A SIMPLE CHALLENGE that you great Mathematicians won't answer...
finite guy
To construct a 'perfect mathematical circle'
requires delta x and delta y to BE zero
from point-to-point in the circle -
not just 'approach zero'.
If delta x and delta y have ANY magnitude
from point-to-point then the 'circle' is a polygon.
It is irrelevant as to how many sides the polygon has -
it could be a billion^billion facets
but it will still be a polygon.
If delta x and delta y are allowed to be zero
from point-to-point in the 'circle'
then we are discussing one point only - not a circle.
How do you try to explain this obvious situation????
Fuckwit
It's called analysis.
http://en.wikipedia.org/wiki/Mathematical_analysis
Btw, the pairs x, y are perfectly defined by
x^2 + y^2 = c.
No delta x and delta y needed for that.
finite guy
>
> - Show quoted text -
Fuckwit is a good name.
You are naive, stupid or indoctrinated...
There must be a delta x and delta y - it is unavoidable.
THAT IS ANALYSIS.
Think again...
at least think sometime.
Try again.
Dustan
> Consider a circle: x^2 + y^2 = c
Ok. This is the mathematical definition of a circle. Who's arguing
with that?
> To construct a 'perfect mathematical circle'
> requires delta x and delta y to BE zero
> from point-to-point in the circle -
> not just 'approach zero'.
Which means it's physically impossible to construct a perfect
mathematical circle. Who's arguing with that?
> If delta x and delta y have ANY magnitude
> from point-to-point then the 'circle' is a polygon.
> It is irrelevant as to how many sides the polygon has -
> it could be a billion^billion facets
> but it will still be a polygon.
And every physical circle is actually a polygon. Who's arguing with
that?
> If delta x and delta y are allowed to be zero
> from point-to-point in the 'circle'
> then we are discussing one point only - not a circle.
This is where we deviate. You, sir, have obviously never heard of
limits or infinitesimals.
> How do you try to explain this obvious situation????
Sorry? Was there a problem there?
finite guy
>
> - Show quoted text -
http://en.wikipedia.org/wiki/Infinite
In mathematics, "infinity" is often used in contexts where IT IS
TREATED AS IF IT WERE A NUMBER (i.e., it counts or measures things:
"an infinite number of terms") but it is a different type of "number"
than the real numbers.
Dear sir (Fuckwit), this is to help you consider your pat and pathetic
reply...
finite guy
Yes, infinite as shown above by another Wiki article is NOT directly
applicable to Real numbers.
You still, as before, have a real conceptual problem.
Think...
finite guy
>
> - Show quoted text -
If you agree that a circle is not mathematically possible and that it
is a polygon -
WHY DO YOU CONTINUE TO USE IT AS IF IT WERE NOT...
Tonico
*************************************************************
It seems to me the only one having any problem here is you. You say
infinite is not directly applicable to the real numbers, whatever
"directly applicable" may mean to you. And you say that it says so in
a Wiki article, which could have been written even by you (go
figure...), for what we know.
Aha...so what? I see you've a problem with that, so you try to solve
it...if you want, of course.
Regards
Tonio
finite guy
>
> - Show quoted text -
I didn't write Wiki.
Is what I quoted from it different to your understanding?
My problem as such is that I understand that it is impossible to make
finite infinite, in actuality or theory.
This is pretty straight forward, and subsequently, a mathematical
circle (which is used daily by you) is invalid.
Easy. In this world of 'quanta', you think that you would consider
it's necessary finitude.
The idea of 'approaching infinity/zero' is understandable but a
nonsense.
Any size number that you choose is NO CLOSER to infinity than any
other.
Really, what is 'trans-finite' - it either is or it isn't.
No number is infinite - except that you deny the know for some other
reason.
Oh, and of course, no number of numbers is infinity.
Either way you try to phrase it.
But you pretend it is so...
Why?
There is no necessity to think that number(s) are infinite.
They can't be - they just keep getting bigger.
So how are your foundations???
finite guy
>
> - Show quoted text -
Tonico,
What does finite and infinite mean to you when you consider them the
same thing, undeniably?
Han de Bruijn
The venom is in the _equals sign_: '=' . What does it MEAN in practice ?
It's possible to make equality less restrictive (that is: less "exact")
by convoluting the delta function representing the circle in an "exact"
image (where it is _invisible_) with a Gaussian distribution function.
Programmed in (Delphi) Pascal as follows:
function G(x,y,sigma : integer) : double;
begin
C := sqrt(sqr(x-a)+sqr(y-b))-R;
g := exp(-sqr(C/sigma)/2);
end;
Form1.Image1.Canvas.Pixels[x,y] := Grijs(G(x,y,2));
Where the 'Grijs' function is black for its argument = 1 and white for
its argument = 0 . Mind the grey / gray scales in between, because they
are representing the _fuzzyfied_ equality.
Here is the picture (for a spread in the Gaussian = 2 pixels):
http://hdebruijn.soo.dto.tudelft.nl/jaar2008/cirkel.jpg
The general theory behind this is called _renormalization_. It's purpose
is to give the _idealizations_ of mathematics hand and feet again in the
real world, by relaxing exactness via a top-down mechanism:
http://hdebruijn.soo.dto.tudelft.nl/QED/index.htm
Han de Bruijn
Virgil
Unless Delphi Pascal is case insensitive, your function is not a
function.
Tonico
*********************************************************
And still, you are the one with some problem, which by the way I
haven't yet figured out.
You say that a "mathematical circle is invalid", whatever that means,
and you say I use it every day. Well, as far as I recall I don't use
circles every day, but even if I do then what? Are you saying actual,
"perfect", circles are impossible to build in our physical world? Ok,
I agree, so...??
You also say, in your rather impetuous and somewhat nonsensical (from
a mathematical point of view) message, that "no number is closer to
infinity than any other"...aha, so what? Who ever, in the mathematical
world, claim such a thing?
What do YOU think that "being close-being far from infinity" could
possibly mean in mathematics?? I've no the slightest idea.
What we mathematicians do sometimes is, for example in limits of
sequences, do some calculations involving the notion of n --> oo ,
which means (now comes a definition. Very important in mathematics.
You should try it) that for any real number R there's only a finite
number of natural numbers s.t. n < R, or what is the same: for every
real number R, all but a finite number of natural numbers fulfill n >
R).
Could it be that this sounds to you the same as claiming that some
number is "closer to infinity" than another one??
Who, again, thinks that "numbers are infinite", as you write? Who ever
convinced you, you poor stray one, that mathematicians believe in such
a thing?
And who ever told you that I do consider finite and infinite the same
thing? Why do you believe such a thing?
Regards
Tonio
finite guy
Are Real numbers defined in mathematics are infinite in quantity or
not????
Tonico
> not????-
**********************************************************
If you meant to ask whether real numbers as defined in mathematics are
infinite the answer is: oh, hollie mollie... not at all!
Although...there're developments including an element, many times
denoted as oo and called infinite, but it STILL is not a "standard"
real number.
Now, if you meant to ask whether the set of all the real numbers, as
defined (both the real numbers and the sets) in mathematics is an
infinite set (infinite set is ALSO a thing defined in mathematics),
then the answer is: yes, of course.
Regards
Tonio
finite guy
OK. Let's look at what you said...
> You say that a "mathematical circle is invalid", whatever that means,
> and you say I use it every day. Well, as far as I recall I don't use
> circles every day, but even if I do then what? Are you saying actual,
> "perfect", circles are impossible to build in our physical world? Ok,
> I agree, so...??
If you agree with the physical world (which is quantised), why do you
use maths in an otherwise fashion?
Mathematics is basically supposed to model reality...
If you cannot make a curve in the real physical world, then why do you
say that 'space' curves??
I guess it you don't like reality...
>
> You also say, in your rather impetuous and somewhat nonsensical (from
> a mathematical point of view) message, that "no number is closer to
> infinity than any other"...aha, so what? Who ever, in the mathematical
> world, claim such a thing?
> What do YOU think that "being close-being far from infinity" could
> possibly mean in mathematics?? I've no the slightest idea.
My apologies for my failings.
Let's set a mirror.
Why do 'mathematicians' babble about "trans-finite" if it is not as I
expressed it?
It is a quasi-religious doctrine that real numbers are infinite in
quantity...
>
> What we mathematicians do sometimes is, for example in limits of
> sequences, do some calculations involving the notion of n --> oo ,
> which means (now comes a definition. Very important in mathematics.
> You should try it) that for any real number R there's only a finite
> number of natural numbers s.t. n < R, or what is the same: for every
> real number R, all but a finite number of natural numbers fulfill n >
> R).
> Could it be that this sounds to you the same as claiming that some
> number is "closer to infinity" than another one??
Ah, you mention only one side of your coin...
How many times a day do you do functions defined as functions of
approaching infnity?
Approaching infinity (calculus and curves) is setting no limit at
all...
"For any real number" but you still express real numbers as being
infinite in quantity, do you not?
You consider One to be infinite when you presume to "divide it to
zero" to make your curves...
>
> Who, again, thinks that "numbers are infinite", as you write? Who ever
> convinced you, you poor stray one, that mathematicians believe in such
> a thing?
> And who ever told you that I do consider finite and infinite the same
> thing? Why do you believe such a thing?
As I said, "dividing to zero" AND any mathematical definition that has
"as x approachs infinity" etc, is used by you every day,. True?
This is a reflection of ancient Greek philosophy, not mathematics...
Be honest to yourself as well as others.
finite guy
Knowing all of this, why do you make 'curves' and 'spheres'?
You are inconsistent...
finite guy
You seem to mix your 'standards' with most equation
interpretations...
Definitions maketh reality not... at least yours do...
Bad Tonico... :-)
finite guy
>
> - Show quoted text -
Why do you say "less exact" when it is a better expression of
reality?
We can't even measure the EXACT number, root2, can we??
Tonico
>
> OK. Let's look at what you said...
>
> > You say that a "mathematical circle is invalid", whatever that means,
> > and you say I use it every day. Well, as far as I recall I don't use
> > circles every day, but even if I do then what? Are you saying actual,
> > "perfect", circles are impossible to build in our physical world? Ok,
> > I agree, so...??
>
> If you agree with the physical world (which is quantised), why do you
> use maths in an otherwise fashion?
> Mathematics is basically supposed to model reality...
*************************************************************
Who told you that? Why do you think you can determine what mathematics
is supposed to model, if anything at all?
**************************************************************
> If you cannot make a curve in the real physical world, then why do
you
> say that 'space' curves??
> I guess it you don't like reality...
>
*************************************************************
I'm very fond of reality, but I don't give a damn about it when doing
mathematics.
*************************************************************
>
> > You also say, in your rather impetuous and somewhat nonsensical (from
> > a mathematical point of view) message, that "no number is closer to
> > infinity than any other"...aha, so what? Who ever, in the mathematical
> > world, claim such a thing?
> > What do YOU think that "being close-being far from infinity" could
> > possibly mean in mathematics?? I've no the slightest idea.
>
> My apologies for my failings.
> Let's set a mirror.
>
> Why do 'mathematicians' babble about "trans-finite" if it is not as I
> expressed it?
> It is a quasi-religious doctrine that real numbers are infinite in
> quantity...
>
***************************************************************
There's a part of mathematics that talks about transfinite stuff, like
transfinite induction, transfinite ordinals, etc. It is pretty well
defined, it has some rules which anyone trying to play with it has to
abide by, and it makes some us pretty happy to talk about it and play
with it.
What is it to you?
**************************************************************
> What we mathematicians do sometimes is, for example in limits of
> > sequences, do some calculations involving the notion of n --> oo ,
> > which means (now comes a definition. Very important in mathematics.
> > You should try it) that for any real number R there's only a finite
> > number of natural numbers s.t. n < R, or what is the same: for every
> > real number R, all but a finite number of natural numbers fulfill n >
> > R).
> > Could it be that this sounds to you the same as claiming that some
> > number is "closer to infinity" than another one??
>
> Ah, you mention only one side of your coin...
> How many times a day do you do functions defined as functions of
> approaching infnity?
> Approaching infinity (calculus and curves) is setting no limit at
> all...
**************************************************************
Uh??
First: I don't usually "do" functions. I'm pretty happily married and
for a rather considerable ammount of time, so far.
Second: as far as I am aware, there are no functions "defined as
functions approaching infinity"....this doesn't make any sense
mathematicalwise!
Third: if by "approaching infinity (calculus and curves) you meant the
different instances where limits are used, say to define derivatives
or Riemann integrals, then I really can't see why you think this is
the same as "setting no limits at all"...
************************************************************
> "For any real number" but you still express real numbers as being
> infinite in quantity, do you not?
**************************************************************
No, I do not. Once again, if you meant whether the set of real numbers
is infinite BY DEFINITION, the answer's pretty simple: yes, that set
is infinite.
**************************************************************
> You consider One to be infinite when you presume to "divide it to
> zero" to make your curves...
>
*************************************************************
Once again: uh???
I don't divide by zero since I've been told, and I've repeated that to
many students, from HS level and up all the way to college, that upon
doing such a thing then world is going to end swallowed by a gigantic
snake.
Who told you, you rather confused, hopefully full-with-good-intentions
one that mathematicians have to divide by zero in order "to make our
curves", whatever that means?
**************************************************************
> > Who, again, thinks that "numbers are infinite", as you write? Who ever
> > convinced you, you poor stray one, that mathematicians believe in such
> > a thing?
> > And who ever told you that I do consider finite and infinite the same
> > thing? Why do you believe such a thing?
>
> As I said, "dividing to zero" AND any mathematical definition that has
> "as x approachs infinity" etc, is used by you every day,. True?
> This is a reflection of ancient Greek philosophy, not mathematics...
>
> Be honest to yourself as well as others.-
***************************************************************
I hope the last line was an unsolicited advise and not an order, and
thus I thank you for it.
I think you really should study some maths. There're LOTS of thing you
don't have much idea about, and you can be easy prey to preachers of
nonsense like some of our anticantorian resident cranks.
Regards
Tonio
Han de Bruijn
^^^^^^
>> end;
>>
>>Form1.Image1.Canvas.Pixels[x,y] := Grijs(G(x,y,2));
>
> Unless Delphi Pascal is case insensitive, your function is not a
> function.
It's indeed case insensitive. But, agreed, " G := " would be neater.
Han de Bruijn
> Why do you say "less exact" when it is a better expression of
> reality?
Please mind the scare quotes.
> We can't even measure the EXACT number, root2, can we??
Worse, we can measure _none_ of the exact real valued numbers exactly,
not even the rationals. But fortunately, we can _count_ the integers :-)
Han de Bruijn
Dustan
> On Feb 11, 8:08 pm, finite guy <adamle...@amnet.net.au> wrote:
After reading some of your responses, I think your argument reduces
to:
No natural number (or real number, for that matter) is infinite,
therefore infinity does not exist.
Unfortunately for you, mathematics doesn't play by those rules.
Infinity may not be a part of the set of natural numbers and real
numbers, but it is still a well-defined mathematical concept. Get over
it.
Dustan
> use maths in an otherwise fashion?
> Mathematics is basically supposed to model reality...
Is art necessarily supposed to model reality? Is music necessarily
supposed to model reality? Are movies necessarily supposed to model
reality? Is literature necessarily supposed to model reality?
Are you necessarily supposed to model reality ('cause you sure are
failin' at it)?
Before you answer any of the above questions, be sure to consider
every word carefully, especially "necessarily".
And BTW, in case you didn't get the message, mathematics is just
another form of art.
Han de Bruijn
Insofar as mathematics purports to be an art, its practitioners have an
obligation to exhibit good taste. (Preston C. Hammer)
Han de Bruijn
The poster formerly known as Colleyville Alan
news:cc79a722-1230-4604...@i7g2000prf.googlegroups.com...
snip>
> If you meant to ask whether real numbers as defined in mathematics are
> infinite the answer is: oh, hollie mollie... not at all!
> Although...there're developments including an element, many times
> denoted as oo and called infinite, but it STILL is not a "standard"
> real number.
>
> Now, if you meant to ask whether the set of all the real numbers, as
> defined (both the real numbers and the sets) in mathematics is an
> infinite set (infinite set is ALSO a thing defined in mathematics),
> then the answer is: yes, of course.
>
> Regards
> Tonio- Hide quoted text -
>
> - Show quoted text -
:Knowing all of this, why do you make 'curves' and 'spheres'?
:You are inconsistent...
You, however, are quite consistent. Your initial post was a troll and you
have continued trolling in every post that follows.
Your posts, if real, would indicate that you do not understand mathematics
and confuse the set of real numbers with physical entities. However, being
a troll, it is not possible to determine whether or not you are that
ignorant.
Dustan
> Fuckwit is a good name.
> You are naive, stupid or indoctrinated...
Ah, yes, name calling.
Dustan
> If you agree that a circle is not mathematically possible and that it
> is a polygon -
> WHY DO YOU CONTINUE TO USE IT AS IF IT WERE NOT...
Actually: it's not *physically* possible. Mathematical impossibility
is a matter of defining the term "impossible" with the chosen axioms.
If you are seriously having trouble distinguishing between physically
impossible and mathematically impossible, then perhaps you should
consider a career unrelated to mathematics or physics.
Perhaps the local McDonald's?
Gonçalo Rodrigues
<Dustan...@gmail.com> fed this fish to the penguins:
No, mathematics is not "just another form of art". Surely, there are
many resemblances, but there are also enough differences to justify
the separation. Of course, you are absolutely right that equating
mathematics with physics is an inanity and saying that "Mathematics is
basically supposed to model reality" is only said by someone who does
neither.
Regards,
G. Rodrigues
Tonico
>
> Insofar as mathematics purports to be an art, its practitioners have an
> obligation to exhibit good taste. (Preston C. Hammer)
>
> Han de Bruijn-
******************************************************
Nonsense. The only requirement so far from mathematics is to be
consistent, and so far it is and it'll continue to be until somebody
else PROVES (and not just whines or cries about it, a la Mueckenheim)
otherwise.
I personally, don't think mathematics is merely a form of art, though
I think it can easily be seen many times as such.
Who's that Preston C. Hammer, anyway?
Regards
Tonio
Marshall
>
> We can't even measure the EXACT number, root2, can we??
What does it mean to measure a number? How much is 5?
We cannot convert the square root of two into a finite decimal
string, if that's what you mean, because there is no finite decimal
string that represents the square root of two. This is better
thought of a limitation of finite decimal strings than a limitation
of numbers.
Marshall
finite guy
I believe that it is his own chosen title, not my choice.
Speak to 'Fuckwit'.
I could have asked him if dimwit, halfwit or the chosen, 'Fuckwit',
was more appropriate.
Bear in mind that as many Mathematicians go, such as Tonico, say,
"I'm very fond of reality, but I don't give a damn about it when
doing
mathematics."
This is saying that he has devoted himself to unreality:
This is a sign of madness or quasi-religious fervour...
Et tu Brute...?
finite guy
>
> - Show quoted text -
Sorry, I thought integers were supposed to be real rationals...
What are you trying to say?
finite guy
You should try to get under it.
I do not say that infinity does not exist - it does exist.
It has nothing at all to do with 'number' and subsequently
mathematics.
This is regardless of your "no need for reality" doctrines.
When don't play but reality's rules, you are simply in fantasy land.
But you love reality...?
finite guy
Then why is there 'applied mathematics' or 'quantum physics'
- all of which rely of mathematical concepts?
But you don't have to worry about the real world, do you?
Are you Alice or the Mad Hatter in your Wonderland?
finite guy
Gee, I thought this was the SCI_math Group?
Doesn't 'sci' stand for science, or is it something else?
finite guy
> On Tue, 12 Feb 2008 05:34:23 -0800 (PST), Dustan
>
> - Show quoted text -
And yet you proudly assert you have no personal need to do so...
Why does physics use mathematics, pray tell?
finite guy
When you confuse finite and infinite, how are you consistent?
How many Pythagorean Triplets are there?
finite guy
So root2 is an 'infinite' decimal string. Decimal relates to number...
Oh... more circularity... approximately. :-)
You are talking about decimal strings as numbers too, aren't you?
Anyway, you don't even want to understand One, it seems. Or 5.
Our human inability to measure is not the same as something being
immeasurable.
finite guy
>
> - Show quoted text -
Ah, but is it 'logical' and 'rational'?
Tonico
*************************************************************
You insist in establishing that I confuse finite and infinite, and you
don't neven know me...
You seem not only to disagree deeply with the non-reality of the
mathematics realm, but you are also very angry and pretty bitter as
well about that. Why? Why does it bother you that much that
mathematicians can play with their toys they way they want, and even
worse (for you, it seems): to enjoy it intensively?
About how many pythagorean triplets are there: I'd tell you that more
than any number you can name, but I'll go with the bait you seem to
think you're teasing me with and I'll tell you the truth: there are
infinite pythagorean triplets.
Regards
Tonio
Tonico
>...................................................
> > No, mathematics is not "just another form of art". Surely, there are
> > many resemblances, but there are also enough differences to justify
> > the separation. Of course, you are absolutely right that equating
> > mathematics with physics is an inanity and saying that "Mathematics is
> > basically supposed to model reality" is only said by someone who does
> > neither.
>
> > Regards,
> > G. Rodrigues-
>
****************************************************
Oh, now you got us. Shoots! Rats! Damn!
Ok, mathematics and neither logical nor rational. There, you win.
Happy now?
Well, now what about leaving us alone with our toys and you go to do
whatever you like, uh?
Regards
Tonio
Gonçalo Rodrigues
<adam...@amnet.net.au> fed this fish to the penguins:
>> >> If you agree with the physical world (which is quantised), why do you
>> >> use maths in an otherwise fashion?
>> >> Mathematics is basically supposed to model reality...
>>
>> >Is art necessarily supposed to model reality? Is music necessarily
>> >supposed to model reality? Are movies necessarily supposed to model
>> >reality? Is literature necessarily supposed to model reality?
>>
>> >Are you necessarily supposed to model reality ('cause you sure are
>> >failin' at it)?
>>
>> >Before you answer any of the above questions, be sure to consider
>> >every word carefully, especially "necessarily".
>>
>> >And BTW, in case you didn't get the message, mathematics is just
>> >another form of art.
>>
>> No, mathematics is not "just another form of art". Surely, there are
>> many resemblances, but there are also enough differences to justify
>> the separation. Of course, you are absolutely right that equating
>> mathematics with physics is an inanity and saying that "Mathematics is
>> basically supposed to model reality" is only said by someone who does
>> neither.
>>
>> Regards,
>> G. Rodrigues- Hide quoted text -
>>
>> - Show quoted text -
>
>And yet you proudly assert you have no personal need to do so...
>
>Why does physics use mathematics, pray tell?
And pray, tell me, what does the fact that there are fields of
mathematics that have no known application to theoretical physics tell
you?
Mathematics is a body of knowledge independent of physics even though
it has many applications to it and there is even a very (emphasize the
very) fruitful dialogue between the two disciplines. I'm really not in
the mood for arguing with you, but wether you agree or not with me it
is really besides the point, because mathematicians *do work* based on
the assumption that mathematics is an independent discipline. And
since it is mathematicians that decide what mathematics is, not you or
me, the case is closed.
Regards,
G. Rodrigues
bill
> Consider a circle: x^2 + y^2 = c
>
> To construct a 'perfect mathematical circle'
> requires delta x and delta y to BE zero
> from point-to-point in the circle -
> not just 'approach zero'.
>
> If delta x and delta y have ANY magnitude
> from point-to-point then the 'circle' is a polygon.
> It is irrelevant as to how many sides the polygon has -
> it could be a billion^billion facets
> but it will still be a polygon.
>
> If delta x and delta y are allowed to be zero
> from point-to-point in the 'circle'
> then we are discussing one point only - not a circle.
>
> How do you try to explain this obvious situation????
Not being a great mathematician, I
don't understand why delta x and
delta y have to be zero. Can you
explain why this is necessary?
TIA,
Bill J
Virgil
Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
> Virgil wrote:
>
> > In article <66242$47b15fe6$82a1e228$17...@news2.tudelft.nl>,
> > Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
> >
> >>finite guy wrote:
> >>
> >>>Consider a circle: x^2 + y^2 = c
> >>>
> >>>To construct a 'perfect mathematical circle'
> >>>requires delta x and delta y to BE zero
> >>>from point-to-point in the circle -
> >>>not just 'approach zero'.
> >>>
> >>>If delta x and delta y have ANY magnitude
> >>>from point-to-point then the 'circle' is a polygon.
> >>>It is irrelevant as to how many sides the polygon has -
> >>>it could be a billion^billion facets
> >>>but it will still be a polygon.
> >>>
> >>>If delta x and delta y are allowed to be zero
> >>>from point-to-point in the 'circle'
> >>>then we are discussing one point only - not a circle.
> >>>
> >>>How do you try to explain this obvious situation????
> >>
> >>The venom is in the _equals sign_: '=' . What does it MEAN in practice ?
Apparently it does not mean the same thing in a physicist's practice
that it means in a mathematician's. Which only means that the physicist
is not doing mathematics.
Virgil
Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
That does not establish HdB as sole arbiter of good taste. In fact,
many, if not most, mathematicians judge his taste, at least in
mathematics, to be execrable.
Dustan
> Then why is there 'applied mathematics' or 'quantum physics'
> - all of which rely of mathematical concepts?
Why is there literature that teaches deep morals about reality, even
though there is no need for it to even represent reality?
Dustan
> I do not say that infinity does not exist - it does exist.
Then there's an infinitely number of points on a circle, no three of
which are collinear.
See how easy that is when you except the existence of infinity?
finite guy
>
> - Show quoted text -
My apologies, Tonico, I must have gone 'Jerry Springer'... :-)
Conversely, you think I am foolish but you don't know me.
It must be most other Mathematicians who think that way...
But no, your truth is, "the number of Pythagorean Triplets is a non-
number: infinity".
Am I not paraphrasing you correctly?
There is an old expression:
Don't let your left hand know what your right hand is doing.
You seem to have a conflict between left and right brain - imagination
and logic.
The problem is that the philosophy of mathematics pollutes the
understanding of the science.
Or maybe it is the other way round - same confused results.
I'm absolutely sure that you believe things like space is infinite...
infinite possibilities... etc.
Space is finite, geometrically flat but 'shaped' - be it one unit or
total units. Do you agree?
No statistical possibilities are infinite, is it?
You can say one thing but do another it seems...
Your method is inconsistent and, by definition, illogical and
irrational.
That is not to say that you are not intelligent - you are probably
quite so.
You hold to mantras, not realities.
Why do you do that?
finite guy
> In article <682c7$47b1a6df$82a1e228$22...@news1.tudelft.nl>,
>
> - Show quoted text -
Yeah, but traditionally mathematicians dress badly. :-)
Maybe except for the celebrity ones with managers...
finite guy
> On Tue, 12 Feb 2008 09:37:56 -0800 (PST), finite guy
Yes, I have some appreciation of the estoteric.
And I do have appreciation of ideas.
You do not seem to understand that the FOUNDATIONS of your discipline
are confused.
The fancy, theoretical stuff is based on extrapolations of the basics
- not independent of themselves.
It is not internally consistent - and you revel in that... you choose
fantasy not discipline.
Is this not true?
finite guy
No, your abject admission is no comfort. Just pretty sad for you...
Petulence flatters no one.
If you would just stay at home and play with/by yourself it would be
best
but you obviously consider yourself a 'teacher' to others.
You want to be a cult leader or something? :-)
finite guy
I'm not sure of what you are asking.
You didn't answer the question.
You seem to think that 'deepness' should be unrelated to truth.
Perhaps this is a bastardisation of relativity or something.
Esops fables are moral fantasies.
Are you amoral?
If so, then your views are, but simple definition, psychopathic.
Let's coin a word: Psychopathetic. :-)
Get real...
man.
finite guy
Opps, sorry, I said "get real" and, to you, that means rational and
irrational. :-)
finite guy
>
> - Show quoted text -
Easy.
If they are not zero from point to point
- then discrete, straight line lengths are expressed between points -
no curve.
This in turn makes the circle not smooth but a polygon.
By extension, nothing 'curves' as such - but it is possibly nearly
smooth to our 'eye'.
Curves and graphs are a useful tool for visualisation but can never be
smooth.
This applies to all possible 'powers' .
Harder - but still easy.
Fermat said:
It is impossible for a cube to be written as the sum of two cubes or a
fourth power to be written as the sum of two fourth powers or, in
general, for any number which is a power greater than the second to be
written as a sum of two like powers.
The philosophy of current mathematics neglects the implications of
this.
Mathematicians, Fermat excluded,
don't understand that a 'cube' is a 4th power entity - not a third
power one.
If you check Fermats phrasing you will see that he uses inconsistent
terminology.
He omits to say 'third power' anywhere but uses the venacular 'cube'.
It is a semantic trick by Fermat.
It is impossible for a cube
to be written as the sum of two cubes
or [IN OTHER WORDS]
a fourth power
to be written as the sum of two fourth powers
or, in general,
for any number
which is a power greater than the second
to be written as a sum of two like powers.
a^3 + b^3 = c^3
The mathematicians here will readily agree that you cannot construct a
c^3.
They fail to realise that it is impossible to make the a^3 or the b^3
in the first place...
There is no cube, or other 'spatial' entity in 3 powers.
It takes 4. And there are no more.
They don't even appreciate why E=mc^2 is a planar relationship - not
'spatial'.
The original Pythagoras Theorem is conceptually flawed.
Send me an email, I'll send you a powerpoint.
finite guy
I accept the existence of infinity - you pointed out that I said
that.
Then you say 'see'... as if you said something smart...
Infinitude has nothing to do with finitude, does it?
STILL YOU MUST HAVE DELTA X AND DELTA Y AS ZERO FROM POINT-TO-POINT.
Your philosophy is errant; along with your terminology...
Go back to the basics - rethink your error rationally and logically.
Please.
Tonico
***************************************************************
What do you care whether I want to be a cult teacher or not? Don't
attend my classes and period.
You say that my "abject admission" (wow, you know how to distinguish
sarcasm....great!) is sad for me. Ok, so you've decided it's sad for
me. Good. Now go away, don't learn mathematics and instead whine about
something you don't have much idea about, and leave in my
"sadness"...what do you care, my boy??
The only one showing a deep and rather abnormal and suspecting
preocupation about stuff that he hasn't learnt at all is you, so far.
Once again, my advice: learn first, construct and write criticism and
bitterness later.
Regards
Tonio
Tonico
...............................
> > > How many Pythagorean Triplets are there?-
>
> > *************************************************************
>
> > You insist in establishing that I confuse finite and infinite, and you
> > don't neven know me...
>
> > You seem not only to disagree deeply with the non-reality of the
> > mathematics realm, but you are also very angry and pretty bitter as
> > well about that. Why? Why does it bother you that much that
> > mathematicians can play with their toys they way they want, and even
> > worse (for you, it seems): to enjoy it intensively?
>
> > About how many pythagorean triplets are there: I'd tell you that more
> > than any number you can name, but I'll go with the bait you seem to
> > think you're teasing me with and I'll tell you the truth: there are
> > infinite pythagorean triplets.
>
> > Regards
> > Tonio-
> My apologies, Tonico, I must have gone 'Jerry Springer'... :-)
> Conversely, you think I am foolish but you don't know me.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Oh, but I know more than enough to claim you're a fool: you are not a
mathematician, you haven't learnt mathematics (how do I know? Pretty
simple: not only you show a pretty basic and deep ignorance in
mathematical knowledge that beginner student in college should know,
but you ALSO don't get along with mathematical terms in an appropiate
way), and yet you think you can make worthwhile criticism of something
you know bananas about.
Ignrant and stupid, indeed.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
It must be most other Mathematicians who think that way...
> But no, your truth is, "the number of Pythagorean Triplets is a non-
> number: infinity".
> Am I not paraphrasing you correctly?
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
I don't know if you are: I told you the truth from a mathematical
point of view. The set of all pythagorean triplets is an infinite set,
and this is, by the way, very easy to prove.
To say that "the number of...is infinite" is just an abuse of
language, but we mathematicians can manage that, don't worry.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> There is an old expression:
> Don't let your left hand know what your right hand is doing.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
This is not just an "old expression" but a rather nonsensical sentence
quoted from a religious book.
**************************************************************
> You seem to have a conflict between left and right brain - imagination and logic.
>
***********************************************************
Perhaps so: what is it to you, again? Why does it bother you THAT
much that conflict or whatever? Are you that jealous of all the joy,
pleasure and satisfaction some of us get from mathematics that you
HAVE to convince yourself that our brain...blah-blah-blah??
Ok, so we've a conflicted brain, ok...what do you care that much? We
don't.
**************************************************************
> The problem is that the philosophy of mathematics pollutes the
> understanding of the science.
> Or maybe it is the other way round - same confused results.
>
**************************************************************
Oh, so you're worried about mathematics polluting science. I
see...aha.
Well, why don't you go out with your impressive credentials and begin
fighting mathematics everywhere where it counts? Here you won't get a
lot since most of us are mathematicians, so we won't take you very
seriously, to say the least.
Go and fight your righteous fight with universities headmasters, with
scientists, in laboratories. I bet you'll harvest a huge success.
****************************************************************
> I'm absolutely sure that you believe things like space is infinite...
> infinite possibilities... etc.
> Space is finite, geometrically flat but 'shaped' - be it one unit or
> total units. Do you agree?
***************************************************************
I can't say for sure since I've no idea what you're talkin about.
Nevertheless, I think not...
***************************************************************
> No statistical possibilities are infinite, is it?
>
> You can say one thing but do another it seems...
**************************************************************
Yeah, I'm pretty talented at that. Thanx for noticing it.
*************************************************************
> Your method is inconsistent and, by definition, illogical and
> irrational.
> That is not to say that you are not intelligent - you are probably
> quite so.
>
> You hold to mantras, not realities.
> Why do you do that?-
****************************************************************
Oh, well...I supose I could tell you, AGAIN, that I've still no much
idea what you're talking about, and that I hardly know what mantras
is, leave alone to hold them, but I'd rather say: and what if I do?
What in the hollie-mollie name of the Great Pumpkin do you give a damn
about what I do, what I hold or not? So I deal with something
irrational, ilogic, stupid...whatever you like. Ok, so what?
Even worse: I'm so damn happy since I discovered maths and since I
deal with it that you can't imagine....and good you can't: you would
probably get a seizure if you knew.
In short: I enjoy my life and my profession very much. Do you enjoy
yours? I hope so, though I suspect something's bugging pretty badly
deep-deep skin...
Regards
Tonio
Pd. By the way, you've noticed I don't get much into mathematical
discussion with you, right? Guess why?...*wink*
finite guy
>
> - Show quoted text -
Jerry! Jerry! Jerry!
You move further away from conclusions and
regress to doctrines which you know to be inconsistent.
Cult 101 - no thanks. You lead... to illogical and irrational
conclusions.
Bad Tonico. :-)
I care for you, bro'.
Stop teaching trailer trash talk of mathematics... correct your
assumptions.
I don't care for your errant philosophical nonsense.
But it is (not even) yours and you love it...
My comment was sarcasm. Sorry.
Your comment wasn't sarcasm though - it was you expressing your
mathematical understanding...
Your doctrinal admissions are surely abject drivel - according to
basic mathematics.
Like mysticism - your special knowledge is only understandable to
'those' who know.
You just should know better...
My views are abnormal, of course, by standard definition
but not by logical conclusion or rational consideration. Try it.
> Once again, my advice: learn first, construct and write criticism and
> bitterness later.
I think I understand your grammar...
I've learned enough to display your error - kids can do it. Easy.
I have constructed - you try to reconstruct that which you have been
indoctrinated.
You method can never work - in reality.
Try reality - I think you said you like it.
Don't 'like' reality but 'love' non-reality. Do it the other way
around.
But you seem to be saying to learn now and then become bitter with
it.
You are a learned man, no doubt??
As with all cultic behaviour, you have lost your logic and
rationality.
What remains? Simply your personal reasons for believing non-reality.
Why go down your rabbit hole, mad hatter?
Wonderland is just a fiction... you love fiction.
I love demonstrable facts - I like fiction.
You know that you reply on all of the errant issues I have discussed.
It is the tension of evidence that upsets you.
That is only human - no matter how 'smart' you believe yourself to be.
Nevertheless, bad Tonico.
Do you know the old definition of insanity - the lunatic doesn't know
anything is wrong?
One definition of wrongful pride is not admitting mistakes.
But when your mistakes are foundational to your thinking - you have to
change.
Tim Little
> STILL YOU MUST HAVE DELTA X AND DELTA Y AS ZERO FROM POINT-TO-POINT.
Oh, now I remember. You're the crank who thinks that for every point
along a line, there is a unique closest neighbour point to each side.
- Tim
Tonico
.................................................
> Do you know the old definition of insanity - the lunatic doesn't know
> anything is wrong?
> One definition of wrongful pride is not admitting mistakes.
> But when your mistakes are foundational to your thinking - you have to
**********************************************************
*Plonk!*
And no: I don't have, and I won't change. Honest.
Bye
Tonio
finite guy
wrote:
> On 2008-02-13, finite guy <adamle...@amnet.net.au> wrote:
>
> > STILL YOU MUST HAVE DELTA X AND DELTA Y AS ZERO FROM POINT-TO-POINT.
>
> Oh, now I remember. You're the crank who thinks that for every point
> along a line, there is a unique closest neighbour point to each side.
>
> - Tim
I'm not that crank...
I must be another.
I'm just stating the simple mathematical fact.
Sjoerd Job Postmus
>
> STILL YOU MUST HAVE DELTA X AND DELTA Y AS ZERO FROM POINT-TO-POINT.
>
> Your philosophy is errant; along with your terminology...
>
> Go back to the basics - rethink your error rationally and logically.
> Please.
Well, point-to-point implies that there is a way to select a next point
on the circle without skipping one. Let me then pose your problem in a
different way...
Let's take a line, for example a line of length 1. Wait, let's even take
the unit interval [0,1] = { x \in R | 0 <= x <= 1 }
Start at the leftmost point, 0. Now, you claim there is a next point,
p > 0, we can choose from the interval. That is, this point satisfies
that { x \in R | 0 < x < p } is empty, since it was the ``next''.
Now, we arise at a problem. We know that (p / 2) is smaller than p, and
larger than 0, so the set above is not empty. Thus, p can not be the
next. Can you see where we have gone wrong? We have assumed there even
was a `next'... I can NOT give you a point p in ]0,1[ s.t. ]0,p[ is
empty.
Suppose on the other hand that the next point existed, than p - 0 = 0.
Suppose also that at a moment in time, n, we're done with our `find
next point' technique. Than, since p_(j+1) - p_j = 0, we get 1 - 0 = p_n
- p_0 =(removing p_j and adding) =
p_n - p_(n-1) + p_(n-1) - p_(n-2) + p_(n-2) + ... - p_1 + p_1 - p_0
bracketing
(p_n - p_(n-1)) + (p_(n-1) - p_(n-2)) + ... + (p_1 - p_0)
knowing that next points have distance 0
0 + 0 + ... + 0
Wait a minute, now our `line segment' is a point, that's certainly
wrong. Why? I assumed there was a next point. There isn't.
Now, let's go back to the circle. Let's mark the center of the circle M.
Pick a point on the circle, p_0. Now, pick the `next' point. The term
point-to-point implies there is a well-described next, with no point in
between. So, let's test. Create the line segment between p_0 and p_1.
Pick a random point on it. Their halve, for instance: r := (p_0 + p_1)/2.
Now, construct the line segment Mr, until it hits the circle at a point,
this point is between p_0 and p_1, but on the arc. So, p_1 was not the
next. The next-point argument fails to make a circle a dot, because it
accepts something which is not true.
Now, of course, let's look at the `approaches 0', instead of `is 0'.
This means, when I call a distance (epsilon) which is larger than 0,
somebody can find two points with distance between eachother less than
epsilon. That's precisely what it means.
Of course, a mathematical is perfectly smooth. A physical circle, which
I don't even want to care about, has the limitation of the size of -per
instance- the atoms. I can take the circle, and numerate the atoms
[1..n] in such a way that between n, and n+1 there is no other *atom*,
but these atoms don't have to be equal.
Just a note about infinity: Most talk about a function `approaching'
infinity, when taking a limit to a certain point (or infinity).
lim f(x) = oo (infinity)
x->a
means: For every N > 0, there is a d > 0, such that for all x
with | x - a | < d, f(x) > N
lim f(x) = b
x->oo
means: For every e > 0, there is a N > 0, such that for all x
with x > N, we have | f(x) - b | < e
I assume you might be able to construct the argument for
lim f(x) = oo
x->oo
Now, one of my teachers says, instead of `goes to infinity', `gets
arbitrarely large', which is arguably a better way to think about
infinity.
Tim Little
Oh. Just the same style then, talking about distances between
successive points.
- Tim
Han de Bruijn
> Sorry, I thought integers were supposed to be real rationals...
Sometimes yes, sometimes no. Depends on whether you are working in an
integer / discrete or in a floating point / continuous environment.
> What are you trying to say?
Hey 'finite guy' ! Why do you think, or rather _desire_ it seems, that
everybody is against you ?
Han de Bruijn
Tonico
wrote:
***************************************************************
Aaaah! Hey, HdB: trying to add this finite, weird, guy to your forces?
Why is everyone "against him"? Yes, why, indeed...?
Regards
Tonio
finite guy
wrote:
> On 2008-02-13, finite guy <adamle...@amnet.net.au> wrote:
>
> > I'm not that crank...
>
> Oh. Just the same style then, talking about distances between
> successive points.
>
> - Tim
Is a crank one who is defined as believing that there is a 'distance'
between points?
I don't understand your comment except that you say I am a crank.
Do you understand that there is some distance between points?
Or do you only have one point - to call me a crank. A rose by any
other name...
Still, I am only expressing logic and rationality.
I hope that you have some congruent interest in them?
Adam.
finite guy
> On Feb 12, 1:59 am, finite guy <adamle...@amnet.net.au> wrote:
>
>
>
> > We can't even measure the EXACT number, root2, can we??
>
> What does it mean to measure a number? How much is 5?
>
> We cannot convert the square root of two into a finite decimal
> string, if that's what you mean, because there is no finite decimal
> string that represents the square root of two. This is better
> thought of a limitation of finite decimal strings than a limitation
> of numbers.
>
> Marshall
I agree. No problem.
Root2 is a unit of its own.
finite guy
wrote:
> On 2008-02-13, finite guy <adamle...@amnet.net.au> wrote:
>
> > I'm not that crank...
>
> Oh. Just the same style then, talking about distances between
> successive points.
>
> - Tim
Tim,
Don't you understand that there is 'distance' between points?
An opposing opinion is usually labelled crank... not just in
mathematics.
No problem.
Adam.
Dustan
> On Feb 13, 9:47 am, Dustan <DustanGro...@gmail.com> wrote:
>
> > On Feb 12, 11:34 am, finite guy <adamle...@amnet.net.au> wrote:
>
> > > Then why is there 'applied mathematics' or 'quantum physics'
> > > - all of which rely of mathematical concepts?
>
> > Why is there literature that teaches deep morals about reality, even
> > though there is no need for it to even represent reality?
>
> I'm not sure of what you are asking.
> You didn't answer the question.
Then reread the thread. Think hard. Think before you respond.
> You seem to think that 'deepness' should be unrelated to truth.
While I do agree with this statement in general, I don't agree with
this statement in this particular context: read what I said, and read
your response. Hopefully you will eventually figure out the shear
stupidity of what you just said. And be glad I didn't just use all
caps on you.
> Are you amoral?
No.
> If so, then your views are, but simple definition, psychopathic.
So my views are, by simple definition, not psychopathic.
Jesse F. Hughes
> Aaaah! Hey, HdB: trying to add this finite, weird, guy to your forces?
> Why is everyone "against him"? Yes, why, indeed...?
Give Han a break. Finite guy is far, far sillier than Han.
--
Jesse F. Hughes
"If you hadn't noticed, basically every result I have destroys some
precious belief of mathematicians and they have from what I've gathered
basically gone collectively bonkers." -- James S. Harris
Dustan
> On Feb 13, 4:07 am, bill <b92...@yahoo.com> wrote:
> > Not being a great mathematician, I
> > don't understand why delta x and
> > delta y have to be zero. Can you
> > explain why this is necessary?
>
[snip]
Your mathematical enlightenment is overwhelming.
bill
Why do the lines between points have to be straight lines?
Theoretically there can be NO line; because a line conists
of more points!
Originally, I was thinking of delta x & y as the x- & y-distances
between two points on a curve. Back in my academic youth
(circa 1945 -1956) we had dx & dy which had something to do
with delta -x, -y This should help explain my confusion!
Bill j
bill
I suppose you are trying to be sarcastic. But since I
profess no mathematical sophistication; it is merely
stupid! It's like saying to a quadriplegic, "Your running
speed is overwhelming."
In retort, I say " Your stupidity is ovrewhelming! "
Bill J
finite guy
Tinio! Tonico! Tonio!
Jerry! Jerry! Jerry!
What is your name, Tonio or Tonico?
If you don't even have that consistent, what value...?
Y'all 'aint against me; only against what I express.
Tonio/Tonico (perhaps a split personality?) would like to think that
disagreement with him equals mental abberation. It is standard
practice among people.
The problem there is that Tonico feels that he is intrinsically
superior.
His thoughts are vast... nah, infinite... :-)
But he's just a finite guy, too.
Tonico, you and I are in the same club. Hey, bro'.
finite guy
Far sillier in some respects perhaps - I don't know Han as well as you
don't.
But never infinitely sillier, eh?
To be infinitely sillier, I would have to devote myself to non-
reality...
finite guy
Your anal-ysis is underwhelming...
I see the Light!!
We know from where your light shines.
It is a little backward.
Jerry! Jerry! Jerry! :-)
Dustan
> On Feb 13, 11:12 pm, Dustan <DustanGro...@gmail.com> wrote:
>
> > On Feb 12, 8:16 pm, finite guy <adamle...@amnet.net.au> wrote:> On Feb 13, 4:07 am, bill <b92...@yahoo.com> wrote:
> > > > Not being a great mathematician, I
> > > > don't understand why delta x and
> > > > delta y have to be zero. Can you
> > > > explain why this is necessary?
>
> > > Easy.
>
> > [snip]
>
> > Your mathematical enlightenment is overwhelming.
>
> Your anal-ysis is underwhelming...
No doubt you were being sarcastic just like I was.
Dustan
> On Feb 12, 7:49 pm, finite guy <adamle...@amnet.net.au> wrote:
> > You seem to think that 'deepness' should be unrelated to truth.
> While I do agree with this statement in general,
Scratch that. I do agree that 'deepness' *can* be unrelated to truth.
Whoops!
finite guy
> On Feb 12, 6:16 pm, finite guy <adamle...@amnet.net.au> wrote:
>
> Why do the lines between points have to be straight lines?
> Theoretically there can be NO line; because a line conists
> of more points!
>
> Originally, I was thinking of delta x & y as the x- & y-distances
> between two points on a curve. Back in my academic youth
> (circa 1945 -1956) we had dx & dy which had something to do
> with delta -x, -y This should help explain my confusion!
>
> Bill j
A good, simple question.
Why indeed...
My poor answer will but the focus of some peoples derision but here
goes.
Firstly, the delta/change in x and y is not the distance between the
points of the circle.
They are of the axes.
Calculus either 'divides to zero' or 'multiplies to infinity' - which
is only nonsense.
But that is the problem - infinitisation of the finite in all
'directions'.
This leads to the acceptance of the fiat statement that 'space is
infinite' and other such follies.
> Theoretically there can be NO line; because a line conists of more points!
Why do you even think that a 'line' is made up of 'points'? Because...
Surely, in "theoretical terms", even points are void.
But all of these things are convenient expressions - useful.
However, we are talking about the idea of going from one point to the
NEXT point - none between.
The idea that you can always put more points 'between'
is a reflection of the misconception of the infinitisation of the
finite.
In practical terms, points are the only physical way we can construct
-
successive marks on a piece of paper, pixels on a computer screen.
The mathematicians here aggressively say that mathematics and reality
are not related.
But regardless of their pontifications and postulations, everyone is
bound by reality.
In mathematical terms, the axes themselves must be 'straight lines' to
be independent of each other.
We go 'from' one 'to' another.
A straight line conceptually means that that we are not going 'via'
elsewhere which would introduce other factors.
I hope that helps.
I'm sure that the guys here can elaborate much more than I
but they will still be expressing things which encapsulate their
misconceptions.
Let's wait and see.
Here is another question.
Why does the Pythagoras Theorem use 'squares'...?
Fermat shows that 'cubes' don't work...
Send me an email and I'll show you why Pythagoras is conceptually
incorrect for E=mc^2.
Tim Little
> Give Han a break. Finite guy is far, far sillier than Han.
Yes, HdB at least *tries* to do mathematics, even if he gets it wrong
a lot of the time. Finite guy is incoherent enough to be a chatbot.
- Tim
Dustan
> Firstly, the delta/change in x and y is not the distance between the
> points of the circle.
> They are of the axes.
And irrelevant to the description of the circle. All that's needed to
describe a circle is:
x^2 + y^2 = r^2
> Calculus either 'divides to zero' or 'multiplies to infinity' - which
> is only nonsense.
Well, when you look at it that way... Oh crap, this really does have
no bearing on reality whatsoever. Errr... That was what you meant,
right? Even though it's not true; calculus is an important application
in physics.
> But that is the problem - infinitisation of the finite in all
> 'directions'.
Ever heard of fractals? They are infinite in complexity but finite in
size. They're mathematical concepts, NOT reality. Reality can only
represent them to a certain extent. But the mathematical concept still
exists. The fact that I'm talking about it proves that.
> This leads to the acceptance of the fiat statement that 'space is
> infinite' and other such follies.
Who said that? I certainly don't believe it.
> > Theoretically there can be NO line; because a line conists of more points!
>
> Why do you even think that a 'line' is made up of 'points'?
By definition.
> Because...
> Surely, in "theoretical terms", even points are void.
You gotta start somewhere, otherwise you'll get nowhere. In this case,
we're starting at the concept of points and sets of points, ie shapes
(those sets, by the way, are, in the vast majority of cases,
INFINITE).
> But all of these things are convenient expressions - useful.
> However, we are talking about the idea of going from one point to the
> NEXT point - none between.
Mathematically impossible with the most commonly accepted premises.
> The idea that you can always put more points 'between'
> is a reflection of the misconception of the infinitisation of the
> finite.
Do you even accept the existence of real numbers?
> In practical terms, points are the only physical way we can construct
> successive marks on a piece of paper, pixels on a computer screen.
Coincidentally, points are also a mathematical concept.
> The mathematicians here aggressively say that mathematics and reality
> are not related.
For a good reason. In case you haven't noticed, math has a tendency to
go on tangents completely unrelated to reality.
> But regardless of their pontifications and postulations, everyone is
> bound by reality.
No, sir, YOU are bound by reality. You're reality, to be exact, which
exists only in your head.
> In mathematical terms, the axes themselves must be 'straight lines' to
> be independent of each other.
And perpendicular, don't forget perpendicular.
> We go 'from' one 'to' another.
On paper, yes. On your graphing calculator, yes. Conceptually, yes.
Mathematically, no, the actual relation (be it a line or a circle or a
parabola or anything else) is not composed of successive points. If it
were, then there would be a finite number of points. Which there
isn't.
> A straight line conceptually means that that we are not going 'via'
> elsewhere which would introduce other factors.
Ummm... What?
> I hope that helps.
Nope.
> I'm sure that the guys here can elaborate much more than I
> but they will still be expressing things which encapsulate their
> misconceptions.
What misconceptions? You mean of reality? Who claimed that any of this
had anything to do with reality?
> Let's wait and see.
>
> Here is another question.
> Why does the Pythagoras Theorem use 'squares'...?
Because that's how it works out. You can actually prove the theorem,
you know.
> Fermat shows that 'cubes' don't work...
Irrelevant and incorrect. The existence of Pythagorean triples has no
bearing on the truth of the Pythagorean theorem.
> Send me an email and I'll show you why Pythagoras is conceptually
> incorrect for E=mc^2.
Pythagorean <=> E=mc^2??? You're connecting this guy to someone over 2
millennia ahead of his time???
I'm not going to argue with you anymore; it's obvious to me that
you're not about to give up on your misconceptions. The fact that I
have had a complete, logical and valid response to every one of your
misconceptions doesn't seem to deter you.
finite guy
> On Feb 13, 5:52 pm, finite guy <adamle...@amnet.net.au> wrote:
>
Here we go again...
> And irrelevant to the description of the circle. All that's needed to
> describe a circle is:
> x^2 + y^2 = r^2
Gee, I thought x and y were axial.
Are you saying they are not?
> Well, when you look at it that way... Oh crap, this really does have
> no bearing on reality whatsoever. Errr... That was what you meant,
> right? Even though it's not true; calculus is an important application
> in physics.
Really...
what do "as x -> ∞" mean then... ?
and the inverse of that... ?
> Ever heard of fractals? They are infinite in complexity but finite in
> size. They're mathematical concepts, NOT reality. Reality can only
> represent them to a certain extent. But the mathematical concept still
> exists. The fact that I'm talking about it proves that.
Fractals are a scaling issue.
And they go on infinitly reducing... according to the mathematical
concept?
What if you 'start' at the minimum and fractal ' upwards'... to a
finite degree?
Gee, same thing happens...
> Who said that? I certainly don't believe it.
Fair enough - it was a generalisation.
Generally, we all use them... :-)
So you believe with certainty that space is finite - 'inward' and
'outward'?
> By definition.
Your errant definitions are the problem...
that's what I have been saying.
Did you miss that?
> You gotta start somewhere, otherwise you'll get nowhere. In this case,
> we're starting at the concept of points and sets of points, ie shapes
> (those sets, by the way, are, in the vast majority of cases,
> INFINITE).
The infinite DOESN"T START ANYWHERE or finish...
Without realising it you are muddling finite and infinite... again...
If I said, "(those sets, by the way, are, in the vast majority of
cases, BLUE)", you would critisize.
But 'blue' is as much a 'number' as infinite.
Infinity is not a number.
Would COW also be as appropriate a description as infinite... ?
> Mathematically impossible with the most commonly accepted premises.
Because you futilely try to infinitise the finite...
Your premise holds no promise... :-)
> Do you even accept the existence of real numbers?
Yes, really...
Both rational and irrational ones.
They shouldn't try to be put on the same number line though.
That's been discussed previously.
I think it was 'lwas?' who pointed out that that is correct.
> Coincidentally, points are also a mathematical concept.
So is a line, a plane, a cube, etc.
Your point being... ?
> For a good reason. In case you haven't noticed, math has a tendency to
> go on tangents completely unrelated to reality.
Yeah, and they are presumably based on the fundamentals... 1, 2, 3...
Why do they try to negate the fundamentals?
Oh, philosophy is why... not mathematics.
True... ?
> No, sir, YOU are bound by reality. You're reality, to be exact, which
> exists only in your head.
Yes, sir. I am bound by reality as best I understand it.
But YOU are proudly not bound by reality...
Haven't you already said that... ?
> And perpendicular, don't forget perpendicular.
I didn't. But thanks anyway.
> On paper, yes. On your graphing calculator, yes. Conceptually, yes.
> Mathematically, no, the actual relation (be it a line or a circle or a
> parabola or anything else) is not composed of successive points. If it
> were, then there would be a finite number of points. Which there
> isn't.
So, once again, you confirm your belief that finite is infinite...
This is the problem...
Is that getting through... ?
> Ummm... What?
Sounded simple. Read it again.
> Nope.
There is always hope...
> What misconceptions? You mean of reality? Who claimed that any of this
> had anything to do with reality?
The one we have been discussing... oops, you can't hear it.
Infinitising the finite and flying off into non-reality.
The real question is:
Are YOU interested in reality since the foundations are built upon
it... ?
> Because that's how it works out. You can actually prove the theorem,
> you know.
Ha, ha, ha...
Why 'squares' was the question.
You are thinking that it is a 'square' relationship.
It isn't - it is an 'area' relationship, silly.
Is proved... is good... I agree.
It still has a misconception... squares...
Circle area is pi*r^2.
Gosh, that's not a square... is it?
> Irrelevant and incorrect. The existence of Pythagorean triples has no
> bearing on the truth of the Pythagorean theorem.
Did I mention triplets?
The reason I mentioned Fermat is that a 'cube' is an extended
'square'.
And Fermat is correct - meaning that there is a problem for you to go
from (1,1,1) to (2,2,2).
Thanks for the valid comment though.
BUT 'squares' have no bearing on the truth of the PT... do they... ?
> Pythagorean <=> E=mc^2??? You're connecting this guy to someone over 2
> millennia ahead of his time???
Come on.. this is a dumb statement...
Of course they are connected.
Bear in mind that Pythagoras was way ahead of BOTH YOU AND ME.
Are you superior to Pythagoras such that you might call him dumb-ass?
I think not...
> I'm not going to argue with you anymore; it's obvious to me that
> you're not about to give up on your misconceptions. The fact that I
> have had a complete, logical and valid response to every one of your
> misconceptions doesn't seem to deter you.
My misconceptions are actually 're-conceptions'...
No one thinks that their held opinion is illogical or invalid.
As you can see above, you misconceive my misconceptions... :-)
Hopefully, you will reply.
If you do reply, please tell me why E=mc^2 is a planar equation in
triangular form.
Regards.
Adam Lewis.
Tim Little
> the NEXT point - none between.
See, I told you he was going to start talking about some crank theory
of successive points.
Let's see what he claims is the NEXT point on the x axis after the
point where it intersects the y axis.
- Tim
Han de Bruijn
Sure. But I also get it _right_ much of the time. You can't have the one
without the other. You don't believe it? Mind the shortest threads! E.g.
http://groups.google.nl/group/sci.math/browse_frm/thread/7a82a8e18f8fa170
Waar gehakt wordt vallen spaanders (You cannot make an omelette without
breaking eggs. Literally: "you can't cleave wood without chips falling"
or something like that ..)
Han de Bruijn
Han de Bruijn
> On Feb 13, 5:52 pm, finite guy <adamle...@amnet.net.au> wrote:
>
>>Firstly, the delta/change in x and y is not the distance between the
>>points of the circle.
>>They are of the axes.
>
> And irrelevant to the description of the circle. All that's needed to
> describe a circle is:
> x^2 + y^2 = r^2
Minor nitpicking .. The original (geometric) definition of the circle is
the place (nowadays most people say: the set) of all points equidistant
to a given point. In algebraic terms:
sqrt(x^2 + y^2) = r with (x,y) e R , r > 0 and r e R .
The original definition is more appropriate when making a visualization.
Han de Bruijn
Tonico
wrote:
*****************************************************************
"Originally"?? It still is the usual definition of circle in analytic
geometry, which takes us at once to the usual analytical description
of the circle centered at (a,b) and with radius r:
(x - a)^2 + (y - b)^2 = r^2 , if we're working with the euclidean
plane and with the euclidean distance.
Regards
Tonio
Pd Have you HdB, read the last posts by that eggregius finite guy? Now
common, be honest: what do you really think of all that?
I mean, besides all the entertainment and the laughs, that is.
finite guy
Coll.
x and y are still axial though, are they not?
finite guy
wrote:
Tim
I think you may have me mixed up with someone else.
I've only ever used my current profile which includes my name.
Must be two different people that you think are cranks.
Regards
Adam Lewis
finite guy
>
> - Show quoted text -
Baby
It's valentines day. Don't be like that...
finite guy
Tinio, Tonio, Tonico... which are you?
Which are you...
now?
I'm only about 5'6", so you could say, "finite, weird, little guy".
More apt.
I guess HbD must be on the Dark Side of the force, eh?
I bet you just want to be a Jedi - Tonocio Wan.
Careful how you handle your lightsabre...
Love and Kisses - it's Valentine's Day.
Adam Lewis.
finite guy
> On Feb 13, 6:58 am, finite guy <adamle...@amnet.net.au> wrote:
> .................................................
>
> > Do you know the old definition of insanity - the lunatic doesn't know
> > anything is wrong?
> > One definition of wrongful pride is not admitting mistakes.
> > But when your mistakes are foundational to your thinking - you have to
> > change.-
>
> **********************************************************
>
> *Plonk!*
>
> And no: I don't have, and I won't change. Honest.
>
> Bye
> Tonio
Bad Tonico...! xoxox ;-)
Did you write that on the toilet?
More a 'plunk' I think.
Like I said:
> > Do you know the old definition of insanity - the lunatic doesn't know
> > anything is wrong?
> > One definition of wrongful pride is not admitting mistakes.
> > But when your mistakes are foundational to your thinking - you have to
> > change.
Like you said:
Wah!!
Regards
Adam Lewis
Han de Bruijn
> On Feb 14, 10:29 am, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL>
> wrote:
>
>>Dustan wrote:
>>
>>>On Feb 13, 5:52 pm, finite guy <adamle...@amnet.net.au> wrote:
>>
>>>>Firstly, the delta/change in x and y is not the distance between the
>>>>points of the circle.
>>>>They are of the axes.
>>
>>>And irrelevant to the description of the circle. All that's needed to
>>>describe a circle is:
>>>x^2 + y^2 = r^2
>>
>>Minor nitpicking .. The original (geometric) definition of the circle is
>>the place (nowadays most people say: the set) of all points equidistant
>>to a given point. In algebraic terms:
>>
>> sqrt(x^2 + y^2) = r with (x,y) e R , r > 0 and r e R .
>>
>>The original definition is more appropriate when making a visualization.
>
> *****************************************************************
>
> "Originally"?? It still is the usual definition of circle in analytic
> geometry, which takes us at once to the usual analytical description
> of the circle centered at (a,b) and with radius r:
> (x - a)^2 + (y - b)^2 = r^2 , if we're working with the euclidean
> plane and with the euclidean distance.
Quoted from an earlier posting in the same thread:
> by convoluting the delta function representing the circle in an "exact"
> image (where it is _invisible_) with a Gaussian distribution function.
> Programmed in (Delphi) Pascal as follows:
>
> function G(x,y,sigma : integer) : double;
> begin
> C := sqrt(sqr(x-a)+sqr(y-b))-R;
> G := exp(-sqr(C/sigma)/2);
> end;
Mind the formula (C) in there. Together with the spread (sigma) it forms
a dimensionless quantity, as _should_ be, when plugged into the 'exp' of
the formula (G). Such a dimensionless quantity cannot be formed with the
other formula: (x - a)^2 + (y - b)^2 = r^2 . Okay? See what I mean?
> Form1.Image1.Canvas.Pixels[x,y] := Grijs(G(x,y,2));
>
> Where the 'Grijs' function is black for its argument = 1 and white for
> its argument = 0 . Mind the grey / gray scales in between, because they
> are representing the _fuzzyfied_ equality.
>
> Here is the picture (for a spread in the Gaussian = 2 pixels):
>
> http://hdebruijn.soo.dto.tudelft.nl/jaar2008/cirkel.jpg
Continuing with the present posting:
> Pd Have you HdB, read the last posts by that eggregius finite guy? Now
> common, be honest: what do you really think of all that?
Well, perhaps he is like the _young_ HdB, somewhat less mature, that is:
http://hdebruijn.soo.dto.tudelft.nl/www/grondig/sci_math.htm
Maybe the year (12.) 1989 reveals something alike 'finitist' behaviour.
> I mean, besides all the entertainment and the laughs, that is.
The truth is that I'm not really amused by this. Think you understand.
Han de Bruijn
Tonico
>
> > I mean, besides all the entertainment and the laughs, that is.
>
> The truth is that I'm not really amused by this. Think you understand.
>
***********************************************************
Yes, that's what I thought, Han...*sigh*. Well, I hoped...you know.
Regards
Tonio
Eric Schmidt
> On Feb 13, 3:29 am, finite guy <adamle...@amnet.net.au> wrote:
>>There is an old expression:
>>Don't let your left hand know what your right hand is doing.
>
>
> +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
>
> This is not just an "old expression" but a rather nonsensical sentence
> quoted from a religious book.
> **************************************************************
It's hardly nonsensical in the original context (which has nothing to do
with what finite guy is saying).
--
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