This Week's Finds in Mathematical Physics [Week 9]

[john baez]

Week 9

1. Surgical invariants of four-manifolds, by Boguslaw Broda, preprint
available as hep-th/9302092.

There a number of attempts underway to get invariants of four-dimensional
manifolds (and 4d topological quantum field theories) by techniques
analogous to those that worked in three dimensions. The 3-manifold
invariants and 3d topological quantum field theories got going with the
work of Witten on Chern-Simons theory, but since this was not rigorous a
number of ways were devised to make it so. These seem different at
first glance but all give the same answer. Two approaches that use a
lot of category theory are the Heegard splitting approach (due to Crane,
Kohno and Kontsevich, in which one writes a 3-manifold as two solid
n-holed tori glued together by a diffeomorphism of their boundaries),
and the surgery on links approach (due to Reshetikhin and Turaev, in
which one builds up 3-manifolds by starting with the 3-sphere, cutting out
thickened links and gluing them back in a different way, allowing one to define
invariants of 3-manifolds from link invariants). In the case of 3
dimensions a nice paper relating the Heegard splitting and the surgery
on links approaches is

Reshetikhin-Turaev and Crane-Kohno-Kontsevich 3-manifold invariants
coincide, by Sergey Piunikhin, preprint, 1992. (Piunikhin is at
ser...@math.harvard.edu.)

People are now trying to generalize all these ideas to 4-manifolds.
There is already an interesting bunch of 4-manifold invariants out
there, the Donaldson invariants, which are hard to compute, but were
shown (heuristically) by Witten to be related to a quantum field theory.
Lately people have been trying to define invariants using category
theory; these may or may not turn out to be the same.

I've already been trying to keep you all updated on the story about Crane and
Yetter's 4d TQFT. This week I'll discuss another approach, with a vast
amount of help from Daniel Ruberman, a topologist at Brandeis. Any
errors in what I write on this are likely to be due to my
misunderstandings of what he said - caveat emptor! Broda's paper is
quite terse - probably due to the race that is going on - and is based
on:

A link calculus for 4-manifolds, by E. Cesar de Sa, in Topology of
Low-Dimensional Manifolds, Proc. Second Sussex Conf., Lecture Notes in
Math., vol. 722, Springer, Berlin, 1979, pp. 16-30,

so I should start by describing what little I understand of de Sa's
work.

One can describe (compact, smooth) 4-manifolds in terms of
handlebody decomposition. This allows one to actually draw pictures
representing 4-manifolds. A lot of times when people first hear about
topology they get they impression that it's all about rubber doughnuts,
Mobius strips, and other Dali-esque wiggly objects in hyperspace. Then,
when they take courses in it, they are confronted with nasty separation
axioms and cohomology theories! This is just to scare away outsiders!
Handlebody theory really *is* about wiggly objects in hyperspace, and
it's lots of fun - though to be good in it you need to know your point
set topology and your algebraic topology, I'm afraid - and much better
than I do!

Recall:

D^n = unit ball in R^n
S^n = unit sphere in R^{n+1}

In particular note that S^0 is just two points. Note that:

the boundary of D^4 is S^3
the boundary of D^3 x D^1 is D^3 x S^0 union S^2 x D^1
the boundary of D^2 x D^2 is D^2 x S^1 union S^1 x D^2
the boundary of D^1 x D^3 is D^1 x S^2 union S^0 x D^3
the boundary of D^4 is S^3

I have written this rather redundant chart in a way that makes the
pattern very clear and will come in handy below for those who aren't
used to this stuff.

To build up a 4-manifold we can start with a "0-handle," D^4, which has
as boundary S^3.

Then we glue on "1-handles," that is, copies of D^3 x D^1.
Note that part of the boundary of D^1 x D^3 is D^3 x S^0, which is two
D^3's; when we glue on a 1-handle we simply attach these two D^3's to
the S^3 by a diffeomorphism. The resulting space is not really a smooth
manifold, but it can be smoothed. It then becomes a smooth 4-manifold
with boundary.

Then we glue on "2-handles" by attaching copies of D^2 x D^2 along the
part of their boundary that is D^2 x S^1. Then we smooth things out.

Then we glue on "3-handles" by attaching copies of D^1 x D^3 along the
part of their boundary that is D^1 x S^2. Then we smooth things out.

Then we glue on "4-handles" by attaching copies of D^4 along their
boundary, i.e. S^3.

We can get any compact oriented 4-manifold this way using attaching maps
that are compatible with the orientations. The reader who is new to this
may enjoy constructing 2-manifolds in an analogous way. Compact
oriented 2-manifolds with boundary are just n-holed tori.

What's cool is that with some tricks one can still *draw* what's going in
the case of 3-manifolds and 4-manifolds. Here I'll just describe how it
goes for 4-manifolds, since that's what Cesar de Sa and Broda are
thinking about. By the way, a good introduction to this stuff is

The Topology of 4-manifolds, by Robion C. Kirby, Springer-Verlag
Lecture Notes in Mathematics (1989), vol. 1374.

So - here is how we *draw* what's going on. I apologize for being
somewhat sketchy here (sorry for the pun, too). I am a bit
rushed since I'm heading off somewhere else next weekend... and I am not
as familiar with this stuff as I should be.

So, when we start with our 0-handle, or D^4, we "draw" its boundary,
S^3. Think of S^3 as R^3 and a point at infinity. Since we use perspective
when drawing pictures of 3-d objects, this boils down to pretending that
our blackboard is a picture of S^3!

As we add handles we continue to "draw" what's happening at the
boundary of the 4-manifold we have at each stage of the game. 1-handles
are attached by gluing a D^3 x D^1 onto the boundary along two D^3's -
or balls - so we can just draw the two balls.

2-handles are attached by gluing a D^2 x D^2 onto the boundary of the
4-manifold we have so far along a D^2 x S^1 - or solid torus, so we just
need to figure out how to draw an embedded solid torus. Well, for this
we just need to draw a knot (that is, an embedded circle), and write an
integer next to it saying how many times the embedded solid torus
"twists" - plus or minus depending on clockwise or counterclockwise - as
we go around the circle. In other words, an embedded solid torus is (up
to diffeomorphism) essentially the same as a framed knot. If we are
attaching a bunch of 2-handles we need to draw a framed link.

Things get a bit hairy in the case when one of the framed links goes
through one of the 1-handles that we've already added. It's easier to
draw this situation if we resort to another method of drawing the 1-handles.
It's a bit more subtle, and took me quite a while to be able to
visualize (unfortunately I seem to have to visualize this stuff to
believe it). So let's go back to the situation where we have D^4, with
S^3 as its boundary, and we are adding 1-handles. Instead of drawing
two balls, we draw an unknotted circle with a dot on it! The dot is
just to distinguish this kind of circle from the framed links we already
have. But what the circle *means* is this. The circle is the boundary
of an obvious D^2, and we can push the interior of this D^2 (which
is sitting in the S^3) into the interior of D^4. If we then remove a
neighborhood of the D^2, what we have left is S^1 x D^3, which is just
the result of adding a 1-handle to D^4.

This is probably easier to visualize one dimension down: if we have a
good old unit ball, D^3, and slap an interval, or D^1, onto its
boundary, and then push the interior of the interval into the interior
of the ball, and remove a neighborhood of the interval, what we have
left is just an S^1 x D^2.

So in short, we can draw all the 1-handles by drawing unlinked,
unknotted circles with dots on them, and then draw all the 2-handles by
drawing framed links that don't intersect these circles.

At this point, if you have never seen this before, you are probably
dreading the 3-handles and 4-handles. Luckily a theorem comes to our
rescue! If we start at the other end of our handlebody decomposition,
as it were, we start with 4-handles and glue on 3-handles. If you
ponder the chart and see what the pattern of what we're doing is, you'll
see that a single 4-handle with some 3-handles stuck on is just the
same as a 0-handle with some 1-handles stuck on. So when we now glue
this thing (or things) onto the stuff we've built out of 0-, 1-, and
2-handles, we are doing so using a diffeomorphism of its boundary. But
a theorem of Laudenbach and Poenaru,

A note on 4-dimensional handlebodies, by F. Laudenbach and V. Poenaru,
Bull. Math. Soc. France 100 (1972), pp. 337-344,

says that any such diffeomorphism extends to one of the interior. This
means that it doesn't make a darn bit of difference which diffeomorphism
we use to glue it on. In short, all the information is contained in the
1- and 2-handles, so we can *draw* 4-manifolds by first drawing a batch
of unknotted unlinked circles with dots on them and then drawing a
framed link in the complement.

[A question for the experts, since I'm just learning this stuff: in the
above we seem to be assuming that there's only one 0-handle. Is this an
okay assumption or do we need something fancier if there's more?]

Now a given 4-manifold may have lots of different handlebody
decompositions. So, as usual, we would like to have a finite set of
"moves" that allow us to get between any pair of handlebody
decompositions of the same 4-manifold. Then we can construct a 4-manifold
invariant by cooking up a number from a handlebody decomposition -
presented as a picture as above, if we want - and showing that it
doesn't change under these "moves".

So, what de Sa did was precisely to find such a set of moves. (There,
that's what I understand of his work!)

And what Broda did was precisely to use the Kauffman bracket invariant
of framed links to cook up an invariant of 4-manifolds from the
handlebody decomposition - which, note, involves lots of links. Recall
that the Kauffman bracket assigns to each link a polynomial in one
variable, q. Here "q" is just the same q that appears in the quantum
group SU_q(2). As I mentioned in "week5," this acts quite differently
when q is a root of unity, and the 3d topological quantum field theories
coming from quantum groups, as well as Crane and Yetter's 4d topological
quantum field theory, come from considering this root-of-unity case. So
it's no surprise that Broda requires q to be a root of unity.

Ruberman had some other remarks about Broda's invariant, but I think I
would prefer to wait until I understand them....

2. Minisuperspaces: symmetries and quantization, by Abhay Ashtekar,
Ranjeet S. Tate and Claes Uggla Syracuse University preprint
SU-GP-92/2-5, 14 pages, available in latex form as gr-qc/9302026

Minisuperspaces: observables and quantization, Abhay Ashtekar,
Ranjeet S. Tate and Claes Uggla Syracuse University preprint
SU-GP-92/2-6, 34 pages, available in latex form as gr-qc/9302027

I was just at the Pacific Coast Gravity Meeting last weekend and
heard Ranjeet Tate talk on this work. Recall first of all that
minisuperspaces are finite-dimensional approximations to the phase space
of general relativity, and are used to get some insight into quantum
gravity. I went through an example in "week6". In these papers, the
authors quantize various "Bianchi type" minisuperspace models. The
"Bianchi type" business comes from a standard classification of
homogeneous (but not necessarily isotropic) cosmologies and having a lot
of symmetry. It is based in part on Bianchi's classification of
3-dimensional Lie algebras into nine types. The second paper gives a
pretty good review of this stuff before diving into the quantization,
and I should learn it!

The most exciting aspect of these papers, at least to the dilettante
such as myself, is that one can quantize these models and show that
quantization does NOT typically remove the singularities ("big bang"
and/or "big crunch"). Of course, these models have only finitely many
degrees of freedom, and are only a caricature of full-fledged quantum
gravity, so one can still argue that *real* quantum gravity will get rid
of the singularities. But a number of general relativists are arguing
that this is not the case, and we simply have to learn to live with
singularities. So it's good to look at models, however simple, where one
can work things out in detail, and not just argue about generalities.

3. Unique determination of an inner product by adjointness relations in
the algebra of quantum observables, by Alan D. Rendall,
Max-Planck-Institut fuer Astrophysik preprint.

I had known Rendall from his work on the perturbative expansion of the
time evolution operators in classical general relativity. He became
interested in quantum gravity a while ago and visited Ashtekar and
Smolin at Syracuse University, since (as he said) the best way to learn
is by doing. There he wrote this paper on Ashtekar's approach to
finding the right inner product for the space of states of quantum
gravity. I had heard about this paper, but hadn't seen it until I met
Rendall at the gravity meeting last weekend. He gave me a copy and
explained it. It is a simple and beautiful paper - such nice
mathematical results that I am afraid someone else may have found
them earlier somewhere.

Ashtekar's idea is to fix the inner product by requiring that the
physical observables, which are operators on the space of states, be
self-adjoint. Rendall shows the following. Let A be a *-algebra acting
on a vector space V. Let us say that an inner product on V is "strongly
admissable" if 1) the representation is a *-representation with respect
to this inner product, 2) for each element of A, the corresponding
linear transformation on V is bounded relative to the norm given by this
inner product, and 3) the completion of V in the inner product is a
topologically irreducible representation of A. Rendall shows the
uniqueness of a strongly admissable inner product on any representation
V of A (up to a constant multiple). Of course, such an inner product
need not exist, but when it does, it is unique. This is as nice a
result along these lines as one could hope for. He also has a more
complicated result that applies to unbounded operators. A good piece of
work on the foundations of quantum theory!

4. Thawing the frozen formalism: the difference between observables and
what we observe, by Arlen Anderson, preprint available in latex form as
gr-qc/9211028.

There were a number of youngish folks giving talks at the gravity
meeting who have clearly been keeping up with the recent work on the
problem of time and other conceptual problems in quantum gravity. In
very brief terms, the problem of time is that in general relativity, we
have not a Hamiltonian in the traditional sense, but a "Hamiltonian
constraint" H = 0, so when we quantize it superficially appears that
there are no dynamics whatsoever (as it seems like we have a zero
Hamiltonian!). That's the reason for the term "frozen formalism" - and
the desire to "thaw" it, or find the dynamics lurking in it. In fact,
the Hamiltonian constraint is just a reflection of the fact that general
relativity has no preferred time coordinate, and we are just learning
how to deal with the quantum theory of such systems. For a good survey
of the problem and some new proposed solutions, I again refer everyone
to Isham's paper:

Canonical Quantum Gravity and the Problem of Time,
Chris J. Isham, 125 pages of LaTeX output, preprint available as
gr-qc/9210011.

In particular, one interesting approach is due to Rovelli, and is called
"evolving constants of motion" (a deliberate and very accurate
oxymoron). While there are serious technical problems with this
approach, it's very natural from a physical point of view - at least
once you get used to it. I have the feeling that the younger
physicists are, as usual, getting used to it a lot more quickly than the
older folks who have been pondering the problem of time for many years.
Anderson is one of these younger folks, and his paper develops Rovelli's
approach in terms of in a toy model, namely the case of two free
particles satisfying the Schrodinger equation.

5. The extended loop group: an infinite dimensional manifold associated
with the loop space, by Cayetano Di Bartolo, Rodolfo Gambini and Jorge
Griego, 42 pages, preprint available as gr-qc/9303010.

Unfortunately I don't have the time now to give this paper the
discussion it deserves. Gambini is one of the original inventors of the
loop representation of gauge theories, so his work is especially worth
paying attention to. He explained the idea of this paper to me a while
back. Its aim is to provide a workable "calculus" for the loop
representation by enlarging the ordinary loop group to a larger group
which is actually an infinite-dimensional Lie group - the point being
that the usual loop group doesn't have a Lie algebra, but this one does.
As one might expect, the Lie algebra of this group is closely related to
the theory of Vassiliev invariants. The paper considers some
applications to quantum gravity and knot theory.

-----------------------------------------------------------------------------
Previous editions of "This Week's Finds," and other expository posts
on mathematical physics, are available by anonymous ftp from
math.princeton.edu, thanks to Francis Fung. They are in the directory
/pub/fycfung/baezpapers. Please don't ask me about hep-th and gr-qc;
instead, read the sci.physics FAQ or the file preprint.info in
/pub/fycfung/baezpapers.

[Archimedes Plutonium]

SAVE// In AP's 151st book TEACHING TRUE PHYSICS, 1st year College, I discuss EM connections in series and in parallel. And I focus in on one sore contention, that as you wire in Parallel and add more resistors, the overall resistance goes down. This is counterintuitive.

However, I believe this is required when you see New Ohm's law as being V = CBE rather than V = CR. I have seen analogies to toll booths on highways to try to ease the discomfort of this counterintuitive. But a better explanation is that Old Physics Ohm's law V = CR is just plain wrong. When we include Resistance = Magnetic field X Electric field the parallel circuit with added resistors making overall resistance go down is now easily explained.

----Quoting from the web---
It is clear from observing the indicator bulbs in the above diagrams that the addition of more resistors causes the indicator bulb to get brighter. For parallel circuits, as the number of resistors increases, the overall current also increases. This increase in current is consistent with a decrease in overall resistance. Adding more resistors in a separate branch has the unexpected result of decreasing the overall resistance!
(snipped)
The Tollbooth Analogy
The effect of adding resistors is quite different if added in parallel compared to adding them in series. Adding more resistors in series means that there is more overall resistance; yet adding more resistors in parallel means that there is less overall resistance. The fact that one can add more resistors in parallel and produce less resistance is quite bothersome to many. An analogy may help to clarify the reason behind this initially bothersome truth.
--- end quoting from the Web ---

AP does not like counterintuitiveness in science. So whenever counterintuitive rears its ugly head, means there is probably something wrong in theory, or something missing in theory. And no analogy is going to rectify the problem, since it is a theory in error.

So it is my hunch that the "Decrease in overall resistance" is because Old Physics Ohm's law has V= CR when it really is V = CBE.

But it is late at night and will work on this tomorrow....


So in Old Physics there Ohm's law was R = V/C while in New Physics we have resistance has two components of magnetic field B and electric field E where R= BE and thus BE = V/C. So in New Physics we have E = V/(CB) and we have B = V/(CE).

So can we begin to see that as you increase the number of resistors of B and E, you cause a decrease in R. Not quite yet.

I vaguely recall constructing series and parallel circuits in High School, but I do not recall if by adding a new resistor to the circuit decreased the overall resistance. And by that, I mean if the light bulbs shone brighter. And that would really be counterintuitive.

[Archimedes Plutonium]

AP requires for John Baez to go to UC Riverside student newspaper publishing a apology, that he was a dumbo in thinking the slant cut in single cone was a ellipse, not realizing the single cone has just 1 axis of symmetry and thus, never possible to produce a ellipse, but the slant cut in cylinder is always a ellipse. So John needs to apologize to all those young students for his mindless geometry mistake.

Mind you, 2 cones connected in this manner <> can yield an ellipse at slant cut and is the reason I keep putting the phrase "single cone".

So John, grow up and be a real mathematician and admit your mistakes, just as you would grade students who make errors.


The 169th book of Science by AP// 4 TESTS of Consistency of Mathematics (1) calculus (2) harmonic series (3) valid functions, (4) dimensions.

Archimedes Plutonium<plutonium....@gmail.com>
Jan 12, 2022, 2:35:35 AM
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The 228th book of Science for AP// Harmonic series of Oresme corrected and where the numerical value of 0.5MeV for monopole comes from// by Archimedes Plutonium

> Decimal 10 Grid
> The summation of all Fractions 0.1+0.2+..+0.9+1.0 in 10 Grid is 5.5
> The summation of all numbers of 10 Grid is 101x5.0= 505.0
>
> Decimal 100 Grid
> The summation of all Fractions 0.01+0.02+..+0.99+1.0 in 100 Grid is 50.5
> The summation of all numbers of 100 Grid is 10001x50.= 500050.
>
> Decimal 1000 Grid
> The summation of all Fractions 0.001+0.002+..+0.999+1.0 in 1000 Grid is 500.5
> The summation of all numbers of 1000 Grid is 1000001x500.= 500000500.
>

Alright, so the curious argument I am going to make is that in the True Numbers of Mathematics, the Decimal Grid Numbers we have a amplification of numbers whose prefix digit is either 5 or 1 and being scale numbers

1, 10, 100, 1000, ....

or

5, 50, 500, 5000, .... only with the 5 prefix it is a bit more than all zero digits after the prefix 5.

In physics we need to explain why the Dirac Magnetic Monopole is 0.5MeV actually in experiments it is 0.51MeV, but since 0.5 and 0.51 are in 2% Sigma Error we can drop the 0.51 and use 0.5.

So we have the monopole at 0.5MeV and the proton at 840MeV with a muon inside of 105MeV totaling 945MeV within sigma error of 938MeV from experiments or the neutron at 940MeV, better yet in sigma error.

So I was not going to write a whole new book, unless I could connect and tie into physics and that is exactly what ended up.

We know the Pair Production requires a gamma ray of 1MeV to split in two particles of 0.5MeV of positron and of monopole.

So, another Physics explanation is that electricity and the magnetic monopole are the summation of all fractions of the EM spectrum of Waves. And, were the summation of all energies in a specific Grid is another value of the 5 prefix.

AP, King of Science, especially Physics
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More to Add on this book:

Yes, so I need not have to write a new book on the fallacy of Old Math's divergence and convergence of series. When you have fake numbers for math, and you have fake ideas like continuum, and like the concept of infinity, you are bound to run into crazy conclusions. Crazy conclusions like that of adding up tiny numbers between 0 and 1 will lead to infinity itself. As if you ever more cut a cherry pie into smaller portions and then think of adding up all the tiny fractions that you will end up with a cherry pie larger than what you started with and a cherry pie that stretches to infinity, all from tiny little pieces. Here the Old Math mathematicians went off the cliff of crazy math in a big glorious manner.

In New Math, the only true numbers of mathematics are Decimal Grid Numbers, and these are discrete numbers meaning empty space in between one number and the next number. The smallest Decimal Grid System is the 10 Grid and it has exactly ten decimal fractions of 0.1, 0.2, 0.3, .. 0.9, 1.0 if we count 1 as a fraction and never count 0 as a decimal fraction.

So for small fraction numbers in 10 Grid we have just 10 numbers to add and that sum is 1.45.

And 1.45 is not a 10 Grid number but a 100 Grid Number. But, 1.45 is in between 1.4 and 1.5.

So here we define Convergence and Divergence for 10 Decimal Grid as being convergence when the sum is a number that exists in 10 Grid or is a number between x and x+0.1 in 10 Decimal Grid where both x and x+0.1 are in 10 Grid. We define Divergence as the sum goes beyond the largest number in the Grid system which is 10 and we view 10 as being infinity borderline so if we add up all the numbers of whole numbers they lie beyond 10 and so that sequence diverges. Or adding up all the numbers from 1.0 to 2.0 diverges to infinity in 10 Grid for it is larger than 10. Notice we do not have to bother with beyond microinfinity in 10 Grid for that is 0.1, for in series we add and the smallest we can add is 0.1+0.1.

You see Old Math never defined what the hell does the concept infinity mean? And in New Math, infinity means a borderline between finite numbers and infinite numbers. Using the Huygens tractrix we nail down, or locate this borderline as being 1*10^604 and for microinfinity the inverse 1*10^-604. Any number larger than 1*10^604 or smaller than 1*10^-604 are infinite numbers and not belonging to mathematics. Yes, I mean what I say, we have departed mathematics when we deal with infinite numbers in the 10^604 Grid. Our conclusions of mathematics are no longer deduction conclusions but probability conclusions. For it is fair to say that mathematics as a science starts to breakdown in the infinite numbers.

So we play a pretend game with 10 Grid that 0.1 is microinfinity and 10 is macroinfinity.

Now we see in every Grid system from 10 to 10^604 that adding up the Fractions in that system all Converge.

And this makes absolute commonsense in Math and Physics for we want not to break Conservation laws in physics the conservation laws of energy which our cherry pie cut into smaller and smaller fractions then adding up all these small fractions, ends up being, in Old Math, larger than infinity.

Now we proven that the sum of all fractions in 10 Grid converges, and by math induction prove that all Decimal Grid Systems converge of their fractions.

The TAKEAWAY--

The takeaway in all of this is that Old Math had several opportunities to see it was all flawed and needed massive overhaul. Old Math could not do a Geometry Proof of Fundamental Theorem of Calculus, should have alerted everyone in Old Math starting with Newton and Leibniz that Old Math was terribly flawed. Old Math could not understand that in Physics it is all discrete and no continuum-- yet the idiots of Old Math ignored quantum mechanics and ventured into more and more absurdities of Cauchy limit analysis in calculus, of Cantor infinities, of continuum hypothesis with Cohen.

Add another to that list of absurdities is the Oresme divergence of fractions, which I just discussed and informally proven Oresme wrong.

No, AP needs not have to write a whole new book on the Oresme divergence of fractions in a sequence, for AP just needs to include this post in his Mathopedia causing there to be 77 huge mistakes and errors and flaws of Old Math.

Thanks, I seemed to have forgotten that the Harmonic series does in fact Converge and needs be added to Mathopedia.
>
> Oresme obviously had not the true numbers of mathematics of Decimal Grid Numbers, instead he had the mindless ignorant Reals with its poppycock continuum, the worst hidden assumption in centuries of mathematics.
>
> When you realize the true numbers of mathematic are Discrete and decimal Grid Numbers then the harmonic series always converges.
>
> The mindless divergence of Harmonic series is a math proof of how banal kooks can become even more banal, and enjoy it.
>
> This would be Mathopedia's 77th fake math.
>
> MATHOPEDIA-- List of 76 fakes and mistakes of Old Math// Student teaches professor
>
> by Archimedes Plutonium
>
> Preface:
> A Mathopedia is like a special type of encyclopedia on the subject of mathematics. It is about the assessment of the worth of mathematics and the subject material of mathematics. It is a overall examination and a evaluation of mathematics and its topics.
>
> The ordering of Mathopedia is not a alphabetic ordering, nor does it have a index. The ordering is purely that of importance at beginning and importance at end.
>
> The greatest use of Mathopedia is a guide to students of what not to waste your time on and what to focus most of your time. I know so many college classes in mathematics are just a total waste of time, waste of valuable time for the class is math fakery. I know because I have been there.
>
> Now I am going to cite various reference sources of AP books if anyone wants more details and can be seen in the Appendix at the end of the book.
>
> I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds questions of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, of that which never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).
>
> ----------------------------
> Table of Contents
> ----------------------------
>
> 1) Introduction
>
> 2) List of 76 errors, mistakes and fakes of Old Math.
>
> 3) Appendix
>
> ---------
> Text
> ---------
>
> 1) Introduction
>
>
> Alright, well, mathematics is a closed subject. What I mean by that is due to the textbook series of Archimedes Plutonium TEACHING TRUE MATHEMATICS, that once you learn the polynomial transform and learn the two Power Rules of Calculus, you reached the peak, the pinnacle of all of mathematics, and anything further in math is just details of what you learn in that textbook series. Math is a completed science because it has this "peak of calculus", unlike the other 5 hard sciences of physics, chemistry, biology, geology, astronomy. Those other five will continue to find new ideas, new things, while math remains static and complete to its peak of calculus understanding. Mathematics is finished complete as far as a science goes because the peak of math is going nowhere. And even though Physics will find new science such as how the proton toruses inside of atoms are configured in geometry, the geometry and calculus used in that configuration, that new science does not change nor does it create or require a new math peak/summit to handle the new physics.
>
> Now I do need to discuss the errors of Math in general and the errors of math in geometry in particular. I have the feeling that Geometry is the more important of the two-- algebra - geometry. This list appears in partial form in most of AP's Teaching True Mathematics textbook series by Archimedes Plutonium, meant to be a guide and orientation, and a organizing of what must be covered before graduating from College, and what math to steer clear of.
>
> Errors mostly, but not always, for some are included because too much time spent on them.
>
> The listings in Mathopedia of errors, mistakes and fakes is based on the idea that Calculus is the supreme achievement of all of mathematics for it is the essential math of doing Physics electricity and magnetism. And in order to have a proof of the Fundamental Theorem of Calculus, we must clean up and clean out all the mistakes, fakes and errors of Old Math, erstwhile, we have no Calculus. So calculus is the consistency maker for the rest of all of mathematics.
>
>
>
> 2) List of 76 errors, mistakes and fakes of Old Math.
>
>
> 1) Calculus requires a geometry proof of Fundamental Theorem of Calculus, a proof that derivative and integral are inverses of one another, just as addition and subtraction are inverses, or, multiplication and division are inverses. The only way to obtain a geometry proof is to clean up and clean out all the fakes, mistakes and errors of Old Math, such as their fake numbers-- the Reals. Their fake definition of function allowing anything be a function. Their fakery of a continuum when even physics by 1900 with Planck onwards in Quantum Mechanics proving the Universe is discrete Space not a continuum, yet by 1900 onwards those in mathematics following the idiotic continuum in the Continuum Hypothesis with even more avid interest, when they should have thrown the continuum on a trashpile of shame.
>
> 2) The true numbers of mathematics are the Decimal Grid Numbers, because you have to need and apply one mechanism only to obtain the true numbers of mathematics-- Mathematical Induction. In Old Math they had just a tiny few intelligent mathematicians, Kronecker, who emerged from the gaggle crowd of kooks to notice that Naturals all come from one single mechanism-- Mathematical Induction. But Old Math never had a crowd of mathematicians with logical brains to say-- all our numbers need to come from the one mechanism of Mathematical Induction.
>
> 3) The true numbers of math have empty space between successor and predecessor numbers. For example the 10 Grid is 0, .1, .2, .3, . . . , 9.8, 9.9, 10.0. Where no numbers exist between .1 and .2, etc. Only discrete numbers allow us to give a proof of Fundamental Theorem of Calculus.
>
> 4) All functions of mathematics must be a polynomial, and if not a polynomial, convert the offering to a polynomial over a specific interval.
>
> Where is that stupid thread in sci.math, poising as a puzzle problem when it had no functions only pretend functions?
>
> A few days back, 11Aug2021 appeared a stupid puzzle problem here in sci.math. Of someone pretending he had 3, 4 even 5 or 6 functions and wanting to prove equality.
>
> Then I stepped into the conversation saying he had no functions at all, until they are converted into polynomials over a specified interval, then you can do calculus on those true real functions.
>
> So, the world wide math community has got to begin to learn, no function is a function, until, and unless they are polynomials. This is an axiom of math and is proven true by the geometry proof of Fundamental Theorem of Calculus. You cannot have a FTC, if you have functions that are not polynomials.
>
> So there is a trade off-- does math want calculus or no calculus? If you want calculus, all your functions have to be polynomials. This has to do with the concept of discrete geometry, not a continuum, for polynomials are discrete.
>
> 5) Space is discrete and all lines in space are strings of attached straight lines.
>
> 6) No curves exist in Geometry, only finer and smaller straight line segments attached to one another.
> We can still keep the name "curve" as long as we know it is a string of fine tiny straightline segments strung together in what looks like a smooth curve. If curves exist, then the Calculus in Fundamental Theorem of Calculus cannot be proven and thus Calculus does not exist. We all know that we have to have Calculus, and so we throw out onto the trash pile the curve of Old Math. And this is reasonable because starting in 1900 in physics there arose the Quantum Mechanics of Space being discrete. And a discrete space has no continuum, has no curve of Old Math.
>
>
> 7) Space has gaps in between one point and the next point. These gaps are empty space from one point to the next point, for example in 10 Grid there is no number between .1 and .2, and in 100 Grid there exists no number between .01 and .02.
>
> 8) Limit analysis was an insane fakery in Old Math, concocted because Old Math needed the excuse of some proof, so they invented the monster con-artist trick that a limit analysis would divert the fact it is no proof at all, but a Non Sequitur argument. Limit analysis is juju totem witchcraft dance around a desire to prove the Fundamental Theorem of Calculus. Just as idiotic as dancing around a sick person of a virus is going to cure the person.
>
> 9) Infinity has a borderline and there is a microinfinity compared to a macroinfinity. For example in 10 Grid, the microinfinity is .1 if we exclude 0 and so there is no number smaller than .1 and no number larger than 10 in 10 Grid, where 10 is macroinfinity.
>
> 10) The 1st Quadrant Only in Coordinate System Geometry. Sad that the first coordinate system of Descartes was correct but soon became corrupted with 4 quadrants. See Mathematical Thought, Volume 1, Kline, 1972, page 303. Where Fermat then Descartes starts the Cartesian Coordinate System as 1 axis only and from 0 rightwards, meaning in our modern day math, 1st Quadrant Only. Why did math screw up on coordinate systems? I suppose some clowns thought negative numbers were true and they wanted ease of drawing a circle with center at 0. When they could have just as easily drawn the circle in 1st Quadrant Only.
>
> 11) Calculus needed a Geometry proof of the Fundamental Theorem of Calculus, but Old Math never provided such, instead they provided some stupid Limit argument. The reason for the creation of the Limit disaster was that the French mathematician Cauchy got sick and tired of hearing his smartest students complain that the width of rectangles in the integral are 0 width, and those smart students could not, for the life of them understand how a rectangle with 0 width has any interior area. So instead of the math community denouncing the limit, instead they elevated the fakery.
Archimedes Plutonium<plutonium....@gmail.com>
Jan 11, 2022, 1:50:22 AM (yesterday)
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Alright, I caught myself in a huge mistake below. Only now did I catch myself for the sum of 0.1+0.2, +.. ,+ 0.9 +1. is not the paltry 1.45 but is the 5.5. I caught that mistake just now in figuring out the fraction summation in 100 Grid and remembering how Gauss computed that as 101 x 50 would be 50.50 which if true, and I made no further mistake would suggest that 1000 Grid would be coming further down in value than is 50.50.

This would suggest that 1000 Grid fractions would be 1001x50 = 50.050. Bringing the total down more than 100 and 10 grids as a percentage of the assumed macroinfinity of those Grids.

So if true would mean a convergence of the fractions the higher the Grid we go. But too tired to compute
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Archimedes Plutonium<plutonium....@gmail.com>
Jan 11, 2022, 11:43:44 AM (15 hours ago)
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Alright, more mistakes until I am in the clear. The 1000 Grid would be 1001 x 500 = 500.5 and not 50.05.

When the True Numbers of mathematics are Decimal Grid numbers what we have is that the Fractions are all concentrated between 0 and 1. There is no Oresme open ended fractions to infinity. There is just a finite set of fractions.

Here is a synopsis of the first three Decimal Grid systems, 10, 100, 1000.


Decimal 10 Grid
The summation of all Fractions 0.1+0.2+..+0.9+1.0 in 10 Grid is 5.5
The summation of all numbers of 10 Grid is 101x5.0= 505.0

Decimal 100 Grid
The summation of all Fractions 0.01+0.02+..+0.99+1.0 in 100 Grid is 50.5
The summation of all numbers of 100 Grid is 10001x50.= 500050.

Decimal 1000 Grid
The summation of all Fractions 0.001+0.002+..+0.999+1.0 in 1000 Grid is 500.5
The summation of all numbers of 1000 Grid is 1000001x500.= 500000500.

Now, in the True Numbers of mathematics, the decimal Grid Numbers we do not come upon a fraction of 2/3 until about the 100 Grid with 0.66 and made more sharper in 1000 Grid with 0.666 and more sharper in 10000 Grid with 0.6666, etc.

In Old Math, they were brainwashed by Reals, where they had infinite supply (ill-defined infinity) of Fractions all the time.

So that Physicists could actually prove the Old Math mathematician was a numbskull, saying to the Old Math mathematician. Look, if you have an infinite supply of fractions all the time you violate the Conservation Laws of Physics with your fractions summing up more than infinity itself.

In New Math, we have the Fractions summed up in any Decimal Grid System as being no-more than a little over 1/2 the largest number in that system, so that 5.5 is a little over 1/2 of 10, and 50.5 is a little over 1/2 of 100, etc. So we also see that a convergence of Fractions to a little over 1/2 of the value of the largest number in that specific Decimal Grid System.

Now, this add-on to my book Mathopedia, need not be a full new book, provided and unless the recurring number sequence of 5.5 , 50.5, 500.5, .... does not show up as any Important Constant of Physics. If it shows up as a important constant of physics, then I am obliged and forced to write a whole new separate book on this topic.

In physics I would start or begin to look at the magnetic monopole of 0.5MeV. Several experiments have placed that value at 0.510 MeV.

If I can tie together the Dirac magnetic monopole of 0.510MeV with the summation of Fractions of Decimal Grid Systems, then I am forced to write a whole new book on this topic.
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Archimedes Plutonium<plutonium....@gmail.com>
Jan 11, 2022, 8:26:30 PM (6 hours ago)
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Now the Sigma Error of 0.51 to 0.5 is 2% and that is easily acceptable. So I will make an enter new book on the Harmonic series Oresme fakery and the AP decimal Grid Numbers convergence of all fractions in mathematics.

AP
Archimedes Plutonium<plutonium....@gmail.com>
Jan 11, 2022, 11:18:35 PM (3 hours ago)
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On Tuesday, January 11, 2022 at 8:25:55 PM UTC-6, Archimedes Plutonium wrote:
> Now the Sigma Error of 0.51 to 0.5 is 2% and that is easily acceptable. So I will make an enter new book on the Harmonic series Oresme fakery and the AP decimal Grid Numbers convergence of all fractions in mathematics.
>

Yes, I am going to make the arguement that the EM spectrum of which the magnetic monopoles of 0.5MeV are a part of, that the number 0.5MeV for Dirac magnetic monopole is a summation of fractional EM waves.

As I pointed out-- the first three Decimal Grid Systems converges to the summation of all the possible fraction values-- those between 0 and 1, including 1 itself, converges to approx, 5, 50, 500, 5000, etc etc.

For many years I was troubled in seeing where a 0.5MeV comes from for the monopole. No trouble in seeing that the muon is 105MeV and proton is 840MeV with proton+muon = 945MeV. No trouble in seeing where those number values come from.

A massive problem in seeing where 0.5MeV comes from.

But also, besides the Summation of fractional energies in the EM spectrum is the 1MeV particle, the gamma ray with 1MeV that decays in Pair Production to two 0.5MeV particles. And of course 1 is the units value. And we can see this sequence in the Decimal Grid System sequences,

10 Grid is of course 10
100 Grid is of course 100 etc

Just as the 5's sequence of summation fractions, 5, 50, 500, 5,000 etc.

These are values of physics, values in motion, but consistently forming around 1 and 0.5.
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Archimedes Plutonium<plutonium....@gmail.com>
Jan 12, 2022, 12:25:51 PM (3 days ago)
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Now this certainly should be the case of when a person has the true numbers of mathematics, that the summation of all the small numbers then the summation of all the numbers would have the very same "prefix" of 5 digit value.
What I speak of, is the idea that the microscopic world of atoms and because the Universe the macroscopic world is one big atom itself that both should have the digit value be the same-- 5 digit value. And this is the case in Decimal Grid Systems, see below.

-Decimal 10 Grid
-The summation of all Fractions 0.1+0.2+..+0.9+1.0 in 10 Grid is 5.5
-The summation of all numbers of 10 Grid is 101x5.0= 505.0


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Archimedes Plutonium<plutonium....@gmail.com>
Jan 12, 2022, 9:41:13 PM (2 days ago)
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One of the most beautiful exquisite tests of the CONSISTENCY OF MATHEMATICS, rivaling the test of geometry proof of Fundamental Theorem of Calculus.

When Old Math cannot ever do a geometry proof of FTC, because it has to throw out the Reals, has to throw out continuum, has to throw out "ill defined infinity", has to well define function as being only polynomial functions and every other type has to convert into a polynomial. Is one TEST of consistency, because without the throwing out of garbage worthless mess of Old Math, you have no calculus at all.

But now, AP has found an even far far easier test of the Inconsistency of Old Math. It comes from series and especially the fake proof of Oresme with his Reals, his ill-defined infinite, his continuum.

SECOND TEST OF CONSISTENCY OF OLD MATH SHOWING OLD MATH to be a cesspool garbage of shit. Sorry for the harsh terms but in science they are needed as a slap in the face of ignorant people brainwashed by Old Math and continue to propagandize and brain wash young students.

SECOND TEST:

The second test merely notes that a Sound and Logical and Consistent Mathematics requires the Small Numbers to summation be containing only the DIGITS that the summation of all the numbers of math has. So when we add up all the Small Numbers in any Decimal Grid System there are only two digits involved the digit 0 and the digit 5, and no others. This tells us that Reals are a cesspool bag of shit. This tells us that the Decimal Grid Numbers are the only valid logical numbers to compose mathematics.

Decimal 10 Grid

The summation of all Fractions 0.1+0.2+..+0.9+1.0 in 10 Grid is 5.5
The summation of all numbers of 10 Grid is 101x5.0= 505.0

Decimal 100 Grid
The summation of all Fractions 0.01+0.02+..+0.99+1.0 in 100 Grid is 50.5
The summation of all numbers of 100 Grid is 10001x50.= 500050.

Decimal 1000 Grid
The summation of all Fractions 0.001+0.002+..+0.999+1.0 in 1000 Grid is 500.5
The summation of all numbers of 1000 Grid is 1000001x500.= 500000500.

Now I should extend this analysis to include only the digits, 1, 0 and 5. And I have to define specifically what is meant by Small Number of a specific Decimal Grid System. A Small Number is one that exists and lies between 0 and 1 and includes 1 but not 0.

So in Old Math, those fools could never list all their numbers, never list all the numbers between any two numbers. Ask a idiot of Old Math to list all the numbers of Reals between 0 and 1 and the magnanmous fool cannot. He/she tries to get away with a list of about 6 numbers and then waves his hand as pretending that 6 suggests all the rest. Most of Old Math is what is commonly called in Logic as "hand waving".

In New Math, we define the true numbers as Decimal Grid Numbers and we define Small numbers as those that lie between 0 and 1, including 1 but not including 0.

We find that, thus, 1,0,5 are the only digits needed for sums of Small numbers, sums of all the numbers.

And this is not a coincidence that 1,5,0 are the digits needed, for to be a Consistent Mathematics demands the summation of small numbers directly related to summation of all the numbers.
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Archimedes Plutonium<plutonium....@gmail.com>
Jan 14, 2022, 2:39:20 AM (yesterday)
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Sorry, I was busy revising my FIRST LIFE = Capacitor book and could not discuss my recent magnificent discovery in math that of a 2nd Consistency Test. But now have the time to discuss it.

Old Math never had Consistency tests. There was much talk, but never any actual consistency tests.

The greatest test of Consistency in Old Math was to do a geometry proof of Fundamental Theorem of Calculus. Of course there was never any valid proof of FTC in Old Math and their silly "limit analysis" is a pack of shit (sorry but that is the only way of getting attention to brainwashed math professors). Old Math never had a valid proof of FTC, they had limit analysis, analyze this analyze that, and analysis is never a proof. From Leibniz and Newton onwards, no-one had the logical brains to realize Calculus is geometry and required a geometry proof.

A limit analysis is not a proof but simply analyzing things. If I analyze a bee flying on a flower, I am not proving anything, yet this is how monsterously silly Old Math was for proving FTC. Analyzing yet not proving.

To prove geometrically FTC, requires you to throw out the Reals, to throw out the Continuum, to Modify what infinity means, to allow only Polynomial functions and no other type of function (if not polynomial, you must convert to polynomial before your piece of crap function is allowed in mathematics, to throw out all quadrants except 1st Quadrant only.

By doing all that throwing out, you thence can do a Geometry Proof of Fundamental Theorem of Calculus.

So that was Math's first and most spectacular Consistency Proof-- do a geometry proof of Fundamental Theorem of Calculus, for it requires you to clean out the entire house of the decayed rotten Old Math.

But there was a more simple streamlined proof of the Consistency and lack thereof in Old Math. This second Consistency Proof takes a look at the Oresme obnoxious alleged proof that the Harmonic series diverges. Meaning that in Old Math, they believed fractions added up can exceed Infinity. Yes, hold your breathe before laughing. In Old Math they thought 1 + 1/2 + 1/3 + 1/4 + .... + 1/n will exceed Infinity.

I did a book in Paleontology saying that the most ludicrous most laughable mistake that science ever endured and took serious was the sabre toothed tiger, never realizing that the teeth were from a walrus that the normal tiger preyed upon.

Was the Saber-Toothed-Tiger, Smilodon, Paleontologists most laughable mistake? // Was the 4 tusked Gomphothere the 2nd joke? Paleontology series, book 1 Kindle Edition
by Archimedes Plutonium (Author)

But here in Old Math, I could just as easily write a book on how laughably crazy are math professors who believed that adding up 1 + 1/2 + 1/3+ .... + 1/n diverges and exceeds infinity.

Which was the worst academic idiot? The paleontologist who could not fathom the walrus tooth laying by a tiger fossil was a different animal. Or the crazy math professor lecturing how small numbers, all smaller than 1 when added up exceed infinity.

We can all see why the Paleontology wants the story of a tiger with enormous teeth because that would rake rake rake in money. But no one can see why the idiot math professor wants to teach Harmonic series sums to infinity.

In my recent posts I showed that the true numbers of mathematics are Decimal Grid Numbers and that causes there to be this.

14) Of course the Calculus geometry proof of Fundamental Theorem of Calculus is a superb test of Consistency of Old Math. Testing whether the (1) numbers used are correct, (2) functions used are correct, (3) infinity correct, (4) continuum or discrete correct. Either all those elements to make a geometry proof of FTC are correct or we have to abandon calculus.

But there is a far more simple and easy measure of Consistency of Old Math numbers coming from the concept of Series addition sums. A far more easy test and it started with Oresme with a fake proof that the Series of small numbers of math, the fractions between 0 and 1 can sum up to be more than infinity itself. Imagine that for a moment, small numbers eclipsing the value of infinity. It defies imagination much like saying you can get energy from a vacuum to run a electric motor in physics.

What went wrong here is that Reals were never the true numbers of mathematics and Old Math had a screwed-up understanding of infinity, for Old Math never had a borderline between what is infinite and what is finite.


One of the most beautiful exquisite tests of the Consistency of Mathematics, rivaling the test of geometry proof of Fundamental Theorem of Calculus.

When Old Math cannot ever do a geometry proof of FTC, because it has to throw out the Reals, has to throw out continuum, has to throw out "ill defined infinity", has to well define function as being only polynomial functions and every other type of so-called-function has to convert into a polynomial first before it is a function. Is one test of consistency, because without the throwing out of garbage worthless mess of Old Math, you have no calculus at all.

But now, AP has found an even far far easier test of the Inconsistency of Old Math. It comes from series and especially the fake proof by Oresme with his Reals, his ill-defined infinite, his continuum.

Second test of Consistency of Old Math showing Old Math to be a cesspool garbage. Sorry for the harsh terms but in science they are needed as a slap in the face of ignorant people brainwashed by Old Math and continue to propagandize and brain wash young students.

Second Test:

The second test merely notes that a Sound and Logical and Consistent Mathematics requires the Small Numbers to summation be containing only the DIGITS that the summation of all the numbers of math has. So when we add up all the Small Numbers in any Decimal Grid System there are only two digits involved for an answer, the digit 0 and the digit 5, and no others. Indicating that the Small Numbers are directly related to the sum total of all numbers. This tells us that Reals are a cesspool. This tells us that the Decimal Grid Numbers are the only valid logical numbers to compose mathematics.


Decimal 10 Grid
The summation of all Fractions 0.1+0.2+..+0.9+1.0 in 10 Grid is 5.5
The summation of all numbers of 10 Grid is 101x5.0= 505.0

Decimal 100 Grid
The summation of all Fractions 0.01+0.02+..+0.99+1.0 in 100 Grid is 50.5
The summation of all numbers of 100 Grid is 10001x50.= 500050.

Decimal 1000 Grid
The summation of all Fractions 0.001+0.002+..+0.999+1.0 in 1000 Grid is 500.5
The summation of all numbers of 1000 Grid is 1000001x500.= 500000500.


Now I should extend this analysis to include only the digits, 1, 0 and 5. And I have to define specifically what is meant by Small Number of a specific Decimal Grid System. A Small Number is one that exists and lies between 0 and 1 and includes 1 but not 0.

So in Old Math, they could never list all their numbers, never list all the numbers between any two numbers. Ask a fool of Old Math to list all the numbers of Reals between 0 and 1 and the magnanimous fool cannot. He/she tries to get away with a list of about 6 numbers and then waves his hand as pretending that 6 suggests all the rest. Most of Old Math is what is commonly called in Logic as "hand waving".


In New Math, we define the true numbers as Decimal Grid Numbers and we define Small numbers as those that lie between 0 and 1, including 1 but not including 0.

We find that, thus, 1,0,5 are the only digits needed for sums of Small numbers, sums of all the numbers.

And this is not a coincidence that 1,5,0 are the digits needed, for to be a Consistent Mathematics demands the summation of small numbers directly related to summation of all the numbers.

AP is exploring the fact that the rest energy of the Dirac magnetic monopole of 0.5MeV, what Old Physics thought was the electron of atoms, but turns out the muon is the true electron of atoms at 105MeV rest mass. So this idea of the Series sum of all fractions is always of a form value involving just digits 5 and 0 is investigated further.
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Archimedes Plutonium<plutonium....@gmail.com>
Jan 14, 2022, 1:51:06 PM (yesterday)
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Alright, far far more on this CONSISTENCY Test of Old Math and Old Math really stinks for you have to throw out Reals, continuum, their dumb and stupid notion of infinity, their -- everything qualifies as a function (only polynomials are functions in true math) their mindless negative numbers and 4 quadrants when only 1st Quadrant exists.

So in Old Math, no-one is able to do a geometry proof of Fundamental Theorem of Calculus. Simply impossible with all the fakery and junk and errors of Old Math. You have to clean out all the trash of Old Math before you can even get started on a geometry proof of FTC.

And Old Math felt the symptoms of their nauseous and banal corruption of the truth of mathematics, for they had to come up with some form of proof of FTC, seeing that they could not have a geometry proof. So what happened, in the 1800s a Frenchman named Cauchy invented the obnoxious and worthless Limit Analysis, preaching that making an analysis is the same as proving FTC. And only the people who take mathematics for "getting a grade" but never learning the truth of calculus buy into that nonsense of a Limit analysis.

For the smart students of math realized almost immediately that Cauchy's obnoxious and error filled limit analysis was saying that a rectangle of 0 width has interior area, defying what we all know that 0 times anything is still 0. For Old Math calculus was summing up rectangles -- all of which were 0 width.

But, but, there is a Geometry proof of FTC provided we clean up many errors of Old Math. One of those huge errors is this notion of the Reals as Numbers, for they are a collection bag of hobbled and cobbled together trash for numbers. You can never tell how many fractions exist between 0 and 1, and Oresme came up with a thoroughly obnoxious error filled proof (fakery spelled in capital letters) Oresme thought he proved that if you add up just the Harmonic series 1+1/2 + 1/3 + ... +1/n+.... That this series of smallest of the numbers on the number line, that Oresme and all later borne mathematicians thought they proved that these small numbers add up to larger than infinity itself. I mean, talk about dunce idiots of mathematics. We all thought the idiots of physics were ones who proclaimed that they could power their electric car from the electricity of a battery out of a lemon. Well, here in mathematics, math professors believe that the Tiny numbers of math add up to more than infinity.

But AP shows us that Decimal Grid Numbers are the true numbers of mathematics and in the first three decimal Grid Systems which is a proof by math induction that the smallest numbers when added up equal a tiny tiny bit more than a value of half of infinity for in 10 Grid 10 is the borderline to infinity and the sum of fractions is 5.5, about halfway.


Decimal 10 Grid
The summation of all Fractions 0.1+0.2+..+0.9+1.0 in 10 Grid is 5.5
The summation of all numbers of 10 Grid is 101x5.0= 505.0

Decimal 100 Grid
The summation of all Fractions 0.01+0.02+..+0.99+1.0 in 100 Grid is 50.5
The summation of all numbers of 100 Grid is 10001x50.= 500050.

Decimal 1000 Grid
The summation of all Fractions 0.001+0.002+..+0.999+1.0 in 1000 Grid is 500.5
The summation of all numbers of 1000 Grid is 1000001x500.= 500000500.


SO THIS TEST OF TRUE MATHEMATICS NUMBERS, is a test that reveals, the total sum of fractions, smallest numbers must be directly related to the total sum of numbers in a Decimal Grid System. Notice the fractions have only the digits 5 and 0 as well as the Total Sum of numbers in a specific Grid System. That is the DIRECT RELATIONSHIP, the mirror image. that the Sum of Fractions reflects the Sum of all the Numbers, for both have only digits of 5 and 0.

But today I want to talk more about the Consistency of the Fundamental Theorem of Calculus and combined with this Test of summation of Series of Fractions. I want to combine the two tests of Consistency.

In the Geometry proof of FTC, we are required a Midpoint between intervals, so for 10 Decimal Grid System we have these numbers to contend with. We are required of the midpoints for that is how the Derivative is constructed geometrically by reforming the rectangle in the interval at its midpoint and lifting up the right-triangle whose vertex is where the derivative lands on.

0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, . . . 0.9, 0.95, 1.0, 1.05, 1.1, ...... 10

Now, those midpoints of intervals do not exist in 10 Grid, no, they exist in 100 Grid, the next higher level Grid System.

But, if we are doing Calculus and using 10 Grid, we are forced to borrow from the 100 grid those midpoints.

If we deal only with 10 Grid strictly, our Series sum is exactly 5.5.

But, now if we add up all the midpoints we have another value of 5.0 exactly

And if we add 5.5 with 5.0 we get a number that is beyond the last finite number in Decimal 10 Grid. We get 10.5, an infinity number within the 10 Grid.

We find that all the other Decimal Grid Systems when summing their Midpoints in Intervals add up to Half of the value of the Grid System working in.

Now this requires careful interpretation, very careful interpretation. If the sum had been 10 outright for 10 Grid and not 10.5, the interpretation would have been immediate, that the sum of the smallest numbers and their midpoint add up to the largest finite number of that Grid system. Unfortunately it adds up to a tiny bit more. Of course we we get to the 10^604 Grid, the summation of fractions and midpoint CONVERGES to the largest finite number of that Grid System.

So in 10 Grid, there is the ominious sum of 10.5 but in 10^604 Grid the summ is virtually the same as the number 1*10^604 itself as we see that tiny dribble spill leftover of a "5 digit".

What I am saying here, is that the TRUE NUMBERS OF MATHEMATICS have to mirror reflect its smallest numbers with the total set of numbers. Reals cannot do any of this because Reals are a "bag of shit".
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Archimedes Plutonium<plutonium....@gmail.com>
1:04 AM (18 hours ago)
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On Friday, January 14, 2022 at 1:38:26 PM UTC-6, Archimedes Plutonium wrote:
> Alright, far far more on this CONSISTENCY Test of Old Math and Old Math really stinks for you have to throw out Reals, continuum, their dumb and stupid notion of infinity, their -- everything qualifies as a function (only polynomials are functions in true math) their mindless negative numbers and 4 quadrants when only 1st Quadrant exists.
>
> So in Old Math, no-one is able to do a geometry proof of Fundamental Theorem of Calculus. Simply impossible with all the fakery and junk and errors of Old Math. You have to clean out all the trash of Old Math before you can even get started on a geometry proof of FTC.
>
> And Old Math felt the symptoms of their nauseous and banal corruption of the truth of mathematics, for they had to come up with some form of proof of FTC, seeing that they could not have a geometry proof. So what happened, in the 1800s a Frenchman named Cauchy invented the obnoxious and worthless Limit Analysis, preaching that making an analysis is the same as proving FTC. And only the people who take mathematics for "getting a grade" but never learning the truth of calculus buy into that nonsense of a Limit analysis.
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> For the smart students of math realized almost immediately that Cauchy's obnoxious and error filled limit analysis was saying that a rectangle of 0 width has interior area, defying what we all know that 0 times anything is still 0.
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> But, but, there is a Geometry proof of FTC provided we clean up many errors of Old Math. One of those huge errors is this notion of the Reals as Numbers, for they are a collection bag of hobbled and cobbled together trash for numbers. You can never tell how many fractions exist between 0 and 1, and Oresme came up with a thoroughly obnoxious error filled proof (fakery spelled in capital letters) Oresme thought he proved that if you add up just the Harmonic series 1+1/2 + 1/3 + ... +1/n+.... That this series of smallest of the numbers on the number line, that Oresme and all later borne mathematicians thought they proved that these small numbers add up to larger than infinity itself. I mean, talk about dunce idiots of mathematics.
>
> But AP shows us that Decimal Grid Numbers are the true numbers of mathematics and in the first three decimal Grid Systems which is a proof by math induction that the smallest numbers when added up equal a tiny tiny bit more than a value of half of infinity for in 10 Grid 10 is the borderline to infinity and the sum of fractions is 5.5, about halfway.
> Decimal 10 Grid
> The summation of all Fractions 0.1+0.2+..+0.9+1.0 in 10 Grid is 5.5
> The summation of all numbers of 10 Grid is 101x5.0= 505.0
>
> Decimal 100 Grid
> The summation of all Fractions 0.01+0.02+..+0.99+1.0 in 100 Grid is 50.5
> The summation of all numbers of 100 Grid is 10001x50.= 500050.
>
> Decimal 1000 Grid
> The summation of all Fractions 0.001+0.002+..+0.999+1.0 in 1000 Grid is 500.5
> The summation of all numbers of 1000 Grid is 1000001x500.= 500000500.

I am slow to interpret this of Summation of Small Numbers with Midpoints.

It would be a easy interpretation if the sum were to equal the last finite number in value but for 10 Grid that sum is 10.5, for 100 Grid that sum is 100.5, for 1000 Grid that sum is 1000.5, for 10^604 Grid that sum is ---- add on a 0.5.

In this sense we can say the Sum of Fractions plus Midpoints is the value of the largest finite number plus tack on a 0.5.

Now I been thinking on this all day long, on and off. And one idea is that a 0.5, is the starting midpoint of the First Infinity Number Interval. Here I have flashbacks to the 1990s where I wasted so much time on P-adics. But here, perhaps, this 0.5 tack on is somehow the first number for Infinite Numbers, sort of like the P-adics going around in a circle, a circuit and coming to -2 which is 9999... 9998 then -1 which is 9999.....99999 and finally 0 and then 0.5 for a new p-adic circuit. Of course, in new true mathematics p-adics and negative numbers are nonexistent.

Anyway, if I fail to make any better of an explanation or interpretation than this, I still have succeeded in showing that the Reals are fake numbers because they are impossible to relate their small numbers with their total numbers.

Decimal Grid System as the true numbers of mathematics, directly relates all the numbers between 0 and 1 and the final largest finite number in that specific Grid System.

And, the most interesting part of this story is a direct link up to physics and the Dirac magnetic monopole of 0.5MeV, of course the gamma ray of 1MeV that in Pair production creates the positron and the antipositron (careful, it is not the electron, for that is the muon).
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I am going to push this book up as being my 169th published book of Science, for I have enough material already to publish. So instead of being 228th, it now becomes 169th.

And the title should be 3 TESTS of Consistency of Mathematics (1) calculus (2) harmonic series (3) valid functions.
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Jan 15, 2022, 7:44:38 PM (6 days ago)
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Alright, I discussed in length the primal greatest consistency test of Old Math-- was-- can it give a geometry proof of Fundamental Theorem of Calculus?? And the resounding answer was-- not unless you throw out the Reals, all functions but polynomials, all numbers except for Decimal Grid Numbers, throw out continuum and its stupid silly limit analysis, throw out all negative numbers and all quadrants except for 1st Quadrant Only, throw out the silly nondefinition of infinity.

My, a lot of throwing out of trash of Old Math.

Then a second consistency test arises in Old Math having to do with the Oresme fakery of a harmonic series diverges. Imagine the ludicrousness of thinking very small tiny numbers can exceed infinity. The resolution of Series of small numbers is obtained by noting that the True numbers in mathematics are the Decimal Grid Numbers. And once you accept these as the true numbers of mathematics, you no longer have the absurd result of Small Numbers added up exceeds infinity.

Now I need a 3rd Test of Consistency of Old Math. A test involving what are valid functions. Throughout Old Math, we see a history of utter lousy logic applied or worse yet, no logic at all. In the history of mathematics, shows a pattern of "acceptance of everything that comes down the road" and never a logical interrogation. Never a test of logic as can be seen by the numbers in Old Math, for even as late as the 20th century we have con-artists with "new silly and stupid numbers" the surreals. And the whole of the numbers of Old Math were a hobgoblin collection of bags of numbers-- junk numbers all accepted and tossed into a huge pile called Reals, and as if that was not good enough to collect trash, they invented complex and p-adics and more.

Where the truth be known, math had only one set of true numbers all along-- Decimal Grid Numbers.

So in this third test of Old Math we examine up close the polynomial functions. And compare them to all the other functions.

Comparing is a form of Consistency testing.

And we quickly note something hugely, hugely important about polynomial functions. Something I learned in college freshman calculus at Univ Cincinnati in 1968. Something I marveled at, and something I held dear, even to this day.

For when you take calculus and doing the derivative or the integral, there is one function and one function type only that is supereasy to solve. Supereasy to solve over all other functions. (And this so much reminds me now of how I solved the unification of the 4 forces of physics-- pick out the one force that is the most perfect force, and then the other 3 forces have to be a form of that perfect force-- the EM force)

Here in math calculus, there is one form of function that is a perfect form for its derivative and integral all follow a simple Power Rule. And once you learned the Power Rule, you never have any trouble with derivative or integral.

So, well, the polynomial functions are the easiest functions as a class of functions to do calculus. This implies that all other functions are likely to be fake functions, until they are turned into polynomials over a prescribed interval.

And there is another beautiful feature of polynomial functions. They are such that you can take a few coordinate points on a graph and turn them into a polynomial function called the Lagrange transform.

Now we ask, do any other class of functions have a transform to turn all other different types of function into this type? The answer is no. Only the polynomial functions have a built in feature of turning any other function into a polynomial.

And now, finally, we have to ask, is the Polynomial function the only valid function and what is its relationship to the Decimal Grid Numbers?
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Jan 15, 2022, 9:48:18 PM (6 days ago)
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So here now, I have not dug deep into whether the Polynomials as functions, the only valid functions is intimately related to Decimal Grid Numbers with their holes and gaps in between one number and the next number. A straight line in 1st Quadrant Only is a polynomial function and does a straight line need and require discrete numbers?

I have not proven that, but I have proven the geometry proof of the Fundamental Theorem of Calculus. With that proof of FTC, then I can safely say, that Polynomial functions require a Discrete Number System.

And I should not have been the only mathematician in the world in 1968 to notice the ease with which polynomials did all of calculus. That if we threw onto the trashpile every function except polynomials, the world of mathematics would be a thousand times better off. I should have not been the only mathematician to see the absolute ease with which polynomials glide through calculus. And this is alarming because the entire rest of the math community was making mathematics a higher and higher trash pile. As the teenager saying goes of math professors PhD, piled higher and deeper.

The ease, utter utter ease of derivative and integral of a polynomial function, yet only AP notices this in 1968. And the utter agony of doing derivatives or integrals of so called other functions that are not polynomials.

And again, the fact that their is a Transform, the Lagrange transform of turning any coordinate points into a polynomial function, yet nothing for other types of functions, should have been clear to everyone in math who does math as a career, that something is peculiar with polynomials as being special. So special they are the only Valid Functions.

AP
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Jan 16, 2022, 3:17:31 PM (5 days ago)
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Let us make it 4 TESTS of consistency, and this is likely to be the easiest test, even far more easy than that of harmonic series testing of consistency. Because in this test we simply note that 3rd dimension covers all of geometry. There is no 4th dimension or higher.

This test covers the need for Calculus to be 1st Quadrant Only, and no 4 quadrants in 2nd dimension, with no negative numbers. Of course the delusional Complex numbers with Imaginary numbers are the furthest reach into insanity. And then we note that Imaginary and Complex and negative numbers stupidity and insanity could have all be staved off if Old Math had simply realized a Axiom of Algebra that they missed-- YOU CAN NEVER HAVE A VALID EQUATION OF MATHEMATICS UNLESS THE RIGHT SIDE OF THE EQUATION HAS A POSITIVE NONZERO NUMBER THERE, ALL ALONE, AT ALL TIMES.

If Old Math had realized this is a crucial axiom of algebra, then much of what inflicts Old Math with its terminal diseased culture of phoniness, would have been abated.

The insanity of 4th dimension and higher even spilled over into physics with their multi dimensions, where even some goon clod physicists believe in a 11th dimension.
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Jan 17, 2022, 1:31:49 AM (4 days ago)
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Now I believe strongly there is this 4th test of Consistency that you can have only 3 dimensions.

And I suspect there is a direct proof out of the 6 EM laws of physics (what was formerly called the Maxwell Equations, only corrected of its many errors).

A direct proof that you cannot have a Faraday law of physics if you had 4th dimension. Something on those lines.

This is not the first time I thought of proving 3rd dimension is the last dimension, for years ago I have been wondering about this. Maybe now I can actually prove it.
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Jan 17, 2022, 2:11:33 AM (4 days ago)
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Yes, I did solve it years ago, and even included it in several of my books on physics.

It is not the Faraday law or Ampere-Maxwell law or Coulomb law or but is rather the New Ohm's law the Voltage = current x magnetic field x electric field.

That is an equation of V = iBE and is a equation of volume in math. To say there is a 4th dimension is tantamount to saying that Volume does not capture all the volume of a prescribed region. That there is something more in geometry than volume, which is not true.

Only I am afraid, dumb people cannot buy that argument. Dumb people want something they cannot understand and hear it from other dumb people that it is true. Take for example Godel's or Cantor's nonsense in logic or math or Hawking's nonsense of black holes or Einstein's nonsense of General Relativity, for dumb people accept that wholeheartedly because they cannot understand it, and hear everyone around them saying-- it is true.

AP
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Jan 18, 2022, 1:58:52 AM (3 days ago)
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Alright, now I am fully working on completing this book. It started as 2 tests of consistency of Old Math, (1) a geometry proof of Fundamental Theorem of Calculus (2) Oresme's Harmonic Series that diverges when it should to any common sense reasonable mind converge.

But I added on two more Consistency challenges to Old Math--- 3rd test-- the polynomial function is the only valid function in mathematics.

And yet a 4th test-- 3rd dimension has to be the last dimension, otherwise Volume in Old Math is no longer all encompassing of Space. Oh, yes, I know, kooks in physics thought of "curled up dimensions" but even here, requires volume. So if you want 4th or higher dimension, you destroy volume of geometry.
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Jan 18, 2022, 1:32:31 PM (3 days ago)
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I decided to place this book in my logic section, rather than mathematics. Mathematicians are far too dumb to correct their field of knowledge, so dumb are they, that they do not require any formal course in logic to learn how to think straight and clear, instead, they can go through college and earn a degree in pure math without ever having to study logic formally.

And this lack of training in Logical Thought-- how to think straight and clear is evident in math history from Leibniz and Newton onwards. That no-one in mathematics realized a slant cut in single cone is a Oval, never the ellipse for a single cone has but 1 axis of Symmetry yet a ellipse to be created from a sectioning requires 2 axes of symmetry such as a cylinder slant cut.

This utter inability to think straight and clear is evident in the entire mathematics community of 2022, where not a single one of these oafs of mathematics is willing to acknowledge the slant cut of single cone is a Oval, never the ellipse, Andrew Wiles, Terence Tao, Thomas Hales, John Stillwell, Ken Ribet, Jill Pipher. Not a single one of them is worth 10 cents in mathematics for not a single one of them has any abilities in Logic-- think straight and think clearly.

And so this book needs to go in the Logic section of AP's science book portfolio.

For the opposite of Logical Reasoning prevailed from Leibniz and Newton's invention of the Calculus around 1670 until AP cleans up Mathematics by 1991-2022 as the writing of this book. No-one in mathematics could think straight and clear that a single cone has 1 axis of symmetry and could never possibly give a ellipse which requires 2 axes of symmetry. And so the opposite of Logical Thought occurred in mathematics history-- the cobbling together of all sorts of junk and silly and stupid ideas, cobbled together into one huge rucksack called mathematics. AP calls it Old Math, for it is mathematics bereft and barren of logical reasoning.

This was the Method of Old Math-- anyone with junk and fake math was accepted into the inner circles of mathematics and this junk and failed and crazy math offerings were accepted and made Old Math, more of a waste dump site than a science of precision. Take a look at Old Math's numbers system, for they cobbled together the Naturals, then tacked on Rationals, then tacked on Irrationals, and not satisfied yet with the garbage collection, they tacked on imaginary numbers and extended it to Complex numbers, and even yet the sewage that was Old Math numbers was not yet satisfied for they took aim at Surreal garbage and P-adics garbage, and then finally along comes AP and says, the only true numbers in mathematics-- all those numbers have to come from a principle of Mathematical Induction, just like the Naturals are produced by mathematical induction. Of course, Old Math was not all losers and fools and idiots of mathematics for there was a Dr. Kronecker who stood up and said-- Naturals were made by God and all the other (crazy numbers) were manmade-- or words to that effect.

But the way Old Math created the Reals, their cesspool collection of numbers is symptomatic of how Old Math treated all subjects of mathematics--- allow everything, because no-one in Old Math had a logical brain of reasoning. No-one in Old Math was forced to train in formal logic. No-one in Old Math understood Logical Thought and Logical Reasoning. And this is proven by Boole and Jevons who in the late 1800s established formal logic but tragically, their system was all error ridden and outright crazy with their 2 OR 1 = 3 with AND connector being subtraction. Yet of course no-one in the mathematics community could ever even spot this tragic error of Boole logic, for mathematics was braindead towards logic. In mathematics history from Leibniz and Newton to AP, the mode of operation was Memorization and Add-on to the mountain of errors. No-one had a sharp logical mind from Newton to AP. Just the reverse where Cauchy tries to invent the Limit Concept to justify rectangles of 0 width, possessing interior positive area for integral. No-one from Leibniz and Newton to AP had a logical brain worth more than 10 cents. Not even those in Logic, had a Logical brain for we see that Cantor and Russell and Whitehead, Turing and Godel doing the Tack and Add on more garbage to the mountainous cesspool sewage that Old Math had become. For if one asks-- Cantor, Russell, Whitehead, Godel were comfortable and happy with Boole logic of 2 OR 1 = 3 with AND as subtraction. So stupid were they-- Cantor, Russell, Whitehead, Turing, Godel in logic that they not only could not see slant cut in single cone is a Oval, never the ellipse, but so stupid in logic that they bought into the mindless idiocy of 2 OR 1 = 3 with AND as subtraction as the foundation of their logical thought and used the mindless 2 OR 1 =3 in all their math proofs.

Even today the foolish math idiots of Wiles, Hales, Tao, Pipher, Ribet, Stillwell think in terms of Boole logic of 2 OR 1 = 3 with AND as subtraction.

So, what AP is going to do with his new book of Mathematics Consistency, is place it in the section of Logic. For Old Math was one huge colossal failure of thinking straight, thinking clear.

As Kronecker noted that Naturals were made by God and all the rest by humanity. AP in correcting Old Math, found that All the True Numbers of Mathematics should be like the Naturals,-- made by God. And that is what the Decimal Grid Number System is all about-- for every number is created by Mathematical Induction.

And only the Decimal Grid Numbers can do a geometry proof of the Fundamental Theorem of Calculus.
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Jan 19, 2022, 12:39:09 AM (2 days ago)
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While watching the Usenet newsgroup of sci.math, a group I have followed ever since late 1993, I saw a post about Oresme's so called proof that the Harmonic Series diverges to infinity. The Harmonic series is 1 + 1/2 + 1/3 + 1/4 + 1/5 + . . . + 1/n.....



Now most people when they come upon this series and its so called or alleged proof of divergence by Oresme in 1350, when they come upon this information for the first time in their studies, are usually set aghast in bewilderment, that the summation of ever tinier fractions when added up, is going to exceed beyond infinity itself. It is like in physics where some charlatan is entertaining us with a gadget that puts out more energy than put into the gadget.



But then no-one from Leibniz and Newton onwards to AP had a good mind of logical reasoning to put a stop to this nonsense of Harmonic series diverging to infinity.



In the case of Oresme, his so called proof is an error of logical reasoning for he reasoned that



1 + (1/2) + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) +....

can be converted to this

1 + 1/2 + 1/2 + 1/2 +1/2 +.... where Oresme concluded that goes to infinity.



Can the reader spot the horrible mistake Oresme and all mathematicians after Oresme made in that argument and its conclusion?



It is a delightful and lovely mistake that a person with Logical brains should find it easy to uncover.



So Oresme argued that he could rearrange the terms in the series and by rearranging that he could generate a sum of all terms after 1 be that of 1/2 (or, even greater than 1/2, but Oresme was satisfied with just using 1/2. For example in rearranging you add 1/3 with 1/4, but Oresme was satisfied with just 1/4+1/4. Same goes for (1/8+1/8+1/8+1/8) where Oresme could have used (1/5+1/6+1/7+1/8). But Oresme was satisfied with just all being 1/8. And with Oresme's poor understanding of what Infinity means-- for the truth of the matter, infinity has a borderline, but no-one in mathematics realized that infinity has a borderline until AP discovered the infinity borderline using Huygens tractrix. If you define infinity as a borderline of 1*10^604 then you have the truth of the Harmonic series. That the addition of fractions is far far less than 1*10^604, for there are only 1*10^604 terms in every series. And since the only number with value equal to 1 is the first term in the Harmonic series and all the other terms are far far less than 1 especially 1/(10^604). Means the Harmonic series converges to a finite number somewhere between 1 and 1*10^604.



This is the problem in mathematics education, in that earning a degree in mathematics to become a professor of mathematics requires no courses or training in formal logic. Logic is the science that helps you think straight and think clear. But in modern day education, a mathematics major in schools is not required to take logic. And thus, in the opinion of AP, most math professors are zombies in logical thought. And not a ghost of a chance that mathematicians from Leibniz and Newton to AP would get the correct understanding of the Harmonic series.

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Jan 19, 2022, 2:05:37 PM (2 days ago)
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Most students of mathematics who have not yet had their logical brain destroyed by a Old Math professor can read the below and figure out the silly mistake Oresme made-- for what Oresme did in his fake proof was allow the "terms of the harmonic series to be unbounded, while stifling the terms in the Truly Infinite Standard Series of Measure of 1+1+1+...... You see, the crux of Oresme's con art fakery is that he allows 1+1/2 + 1/3 + 1/4 +........ He allows that series to have far far far more terms than he allows 1+1+1+1+..... to have terms. And thus, a con-art fake is born into mathematics and math education as mindless math professors bought into that magician trick of fakery. Which reminds me of the con-art fake in 1973. This is where Geller claimed to bend spoons from this brain waves. And Johnny Carson was himself a magician and invited Geller spoon bending on his show but knowing what the deception and fakery was of Geller, and throughout the show Geller was unable to perform his magic trick act.



But in the case of Oresme, the delusion or optical illusion is quite plain to see-- Oresme allows more terms for his fractions of Harmonic series than he allows for integer terms of 1 for infinity. Oresme's mistake and all the Old Math Professors after Oresme is their Dis-Comparison, they compare more terms for 1/2, 1/3,.... than they compare with 1,1,....



It is sad and silly that Old Math was full of con-art magic tricks than ever the truth of mathematics.



And it is sad and silly that math was hoodwinked, yet no physicist was hoodwinked by spoon bending. At least, spoon bending was never taught in physics classrooms.









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Jan 20, 2022, 3:03:57 PM (yesterday)
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First let me remark, that it is a blessing to write so many books of science for one just feeds off the other once you write 169 books of science. For example, just recently I wrote the book that dispels the myth that the cheetah was the fastest land animal on Earth, by proving the racehorse is the fastest land animal on Earth. You are never going to get a cheetah to run what Secretariat ran the 2.4km in 1.59 minutes, and that is with a weight of a jockey on Secretariat's back, not included in that ultimate speed of a racehorse compared to cheetah.

Anyway this book of 169th on science is about Consistency in Mathematics and one item of consistency is the fallacy of Old Math with their dimensions exceeding 3rd. For in truth, the 3rd dimension is the last and final dimension. And the easy Proof of Consistency is that of Volume, for if you had 4th or higher dimension, then your formula of Volume cannot be V= LWH, but must have an additional term beyond length, width, height. In other words, 4th dimension causes Volume to be wrong as LWH.

But, today, I have another stunning proof other than using volume but using calculus of Speed and Acceleration, just like the racehorse Secretariat. By the way I read some more on Secretariat and some people say he had 4 times the heart that a average racehorse has and another web site saying he had 2X the heart size. I have no way of untangling which is the more accurate.

So, now, it is indubitable that Speed equals meter/second and that acceleration equals meters/seconds^2.

If you look at the cover picture of my book on racehorses you see that Secretariat had the largest angle of a stride at 110degrees.

So in physics we can say that Speed is Stride divided by Time.

In physics we can say that in running we have a concept of 1/second^2 as a internal electric motor of the speed at which you through your forleg out and your hindleg pushing forward. So that 1/second^2 is a motor rotor.

I wrote another book explaining Angular Momentum and another book explaining what is 3rd Dimensional Calculus.

Here is where I can tie in all those books of science in explaining that 3rd Dimension has to be the last and final dimension of science or math.

To say that there is a 4th dimension would be saying there is something beyond acceleration. That there is more math beyond acceleration.
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Jan 20, 2022, 3:33:07 PM (yesterday)
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So what we have here is extremely fascinating and extremely important, because we all can see the derivative in 2 dimensional calculus is dy/dx.

And here is an opportunity for the first time to see Derivative in 3rd dimension where the motor rotor of a 1/second^2 is involved with the dy/dx of 2nd dimension. The motor rotor of a Distance/ motor rotor is acceleration.

So we see the 2nd dimension calculus of purely dy/dx.

But now we can see the 3rd dimension calculus-- acceleration --- as the dy/motor rotor.

In one of my books I explain 3rd dimensional calculus as being in fact the Faraday Law. But now, today, I can tie into that with acceleration is dy/motor rotor.

And the way we see or view this is our own running or the running of Secretariat. The dy for Secretariat is his 110degree forleg to hindleg-- the stride in the run. But now we have a 1/seconds^2 and that is what is called by me the motor rotor. Do we have a fast 1/sec^2 a fast motor rotor or do we have a slow motor rotor.

I myself as a runner knows I have a very fast motor rotor, the energy I can burst forth with throwing my legs out on a run. However, I lack a huge stride. If I had a huge stride along with my motor rotor, I would have in my youth probably won a Olympic medal in racing. But because I have a short stride, means I was never Olympic material.

So in running, there are two dynamics at play, there is the stride-- how far apart can you throw your front leg to hind leg, and Secretariat was champion of that with 110 degrees separation. But the other dynamic is how fast that internal motor of the runner is going, how fast or rpm's or motor rotor is the runner producing. And in Secretariat with his heart so much larger than the average race horse could have a high high rpm. And that is the reason Secretariat won the triple crown in his last of 3 races beating the field by 31 lengths. When you put a racehorse with a 110 degree stride and a motor rotor of Secretariat, he is going to win by 31 lengths.

And the point in all of this, is that just like Volume is all consuming of a measure of Space. So is Acceleration all consuming of calculus Derivative in 3rd dimension. There cannot be a 4th dimension for it destroys geometry. Which in proofs of Math Consistency, means geometry has contradictions if inconsistent. A 4th dimension causes geometry to be inconsistent.
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Jan 20, 2022, 7:08:16 PM (yesterday)
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Physics had a concept for 1/seconds and called it frequency and called it rpm revolutions per minute (or seconds).

But physics had no concept for 1/seconds^2.

Sure, 1/sec^2 is the derivative of 1/sec, but physics had no developed concept for 1/sec^2 and no term for it.

So let me name 1/seconds^2 as being motor-rotor. The motor-rotor is the rate of change of 1/sec. This rate of change is 1/seconds times 1/seconds equals 1/seconds^2. Since rpm is in minutes we include 60 seconds in a minute and so the Motor-Rotor is rpm times rpm, also new to physics.

In Running whether human or racehorse there are two components, the stride is 1st component and the motor-rotor is the 2nd component. The stride is throwing your legs forward. The motor-rotor is a measure of the body to keep on throwing the legs forward. The fastest runners have a large stride and have a fast rotation of motor, some would call this the pace. So that if you as a runner can throw your legs 2 times against another runner with the same stride who throws his legs once to your 2 times, then your legs are faster than the other runner for you will have covered 2 times the distance.

There are four kinds of runners:
1) short stride and slow motor-rotor
2) long stride but slow motor-rotor
3) short stride and fast motor-rotor
4) long stride and fast motor-rotor

Someone running in place is short stride and fast motor-rotor. Olympic champions want as long a stride as possible hooked up to a fastest possible motor-rotor.
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Archimedes Plutonium<plutonium....@gmail.com>
3:56 PM (7 hours ago)
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Now yesterday I defined a brand new concept of both math and physics in that of 1/seconds^2. Of course, Old Math and Old Physics defined Frequency for that of 1/seconds, but they were too stupid to define 1/seconds^2. I defined it as Motor-Rotor as the rate of change of rps, revolutions per second.

This is extremely important for both math and physics because it is the 3rd dimension calculus. Being dunces in Old Math and Old Physics, they never had a 3rd dimensional calculus. With their 2 dimension dumb minds, they could not even go from their 2nd dimension calculus to where AP is at now,-- 3rd dimension calculus.

So yesterday I defined the concept of Motor-Rotor which is dy/(dx^2) the 2nd derivative of 1/seconds. And this is a concept, a phenomenon we easily recognize in Runners and Racehorses. In running the Stride- the throwing out of legs in the next step forward is the dy of calculus, and the repeating of stride is the frequency the 1/seconds. But now, we have 3rd dimension calculus and here we have the Stride , but we also have the math of Repeating-that-Stride involved in what I call the Motor-Rotor, of 1/seconds^2. We can think of it as the body energy in rotating the Stride legs to repeat another new stride.

So if we have a Runner like Secretariat with a Stride of 110degree angle from forleg to hindleg, which is the largest stride recorded in horse racing and if we couple that stride with a huge Motor Rotor-- the ability to repeat that throwing of stride, then you have a champion racehorse.

But today I am going to talk about the numerator of dy/dx which is speed. And instead of squaring the denominator for acceleration as dy/(dx^2) I am going to square the numerator of dy/dx and have (dy^2)/dx. And many of those in physics already knows what that is, for it is angular momentum.

So in the dumb and silly and stupid Old Math and Old Physics that had only 2nd dimension calculus. New Math and New Physics has 3rd Dimension Calculus with its (dy^2)/dx and its dy/(dx^2).

In 3rd Dimension Calculus I need not define dy^2 as it is meters^2 and we all know what meters squared is that of area. But it gives us greater insight into a concept that no-one in Old Physics ever mastered-- angular momentum, for every physicist of the 1900s never understood angular momentum, absolutely not a single physicist of the 1900s had a understanding worth more than 10 cents of what is angular momentum. And the proof of this is that everyone in the 1900s saw the 0.5MeV particle flying around a 938MeV proton at over 99% the speed of light. There is no angular momentum in that for the 0.5MeV particle would immediately fly off. There is angular momentum when we take the Muon as the true real electron of atoms, but it still is moving at too fast a speed to be bound to a proton. So we have to realize and understand that the Muon of 105MeV is stuck inside a proton torus of 840MeV. Being stuck inside so that the 8 rings of the proton hold and bound the Muon inside and doing the Faraday Law with the proton torus, gives Angular Momentum.
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[Archimedes Plutonium]

Blonde airhead Marjorie Taylor Greene, Georgia, running US Foreign policy more than weakling Joe Biden. Marjorie wants Russia to run over Ukraine, next stop Poland. So Marjorie refuses $61 billion aid to Ukraine and she has the backing of other Republicans as they follow the airhead of Congress.

Mathin3D, are you worried more about Marjorie in politics or Marjorie in math classrooms, teaching the slant cut of cone is ellipse, while AP says it is a Oval. And Marjorie could never do, nor understand what a geometry proof of Fundamental Theorem of Calculus is all about.

But the tragedy of Marjorie, is that Joe Biden is so weak, weak of a president, he is in the back seat while Marjorie is driving US foreign policy.

If AP were president, not saying I want that job, but if president, AP would bulldoze all 10 Republicans who block and throttle the govt from getting things done-- F-16s and $61billion in aid to Ukraine. And finish the Two State Solution for Palestine by the end of the month.

No, Joe Biden is weak weak weak and I think he should immediately resign and let Kamala finish out his term.

Nothing more ghastly to see than a blonde airhead Greene running USA foreign policy. As reported by Mathin3D who is also in the back seat.

On Friday, January 5, 2024 at 9:25:53 AM UTC-6, Mathin3D wrote:
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> Shut up fool.
>
> The Supreme Court will rule in favour of the shyster. You are as clueless about American politics as you are of mathematics and science.


Very crude dot picture of 5f6 magnetosphere of 231Pu Atom Totality

A torus shape doing the Faraday Law inside of each and every atom.
             ____
       .-'               `-.      
   .'     ::\ ::|:: /::   `.
 /        ::\::|::/::        \               
;             _ _             ;
|      ___( O )___      |     
;               - -             ;
 \         ::/::|::\::         /      
   `.     ::/ ::|:: \::      .'             
      `-    _____   .-'
     
One of those dots in the magnetosphere is the Milky Way galaxy. And
each dot represents another galaxy. The O is the Cosmic nucleus and
certainly not as dense as what Old Physics thought because in New Physics
the interior of atoms has the Faraday law with the donut hole occupied by neutrons as storage capacitors.

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, govt-police drag net spam,off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.  

Read my recent posts in peace and quiet. If you, the reader, is wondering why AP posts this to a thread which is off topic in sci.math or sci.physics, is because some stalkers track AP, such as kibo, dan, jan who have been paid to stalk for 3 decades and when they see AP trying to post to his own thread that is on-topic they throw a impossible reCAPTcha suppression and repression at me that only wastes my time. From what AP can make out-- Google is not the only one using reCAPTcha, apparently the US govt rents out reCAPTcha. So if you see a AP post in a thread off topic, is because kooks of reCAPTcha are making it impossible for AP to post to the on-topic thread.

Read all of AP's post in peace and quiet in his newsgroup-- what sci.physics and sci.math should look like when govt spammers are not allowed in a newsgroup to wreck the newsgroup. Govt spammers have their agenda of drag net spam, and then their agenda of spy message codes, such as the "i sick, i cry" baloney, which only ends up ruining the newsgroups and why Google decided to close shop having fought govt bureaucrat mind sets for 30 years, and time to close shop.

AP kindly asks Google to let AP run all three, sci.math, sci.physics, PAU as he runs PAU, now--- all pure science, no spam and no govt b.s.

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Archimedes Plutonium