimedes Plutonium
>From Wikipedia, the free encyclopedia
· Interested in contributing to Wikipedia? ·
Jump to: navigation, search
This article is being considered for deletion in accordance with
Wikipedia's deletion policy.
Please share your thoughts on the matter at this article's entry on
the Articles for deletion page.
Feel free to edit the article, but the article must not be blanked,
and this notice must not be removed, until the discussion is closed.
For more information, particularly on merging or moving the article
during the discussion, read the guide to deletion.
Steps to list an article for deletion: 1. {{subst:afd}} 2.
{{subst:afd2|pg=Archimedes Plutonium|cat=|text=}} ~~~~ (categories)
3. {{subst:afd3|pg=Archimedes Plutonium (4th nomination)}} (add to top
of list) 4. Please consider notifying the author(s) by placing
{{subst:adw|Archimedes Plutonium|Archimedes Plutonium (4th
nomination)}} ~~~~ on their talk page(s).
For a list of other Usenet personae, see Notable Usenet personalities.
Archimedes Plutonium (born July 5, 1950), also known as Ludwig
Plutonium, wrote extensively about science and mathematics on Usenet.
In 1990 he became convinced that the universe could be thought of as
an atom of plutonium, and changed his name to Ludwig Plutonium to
reflect this idea. He is notable for his offbeat theories about
physical constants, human evolution, and nonstandard models of
infinite arithmetic [1][2].
Archimedes Plutonium, in his Usenet posts, was the first to describe
the process of biasing search-engine results by planting references,
and coined the phrase search-engine bombing to describe it. This later
became well-known as google bombing[3][4][5].
Contents
[hide]
* 1 Biographical Sketch
* 2 Theories
o 2.1 Plutonium Atom Totality
o 2.2 Plutonian Integers
o 2.3 Other
* 3 Quotes
* 4 References
[edit] Biographical Sketch
Plutonium was born under the name Ludwig Poehlmann in Arzberg,
Germany. His family moved to the United States and settled near
Cincinnati, Ohio, where Plutonium was adopted into the Hansen family
and brought up under the name Ludwig Hansen. After changing his name
to Ludwig Plutonium, he began posting to Usenet in 1993. His prolific
posts quickly made him an internet celebrity.
[edit] Theories
Archimedes Plutonium is the author of many notable theories, most of
which claim to displace currently accepted scientific theories.
[edit] Plutonium Atom Totality
Plutonium Atom totality is a metaphysical idea that the universe
should somehow be thought of as a gigantic atom of the element
plutonium, Pu 231. It is not believed by most scientists that the
universe considered as a whole is any type of atom, let alone an atom
of plutonium. The cosmic atom, often written ATOM, is a manifestation
of god, or the totality of all things. It is attributed with some
divine properties, although the physical universe in Plutonium
philosophy only obeys natural laws and does not include supernatural
phenomenon [6]
[edit] Plutonian Integers
An integer in Plutonium's philosophical view includes objects which
have a decimal expansion which never ends. Just as the real number 1/3
can be represented as
\frac{1}{3} = .33333...
the infinite integer whose decimal expansion consists solely of 3s is
a valid Plutonian integer
x = ....33333.\,
This type of number resembles the p-adic integers, but it is very
different because it is not considered as a convergent sequence, but
as a philosophically primitive element of the mathematical universe,
an integer. This type of object has no counterpart in standard
mathematics, and all of the results that Plutonium claims for them are
not accepted as part of mainstream mathematics.
The addition and multiplication of Plutonian integers is defined by a
digit-wise procedure. Any product or sum which produces integers with
equal digits are equal. So for example, in Plutonian arithmetic
.....999999 + 1 \,
is a number with a decimal expansion which ends in an infinitely long
string of zeros, but starts with a 1 in the "front end".
1.....000000 \,
This number in Plutonium's understanding is analogous to the antipode
of zero on a large geometric sphere, like the Riemann sphere.
Plutonium does arithmetic on infinite Integers by adding and
multiplying ever larger finite subsequences until the place values
stop changing. The operations of addition and multiplication violate
some of the usual laws of arithmetic, and Plutonium uses this to find
counterexamples to many problems in number theory. For example, he
finds Plutonian integers which have the property that:
a^3 + b^3 = c^3,\,
the counterpart in Plutonian arithmetic to the well known p-adic
statement that there are counterexamples to Fermat's Last Theorem in
any p-adic base. Accepting the Plutonian integers as the true integers
leads to a philosophical idea of counting which is explicitly
infinitary. In this philosophy, Fermat's Last Theorem, which was
proved to be true of the standard integers by Andrew Wiles, is false.
Plutonium often insists that the set of all integers is of the same
cardinality as the real numbers because both the real numbers and the
integers consist of "All Possible Digit Arrangements". He often refers
to the integers as Adic Integers, which derives from the loose analogy
with p-adics. In later writing, he extends such infinite integers to
sometimes include arbitrary ordinal-like sequences of digits, with
some difficult-to-follow and admittedly inconclusive results [7].
[edit] Other
Plutonium has supported some well known scholarly positions in his
writing. He has questioned the accuracy of narratives about the
historical Jesus, a popular non-mainstream view in early Christian
scholarship[8]. He also formulated a theory of group selection, caused
by warfare, as the source of human intelligence[9]. He has tried to
revive a once mainstream but currently obsolete view that the charge
of the nucleus is due to nuclear electrons, a view which fell out of
favor with the 1934 discovery of the neutron[10].
[edit] Quotes
* "The whole entire Universe is just one big atom where dots of
the electron-dot-cloud are galaxies."
* "God is Science, and Science is god."
* "God is this one big atom that comprises all the Universe, much
like what Spinoza discovered some centuries past, called pantheism.
Where we are a tiny part of God itself. And where there is a heaven
and hell in part of the atom structure. And where we will be judged by
God when we die and our photon and neutrino souls will reincarnate
once again in a future life somewhere in the Cosmos."
* "The world's finest Bibles are current physics textbooks or
biology or chemistry textbooks such as the Feynman Lectures on
Physics."
* "When you have a foggy notion of what you are working with, it
is impossible to prove much about them."
[edit] References
1. ^ Joseph C. Scott. "Sometime-scientist Plutonium says science is
'gobbledygook'", The Dartmouth, September 25, 1997.
2. ^ Jennifer Kahn. "Notes from Another Universe", Discover, April
2002.
3. ^ http://www.ifergan.org/google-bombing.html
4. ^ Law and Order on Net and Web (September 17, 1997).
5. ^ http://www.kibo.com/exegesis/search_engine_bombing.shtml
6. ^ http://www.iw.net/~a_plutonium/
7. ^ http://www.iw.net/~a_plutonium/, for further information, see
http://mathforum.org/kb/forum.jspa?forumID=13 , Archimedes Plutonium ,
article: 10/16/07 11 #104 In fact the definition of Reals as *all
possible digit arrangements* bars or precludes Cantor ever applying a
diagonal method ; new textbook: "Mathematical-Physics (p-adic primer)
for students of age 6 onwards"
8. ^ http://www.iw.net/~a_plutonium/
9. ^ http://www.iw.net/~a_plutonium/ , see also
http://forum.lowcarber.org/archive/index.php/t-80681.html
10. ^ http://wee.iw.net/~a_plutonium , see also H.E. White Phys.
Rev. 35, 441 - 444 (1930) for an entry point into the mainstream
discussion.
a_plutonium
(much clipped)
>
> I am archiving these tidbits because I am sure that my writings will
> survive
> far longer than Wikipedia, and that deep into the future, about the
> only human
> that people will want to know alot about is Archimedes Plutonium. At
> some point
> in the future history of humanity, AP will eclipse even Jesus.
>
> *** quoting what Wikipedia article on Archimedes Plutonium ***
>
> [edit] Plutonium Atom Totality
>
> Plutonium Atom totality is a metaphysical idea that the universe
> should somehow be thought of as a gigantic atom of the element
> plutonium, Pu 231. It is not believed by most scientists that the
> universe considered as a whole is any type of atom, let alone an atom
> of plutonium. The cosmic atom, often written ATOM, is a manifestation
> of god, or the totality of all things. It is attributed with some
> divine properties, although the physical universe in Plutonium
> philosophy only obeys natural laws and does not include supernatural
> phenomenon [6]
>
> *** end quoting Wikipedia ***
>
I realized before I wrote those lines "even Jesus" that I would turn
away
alot of people to ever want to read me again. I wrote those lines
because
I am not a megalomania but rather very humble and down to earth. I
know
and realize that the ancient scientist of Democritus eclipsed all the
religions
of his time-- the Greek and Roman Gods yet today almost every human
knows
their bodies are made up of atoms like carbon, oxygen, hydrogen etc.
Some
one quoted as saying words to the effect "Gods come and go, but the
Atomic
theory endures". So am I a megalomania about my worth to science? I
would
say no. I would say that scientists as a whole are cowards who seldom
if ever
come forth in public to state their views of religion versus science.
Where they
spend their entire working life doing science but never brave enough
to come
forth and say that religion is a harm to humanity.
Never saying that unless we curb human overpopulation that noone in
the
future will eclipse anyone because there will not be a human around.
To
voice out against overpopulation and global warming and nuclear
weapons
proliferation. To voice out that religion is counter to human
population control
and counter to global warming and counter to nuclear deterrance.
It is science that has brought humanity to modern living but it is
religion that has
the political control over most of humanity and which is not looking
to make humanity
live long and prosper but is only looking to increase that specific
religion. We see it
in South America where the Catholic religion is saying have as many
kids as you can.
We see it in the Middle East and Asia where religion encourages dense
populations in
order to have plenty of warriors and fighting soldiers. We see it here
in the USA where
immigration is rapidly filling up this country.
Am I am misanthrope? I would say no, for honestly I never heard of
this word until about
1994 or thereabouts on the Internet reading a post from someone who
called someone a
misanthrope. So I looked it up and saw that it meant a hatred of
humanity. How bizarre, I
thought, that some people can actually hate humanity. But I guess if
people commit suicide
then misanthrope is not so distant. I am not a misanthrope for if I
were, it would not explain why
I spent my life in doing discovery of science and to understand the
world around us. If I hated
humanity, I sure would not like to find out the wonders of the world
and share them with others.
No, I am neither a megalomania nor a misanthrope. I am a scientist who
recently amassed
a book titled the possible extinction of our species in the future and
because I wrote that
book as well as another book titled where science replaces religion in
the future, that I feel
obliged to make comments such as the above "eclipse Jesus".
Just within my own lifetime I turned 180 degrees where in youth I
would have said it is almost
impossible for the human species to go extinct, and now, here in the
last decades of my life
I come to the sobering view that not only is extinction possible of
humanity, but at the slow rate
of response to our looming crisis of (1) Nuclear weapons (2) human
overpopulation (3) Global
Warming that the chances of a human extinction are larger than 50 to
50. And religion is not
helping but one of the accelerants.
By this time in our history, many countries and continents should have
laws restricting human
births, so that we freeze human population so that everyone can have a
decent life. Instead, we
populate like rabbits and then have a nuclear war winnow the numbers
down. We encourage
families to have as many kids so that they will demand of limited
resources and create economic
expansions all so that we can make more money while we destroy
environments of continents
and send thousands of animal and plant species into extinction.
Instead of seeking energy independence by destroying and using up
resources it is better
to have limited human population that can sustain itself totally on
renewable. Back in the
year 1899, the entire human population could live on renewable energy
sources. But instead,
the crazy modern society wants to fill Earth with 15 billion humans so
that every corner of the
globe is chock full of people, mostly miserable and with the only way
out is a nuclear war.
So, unless Scientists who know the best about the world, step forward
and be brave and be
honest and tell the world, either you curb population and curb nuclear
weapons and solve
global warming that this species we belong to, will go extinct.
For instance, in the presidental campaigns in the USA, our candidates
are talking about politics
that is roughly 150 years back in time appropriate with health care
reform if you vote form me.
What they should be talking about is (1) laws to curb population (2) a
M.A.D. Fleet to deterr
nuclear weapons (3) thistle seed dropped by airplanes in apogee of
flight to solve global warming.
Our politicians are 150 years back in time about what we need to solve
and fix.
And it is sad that a TV actor has more of a chance to become USA
president than any of our
scientists who know what the problems are and have solutions.
So I will continue to make statements like "eclipse Jesus" if I think
it can do any good.
I now believe that pulsars we see in outer space of those star systems
that give a constant
steady pulse are civilizations much older than us and who have reached
their oncoming extinction.
That they then burst out in a last communique to the rest of the
Cosmos "we were here but not
smart enough to have marshalled the resources of our Solar System and
on the brink of
extinction."
We need scientists who are brave to post what they see and feel, not
cower away.
a_plutonium
everyone that in the past 20 years
this planet is showing so many symptoms of "going wrong" whether
economics or environment
or social respect, that the politics of old need to be changed. Here
in the USA, the president
candidates are saying "vote for me and I will put health care money in
your pockets" whereas the
world needs to solve (1) nuclear weapon proliferation (2) human
overpopulation and (3)
global warming.
So if politics is 150 years behind the times. I ask for all scientists
and all those people in
environment and all those connected with science instead of religion
to come together. That
we need scientists running the show.
That countries which run democratic elections generally never elect
the best qualified people to
run the country. And the best qualified people come from the ranks of
science.
So scientists should all get together and form a union or en-masse and
list the 3 major political
problems of our time and to then act upon solving them. That politics
of the past is no longer
able to fix problems and that scientists have to join together. We
should no longer look upon
ourselves as servants of elected leaders, but rather instead, as
superiors of politicians who lack
the wisdom in solving the most important problems.
In movies, the scientists are always those guys with a minor role
where the politicians are
doing all the decisions. We reached a point in history where that has
to change and where
the scientists are leading.
All those pulsars in the night sky, I bet 90 percent are failed
civilizations on distant and lonely
planets where their life is about to go extinct. I bet most of those
could have avoided extinction
if their scientists ran the politics.
It is funny and ironic that in the USA, as for the economics we hire a
Princeton University
professor of economics to run the show for economics, yet we have a
TV actor candidate
for president who if elected would run the show for the entire
country. I do not know why
I am the only one to raise concerns that our country is in such bad
shape that a TV actor
has more of a chance than thousands of better qualified persons.
Proginoskes
Cthulhu on a cracker!!! An entire AP post which I agree with!!!
As for why qualified (scientific) people don't run for political
office, well he should look at what the media do: expose every single
dirty secret which ever occurred in someone's life, and spin the good
ones into bad ones. (Kerry was a decorated Vietnam vet, and yet he
lost to a ... a ... draft dodger ...) The qualified people are smart
enough to not put themselves through this process.
Plus, you need money -- lots of it -- unless you want to run as a
Republocrat.
--- Christopher Heckman
The Dark Ages never ended.
Archimedes Plutonium
its unnecessary war in Iraq to Global Warming to nuclear arms
proliferation in North Korea and Iran. A world that seems to be caroming
from one disaster to another disaster.
And one of the problems is the lack of qualified leaders in the world
where the USA has a election system that just fails miserably to place
qualified people into high ranking jobs. About the only suitable
qualified people for the job they hold is the Federal Reserve. A country
which is supposed to lead the world, has a better chance of electing a
TV actor than thousands of better qualified people.
The world has changed dramatically since 1899 where the 20th century
politics of "vote for me and I will fill your pockets with health care
reform". Politics of the 21st century needs to address worldwide trends
of human overpopulation, global warming, nuclear weapons which are
antithema to present politicians.
So I propose that a new organization be borne and headquartered
somewhere. Where all scientists and anyone interested can join and
become a member. The goal of this organization is to lead the world out
of troubles and looming disasters. Since present politicians lack the
foresight and ability to lead properly, this new organization is out in
front on all the major issues. It will raise alot of money and with the
money it will educate the citizenry of the world via newsmedia and
movies and books. It will not have an army and can not force countries
to do things but it will bring to light what countries are astray
and doing bad things.
It will endorse some political leaders and will be active informing
about corrupt ones.
Up till now, the scientists and engineers and the professional class of
society have been mostly quiet deer in the forest of world politics, and
have come out of the forest only to act as a servant to the political
powers. Since most of our pressing problems are of a scientific nature,
it stands to reason that scientists need to become more active in
politics. Instead of sitting in the backseats, scientists should be in
the drivers seat.
So the world needs to form and give birth to such an organization, which
daily gives news reports and data on what needs to be done on the three
most important challenges of our time.
Dik T. Winter
>
> Dik T. Winter wrote:
> > In article <4715E990...@hotmail.com> Archimedes Plutonium <a_plu...@hotmail.com> writes:
> > ...
> > > Note to Dik Winter: you told me in the mid 1990s that if I get the
> > > operations defined on "my P-adics" that you would then tell me what
> > > its algebra was such as field or ring. Well I have those operations
> > > defined for the Decimal P-adics, so could you kindly tell what the
> > > algebra is over my p-adics? I am guessing it is either a no-algebra or
> > > a completed-field matching the Reals.
> >
> > It has also been shown to you in the mid 1990s that the 10-adics are the
> > cartesian product of the 2-adics and the 5-adics. They are not a field
> > because there are zero-divisors. You already know that in the 10-adics
> > there are two idem-potents not equal to either 0 or 1. Call them a and
> > b, it is easy to show that (a - 1) * a = (b - 1) * b = 0.
> >
> > In general, each 10-adic can be written as a pair (p, q) where p is a
> > 2-adic and q a 5-adic. One of the idempotents a and b corresponds to
> > the pair (1, 0) and the other to the pair (0, 1).
>
> Would you care to comment not on the 10-adics.
As you mention "p-adics" I thought you meant "p-adics" as normally used
in mathematics, but obviously you have your own private terminology.
> Would you care to comment on "All Possible Digit Arrangements" for
> ......000001 to ....99999999999
>
> Where the operations of these numbers are not P-adics.
>
> Where the operations are borrowed from Reals between 0 and 1 in Reals
> and the final answer of any operation is what digits do not change such
> as
If you mean mirroring, doing the operation on the reals, and mirroring back
again, I am wondering what the difference is between 1 and ...999990.
And is ...00018 * ...00028 = ...0006642?
Or do you mean something else with your "borrowing"?
> So I am asking you, whether these Decimal P-adics also transfer all
> the Field Algebra properties for which the Reals possess? Keep in mind
> that these Decimal P-adics do not end with ....999999 but continue with
> (pi) as South Pole and come back around a circle to the North Pole of
> 2(pi).
This makes no sense at all.
> Mine are totally different in that they are not Reals but having the
> same operations as Reals.
In what way are they different, except that the notation is reversed?
> P.S. someone has found a way of blocking my posts from ever reaching
> the newsgroup so that once I send this post, the thread increases by
> one more number, but this post never actually shows up in the thread
> for anyone to read. As the above #135 never appeared and #133 appeared
> almost 12 hours later and only after I reposted #133 from a different
> ISP. So I am afraid some clowns have utilized some method where a post
> never shows up on sci.math. It maybe that Google is fixing something,
> but why would another ISP not have the trouble?
I think the problem is with you. #133 and #135 both show up here as
posted through google.group. Dated:
#133 16 Oct 2007 19:53:28 -0700
#135 17 Oct 2007 03:29:28 -0700
A bit of paranoia can be healthy, but too much is bad.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Dik T. Winter
> it is the world's largest prime number, since no number prior divides
> into it evenly.
What is the remainder when you divide it by 7? I would think it is
divisible by 7, but perhaps I do not understand the operations as you
define them well-enough.
Dik T. Winter
...
> The P-adics as defined in this book are infinite leftward strings of
> all possible
> digit arrangement and whose operations are the same as for Reals as
> a Cauchy sequence to the final answer.
What is 7 * 142657...1428571?
> Dividing 3 into 88888......88888871 in the new P-adics which I call
> Decimal P-adics not 10-adics is this:
>
> 3 into 8 is 2 with 2 remainder. Carry the 2 and we have 28.
> Then 3 into 28 is 9 with 1 remainder. Carry the 1 and we have 18.
> Then 3 into 18 is 6 and we repeat the block of 296 where we have
> 296296296 and 3 does not divide 71 evenly so the entire
> number is prime.
No, by that method you will see that the number is divisible by 71.
> .....999997
Is divisible by 7. Using your method:
7 into 9 is 1 with 2 remaining
7 into 29 is 4 with 1 remaining
7 into 19 is 2 with 5 remaining
7 into 59 is 8 with 3 remaining
7 into 39 is 5 with 4 remaining
7 into 49 is 7 with nothing remaining.
We repeat the block of 142857 where we have 142857142857 and 7 dies
divide 7 evenly, so the entire number is divisible by 7. Note that
using this method the number is also divisible by 97, 997, 9997, etc.
Jesse F. Hughes
> So I propose that a new organization be borne and headquartered
> somewhere.
See, it's this sort of forward-thinking that sets you a breed apart.
--
Jesse F. Hughes
"/Monster Ballads/ is packed with pure hits from the artists who taught
us how to love." -- As seen on TV
Archimedes Plutonium
Good try but not true.
The definition as setup in what I am going to rename as AP-adics so as
to not confuse with P-adics (as Wikipedia teaches me to call them
something different).
Anyway the definition of multiplication and division uses a radix if
there is a remainder. And the final answer is a Cauchy Sequence over all
the piecewise divisions. So if the radix disappears and never again
shows up then the number is composite, but if the radix continually
shows up, even though one or two piecewise divisions is even, means the
final answer is composite.
7 into 97 is 13.8
7 into 997 is 142.4
7 into 9997 is 1428.1
7 into 99997 is 14285.2
7 into 999997 is 142856.7
7 into 9999997 is 1428571
7 into 99999997 is 14285713.9
and the fractional radix repeats in a block
So the Cauchy sequence of the above never eliminates the radix, does it,
so it is Prime not composite.
Just because you can find one smooth even division every periodically in
the sequence does not make it overall Composite. To be overall Composite
then the Cauchy Sequence stops yielding a radix answer.
By the way, I was doing some checking and quantity of Primes in the
...999 series matches the quantity of primes in the ....00000 series.
Mathematicians have never explored the fact that the number of primes at
the end of the Counting Numbers is the same quantity as the beginning
where you have 25 Primes in the first 100 counting numbers and you have
25 Primes in the last 100 Counting Numbers where ....999997 is the
world's largest prime. But the same quantity exists in ....11111 series
as well as .....22222 series as well as ....33333 series etc.
I have not checked whether the series such as .....454545 would have
25 Primes in their first 100 Counting Numbers but suspect that is true.
What this tells us is that the Prime Distribution Theorem in mathematics
is only locally true for a Series of Primes out to a large number but
not true overall for Mathematics. For the Primes are distributed in the
Counting Numbers as a layered structure that repeats itself such as a
onion layering.
Archimedes Plutonium
Dik T. Winter wrote:
> In article <471706E4...@hotmail.com> Archimedes Plutonium <a_plu...@hotmail.com> writes:
> ...
> > But we look at the two preceding numbers and particularly .....9999997 and
> > it is the world's largest prime number, since no number prior divides
> > into it evenly.
>
> What is the remainder when you divide it by 7? I would think it is
> divisible by 7, but perhaps I do not understand the operations as you
> define them well-enough.
In a previous post I outlined that division. Division is the same as
Reals only the final answer is a Cauchy Sequence of those digits that
remain the same in place value in further divisions. So the number
99999....99997 is Prime because although a few periodic divisions do
turn out to be evenly divided the next block is a radix fraction. To
be composite means the Sequence never yields a radix fraction to infinity.
2 divided into .....66666668 never yields a radix fraction and so is
Composite.
Question Dik: what algebra exists for the points on the unit circle? Do
those points have an algebra?
a_plutonium
online encyclopedia
where they used anyone as an editor. So anyone could access this
encyclopedia and read
what they had on a topic, but more than that, they could edit and
change what was written on
the topic. They did this because normally a encyc takes alot of human
man hours of work,
whereas if you allow free editing you can build a encyclopedia in a
hurry, although the
accuracy and quality is alot to be desired. I experimented with
Wikipedia with an entry of
John Bell's Superdeterminism and to my horror found that my entry
which is the world's finest
entry on John Bell's Superdeterminism explained in a paragraph that
some "other" editor
quickly destroyed it with philosophical gobbledygook. So the trade off
is that Wikipedia
company has a online free encyclopedia but the quality is a low
quality. I still use
Wikipedia for convenience items but not for anything that requires
accuracy.
I want to save this discussion page in Wikipedia on the recent entry
of "Archimedes Plutonium"
because of the habit that where one editor spends a 8 hours of work in
establishing a page
and another editor comes along and trashes the entire page for some
bureacratic or bully-hate
reason. So one guy spends 8 hours while the other spends 8 seconds to
remove.
And my archive, I am confident will last longer than any Wikipedia
encyclopedia, just as
Democritus outlasted everybody and every form of communication with
his Atomic Theory.
So in the far future, everyone will know Democritus and Archimedes
Plutonium, but where
Wikipedia encyclopedia had disappeared in the intervening centuries.
*** quoting discussion page of Wikipedia under "Archimedes
Plutonium"***
Talk:Archimedes Plutonium
>From Wikipedia, the free encyclopedia
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Contents
[hide]
* 1 Subject's writing as source for subject's views
* 2 Er, what is this page doing here?
* 3 Explanation-- For everybody
* 4 Another approach
* 5 Harrasment, specious, etc.
* 6 Plutonium arithmetic
* 7 Please No Undue Weight
* 8 Yet another reason not to discuss AP's arithmetic.
[edit] Subject's writing as source for subject's views
Hi! Arthur, I see you just deleted a large chunk about his views with
the comment Remove things based only on self-published USENET
nonsense. It would seem to me that in writing about a person's views,
their own writing is a perfectly good source. Are you questioning the
quality of the summarization? If not, it seems like the material is
sourced and relevant, and would be worth keeping. Thanks, William
Pietri 23:23, 17 October 2007 (UTC)
Whether a particular Usenet post actually came from AP or not is not
verifiable. Now, I know that AP almost doesn't exist except on Usenet,
but that doesn't mean that Usenet posts magically become reliable
sources for AP's views. If we can't verify they come from AP, I'm
afraid they're worth little. Phiwum 01:40, 18 October 2007 (UTC)
I didn't suggest that magic was involved, thanks. Especially given
that we are talking about a Usenet personality, I think the
presumption that the linked posts represent his views is reasonable
absent some reason to think otherwise. We should and do make similar
presumptions about who owns a web site or that a reporter has quoted
somebody accurately. If you think that these are forged, you could
probably contact him directly. William Pietri 03:38, 18 October 2007
(UTC)
We must understand the reason for this editorial policy.
People who made comments online that they would rather forget are
annoyed if someone digs up a usenet post that they do not agree with
anymore or that they wrote in a moment of pique. They want to stick
with the line that "usenet is not verifiable". Let them. AP posts have
been archived by himself, and are available through his website. They
have content which is relatively stable, and they are reliable
references for his writings. He refers to them as "books published
online" on his website, which suggests that they are not going to
change very much in the future.Likebox 05:45, 18 October 2007 (UTC)
No, the policy is not motivated by editors' desire to deny
their own postings. Indeed, I'd guess that most of the editors arguing
Usenet is not a reliable source are not Usenet posters. But if AP
archives his posts on his website, then you could consider citing his
website rather than Usenet. (That he calls certain posts "books" does
not mean they are stable, by the way.) Phiwum 10:25, 18 October 2007
(UTC)
To William: I'm sympathetic to that view, but this discussion
has occurred repeatedly in the past and consensus has been that Usenet
posts are, by and large, not RS. On the one hand, it does seem an odd
policy to apply to a fellow known almost exclusively for his Usenet
presence. On the other hand, given that we cannot verify authorship,
the policy has some sense to it. As far as contacting AP to ask him if
this or that post is his, well, I suspect that there would be some
resistance to that notion. But before settling that question, let's
see whether this resurrected article lives through the week. Phiwum
10:25, 18 October 2007 (UTC)
[edit] Er, what is this page doing here?
As much as I'm interested in AP, this page was deleted and redirected
to Notable Usenet personalities (as we all know). Now, I didn't vote
in favor of deletion, but recreating this page just doesn't seem
particularly kosher to me. What new justification has been found?
Phiwum 01:37, 18 October 2007 (UTC)
Good question. I hadn't noticed that. Looking at the three different
AfDs, it seems there's a lot of controversy. On a strict numeric
basis, the last AfD was a keep, but the closing admin decided it as a
delete mainly due a concern that it was mocking the subject. This
article doesn't seem to do that, so I don't see a big issue with the
recreation. Perhaps the creator of this version could explain his
intentions? William Pietri 03:46, 18 October 2007 (UTC)
Yep, it's been discussed three times (2nd AfD, 3rd AfD) and the last
decision was to delete, primarily because AP's theories were not
notable (WP:OR), he was considered marginally notable enough for a WP
article, and mostly because of the lack of sources. Which is why I
moved his info to a single paragraph summary at Notable Usenet
personalities (talk). In fact, that was the whole reason for creating
that page, in order to have a place to list "notable" Internet posters
who otherwise were not noteworthy enough for an entire separate
article. User:Likebox says AP is interesting, but that is obviously
not sufficient criteria to justify a WP article. Unless there are
compelling reasons to list all of AP's theories on WP, I don't see why
a simple short entry on Notable Usenet personalities is not good
enough. - Loadmaster 15:14, 19 October 2007 (UTC)
[edit] Explanation-- For everybody
The reason I wrote this page is because I find Archimedes Plutonium's
intriguing, and I think he is a notable personality. Many other people
agree, but there was controversy about this page in the past. The
controversy centered on the following points:
1. The article did not adhere to Wikipedia standards for
biographies of living persons. Large parts of it were defamatory.
There were many mocking comments of a personal nature. Archimedes
Plutonium asked that the page be removed for that reason specifically.
2. The article did not include all notable references, and large
parts were unsourced.
3. AP has a history of antagonism toward Wikipedia in general.
I tried to fix all these problems in the rewrite. The article is
properly sourced, it includes a fair summary of his writings, and is
respectful. The summary of his work has been deleted for some reason,
but I hope the editor will change his mind. The biographical material
sticks to bare-bones stuff, and does not have anything of a defamatory
nature.
One reason I wrote this page is because the AfD discussion was biased
by a voting paradox. Although most people wanted the page to stay, the
voting procedure lumped together those who thought "it should stay,
but my second choice is that it should be merged", with "it should be
deleted, but my second choice is it should be merged" together with
"it should be merged". This means the article was going to get merged
even if nearly everyone thought it should stay. Combined with
Plutonium's objections, the outcome of the editorial decision making
process was, in my opinion, preordained.
AP is definitely notable, he has been something of an inspiration to
me personally, because of he was such a prolific source of original
unconventional ideas. His infinite integer arithmetic continues to be
a source of new ideas for me, personally. I hope this presentation
will satisfy everyone, including Mr. Plutonium.Likebox 05:18, 18
October 2007 (UTC)
This is a misleading summary of the deletion debate. As I recall it,
the most popular reason to delete was notability, not BLP, sourcing or
especially AP's antagonism. And, in general, one doesn't fix BLP
problems by removing every acknowledgment that AP's theories are not
regarded as acceptable science or mathematics by any trained scientist
or mathematician. BLP does not mean: ignore all criticisms.
(Pretending, for instance, that AP's discussion of P-adics involves a
well-defined mathematical structure is extremely misleading.) Phiwum
10:31, 18 October 2007 (UTC)
It is only misleading summary of the AfD if you don't see the
paradox that a guy who has worldwide fame which could only be gained
through the internet is the only thing that the internet encyclopedia
does not cover at excessive length.
Ludwig's discussion of P-adics is not a well-defined discussion of
the p-adics, but that's because he is not discussing P-adics. He is
discussing infinite integers. He wants a model where the set of all
integers have equal cardinality to what we usually think of as the
real numbers. Models like that are well known to exist in formal set
theory, for essentially logical reasons, but they don't have the other
properties which you want, in particular Fermat's Last Theorem is
still true. I don't know if it is possible to make a good model of the
integers this way, but I think it likely is. I personally tried to
make it a rigorous construction for a while. It's certainly an
inspiring conjecture that nobody else would have been brave enough to
think of, and of course he has a lot of confusion about it--- that's
what happens when you're doing something new. I talked it over with
people, and they had some ideas, but it wasn't obviously false or
obviously true. It's only obviously false in Cantor's philosophy of
infinity, which he obviously doesn't adhere to. Just because all
mathematicians, for convenience, have decided to settle on exactly one
view of the infinite does not mean that they are in any objective
sense "right". And it isolates and marginalizes people with a
different philosophy of the infinite, like AP.
Although his confusions are understandable, they are colored by
his personality and biased by his self-aggrandizement. He is also
never very careful about his arguments, so it is difficult to make
sense of a lot of them. As far as "trained scientists and
mathematicians", yes, I agree that most mathematicians and scientists
think that the integers are a stable structure that they understand.
This is not so for logicians or set theorists, who are well aware that
the infinite set of integers is a very difficult structure to define,
and that any new models are welcome. This is not to say that his views
should be presented anywhere other than on a short page devoted to his
ideas. If in the future people will become interested in non-standard
models of arithmetic based on the p-adics (as many publicly are and
were in history) then things will be different.Likebox 14:26, 18
October 2007 (UTC)
Well, the idea of a non-standard model bases on p-adics may be
feasible. The idea of a non-standard model based on the 10-adics is
not; it's not an integral domain. But an unpublished mathematical
concept, no matter how earth-shaking it may be, has no place on
Wikipedia unless it has news coverage. AP, or Archie, has only limited
coverage outside of Usenet. - Arthur Rubin | (talk) 15:03, 18 October
2007 (UTC)
There is no problem with using 10-adics. They just don't
have the property that for all x,y, xy=0 implies x=0 or y=0. So what.
So maybe that's not true for infinite integers. Who can tell? When was
the last time you saw an infinite integer? So the model of arithmetic
is wacky, it is zany, and it is sort-of non-canonical. Big deal. It's
still a fun idea. It's notable because he got the whole scientific and
mathematical world thinking about it and talking about it, and that's
well documented.Likebox 16:44, 18 October 2007 (UTC)
To Likebox: One does not need to depend on Cantor's philosophy
in order to judge that AP has no coherent mathematical theory at all.
To take one recent example: he has concluded that e^(pi * i) = 1
because i = 0. But, in any case, this isn't a referendum on the
quality of AP's work. My questions are the following: (1) Is it
reasonable to revive a recently deleted page when there is no new
argument for notability? (2) Is it reasonable to write about AP's
mathematics without an explicit acknowledgment that neither AP nor
anyone else has never given a coherent description of his theory? That
is, does BLP require ignoring existing (on Usenet) criticism of AP's
theory, or would this violate Undue Weight?
Well, if i is zero, then e^(pi *i ) does equal 1, doesn't
it? Who else in the history of the world has written things like this?
There is absolutely no need to criticize it yet again. The whole world
already does that in every textbook and every lecture. There is a need
to preserve it, because it is stimulating, and it is original, and it
is funny, and it is thought-provoking.Likebox 16:44, 18 October 2007
(UTC)
Wikipedia does not exist to preserve every
stimulating, original, funny and thought-provoking idea (not that I
consider this idea either stimulating or thought-provoking). Phiwum
17:40, 18 October 2007 (UTC)
That's exactly why I didn't mention that
particular idea in the article.Likebox 18:03, 18 October 2007 (UTC)
But I don't know that (2) matters, since I think the answer to
(1) is "no".
And I think the answer is "yes", and that it was "yes"
during the last AfD, and will be "yes" in the foreseeable future. I
think the majority of editors in the last AfD thought the same
thing.Likebox 16:44, 18 October 2007 (UTC)
Finally, in passing, I dispute your claim that set theorists
and logicians regard the integers as very difficult to define or that
they welcome AP's contributions. Yes, unusual constructions of numbers
are interesting (say, Conway's work), but what AP has written about is
much too confused to count as a contribution. And even if people
become interested in infinite digit strings, it would be doubtful in
the extreme that AP contributed significantly to that interest, much
less contributed to a foundation of such structures. But, of course,
this aside is irrelevant to the real issues here. Phiwum 15:06, 18
October 2007 (UTC)
Of course they don't welcome them into the journal of
symbolic logic. But I welcome them as informal ideas! There are other
people who welcome them too, and why not? It does no harm to think
about things that turn out to be nonsense, and it sometimes does a lot
of good.
I would urge you to try to define the integers in a way that includes
all finite integers but excludes infinite integers. That's well known
to be impossible, because if it is consistent that there are
arbitrarily large integers, you can add a symbol C (which represents
an infinite integer) and the axioms that C>1, C>2 ... C>n..., for all
finite n. This is arithmetic a-la Abraham Robinson. Now if you can
have digit expansions which are "C" long, you get some version of
Plutonium arithmetic, except without the wacky identities. Many
people, including AP, understand this intuitively. The only debate in
logic is over what kind of structures are interesting to play with.
Logicians have their own sandbox with their own toys, and AP has his
own too. It is not obvious that AP's version is significantly less
consistent, although he changes his mind a lot because there is a lot
of freedom. The reason AP's integers are so cute and funny is because
they are uncountable, because there is a map from the usual real
numbers to the Plutonium integers. So it gives a weird new picture of
the mathematical universe where the real numbers are countable! That's
the weirdest and funniest mathematical idea I've heard since Cantor.
It's mind bogglingly original.
It is not impossible to define the set of natural
numbers in ZFC so that it includes only finite numbers. Indeed, it is
common to do so. Now, you may be thinking instead of the problem of
defining a first-order theory for N that does not allow non-standard
models. So, let's agree this cannot be done. It does not follow that
non-standard models are "some version of Plutonium arithmetic" (or,
indeed, that AP has a version of arithmetic). (I thought about
discussing whether AP's "theory" is "significantly less consistent"
than alternatives, but I just couldn't make out what that might mean.)
Phiwum 17:40, 18 October 2007 (UTC)
It is impossible. Every consistent model of
mathematics which can talk about integers can embed nonstandard model
of the integers. Even in ZFC it is consistent to add the axioms "C is
an ordinal" "C is less than omega", "C>1" , "C>2", "C>3", etc... and
these axioms are always consistent. Now make a model for these axioms
and you get a nonstandard model of ZFC which has a nonstandard model
of the integers inside. It has nothing to do with Peano Arithmetic,
first order, or second order, or any order. It's a philosophical
problem which follows from the compactness theorem. You are right that
they are not usually similar to AP's integers. That's why AP is
notable, this is why he is famous. He has many, many, original
ideas.Likebox 18:11, 18 October 2007 (UTC)
No, it is not impossible to define the set of
natural numbers. Here is my definition: Let x be any infinite ordinal.
The set N is the set { n in x | n is finite }. We may define "y is
finite" by "y is not equinumerous with any proper subset of y", where
equinumerosity is defined in terms of bijections as usual. There are,
of course, other common definitions.As I said before, what I think you
mean is that one cannot characterize N by a first order theory-every
such theory would admit non-standard models. That's a different
question than whether one can define the set N of natural numbers.
Phiwum 18:30, 18 October 2007 (UTC)
That is not what I mean, I mean exactly what I said. Your definition,
while it seems to your intuition to exclude infinite integers, can be
proven not to exclude infinite integers. If you add to your axioms the
axiom list 1. "there exists an ordinal C" 2. "C is finite/C has no
self-bijection" 3. "C>1" 4. "C>2", 5. "C>3", and so on, you get an
infinite list of axioms. Any finite subset of this infinite axiom
system does not lead to contradiction, because if you truncate this
system at axiom N you can take C=N-1 and there's no contradiction. But
by the compactness theorem this means that the infinite list of axioms
does not have a contradiction either. In the infinite list of axioms
there is a nonstandard integer C. This is a well known and
uncontrovertial property of axiomatic systems which include the
integers. It is a basic fact in logic. But it is not so well
advertized in other parts of mathematics or to the lay public. I think
it is notable that AP noticed this without the benefit of formal
training.Likebox 19:18, 18 October 2007 (UTC)
I see your point now and I think
you're correct. It is a bit strange to claim that AP noticed this,
however. The fact is that AP, like many cranks, concluding that the
set N can be infinite only if some integers have infinitely many
digits. It has nothing to do with "noticing" this application of the
compactness theorem. (The above was written by User:Phiwum)
65.78.2.122 21:30, 18 October 2007 (UTC)
I agree that AP, like many cranks
before him, noticed this fact. But AP had an internal conviction that
this was the _proper_ notion of integer, and he went much, much
further and did explicit calculations over many years trying to show
that Fermat's Last Theorem fails, and that arithmetic has weird
objects like -1/3, and exactly how Cantor's proof fails when you make
a "list" in his model, and all sorts of other things that he could
never get straight. But boy did he try. This is not your garden-
variety crank, this is a crank on steroids! That's why I respect him.
If he falls a bit short of his goals, well, his goals are very lofty
(I wrote this Likebox 03:11, 20 October 2007 (UTC) ).132.236.54.83
21:43, 18 October 2007 (UTC)
This discussion sounds like it is predicated on the idea
that to discuss AP is to endorse AP's views. Of course not! But his
ideas are philosophical in nature. You don't need to advocate flat
Earth to write about it. And there is no need to be disrespectful.
He's a living person, who has done a lot to contribute to people's
enjoyment of life, and unlike most, he never got paid a cent for
it.Likebox 16:44, 18 October 2007 (UTC)
Presenting his "theories" without criticism is a clear
violation of the undue weight principle. Phiwum 17:40, 18 October 2007
(UTC)
Presenting his theories without criticism is
perfectly acceptable on his page. If you want to criticize, say
somewhere early (as I tried to do) "Most of these ideas are held by
Plutonium and Plutonium alone".Likebox 18:11, 18 October 2007 (UTC)
This is simply not consistent with
WP:NPOV#Undue_weight:
"Minority views can receive attention on
pages specifically devoted to them-Wikipedia is not a paper
encyclopedia. But on such pages, though a view may be spelled out in
great detail, it must make appropriate reference to the majority
viewpoint, and must not reflect an attempt to rewrite majority-view
content strictly from the perspective of the minority view."
Seems pretty explicit to me. Phiwum 18:30, 18
October 2007 (UTC)
All right already, I see that you can back your opinions up with the
inviolate Wiki standards. I'll make sure that the mainstream view is
presented fairly. The mainstream view is that the universe is not a
gigantic atom of plutonium, and that the integers are not the same as
the real numbers with the digits going up. I'll write that. But,
honestly, nobody will ever get confused about this.Likebox 19:30, 18
October 2007 (UTC)Phiwum, that doesn't require criticism. The goal is
just to make sure people don't mistake a fringe theory for the truth.
To achieve that, we just have to note that his view is unique and link
to the mainstream understanding. Likebox had already previously linked
from his quirky mathematical concepts to real ones. How do you feel
that isn't sufficient? Thanks, William Pietri 03:09, 19 October 2007
(UTC)
To call AP's view "unique" hardly
expresses the real facts: His so-called theories are incoherent and
are more similar to poetry than to mathematics. Failing to convey this
basic observation is to give AP more credit than he is due. To refer
to AP's theory as merely unique and different from the mainstream view
gives the utterly false impression that they are an alternative
mathematical view. They clearly do not qualify as such, since there is
no real theory there at all. Phiwum 11:16, 19 October 2007 (UTC)
Do you have a source saying that?
If so, by all means include it. Even if not, I don't think you have
cause to worry. By making clear the circumstances of and response to
his theorizing, we can also make clear that nobody takes these
theories seriously. Readers can judge for themselves to what extent
they should place trust in the Usenet postings of a long-time campus
dishwasher. I'd also encourage you to find quotes that you feel
accurately convey the situation. Time Cube does that pretty well, I
think. William Pietri 01:35, 20 October 2007 (UTC)
This is exactly the concern of
the undue weight theory. No one has ever published a response to AP in
a reliable source. Thus, if we follow your plan (print the theory, do
not acknowledge the elephant in the room), we give undue weight to his
theory. Don't get me wrong: I also agree that we can't publish
original criticisms of the same, but as the article stands (last I
read it), it is rather overly credulous that AP has a mathematical
theory and this just simply isn't so. (You're right that the Time Cube
article does a decent job acknowledging the concept is nonsense, but
it appears to do so without citation.) Phiwum 03:35, 20 October 2007
(UTC)
[edit] Another approach
My preferred approach to this article would be to excise any
indication that he's a real person, but write only about the Internet
(primarily Usenet) persona. Then we wouldn't have to deal with WP:BLP,
and could clearly use sources apparently written by "him" on Usenet
without worring about the true provenance. But that still leaves the
question of notability. - Arthur Rubin | (talk) 15:08, 18 October 2007
(UTC)
I like the idea, but I imagine it will be a hard sell. Especially the
part where you ignore BLP on the grounds that he's a persona and not a
person. (Okay, that's probably an unfair characterization of your
proposal, but I hope it's close enough.)And you're right that
notability is still an issue. The folks who thought he wasn't notable
before have been given no reason to change their minds. Phiwum 15:36,
18 October 2007 (UTC)
My idea is to start a page on the internet persona "Arthur Rubin".
Preferably emphasizing his nose-picking and belching. Come on people!
This is a real person that every one of us knows. He's the neighbor
down the street that let his weeds grow tall.Likebox 16:50, 18 October
2007 (UTC)
If he's a real person (which I think has been demonstrated as
"his" postings were significantly reduced after he was ...
discharged ... from his employment at Dartmouth), then his Usenet
postings cannot be used in this article unless he publicly
acknowledges them. My Usenet postings have been sporged (in response
to a generally favorable article toward Scientology, for what it's
worth); I've cleared a few thousand out of the Google (then Deja) news
archives, but I may have missed a few, and would certainly consider it
a WP:BLP violation if they were mentioned in my article as if I had
written them. - Arthur Rubin | (talk) 17:08, 18 October 2007 (UTC)
Ok, ok. No usenet posts. But he has them all archived
somewhere. That's easy to fix.Likebox 17:09, 18 October 2007 (UTC)
That's an intriguing approach. Kind of like treating him as a
fictional character. Or perhaps like JT LeRoy. But since he is in fact
a real person and not a fictional character, I think we have to write
about him as a real person. Unless we have evidence that he, like
Laura Albert, was faking it. William Pietri 03:14, 19 October 2007
(UTC)
[edit] Harrasment, specious, etc.
I think those words may be inherently WP:POV or WP:OR unless someone
(other than AP, himself) actually used them. "Inventive" is certainly
WP:OR on the part of the editor. "Insane", which is what I would have
called them, is also WP:POV / WP:OR, and shouldn't be in the article.
Of course, the previous deletion may make all of this moot. - Arthur
Rubin | (talk) 19:04, 18 October 2007 (UTC)
What previous deletion ?? There was no deletion except me removing all
the [original research?] tags. Maybe it's a NPOV violation, but it's
not that bad. You need to say that AP was targeted because he was a
notable individual, crazy acting and such, and in a non-libelous
way.Likebox 19:39, 18 October 2007 (UTC)
"Inventive" means full of new inventions. Stuff you've never
heard. "The moon is kept on orbit by angels that push it from behind"
is not inventive, people used to say that all the time. "Let's blow up
the moon!" is inventive. Nobody ever said that before Abian. You have
to exercise some judgement. I am doing my best. "Prolific" means "lots
and lots of it", I think that's universally agreed upon. It is
reasonable to write "Prolific, madly inventive, incoherent, insanely
phrased, rambling, wide-ranging, unfocused", what's wrong with that?
It's accurate. Also "deranged" or "incomprehensible" (although they're
not that incomprehensible if you have an open mind, and
incomprehensible has connotations of boring, which they never were).
Whatever, just as long as its accurate and respectful.Likebox 19:39,
18 October 2007 (UTC)
Inventive is literally WP:OR unless either (1) some reliable
source has said that, (2) it's a neutral summary of what a reliable
source said. We are not supposed to introduce our own opinions into
Wikipedia. EdJohnston 19:54, 18 October 2007 (UTC)
It's an obvious comment. I didn't say "syphilitic" or "ADD
indicating", I described a characteristic of his postings. "The
integers are uncountable" is inventive, it might also be kooky, in
which case "Zanily inventive" might be more appropriate, or "there's
no father to his style". It's not OR just because it's an adjective
you think is positive applied to someone you don't like. It did not
require a new idea or synthesis on my part.132.236.54.80 20:07, 18
October 2007 (UTC)
Oops--- that was me. Jeepers, I didn't realize this page would
raise such a ruckus.Likebox 20:10, 18 October 2007 (UTC)
Likebox, where did you get the information that 'he was
never seriously suspected of any wrongdoing?' If the police did not
think he could have been involved in the murders, why would they
question him? I think this unsourced statement will need to be taken
out due to WP:V. EdJohnston 22:25, 18 October 2007 (UTC)
From the newspaper article that was just added. First,
The crime was later solved and AP had nothing to do with it, but I
quote:
Another false lead turned investigators' attention
to Poehlmann, who used a pseudonym, Archimedes Plutonium. Police were
piqued by Poehlmann's suspicious postings online about his contempt
for Dartmouth and his anger over how he was treated during his time
working at the campus hotel.
It was [Hanover Police Chief Nick] Giaccone's
impression that Plutonium, although a very odd individual, was not
associated with the murders ... and that no further investigation was
required into Plutonium, a police report states.
Given the facts, it would be libelous not to say
this.Likebox 22:35, 18 October 2007 (UTC)
I would also add that the facts support the suggestion
of police harassment by Plutonium, as a direct result of his online
activities.Likebox 22:37, 18 October 2007 (UTC)
That assertion states only that Giaccone did not
seriously believe Plutonium was associated with the murders. It
doesn't state that "he was never seriously suspected of any
wrongdoing", or even "he was never seriously suspected of being
associated with the murders." - Arthur Rubin | (talk) 23:05, 18
October 2007 (UTC)
I think the Boston Globe article was contrasting the
views of the 'investigators' (who are presumably the New Hampshire
State Police) with those of the local Hanover police chief. The local
guy believed that no further investigation was required, but it seems
that the state police thought differently. There is more detail about
why Plutonium was investigated at [1] but this site can't be assumed
to be a reliable source.
The crime is solved, the case is closed[2]. I ask
that you do not bring this up again. It is a blight on wikipedia, and
upon the character of contributors.Likebox 03:01, 19 October 2007
(UTC)
Now that Arthur has convinced some of us that Usenet
postings can't be used as references about A.P., I think this article
is swinging back towards AfD territory. It's fine to include A.P. as
one guy in an article on Notable Usenet personalities, but I certainly
don't think his inclusion in a long list of suspects in a NH murder
investigation will make him notable enough for an article. EdJohnston
01:58, 19 October 2007 (UTC)
Except for his very notable views, which are now
lacking representation on this page.Likebox 03:03, 19 October 2007
(UTC)
Personally, I'm not persuaded that his Usenet posts can't be treated
as sufficiently reliable sources of his views. Sure, they could be
faked. But almost any source could be faked, as Jayson Blair can tell
us. I have heard no reason to suspect these posts in particular,
especially given Plutonium specifically claims authorship of them on
his website. That aside, Likebox has offered to go through his current
website, and although the Wayback Machine is down right now, it's
worth checking to see what they have on his previous home pages: [3]
[4]. So I ask all participants to avoid bringing this to AfD until
Likebox has done the work he's offered to do on this. William Pietri
03:26, 19 October 2007 (UTC)
[edit] Plutonium arithmetic
This section pretends that there is some coherent theory found in AP's
writings. This is not at all clear and to speak of Plutonian
arithmetic as if operations were clearly defined is, I think,
misleading in the extreme. Phiwum 15:03, 19 October 2007 (UTC)
Anyone who's been following his recent "publications" on sci.math can
see that his beliefs about p-adics, spherical/elliptical number
system, irrational and transcendental numbers, etc., are, to put it
kindly, patent nonsense. A simple example is his declaration that "the
infinite P-adic ...9997 is the largest prime"; another is his claim
that "transcendental numbers are incomplete but continually growing
decimal expansions with digit holes". Any mention of his mathematical
musings should be labeled quite clearly as being unsubstantiated,
unproven, and not based on any coherent methodology. - Loadmaster
15:24, 19 October 2007 (UTC)
The phrase "not even wrong" comes to my mind, so I'm not sure that
unproven quite captures the situation. Phiwum 16:13, 19 October 2007
(UTC)
That's closer to describing it, although "unprovable" (just a
step above "incoherent") might also be appropriate. His latest musings
are his proofs of the Poincaré Conjecture[5], Riemann Hypothesis, and
Goldbach Conjecture using his P-adics. Hilarious, to say the least. He
employs the time-tested crank approach of presenting incoherent
arguments based on terms and concepts of his own invention that are
practically impossible to ///disprove using normal logic. It can be
truly wondrous at times. - Loadmaster 17:00, 19 October 2007 (UTC)
(deindent) Not even wrong only if you don't understand what he's
doing. These are all standard problems for the many millions of people
who have tried to make sense of infinite arithmetic at some point in
their lives.
The number ...9997 in Archimedes' system is also known as the number
-3, which almost is the "largest prime" in Ludwig's order on the
Plutonian integers. You would think ...99998 might be the right one,
but that's -2, and it is clearly divisible by two. So maybe ...9997
should be thought of as divisible by three, but dividing by three is
different than dividing by two in base-10, because two divides 10 and
three does not. So maybe that's a self-consistent definition in a 10-
based infinite arithmetic with the order he chooses. Maybe not. I
don't know, but neither do you, and to pretend otherwise is insincere.
It's not incoherent, just original, and incomplete. The methodology is
obviously many, many, painstaking infinite digit calculations, with
the extra burden that the rules keep shifting whenever he finds an
inconsistency.
The reason he claims transcendental numbers are incomplete is because,
if you accept that the integers are Plutonian, the real numbers are
only "finitely" wide. Normally, a real number can be thought of as a
map from Z->digits, giving it's digit sequence. Unfortunately,
Plutonium's "Z" is just as large as the real numbers, so that a real
number is really only a sequence of digits, because a sequence in this
view cannot be viewed as a map from Z-> digits. In this view Z is
larger than any sequence (the integers are "uncountable"). So the real
numbers have "gaps" which would be filled by reciprocals of infinite
integers. But large integers don't have reciprocals in Plutonium's
system, because he can't make any sense out of bi-infinite sequences:
Numbers like ... 999123.3333..... are not allowed because you can't do
multiplication digit by digit.
So he doesn't think of the real numbers as containing the integers, he
has two classes of numbers the "Adic integers" which are infinite to
the left and finite to the right, and the "real numbers" which are
infinite to the right and finite to the left, and it is illegal to add
an adic integer and a real number.
The reason Archimedes Plutonium keeps working on the Riemann
Hypothesis is because he feels he can say something new about the
distribution of primes because he has knowledge of some infinite ones.
This is because he can ask questions like "if I choose an infinite
integer at random, digit by digit, do I get a prime number?" Those
sorts of questions have analytic counterparts about real numbers
(complex numbers really). He probably feels the twin-prime conjecture
is false, becuase, what's the chance that the infinite integer ....
321113 and ....321115 are both prime? He also probably feels that an
infinite even number can always be the sum of two primes because there
are so many ways to express an infinite number as the sum of two
things. These last two statements are both based on my own thinking.
He might thinks that there are very many primes at infinity, I don't
know for sure.
Look, I am not saying his mathematical musing are not crankish. But
recognize that Archimedes Plutonium is to crank science as Isaac
Newton is to mainstream science. He has seen further than others even
though he stands on the shoulders of no-one.Likebox 19:49, 19 October
2007 (UTC)
"The methodology is obviously many, many, painstaking infinite digit
calculations, with the extra burden that the rules keep shifting
whenever he finds an inconsistency." Wow. I don't think I could have
summed up the project better than that. As to whether this method
actually allows him to see further, well... Phiwum 21:06, 19 October
2007 (UTC)
Laughable and pathetic as it is, it is the only avenue available
to any scientist, even the most respected, when groping their way in
the dark towards a new idea. Sometimes you succeed, sometimes you
fail. But it's the same process.Likebox 21:20, 19 October 2007 (UTC)
Most theories don't involve many painstaking infinite
calculations and discoveries of inconsistencies require rather more
careful deliberation than "shifting" the rules whenever they pop up.
Phiwum 21:38, 19 October 2007 (UTC)
Spoken by someone who has probably never agonized to come
up with a new theory. It requires many tentative calculations, and
reworking the rules, and eventually, if you're lucky, everything
crystallizes. It probably won't crystallize for Archimedes Plutonium,
but it might for the next person who considers his system, or
something like it. Then we'll have a good alternate model of
arithemtic, and we might be able to prove some real independence
results.Likebox 02:23, 20 October 2007 (UTC)
On the contrary, I have done such work. And when I
find an inconsistency, I don't just shift rules regarding how to add
numbers. I revisit my axioms and consider where my intuitions went
wrong and I proceed by clearly stating the new theory (axiomatically).
An inconsistency is not typically avoided by adding a new ad-hoc
exception. (Note: I'm using your description of AP's method!)In the
meantime, you give AP rather more credit than I think he's due. He's
an interesting crank. He is not an influential father of an
alternative arithmetic. Now, I could be wrong, of course, but I doubt
it. Phiwum 03:29, 20 October 2007 (UTC)
You are right. You don't make ad-hoc exceptions.
But Plutonium, unlike most cranks, tries his best to be consistent,
and to formulate the rules as clearly as he can. He also tries to
widen the applicability of his system. He is not completely
successful, but considering the type of work he is doing, and how many
other people have tried to examine these ideas, it is unbelievable he
got as far as he did.Likebox 04:04, 20 October 2007 (UTC)
[edit] Please No Undue Weight
When discussing cranky ideas, it is not appropriate to go into great
length. That's a violation of WP:UNDUE_WEIGHT A short summary and a
link is enough. When discussing ideas which have well-accepted
counterparts, it might be appropriate to go into greater length, but I
am not sure about that, considering the ongoing ruckus about the
"plutonian integers".Likebox 20:55, 19 October 2007 (UTC)
An additional comment--- I urge anyone who thinks Plutonium's model of
the integers is totally wacked to consider that many logicians think
it is not that bad an idea. If you are not involved in mathematical
logic, you don't understand how ideas such as these have led to
progress in the past. Forcing is one example, as is Robinson's
nonstandard analysis. The original notion of infinitesimal by
Cavalieri was laughed at, and Cavalieri was a bit of a crank in his
own time (although Plutonium dwarfs all previous crancks in both
output and magnitude of crackpottery). It is something many people
have played with, myself included, and yet I missed some stuff--- I
didn't see that the integers could be uncountable in the sense of no
list, because I didn't see that Cantor's argument could fail. I lacked
the imagination to see that the "height" of the integers in digits
might be different than their "width" as a cardinal. He might be
mentally unstable, but in my opinion, he has contributed a little bit
to mathemtical thinking, which is more than all other living crancks
combined.Likebox 02:32, 20 October 2007 (UTC)
"Many logicians think [Plutonium's so-called model] is not that bad an
idea." Wow, that is interesting! Can you name a single logician who
has gone on record suggesting that AP has a theory of integers and
that this theory of integers isn't utterly nuts? Phiwum 03:23, 20
October 2007 (UTC)
No, but I tell you the following (I won't name names, so you have to
take my word) of a famous logician who I asked this--- "can we do
Cohen forcing on the integers by first constructing a non-standard
model and then performing forcing operations on digit sequences of
nonstandard length". I was embarassed to say this, because I knew it
wasn't my idea, that it is AP's. He thought it was nuts at first, but
later he searched me out to tell me it might be interesting and
requires more exploration.This logician is very, very, famous.Likebox
04:47, 20 October 2007 (UTC)
To see that Fermat's Theorem Fails for Plutonium integers (this is a
true fact, not only an unsupported claim by Plutonium), consider the
following:
X^3 + Y^3 = Z^3 (\mathrm{mod}\;\; 10^n) \,
has solutions for all n in normal mathematics, and each solution for n
one larger can be thought of as adding one more digit to the left of
the previous solution. By considering the nonstandard model of
arithmetic constructed a-la Robinson and letting n be an infinite
integer, it follows that X^3 + Y^3 = X^3 has infinite integer
solutions, in a non-standard model of arithmetic. This model does not
obey induction axioms, because then certain identities which Plutonium
takes for granted will necessarily fail. The cubic example was proven
by Euler to have no solution by a simple induction-style argument, so
that this example will no longer be solvable. But maybe other
exponents will still be solvable even after adding the induction
constraints. Since Plutonium's integers are uncountable, Cohen's
method might be usable on them, and then there might be independence
results. Maybe not. But maybe we can find out once and for all if
Fermat (who had no recourse to methods more advanced than PA or maybe
one or two reflections) had a proof of Fermat's Last Theorem or not.
These are burning questions in logic, and any new idea, no matter how
crazy, is sorely needed.Likebox 02:53, 20 October 2007 (UTC)
The claim that this is a true fact depends on whether there is a
structure with exponentiation and addition satisfying the various
things AP has said about his toy, don't it? Phiwum 03:23, 20 October
2007 (UTC)
You're absolutely right. Exponentiation might be uncomputable
for A^B for general Plutonian integers, but cubing is fine and can be
worked out from multiplication. I know how to write down explicit
digit sequences for A,B,C that make the cubic identity work. It's the
same construction as for the p-adics. I read in a number theory book
once "Fermat's last theorem is considered difficult becuase it has
solutions for all p-adic bases". I couldn't understand why
mathematicians thought that this mattered at all, until I saw
Plutonium's posts. Then I understood that the p-adics are a sort of
"interim" alternate model for the integers until we can find something
better. This was also the first time I felt that there was some method
to Plutonium's madness, and I read his stuff after that.Likebox 03:45,
20 October 2007 (UTC)
[edit] Yet another reason not to discuss AP's arithmetic.
The article currently claims that ...9999 = -1 in AP's "theory". Just
today, however, AP wrote the following on sci.math:
"This book defines P-adics far differently than yours and the old way.
The old
way was a costumed-acting-Reals where they had ....99999 = (-1)
"The P-adics as defined in this book are infinite leftward strings of
all possible digit arrangement and whose operations are the same as
for Reals as a Cauchy sequence to the final answer."
Now, I don't pretend to understand any of AP's theory, but it appears
to me that he is denying that ...99999 = -1. Of course, that's just
today. Tomorrow, it might change again. In any case, seems to me that
the current section on arithmetic is not an accurate account of AP's
theory (and how could it be, when his half-completed notions change on
a whim?). Phiwum 20:10, 20 October 2007 (UTC)
Please understand, Plutonium has long ago extended his theory to
describe the infinite number
1....0000 = ....9999 + 1
and related ordinal-like constructions. I didn't want to get into this
because, while I find this stuff fascinating, it has no connection to
anything else (including p-adics) and would be UNDUE WEIGHT. He no
longer accepts that ....9999= (-1) because he doesn't want it to be
negative and small, but positive and large. There is, as I said, a
huge amount of freedom here, and he keeps changing his mind. This is
why he isn't writing in "The Journal of Symbolic Logic".Likebox 20:16,
20 October 2007 (UTC)
Just to expand--- Ludwig was extremely surprised to learn about p-
adics (I remember). He really thought that he was the first to think
of this construction. But when he learned about them, he didn't
dismiss them as "inconsistent rantings of the mathematical world", he
read about them, learned them as best he could, took what he wanted,
and then went on to construct even larger infinite integers! His
current system is currently best described in well-accepted language
as follows:
A Plutonian integer is an ordinal sequence of digits. The sum is
defined by a digit-by-digit construction, with an ordinal "carry"
whenever there is a consistent rule to give you the carry at digit
position , 2 , and any other limit ordinal that the integer reaches.
The "largest prime" is the number "...9997" only if you interpret ...
as meaning "over all ordinal positions" not "over all integer
positions". But as I said in the article, he hasn't sorted this out
even to his own satisfaction, let alone anybody else's.Likebox 20:26,
20 October 2007 (UTC)
I would like to give a comprehensible translation of the "Plutonium-
speak" you quoted into normal sounding mathematics, for the benefit of
those who have not been following Plutonium's writing--- "The
Plutonian integers defined in this work are different than the p-adic
integers as they are usually defined, where there is an obvious
constructible one-to-one map from the set of all possible p-adics to
the set of all real numbers. In particular, in the old system the
number ...9999 is not larger than all other numbers, but identified
with its limit in the p-adics, which is -1. The Plutonian integers
defined here are all possible infinite ordinal arrangements of digits
whose operations are defined by transfinite induction. Each step in
the induction is produced by the usual algorithms to multiply digits
of integers, extended to all admissable ordinals in a consistent way,
much as operations on the real numbers are defined by an inductive
process on the integers which produces the real number from
approximating Cauchy sequences". I have gotten pretty good at
translating this stuff by now. You have to believe that I am really
acting as interpreter here, not originator. I am way too conventional
in my thinking to ever come up with stuff like this myself.Likebox
20:47, 20 October 2007 (UTC)
*** end quoting discussion page of Wikipedia under "Archimedes
Plutonium"***
David R Tribble
>> You might try reading the question more closely.
>> I asked for the two primes that sum to 8888888888888.
>
Archimedes Plutonium wrote:
>> No harm to the argument, as I said you first look to the Induction of 80
>> to 90 with the 1st induction as 0 to 10 and the 2nd of 10 to 20 and if
>> those primes are not the answer then you look at the primes below 88
>> and they are 71 and 17.
>
David R Tribble wrote:
>> You still have not answered my question:
>> What are the two primes that sum to 8888888888888?
>
Archimedes Plutonium wrote:
> ....88888871 and ......888888817 are primes as both generate radix
> fractions in their Cauchy sequence
I've asked you three times now to identify the two primes
that sum to 8888888888888, and three times you have
failed to do so. You seem to trying to answer a different
question having to do with ...888, which has nothing to do
with what I asked.
I am forced to assume that you don't know, and therefore
your proof of the Goldbach Conjecture is wrong.
Archimedes Plutonium
Dik T. Winter wrote:
(snipped)
>
> As you mention "p-adics" I thought you meant "p-adics" as normally used
> in mathematics, but obviously you have your own private terminology.
>
> > Would you care to comment on "All Possible Digit Arrangements" for
> > ......000001 to ....99999999999
> >
> > Where the operations of these numbers are not P-adics.
> >
> > Where the operations are borrowed from Reals between 0 and 1 in Reals
> > and the final answer of any operation is what digits do not change such
> > as
>
> If you mean mirroring, doing the operation on the reals, and mirroring back
> again, I am wondering what the difference is between 1 and ...999990.
If you are asking for subtraction, then ...999999 + 3 = (pi) + 2
So that
1 - ....9999990 = (pi) + 11
If you are asking where is 1 and ....999990 then 1 is one unit on a line
of longitude from the North Pole and ....999990 is ten units distance
from the South Pole. And (pi) + 11 is 11 units on the other
semilongitude from the South Pole.
The numbers 1 to 999...99999 are a semilongitude and the other
semilongitude are numbers (pi) to 2(pi)
> And is ...00018 * ...00028 = ...0006642?
>
Multiplication is simply the same as Reals so that equals ....0000504
> Or do you mean something else with your "borrowing"?
>
Everything is the same as Reals, except the final answer is a Cauchy
sequence of what digits remain the same in place value. This way I
eliminate the base in P-adics. So that people can look at all the Reals
as Decimal Reals and look at all the Counting Numbers as AP-adics.
> > So I am asking you, whether these Decimal P-adics also transfer all
> > the Field Algebra properties for which the Reals possess? Keep in mind
> > that these Decimal P-adics do not end with ....999999 but continue with
> > (pi) as South Pole and come back around a circle to the North Pole of
> > 2(pi).
>
> This makes no sense at all.
Okay, let me ask you a different question that will answer my above.
Tell me if the points on a circle have any algebraic structure. I
believe someone gave me a full answer to that question in 1994 but
I have not located that post. I have it my archive but not tracked
it down.
So do the points on a circle have an algebraic structure. My intuition
says they have none. My foggy memory of what the poster (I believe it
was KH) said was that there is no algebraic structure and his post led
me to believe noone has proven in mathematics that the circle points
have no algebraic structure.
So please fill me in on what is known about the points on a circle and
whether they have any algebraic structure.
I was looking through my meager set of geometry books for structure of
the Elliptic and Hyperbolic Geometries to no avail.
>
> > Mine are totally different in that they are not Reals but having the
> > same operations as Reals.
>
> In what way are they different, except that the notation is reversed?
>
WEll, for one, both the Reals and AP-adics are countable since they both
are ALL Possible Digit Arrangements. And Reals are infinite rightwards
and AP-adics the opposite in infinite leftwards. The greatest difference
is that REals can only be used in Euclidean Geometry and AP-adics only
in Elliptic Geometry. So the Poincare Conjecture and Riemann Hypothesis
are math works that exist only in Elliptic Geometry where the Counting
Numbers are these AP-adics. That is a tall difference, I would say.
Proginoskes
wrote:
> [...]
> Anyway the definition of multiplication and division uses a radix if
> there is a remainder. And the final answer is a Cauchy Sequence over all
> the piecewise divisions. So if the radix disappears and never again
> shows up then the number is composite, but if the radix continually
> shows up, even though one or two piecewise divisions is even, means the
> final answer is composite.
>
> 7 into 97 is 13.8
> 7 into 997 is 142.4
> 7 into 9997 is 1428.1
> 7 into 99997 is 14285.2
> 7 into 999997 is 142856.7
> 7 into 9999997 is 1428571
> 7 into 99999997 is 14285713.9
> and the fractional radix repeats in a block
>
> So the Cauchy sequence of the above never eliminates the radix, does it,
> so it is Prime not composite.
Thus, there is an interesting property in this set of numbers: There
is an AP-adic N such that (7*N) is not divisible by 7 (namely ...
1428571428571).
> Just because you can find one smooth even division every periodically in
> the sequence does not make it overall Composite. To be overall Composite
> then the Cauchy Sequence stops yielding a radix answer.
How do you divide 3 by ...11111?
I thought up an interesting problem last night, based on AP's new
definition of division. Given two (finite, "traditional") integers m
and n, say that m is "dirvisible" by n if the last k digits of m are
divisible by n, for all appropriate k. (Thus, 312 is not dirvisible by
3, since 2 is not divisible by 3.) Find suitable dirvisibilty tests
for n=2 through 10.
(The extra "r" is short for "recursive".)
--- Christopher Heckman
SPOILER BELOW.
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n = 1, 2, 5, 10: m is dirvisible by n iff m is divisible by n.
n = 3, 7, 9: m is dirvisible by n iff every digit of m is divisible by
n.
n = 6: combine n = 3 and n = 6. (Every digit is 0, 3, 6, or 9, and the
number ends in 6.)
n = 4: the last digit is 4, 8, or 0, and the tens digit is even.
n = 8: the last digit is 8 or 0, the tens digit is 0, 4, or 8, and the
hundreds digit is even.
Bonus fact: If n > 10 and n is relatively prime to 10, then the only
integer dirvisible by n is 0.
Dik T. Winter
> Dik T. Winter wrote:
I asked a question that you did not answer, I will repeat it later.
> > > 3 into 8 is 2 with 2 remainder. Carry the 2 and we have 28.
> > > Then 3 into 28 is 9 with 1 remainder. Carry the 1 and we have 18.
> > > Then 3 into 18 is 6 and we repeat the block of 296 where we have
> > > 296296296 and 3 does not divide 71 evenly so the entire
> > > number is prime.
> >
> > No, by that method you will see that the number is divisible by 71.
...
> > We repeat the block of 142857 where we have 142857142857 and 7 dies
> > divide 7 evenly, so the entire number is divisible by 7. Note that
> > using this method the number is also divisible by 97, 997, 9997, etc.
>
> Good try but not true.
I repeat your argument. So why is it not true when I state it, but is it
true when you state it?
> Anyway the definition of multiplication and division uses a radix if
> there is a remainder.
When does multiplication have a remainder?
> And the final answer is a Cauchy Sequence over all
> the piecewise divisions.
How do you *define* Cauchy Sequence? You do not use the standard definition.
> Just because you can find one smooth even division every periodically in
> the sequence does not make it overall Composite. To be overall Composite
> then the Cauchy Sequence stops yielding a radix answer.
Hence my first question that you did not answer:
> > What is 7 * 142657...1428571?
According to your technique it should be 9999...99997. So I repeat
my question, is that true or not, and if not true what *is* the
result of that multiplication? If it is true we have when we
define:
a = 999999...9999997
and
b = 142857...1428571
the following:
b * 7 = a
a / 7 != b
which appears to me to be inconsistent. So apparently b * 7 is
something different. What is it? Pray give the answer. If you do
not give an answer I can only conclude that you have not properly
defined your arithmetic.
Dik T. Winter
> Dik T. Winter wrote:
> > In article <471706E4...@hotmail.com> Archimedes Plutonium <a_plu...@hotmail.com> writes:
> > ...
> > > But we look at the two preceding numbers and particularly .....9999997 and
> > > it is the world's largest prime number, since no number prior divides
> > > into it evenly.
> >
> > What is the remainder when you divide it by 7? I would think it is
> > divisible by 7, but perhaps I do not understand the operations as you
> > define them well-enough.
>
> In a previous post I outlined that division. Division is the same as
> Reals only the final answer is a Cauchy Sequence of those digits that
> remain the same in place value in further divisions. So the number
> 99999....99997 is Prime because although a few periodic divisions do
> turn out to be evenly divided the next block is a radix fraction. To
> be composite means the Sequence never yields a radix fraction to infinity.
Which does not answer my question. What *is* the remainder when 999...9997
is divided by 7? You should be able to answer that because you defined the
arithmetic on those numbers.
> Question Dik: what algebra exists for the points on the unit circle? Do
> those points have an algebra?
What do you actually *mean* with "an algebra"? If you mean that there exist
operations like addition, subtraction, multiplication and division, yes
there are. And not even a single set. Consider the unit circle as the
pair (cos(x), sin(x)), and do operations on the x's mod 2.pi. There you
are, the only problem is that there are zero divisors. And there are
many other possibilities.
Dik T. Winter
> Dik T. Winter wrote:
> If you are asking for subtraction, then ...999999 + 3 = (pi) + 2
> So that
> 1 - ....9999990 = (pi) + 11
What is (pi) * (pi)? What is ...999999 + 3 * (pi)? How do I calculate
with (pi)? Where did you define those calculations?
> > Or do you mean something else with your "borrowing"?
>
> Everything is the same as Reals, except the final answer is a Cauchy
> sequence of what digits remain the same in place value.
That is *not* the definition of Cauchy sequence.
> This way I
> eliminate the base in P-adics.
No, you do not. Consider the sequence (in decimal) of 1, 11, 111, 1111,
11111, ...; according to you it is a Cauchy sequence. Base 3 it becomes
1, 102, 11010, 1112011, 120020112, 12122102020, 2002110011021, which is
not a Cauchy sequence in your terminology at all. So what is a Cauchy
sequence in one base is not a Cauchy sequence in another base in your
terminology. You do *not* eleminate base.
> Tell me if the points on a circle have any algebraic structure. I
> believe someone gave me a full answer to that question in 1994 but
> I have not located that post. I have it my archive but not tracked
> it down.
Perhaps I was the one who gave an answer?
> So do the points on a circle have an algebraic structure. My intuition
> says they have none. My foggy memory of what the poster (I believe it
> was KH) said was that there is no algebraic structure and his post led
> me to believe noone has proven in mathematics that the circle points
> have no algebraic structure.
Or perhaps KH. Why is it that you have to ask questions multiple times?
> So please fill me in on what is known about the points on a circle and
> whether they have any algebraic structure.
Have a look at the web. There is a lot of algebraic structure possible,
but whether they have the properties you need remains a question.
> I was looking through my meager set of geometry books for structure of
> the Elliptic and Hyperbolic Geometries to no avail.
Looking for algebraic structures in geometry books seems to me the wrong
track.
> WEll, for one, both the Reals and AP-adics are countable since they both
> are ALL Possible Digit Arrangements. And Reals are infinite rightwards
> and AP-adics the opposite in infinite leftwards. The greatest difference
> is that REals can only be used in Euclidean Geometry and AP-adics only
> in Elliptic Geometry. So the Poincare Conjecture and Riemann Hypothesis
> are math works that exist only in Elliptic Geometry where the Counting
> Numbers are these AP-adics. That is a tall difference, I would say.
Your linking of geometry with arithmetic makes no sense.
Archimedes Plutonium
Dik T. Winter wrote:
>
> According to your technique it should be 9999...99997. So I repeat
> my question, is that true or not, and if not true what *is* the
> result of that multiplication? If it is true we have when we
> define:
> a = 999999...9999997
> and
> b = 142857...1428571
> the following:
> b * 7 = a
> a / 7 != b
> which appears to me to be inconsistent. So apparently b * 7 is
> something different. What is it? Pray give the answer. If you do
> not give an answer I can only conclude that you have not properly
> defined your arithmetic.
I made a mistake for I agree that
142857142857....1428571428571 X 7 = 9999....999997
and so ....999997 is not prime.
So that makes ......99999991 the world's largest prime.
I am using the term Cauchy Sequence in the sense that as I operate digit
by digit from place value to place value that the digits no longer
change in that place value. Perhaps I should eliminate the term "Cauchy"
from this book as it seems to mislead rather than clarify.
Perhaps I should call it "Unchanging Digit Sequence"
Archimedes Plutonium
Dik T. Winter wrote:
>
> > Question Dik: what algebra exists for the points on the unit circle? Do
> > those points have an algebra?
>
> What do you actually *mean* with "an algebra"? If you mean that there exist
> operations like addition, subtraction, multiplication and division, yes
> there are. And not even a single set. Consider the unit circle as the
> pair (cos(x), sin(x)), and do operations on the x's mod 2.pi. There you
> are, the only problem is that there are zero divisors. And there are
> many other possibilities.
I mean an algebraic structure such as Group or Ring or Field. Has it
been proven that the points on a unit circle are impossible to be a
group, to be a ring to be a field? And why has it not been proven?
Archimedes Plutonium
Dik T. Winter wrote:
> In article <471D8311...@hotmail.com> Archimedes Plutonium <a_plu...@hotmail.com> writes:
> > Dik T. Winter wrote:
> ...
> > If you are asking for subtraction, then ...999999 + 3 = (pi) + 2
> > So that
> > 1 - ....9999990 = (pi) + 11
>
> What is (pi) * (pi)? What is ...999999 + 3 * (pi)? How do I calculate
> with (pi)? Where did you define those calculations?
(pi) X (pi) = (pi)^2 or if not satisfied
It is 180 degrees radians X 180 degrees radians
Pi and 0 are imaginary in AP-adics so asking that is like asking what
is 0 X 0 = 0.
....999999 + 3 X (pi) is
.....99999 + 3 = (pi) + 2 and now ((pi) + 2)x (pi)
or if not satisfied is 182 degrees radians X 180 degrees radians
Dik, the sphere is divided into two where one Hemisphere is the numbers
1 to 9999....99999 and the other hemisphere is imaginary with 0 and
(pi) from 180 degrees to 360 degrees. The reason for this is because
Elliptic geometry shares the sphere with Hyperbolic Geometry. So the
hemisphere that is imaginary is in fact Hyperbolic. The numbers
1 to ...99999 are Elliptic and cannot make a complete circuit and
so the other hemisphere is imaginary.
>
> > > Or do you mean something else with your "borrowing"?
> >
> > Everything is the same as Reals, except the final answer is a Cauchy
> > sequence of what digits remain the same in place value.
>
> That is *not* the definition of Cauchy sequence.
Alright, I stop using that term and use the term "Unchanging Digit
Sequence"
>
> > This way I
> > eliminate the base in P-adics.
>
> No, you do not. Consider the sequence (in decimal) of 1, 11, 111, 1111,
> 11111, ...; according to you it is a Cauchy sequence. Base 3 it becomes
> 1, 102, 11010, 1112011, 120020112, 12122102020, 2002110011021, which is
> not a Cauchy sequence in your terminology at all. So what is a Cauchy
> sequence in one base is not a Cauchy sequence in another base in your
> terminology. You do *not* eleminate base.
Agreed. I do not eliminate bases. But I make bases as irrelevant. Just
as bases are irrelevant when talking about the Reals, for all the
information is contained in the Decimal Reals and no need to change
bases. Same thing here in that AP-adics are Decimal Adics and no need to
change base. All the mathematical information and content of the Reals
is contained in Decimal Reals, likewise for AP-adics.
>
> > Tell me if the points on a circle have any algebraic structure. I
> > believe someone gave me a full answer to that question in 1994 but
> > I have not located that post. I have it my archive but not tracked
> > it down.
>
> Perhaps I was the one who gave an answer?
>
> > So do the points on a circle have an algebraic structure. My intuition
> > says they have none. My foggy memory of what the poster (I believe it
> > was KH) said was that there is no algebraic structure and his post led
> > me to believe noone has proven in mathematics that the circle points
> > have no algebraic structure.
>
> Or perhaps KH. Why is it that you have to ask questions multiple times?
>
I do not have a photographic memory like you.
> > So please fill me in on what is known about the points on a circle and
> > whether they have any algebraic structure.
>
> Have a look at the web. There is a lot of algebraic structure possible,
> but whether they have the properties you need remains a question.
>
> > I was looking through my meager set of geometry books for structure of
> > the Elliptic and Hyperbolic Geometries to no avail.
>
> Looking for algebraic structures in geometry books seems to me the wrong
> track.
>
> > WEll, for one, both the Reals and AP-adics are countable since they both
> > are ALL Possible Digit Arrangements. And Reals are infinite rightwards
> > and AP-adics the opposite in infinite leftwards. The greatest difference
> > is that REals can only be used in Euclidean Geometry and AP-adics only
> > in Elliptic Geometry. So the Poincare Conjecture and Riemann Hypothesis
> > are math works that exist only in Elliptic Geometry where the Counting
> > Numbers are these AP-adics. That is a tall difference, I would say.
>
> Your linking of geometry with arithmetic makes no sense.
I would say you never considered the question before. And perhaps that
is why I am the first to discover this mathematical important knowledge.
That a circle or a sphere or any Riemannian surface cannot handle the
Reals mapped onto them. Reals are native only to Euclid geometry and
that a circle is not composed of Real Numbers but is composed of
AP-adics with radix fraction.
Noone can shape a tin foil or aluminum foil rectangle into a sphere
surface without cutting and tearing and leaving breaks and creases.
And it should be intuitive to any thinking mind that if you cannot shape
a rectangle into a sphere surface, that you cannot call the points on a
circle or sphere Reals. Noone in math has proven that a sphere surface
or Riemannian surface or Lobachevskian surface has a continuum of
points. They all assumed it to be the case.
What I am slowly showing is that only Euclid geometry has a continuum of
points and so Reals are intrinsic to Euclid geometry. But that AP-adics
are intrinsic to any circle, any sphere and to Riemannian and
Lobachevskian geometries.
Oh, of course you can say the unit circle points are the Reals from 0 to
1, but saying is not proving.
Eventually my program will reveal that every and all circles and spheres
and Riemannian and Lobachevskian geometries are ridden with holes. We
can get as close as we want to a point via the radix fraction but since
it is finite, means it is not a continuum. The reason you have a
continuum in the Reals is because the rightward string is infinite. And
because the Reals are finite in the leftward allows the Reals to form
straight lines in Euclid geometry. However, lines in Euclid geometry
cannot go to infinity, so the parallel postulate needs to be revised and
updated because a finite leftward string in Reals negates the lines from
going to infinity. For Riemannian and Lobachevskian geometry, since the
leftward string is infinity, does not mean a continuum there, but rather
it means a curvature. So the reason Euclid geometry is 0 curvature is
because the leftward string is finite.
So, yes, Dik, to the contrary, numbers and arithmetic and geometry are
intertwined. They are not some puffed up definitions and run out and
apply definitions as old folks of math see math. Math, like physics
exists independent of the human mind.
Proginoskes
wrote:
> [...]
> I made a mistake for I agree that
>
> 142857142857....1428571428571 X 7 = 9999....999997
> and so ....999997 is not prime.
>
> So that makes ......99999991 the world's largest prime.
Nope. ...14285714285713 * 7 = ...99991, so ...99991 isn't prime,
either.
Furthermore, ...1428571428571427 * 7 = ...999989, so don't bother
saying that ...999989 is prime, either.
And forget about 3 being prime. ...1428571428571429 * 7 = ...00003.
In fact, for every AP-adic N, there is an AP-adic M such that
M * 7 = N.
Which means the only possible prime is 7 itself (which is when
M = 1 works above; otherwise there is a non-trivial factorization of
N).
But: ...666666669*3 = ...00007, so I guess that throws out 7 as well.
Golly ... AP proved that there are infinitely many primes, but there
don't seem to be any at all!!!!
--- Christopher Heckman
Dik T. Winter
> Dik T. Winter wrote:
...
> > my question, is that true or not, and if not true what *is* the
> > result of that multiplication? If it is true we have when we
> > define:
> > a = 999999...9999997
> > and
> > b = 142857...1428571
> > the following:
> > b * 7 = a
> > a / 7 != b
> > which appears to me to be inconsistent. So apparently b * 7 is
> > something different. What is it? Pray give the answer. If you do
> > not give an answer I can only conclude that you have not properly
> > defined your arithmetic.
>
> I made a mistake for I agree that
>
> 142857142857....1428571428571 X 7 = 9999....999997
> and so ....999997 is not prime.
>
> So that makes ......99999991 the world's largest prime.
Ok, now try:
076923976923...07692307 * 13.
Is it 999999...99999991 or not? If not, what is the value?
> I am using the term Cauchy Sequence in the sense that as I operate digit
> by digit from place value to place value that the digits no longer
> change in that place value. Perhaps I should eliminate the term "Cauchy"
> from this book as it seems to mislead rather than clarify.
>
> Perhaps I should call it "Unchanging Digit Sequence"
Yes, because it is not a Cauchy sequence.
Dik T. Winter
> Dik T. Winter wrote:
>
> > > Question Dik: what algebra exists for the points on the unit circle? Do
> > > those points have an algebra?
> >
> > What do you actually *mean* with "an algebra"? If you mean that there
> > exist operations like addition, subtraction, multiplication and division,
> > yes there are. And not even a single set. Consider the unit circle as
> > the pair (cos(x), sin(x)), and do operations on the x's mod 2.pi. There
> > you are, the only problem is that there are zero divisors. And there are
> > many other possibilities.
>
> I mean an algebraic structure such as Group or Ring or Field. Has it
> been proven that the points on a unit circle are impossible to be a
> group, to be a ring to be a field? And why has it not been proven?
Can't you read? What I defined above for the points on the unit circle
is a ring. It is even possible to make it a field, but the structure is
not natural. So the reason that it has not been proven that it is not
possible is because it is possible. That has already been told to you
back in 1994 or so.
Dik T. Winter
> Dik T. Winter wrote:
> > In article <471D8311...@hotmail.com> Archimedes Plutonium <a_plu...@hotmail.com> writes:
> > > Dik T. Winter wrote:
> > ...
> > > If you are asking for subtraction, then ...999999 + 3 = (pi) + 2
> > > So that
> > > 1 - ....9999990 = (pi) + 11
> >
> > What is (pi) * (pi)? What is ...999999 + 3 * (pi)? How do I calculate
> > with (pi)? Where did you define those calculations?
>
> (pi) X (pi) = (pi)^2 or if not satisfied
But I assume that (pi) is an adic. If not, your adic arithmetic is
not complete, while earlier you asked me to tell you what it was
because you said you had "defined arithmetic" on the adics. Sorry,
with that kind of arithmetic the adics do not even form a group with
respect to addition.
> It is 180 degrees radians X 180 degrees radians
Makes no sense at all. What are "degrees radians"?
> >
> > > This way I
> > > eliminate the base in P-adics.
> >
> > No, you do not. Consider the sequence (in decimal) of 1, 11, 111, 1111,
> > 11111, ...; according to you it is a Cauchy sequence. Base 3 it becomes
> > 1, 102, 11010, 1112011, 120020112, 12122102020, 2002110011021, which is
> > not a Cauchy sequence in your terminology at all. So what is a Cauchy
> > sequence in one base is not a Cauchy sequence in another base in your
> > terminology. You do *not* eleminate base.
>
> Agreed. I do not eliminate bases. But I make bases as irrelevant.
Darn, in one base the sequence above converges in your terminology, in
another base it does not converge. And you are stating that the base
is irrelevant, while convergences is of prime concern for your arithmetic?
Suppose that in a multiplication done in base 10 the sequence of partial
results does not converge while it does converge in base 7. What is the
product?
> > > WEll, for one, both the Reals and AP-adics are countable since they
> > > both are ALL Possible Digit Arrangements. And Reals are infinite
> > > rightwards and AP-adics the opposite in infinite leftwards. The
> > > greatest difference is that REals can only be used in Euclidean
> > > Geometry and AP-adics only in Elliptic Geometry. So the Poincare
> > > Conjecture and Riemann Hypothesis are math works that exist only
> > > in Elliptic Geometry where the Counting Numbers are these AP-adics.
> > > That is a tall difference, I would say.
> >
> > Your linking of geometry with arithmetic makes no sense.
>
> I would say you never considered the question before. And perhaps that
> is why I am the first to discover this mathematical important knowledge.
> That a circle or a sphere or any Riemannian surface cannot handle the
> Reals mapped onto them. Reals are native only to Euclid geometry and
> that a circle is not composed of Real Numbers but is composed of
> AP-adics with radix fraction.
And this also makes no sense. A circle can be contained in Euclidean
geometry.
Archimedes Plutonium
It looks like AP-adics caught up with alot of regular P-adic theory, but
they differ so much that the above is only a minor temporary victory for
those opposed to AP-adics.
Well, at the moment the picture is looking rosy for me, although I lost
the easy way of showing the Prime Distribution theorem is false. Looks
like I have to give you the "prime busters" between ...999999 and
.....999999901
So here is one Prime Buster:
99999.......1716151413121110987654321
And I reckon it is now the world's largest prime
then there are many prime numbers to be manufactured like this
where it elminates compositery. It is like a target that moves
whereas ....9999997 or ....99999991 are standing still targets.
99999......89999899989989
I dare either Chris or Dik to find those composite.
Many will say those are rigged numbers. I reply that under All Possible
Digit Arrangements they are just as valid and legitimate as ....999997
The difference between primes in P-adics and AP-adics is that there are
an infinitude of Primes missed in P-adics because of their lack of
understanding of All Possible Digit Arrangements.
P.S. the Prime Distribution Theorem is still false, but not as horribly
false as what I previously suspected. And as to whether the distribution
of primes is like a onion layering, well, I am not quite so sure about
that. First I have to be sure of what is the world's largest prime
and so far it looks as though this is:
99999.......2019181716151413121110987654321
Archimedes Plutonium
Dik T. Winter wrote:
> In article <471ED8BF...@hotmail.com> Archimedes Plutonium <a_plu...@hotmail.com> writes:
> > Dik T. Winter wrote:
> >
> > > > Question Dik: what algebra exists for the points on the unit circle? Do
> > > > those points have an algebra?
> > >
> > > What do you actually *mean* with "an algebra"? If you mean that there
> > > exist operations like addition, subtraction, multiplication and division,
> > > yes there are. And not even a single set. Consider the unit circle as
> > > the pair (cos(x), sin(x)), and do operations on the x's mod 2.pi. There
> > > you are, the only problem is that there are zero divisors. And there are
> > > many other possibilities.
> >
> > I mean an algebraic structure such as Group or Ring or Field. Has it
> > been proven that the points on a unit circle are impossible to be a
> > group, to be a ring to be a field? And why has it not been proven?
>
> Can't you read? What I defined above for the points on the unit circle
> is a ring. It is even possible to make it a field, but the structure is
> not natural. So the reason that it has not been proven that it is not
> possible is because it is possible. That has already been told to you
> back in 1994 or so.
Okay thanks. Now it is my duty to show that those points are impossible
to form a ring or a field. Impossible because the points on a circle do
not obey transitivity.
My duty, because there is a fundamental difference between Euclid
geometry and both Elliptic and Hyperbolic geometry. In Euclid the
triangle sum is exactly 180 degrees and in Elliptic and Hyperbolic it
is never 180 degrees. That fundamental difference destroys there ever
being a ring or field for Elliptic and Hyperbolic geometry and any
alleged proof would have major flaws.
Any alleged concoction that the points on a circle form a ring or field
would be tantamount to saying that there are some Elliptic and
Hyperbolic triangles whose angle sum is exactly 180 degrees.
Archimedes Plutonium
Proginoskes wrote:
> On Oct 23, 10:23 pm, Archimedes Plutonium <a_pluton...@hotmail.com>
> wrote:
>
>>[...]
>>I made a mistake for I agree that
>>
>>142857142857....1428571428571 X 7 = 9999....999997
>>and so ....999997 is not prime.
>>
>>So that makes ......99999991 the world's largest prime.
>
>
> Nope. ...14285714285713 * 7 = ...99991, so ...99991 isn't prime,
> either.
>
> Furthermore, ...1428571428571427 * 7 = ...999989, so don't bother
> saying that ...999989 is prime, either.
>
> And forget about 3 being prime. ...1428571428571429 * 7 = ...00003.
>
Not true for it leaves a front view remainder where you can never
get all the front view digits as 0
And because you cannot, means the definition of Prime still stands as
a good working definition.
The P-adic fans are falling into the trap of thinking that ....99999
is 1 as in 2.99999.... is 3
> In fact, for every AP-adic N, there is an AP-adic M such that
> M * 7 = N.
>
> Which means the only possible prime is 7 itself (which is when
> M = 1 works above; otherwise there is a non-trivial factorization of
> N).
>
> But: ...666666669*3 = ...00007, so I guess that throws out 7 as well.
>
> Golly ... AP proved that there are infinitely many primes, but there
> don't seem to be any at all!!!!
>
> --- Christopher Heckman
>
In the above, to those P-adic fans it may look bleak to AP-adic fans,
but in fact it is the opposite where AP-adics look rosy.
Although it looks bad for the 999prefix-series since the 142857 block
destroys the 99999 blocks, however one can manufacter a prefix series
that is a prime series such as these:
......2019181716151413121110987654321
or
.....9999909999099909909
So there are infinite number of such prefix series that are prime
and then the backend tacked on number is prime if odd and not 5.
a_plutonium
Proginoskes wrote:
> On Oct 23, 10:23 pm, Archimedes Plutonium <a_pluton...@hotmail.com>
> wrote:
> > [...]
> > I made a mistake for I agree that
> >
> > 142857142857....1428571428571 X 7 = 9999....999997
> > and so ....999997 is not prime.
> >
> > So that makes ......99999991 the world's largest prime.
>
> Nope. ...14285714285713 * 7 = ...99991, so ...99991 isn't prime,
> either.
>
> Furthermore, ...1428571428571427 * 7 = ...999989, so don't bother
> saying that ...999989 is prime, either.
I accept the fact that 142857 destroys the block 999999 and so one
only needs to find out where the 989 or 9989 or 99989 so on is
divisible
evenly by 7. So that there are probably no primes in the last 100
Counting numbers leading up to ....999999. Probably none
>
> And forget about 3 being prime. ...1428571428571429 * 7 = ...00003.
>
> In fact, for every AP-adic N, there is an AP-adic M such that
> M * 7 = N.
No, this tangent is not true, for this is a vestige of P-adic thinkers
of the Reals
where they in their *sloppiness* remember that 1.9999..... is that of
2
but here in frontview AP-adics we eliminate that sloppiness and
realize
that .....9999999 +1 is not 0 but is one unit distance further which
is 180 degrees
or (pi) radians which is imaginary in AP-adics.
So the old and sloppy P-adics saw that ....9999999 +1 as 0 but what
the AP-adics
teaches us is that the frontview is important and precise
and that the above is not ....0000003 but is in fact 100000.....00003
So the definition of Prime still stands good, it is the sloppiness of
the old P-adics
that needs attention.
>
> Which means the only possible prime is 7 itself (which is when
> M = 1 works above; otherwise there is a non-trivial factorization of
> N).
>
> But: ...666666669*3 = ...00007, so I guess that throws out 7 as well.
>
> Golly ... AP proved that there are infinitely many primes, but there
> don't seem to be any at all!!!!
>
> --- Christopher Heckman
So if nothing else, the AP-adics draws much attention to the
sloppiness of the old
P-adics.
The important thing now is to nail down what the world's largest prime
is. I made a typing
mistake by calling this number 9999.........1110987654321 as between
that of the
Counting Numbers from ......9999999 to .....999999901 which obviously
it is not between those
last 100 Counting Numbers but far smaller than any of those last 100.
What I need to do is find out exactly what is the world's largest
Prime number as an anchor
to better understand the whole view of Counting Numbers. The largest
prime is going to have
alot of 9s in its digit arrangement. So can I think of a irrational
digit arrangement with alot
of 9s in it or is the above the best there is?
a_plutonium
>
> What I need to do is find out exactly what is the world's largest
> Prime number as an anchor
> to better understand the whole view of Counting Numbers. The largest
> prime is going to have
> alot of 9s in its digit arrangement. So can I think of a irrational
> digit arrangement with alot
> of 9s in it or is the above the best there is?
I think perhaps this is the worlds Largest Prime number root of
999999.........2019181716151413121110987654321
If we try this irrational root sequence:
999999.......99999989999989999899989989
although it has alot more 9s in its sequence, the important 9s are
close to the
frontview where they matter the most as being large.
So if I had to make a choice, I would pict the first entry as the
world's largest
irrational root and thus yielding the world's largest prime.
Archimedes Plutonium
a_plutonium wrote:
> Archimedes Plutonium wrote:
>
>
>>What I need to do is find out exactly what is the world's largest
>>Prime number as an anchor
>>to better understand the whole view of Counting Numbers. The largest
>>prime is going to have
>>alot of 9s in its digit arrangement. So can I think of a irrational
>>digit arrangement with alot
>>of 9s in it or is the above the best there is?
>
>
> I think perhaps this is the worlds Largest Prime number root of
>
> 999999.........2019181716151413121110987654321
>
> If we try this irrational root sequence:
>
> 999999.......99999989999989999899989989
>
> although it has alot more 9s in its sequence, the important 9s are
> close to the
> frontview where they matter the most as being large.
>
> So if I had to make a choice, I would pict the first entry as the
> world's largest
> irrational root and thus yielding the world's largest prime.
>
Nay, another mistake. There are alot of mistakes when a new theory
enters science. I should have picked the second choice above
and then get an ever increasing presence of 9s into the sequence of
digits so as to manufacture or construct a string of 9s and 8 digits to
where it is irrational and possessing the maximum number of 9s digits.
So that is a tough order to place in a manufacturing facility. I want a
string that goes to infinity and ends in the front view with alot of
9s such as 9999999....8....89
While sprinkling in 8s just to make it irrational. It would have
to be a good manufacturing facility.
David R Tribble
> Mathematicians have never explored the fact that the number of primes at
> the end of the Counting Numbers is the same quantity as the beginning
> where you have 25 Primes in the first 100 counting numbers and you have
> 25 Primes in the last 100 Counting Numbers where ....999997 is the
> world's largest prime. But the same quantity exists in ....11111 series
> as well as .....22222 series as well as ....33333 series etc.
>
> is only locally true for a Series of Primes out to a large number but
> not true overall for Mathematics. For the Primes are distributed in the
> Counting Numbers as a layered structure that repeats itself such as a
> onion layering.
So now you claim to have disproven the Prime Number Theorem.
You state it's only true "out to a large number" - any idea what
number that might be?
David R Tribble
>> Question Dik: what algebra exists for the points on the unit circle? Do
>> those points have an algebra?
>
Dik T. Winter wrote:
>> What do you actually *mean* with "an algebra"? If you mean that there
>> exist operations like addition, subtraction, multiplication and division,
>> yes there are. And not even a single set. Consider the unit circle as
>> the pair (cos(x), sin(x)), and do operations on the x's mod 2.pi. There
>> you are, the only problem is that there are zero divisors. And there are
>> many other possibilities.
>
Archimedes Plutonium wrote:
> Okay thanks. Now it is my duty to show that those points are impossible
> to form a ring or a field. Impossible because the points on a circle do
> not obey transitivity.
If I'm reading it right, Dik's simple scheme is to use the points
on a circle of radius 1. Addition a+b is defined as adding
the arc lengths of points a and b. Point a has coordinates
(xa,ya), so Len(a) = arccos(xa). So adding a+b = c means
that Len(a)+Len(b) = Len(c), or arccos(a)+arccos(b) = arccos(c),
all modulus 2pi, of course (to handle wrap-around).
0 rad is the additive identity.
Multiplication is likewise simply the product of arc lengths.
So a x b = c means Len(a) x Len(b) = Len(c) (mod 2pi).
1 rad is the multiplicative identity.
Addition and multiplication are obviously commutative,
associative, and distributive.
Thus we have a ring. Defining subtraction and division is
also straightforward, so we have a field as well (with 0 rad
as the only undefined divisor).
(Apologies if I made any mistakes.)
And like Dik said, there are many, many other possibilities
for algebraic structures on the unit circle.
> Any alleged concoction that the points on a circle form a ring or field
> would be tantamount to saying that there are some Elliptic and
> Hyperbolic triangles whose angle sum is exactly 180 degrees.
Good luck with your proof.
Proginoskes
wrote:
> Proginoskes wrote:
> > On Oct 23, 10:23 pm, Archimedes Plutonium <a_pluton...@hotmail.com>
> > wrote:
>
> >>[...]
> >>I made a mistake for I agree that
>
> >>142857142857....1428571428571 X 7 = 9999....999997
> >>and so ....999997 is not prime.
> > And forget about 3 being prime. ...1428571428571429 * 7 = ...00003.
>
But the "Unchanging Digit Sequence" 9*7, 29*7, 429*7, etc., converges
to ...0003.
Another question along this line is: You don't have to worry about the
"front view remainder" for the product ....1428571428571 * 7 (which
you acknowledge above), so why do you insist on it for ...
1428571428571429 * 7? This tells me that different (ad hoc) rules are
used for calculating
....1428571428571 * 7 and ...1428571428571429 * 7.
--- Christopher Heckman
Proginoskes
wrote:
> [...]
> Nay, another mistake. There are alot of mistakes when a new theory
> enters science. I should have picked the second choice above
> and then get an ever increasing presence of 9s into the sequence of
> digits so as to manufacture or construct a string of 9s and 8 digits to
> where it is irrational and possessing the maximum number of 9s digits.
>
> So that is a tough order to place in a manufacturing facility. I want a
> string that goes to infinity and ends in the front view with alot of
> 9s such as 9999999....8....89
>
> While sprinkling in 8s just to make it irrational. It would have
You need an infinite number of 8's here. A finite number of them (it
seems) would result in a rational AP-adic.
A better example is this. ...232323832 is rational since, going from
right to left, you eventually find a pattern that repeats itself
verbatim, ad infinitum (namely 32). For the example above, if there
are only finitely many 8's, and the rest of the numbers are 9's,
you'll eventually find that 9 repeats itself over and over again.
--- Christopher Heckman
Archimedes Plutonium
I am wondering if there is some sort of shortcut such as a concept
of midpoint of an infinite string. I think this makes sense because
All Possible Digit Arrangements.
So that somewhere in this number string:
99999............midpoint .........9999999
And the 1/2 of that number is 49999....99999r5
So, now, there is a number in All Possible Digit Arrangements as such
99999.........m.......9997
where m is the midpoint of that string.
Now, if I place a 8 in the midpoint as such:
9999999......99989999.....99997
So the question would be, is it Prime and is it the World's largest prime?
The other thing I thought of is the manufacturing process
such as 9999..........99999989999989999899989989
But the trouble with manufacturing is that it does not tell
me what the largest prime is because I can always build a sparser
8 digit appearance.
What I want is to pinpoint the largest prime.
So I wonder if the midpoint place value of a number can render it
prime and whether this is the world's largest prime.
Archimedes Plutonium
Proginoskes wrote:
> On Oct 24, 9:58 am, Archimedes Plutonium <a_pluton...@hotmail.com>
> wrote:
>
>>Proginoskes wrote:
>>
>>>On Oct 23, 10:23 pm, Archimedes Plutonium <a_pluton...@hotmail.com>
>>>wrote:
>>
>>>>[...]
>>>>I made a mistake for I agree that
>>>
>>>>142857142857....1428571428571 X 7 = 9999....999997
>>>>and so ....999997 is not prime.
>>>
>>[...]
>>
>>>And forget about 3 being prime. ...1428571428571429 * 7 = ...00003.
>>
>>Not true for it leaves a front view remainder where you can never
>>get all the front view digits as 0 [...]
>
>
> But the "Unchanging Digit Sequence" 9*7, 29*7, 429*7, etc., converges
> to ...0003.
I need to sharpen the definitions of operations as the radix fraction
was incompetent to treat the 142857 for 999999
>
> Another question along this line is: You don't have to worry about the
> "front view remainder" for the product ....1428571428571 * 7 (which
> you acknowledge above), so why do you insist on it for ...
> 1428571428571429 * 7? This tells me that different (ad hoc) rules are
> used for calculating
> ....1428571428571 * 7 and ...1428571428571429 * 7.
I have always been consistent in looking at both ends of the string, the
frontview and rearview. I would rather say that the P-adic fans have
been inconsistent such as their insistence that ......999999 + 1 in
P-adics is 0.
I think much of that confusion was due to the fact the concept of
"frontview" was only a recent discovery. I see nowhere in the math
literature that anyone raises the issue of "frontview". So it looks as
though I discovered "frontview" and then the number ....9999+1 goes
under closer scrutiny. Even I myself in the 1990s accepted
.....999999 + 1 as being 0. But once frontview is set forth then
closer inspection of .....99999 + 1 reveals a different truth.