Might pi be rational?

It is common knowledge that pi is trandencental, but have you ever read a proof of that? Well this guy is challenging that, contrary to everyone he is claiming that pi is rational!

http://webonastick.com/pi/

I'm hope this is of interest to some flat earthers.

It is common knowledge that pi is trandencental, but have you ever read a proof of that? Well this guy is challenging that, contrary to everyone he is claiming that pi is rational!

http://webonastick.com/pi/

I'm hope this is of interest to some flat earthers.

I actually have read a proof of that.  It was very similar to the proof regarding the irrational nature of 2^(1/2)

There is no such thing as an irrational number.

There is no such thing as an irrational number.

Sure there is, it is a real number that is not rational.

There is no such thing as an irrational number.

The numbers I have met were rather rational, but that does not mean the ones we have not met are rational also. Please do not make such  broad assumptions.

There is no such thing as an irrational number.

There is no such thing as you.

http://en.wikipedia.org/wiki/Irrational_number

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

Since this page was published on the Internet sometime in November 1994 (it was available as my .plan file for a while before then), a few visitors have explained to me a supposed hole in my theorem concerning division by zero, or something else. If you are one of those people, then you can safely rest assured that that this page is a joke, and that the only reason I didn't respond to some of you was simply that I couldn't figure out what to say.

taken from the bottom of the page

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

In the physical world, there are no irrational numbers, or rational numbers with never ending periodic decimal parts; these are, by definition, abstract concepts, invented in the XIXth century by mathematicians.

The works of "Pythagoras", "Plato", "Socrates" were made up during the first half of the XVIIIth century, in the radical new chronology (see the proofs at my alternative flat earth theory links).

As such, the concept of the irrational number was injected in the western thought stream in order for these conspirators to be able to present the heliocentric planetary system to the world.

The only mathematician who realized that there were no irrational numbers in the real/physical world, and who continuously attacked R. Dedekind and G. Cantor for their mathematical pipe dreams, was Leopold Kronecker.

Kronecker is well known for his remark:-

God created the integers, all else is the work of man.
Irrational numbers are totally man-invented.

Kronecker believed that mathematics should deal only with finite numbers and with a finite number of operations. He was the first to doubt the significance of non-constructive existence proofs. It appears that, from the early 1870s, Kronecker was opposed to the use of irrational numbers, upper and lower limits, and the Bolzano-Weierstrass theorem, because of their non-constructive nature. Another consequence of his philosophy of mathematics was that to Kronecker transcendental numbers could not exist.

In 1870 Heine published a paper On trigonometric series in Crelle's Journal, but Kronecker had tried to persuade Heine to withdraw the paper. Again in 1877 Kronecker tried to prevent publication of Cantor's work in Crelle's Journal, not because of any personal feelings against Cantor (which has been suggested by some biographers of Cantor) but rather because Kronecker believed that Cantor's paper was meaningless, since it proved results about mathematical objects which Kronecker believed did not exist. Kronecker was on the editorial staff of Crelle's Journal which is why he had a particularly strong influence on what was published in that journal. After Borchardt died in 1880, Kronecker took over control of Crelle's Journal as the editor and his influence on which papers would be published increased.

Although Kronecker's view of mathematics was well known to his colleagues throughout the 1870s and 1880s, it was not until 1886 that he made these views public. In that year he argued against the theory of irrational numbers used by Dedekind, Cantor and Heine giving the arguments by which he opposed:-

... the introduction of various concepts by the help of which it has frequently been attempted in recent times (but first by Heine) to conceive and establish the 'irrationals' in general. Even the concept of an infinite series, for example one which increases according to definite powers of variables, is in my opinion only permissible with the reservation that in every special case, on the basis of the arithmetic laws of constructing terms (or coefficients), ... certain assumptions must be shown to hold which are applicable to the series like finite expressions, and which thus make the extension beyond the concept of a finite series really unnecessary.

Lindemann had proved that π is transcendental in 1882, and in a lecture given in 1886 Kronecker complimented Lindemann on a beautiful proof but, he claimed, one that proved nothing since transcendental numbers did not exist.


How does the irrational number concept play into our theory discussed here, flat earth vs. round earth?

Stability of the heliocentric solar system

It is only at the highest level of academic circles specialized in bifurcation theory (thus, well-hidden from public view) where we find the truth about the original H. Poincare quotes, which do show that a differential equation (initial value d.e.) approach to celestial mechanics IS IMPOSSIBLE.

As Poincare experimented, he was relieved to discover that in most of
the situations, the possible orbits varied only slightly from the initial
2-body orbit, and were still stable, but what occurred during further
experimentation was a shock. Poincare discovered that even in some of the
smallest approximations some orbits behaved in an erratic unstable manner. His
calculations showed that even a minute gravitational pull from a third body
might cause a planet to wobble and fly out of orbit all together.

Here is Poincare describing his findings:

While Poincare did not succeed in giving a complete solution, his work was so impressive that he was awarded the prize anyway. The distinguished Weierstrass, who was one of the judges, said, 'this work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics.' A lively account of this event is given in Newton's Clock: Chaos in the Solar System. To show how visionary Poincare was, it is perhaps best if he described the Hallmark of Chaos - sensitive dependence on initial conditions - in his own words:

'If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. but even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.' - in a 1903 essay 'Science and Method'

That is why the conspirators had to invent a very complicated new theory, called chaos theory, with the help of G.D. Birkhoff and N. Levinson; their work was the inspiration for S. Smale's horseshoe map, a very clever way to describe Poincare's original findings as "workable" and "manageable". The formidable implications are, of course, that chaotical motion of the planets predicted by the differential equation approach of the London Royal Society is a thing that could happen ANYTIME, and not just some millions of years in the future, not to mention the sensitive dependence on initial conditions phenomenon.

Even measuring initial conditions of the system to an arbitrarily high, but finite accuracy, we will not be able to describe the system dynamics "at any time in the past or future". To predict the future of a chaotic system for arbitrarily long times, one would need to know the initial conditions with infinite accuracy, and this is by no means possible.


http://essay.studyarea.com/old_essay/science/chaos_theory_explained.htm (exceptional analysis of the differential equation approach and the implications thereof)

http://ptrow.com/articles/ChaosandSolarSystem5.htm

(superb analyses of the long term stability of the solar system)


Smale Horseshoe concept:

http://www.its.caltech.edu/~mcc/Chaos_Course/Lesson23/Predicting.pdf
http://en.wikipedia.org/wiki/Horseshoe_map


KAM theory:

http://www.math.rug.nl/~broer/pdf/kolmo100.pdf


Stability of the Solar System:

http://chaos.if.uj.edu.pl/~karol/pdf/solar.pdf (if it cannot be accessed directly, list the link on google search and use the quick view option)


Velikovsky stability theory:

http://www.ralph-abraham.org/interviews/abraham-ebert.html


Butterfly effect:

http://en.wikipedia.org/wiki/Lorenz_attractor
http://en.wikipedia.org/wiki/Butterfly_effect

E. Lorenz did not realize that a system of three nonlinear differential equations could not approximate at all such a complicated natural phenomenon; there is no butterfly effect, the weather in Asia will not change due to the movement of a butterfly's wings in North America (sensitive dependece on initial conditions).

http://www.physicsforums.com/archive/index.php/t-196680.html
http://findarticles.com/p/articles/mi_m0QZX/is_68/ai_n9507766/pg_52/

http://homepages.ulb.ac.be/~gaspard/G.Acad.00.pdf

Homoclinic orbits:

http://arxiv.org/PS_cache/nlin/pdf/0702/0702044v2.pdf


Poincare chaos:

http://web.archive.org/web/20061208155727/http://pims.math.ca/pi/current/page25-29.pdf

Dynamics and Bifurcations, J. Hale and H. Kocak (pages 248, 477, 486-490)
Introduction to Applied Nonlinear Dynamical Systems and Chaos, S. Wiggins (pages 286, 384, 420-443, 550, 612), both edited by Springer-Verlag; the information in these pages actually show the mathematical and physical implications of chaos theory.

The Duffing oscillator (prototype for nonlinear oscillations), the driven Morse oscillator, Poincare's three body problem equations, the librational motion of a satellite equations, the Ginzburg-Landau equation (nonlinear Schrodinger eq.) which reduces to the Duffing oscillator, all will have parameter values for which the stable/unstable manifolds of a saddle point will come into contact tangentially - homoclinic tangency.

Differential equations can be used on a very limited base (classical mechanics, quality-control, electronics/electrical engr., thermodynamics, and even here with certain assumptions/simplifications) and not at all in order to describe/predict biological processes and cosmological theories, where the aether theory comes into play to explain all the details.

Moreover, the system parameters will be varying functions of time, not to mention that the coefficients of the forcing/damping functions will not be "sufficiently small" in actual practice.

The assumptions actually made in describing various phenomena in several branches of physics are very well described in the classic Mathematics applied to deterministic problems in natural sciences by C.C. Lin and L. Segel (chapters 1, 4, 6, 8 ); page 43 exemplifies the extraordinary philosophical implications of the differential equation approach in modern physics:

http://www.ec-securehost.com/SIAM/CL01.html


An analysis of the calculus approach errors:

http://milesmathis.com/are.html
http://milesmathis.com/calcsimp.html
http://milesmathis.com/flaw.html
http://milesmathis.com/lemma.html
http://milesmathis.com/avr.html


Now we know that Pythagoras never existed actually, as there were no ancient Greece/Rome/Egypt in our radical new chronology, and that the conspirators invented the irrational number concept in order to deceive the public regarding the Pythagorean comma (instead of a circle of fifths, we would have a spiral of fifths); they also invented, through J.S. Bach, the equal temperament scale in order to hide the real scale they used to produce levitation of large blocks of stone.


D. Hempel on Pythagoras' irrational numbers:

http://www.davidicke.com/forum/showthread.php?t=10283
http://www.breakingopenthehead.com/forum/showpost.php?s=b7d281def62a68bb3f0971352e1ed848&p=30829&postcount=5


From http://essay.studyarea.com/old_essay/science/chaos_theory_explained.htm


Scientists used to, before the chaos theory, believe in the
theory of reductionism, many still do. Reductionism imagines nature as equally
capable of being assembled and disassembled. Reductionists think that when
everything is broken down a universal theory will become evident that will
explain all things. Reductionism implied the rather simple view of chaos
evident in Laplace's dream of a universal formula: Chaos was merely complexity
so great that in practice scientists couldn't track it, but in principle they
might one day be able to. When that day came there would be no chaos,
everything in existence would be perfectly predictable, no surprises, the
world would be safely mutable. The universe would be completely controlled by
Newton's laws.

Chaos touches all things in existence, and all sciences,
mathematics, physics, biology, anthropology, entomology, astronomy, even the
Ivory Tower science of Newtonian physics. In the last years of the 19th
century French mathematician, physicist and philosopher Henri Poincare
stumbled headlong into chaos with a realization that the reductionism method
may be illusory in nature. He was studying his chosen field at the time; a
field he called the mathematics of closed systems, the epitome of Newtonian
physics. A Closed system is one made up of just a few interacting bodies
sealed off from outside contamination. According to classical physics, such
systems are perfectly orderly and predictable. A simple pendulum in a vacuum,
free of friction and air resistance will conserve its energy. The pendulum
will swing back and forth for all eternity. It will not be subject to the
dissipation of entropy, which eats its way into systems by causing them to
give up their energy to the surrounding environment. Classical scientists were
convinced that any randomness and chaos disturbing a system such as a pendulum
in a vacuum or the revolving planets could only come from outside chance
contingencies. Barring those, pendulum and planets must continue forever,
unvarying in their courses.

It was this comfortable picture of nature that
Poincare blew apart when he attempted to determine the stability of our solar
system. For a system containing only two bodies, such as the sun and earth or
earth and moon, Newton's equations can be solved exactly: The orbit of the
moon around the earth can be precisely determined. For any idealized two-body
system the orbits are stable. Thus if we neglect the dragging effects of the
tides on the moon's motion, we can assume that the moon will continue to wind
around the earth until the end of time. But we also have to ignore the effect
of the sun and other planets on this idealized two-body system. Poincare's
problem was that when an additional body was added to the situation, like the
influence of the sun, Newton's equations became unsolvable. What must be done
in this situation is use a series of approximations to close in on an answer.
In order to solve such an equation, physicists were forced to use a theory
called Perturbation. Which basically works in a third body by a series of
successive approximations. Each approximation is smaller than the one before
it, and by adding up a potentially infinite amount of these numbers,
theoretical physicists hoped to arrive a working equation. Poincare knew that
the approximation theory appeared to work well for the first couple of
approximations, but what about further down the line, what effect would the
infinity of smaller approximations have? The multi-bodied equation Poincare
was attempting was essentially a Non-linear equation. As opposed to a
differential or linear equation. For science, a phenomenon is orderly if its
movements can be explained in the kind of cause-and-effect scheme represented
by a differential equation. Newton first introduced the differential idea
throughout his famous laws of motion, which related rates of change to various
forces. Quickly scientists came to rely on linear differential equations.
Phenomena as diverse as the flight of a cannonball, the growth of a plant, the
burning of coal, and the performance of a machine can be described by such
equations. In which small changes produce small effects and large effects are
obtained by summing up many small changes. A non-linear equation is quite
different. In a non-linear equation a small change in one variable can have a
disproportional, even catastrophic impact on other variables. Behaviors can
drastically change at any time. In linear equations the solution of one
equation allows the solver to generalize to other solutions; in non-linear
equations solutions tend to be consistently individual and unrelated to the
same equation with different variables. In Poincare's multi-bodied equation,
he added a term that added nonlinear complexity to the system (feedback) that
corresponded to the small effect produced by the movement of the third body in
the system. As he experimented, he was relieved to discover that in most of
the situations, the possible orbits varied only slightly from the initial
2-body orbit, and were still stable but what occurred during further
experimentation was a shock. Poincare discovered that even in some of the
smallest approximations some orbits behaved in an erratic unstable manner. His
calculations showed that even a minute gravitational pull from a third body
might cause a planet to wobble and fly out of orbit all together.

Poincare's discovery was not fully understood until 1953 by Russian physicist A. N. Kolmogorov. Initially
scientists believed that in theory they could break up a complicated system
into its components before experimentation because any changes in patterns
would be small and not effect an established construct such as an orbit.
Kolmogorov was not prepared to accept that the whole universe is a fraction of
a decimal point away from self-destruction. Unfortunately his research didn't
help. Kolmgorov concluded, from his own calculations, that the solar system
won't break up under its own motion provided that the influence of an
additional gravitational source was no bigger than a fly approximately 7000
miles away, and the cycles per planetary year did not occur in a simple
ratio like 1:2 1:3 or 2:3 and so on.

But, what happens when the planet's years form a simple ratio? Well, that would mean that with each orbit, the
disturbance is amplified due to a steady input of gravitational energy. It
creates a resonance feedback effect much like a normal microphone amplifier.
Say you lie an amplifiers input mic directly in front of its output speaker.
Any sound that enters the microphone will be played back through the speaker
louder, that playback will be picked up by the mic and amplified once again,
eventually the volume will reach its critical point and the speaker will blow
out. Well, if this were so, is there proof? Does this really happen in space?
Could this occur in our solar system? The answer is yes.

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

In the physical world, there are no irrational numbers, or rational numbers with never ending periodic decimal parts;

A pie is divided in 3 equal parts. Please express the part as a decimal number. Similarly, a circle has a radius 1. Please express its circumference as decimal number.

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

In the physical world, there are no irrational numbers, or rational numbers with never ending periodic decimal parts; these are, by definition, abstract concepts, invented in the XIXth century by mathematicians.

I agree.  I also agree with much of the rest of your post, save the historical revisionism. Whenever I read your theories concerning this, it always comes down to this simple decider for me.  

"Is it more likely people are dumb, or is more likely that malice occured?"

Ignoring all that, in the physical world there are no numbers at all.  Math only makes sense based on what axioms we defined for it.  In other words, the physical world has nothing to do with math, except by coincidence.   Hartry Field's Science Without Numbers is a good starting point down this argument.

If I define "blue" numbers to exist, they exist as much as any other number.  

Obviously, you are familiar with the argument of fictionalism and axiom central math, as well as the counter arguments; I am too;  I think we can leave it as we agree to disagree unless there is any material I would not be aware of you wish to share here.

On a personal note, I am interested in burying whatever issues we have with each other.  Obviously I don't agree with everything you say, but you are a lot closer to the truth than many others here.  I don't like how things went down, but they had to happen that way.  We have enough round earthers at our throats to be trying to tear each other down.  Obviously, I invite discourse tearing down my theories or others.  I just mean on a personal level.

Cheers, and Merry Christmas.

A good starting point is to expand your bibliographical research, such as the thoughts of N. Tesla on the abstract nature of mathematics:

The inventor of the electric world we live in, Nikola Tesla was spot-on when he remarked that "modern non-applied science has become nothing more than manipulative indulgence in fancy "thought experiments" and abstract, fuzzy math which have no relation to reality. Instead of the theories being made to fit reality, what we have is the opposite: reality being adjusted or in fact completely overthrown, in order to fit agenda-driven theories and models."

Might pi be rational?

nope. next question, please.

While levee may want you to believe that, his point falls flat.

This is a tautology.

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

If you now say that you only meant "there are no numbers in the world" then that is meaningless garble. A number is simply a representation of amount.

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

If you now say that you only meant "there are no numbers in the world" then that is meaningless garble. A number is simply a representation of amount.

No, its not. Its an abstraction that can be used, among many other things, as a tool to the ends you state.

block of copy pasta

does anyone ever read his posts?

Quote from: Raist on December 27, 2010, 09:22:48 PM

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

If you now say that you only meant "there are no numbers in the world" then that is meaningless garble. A number is simply a representation of amount.

No, its not. Its an abstraction that can be used, among many other things, as a tool to the ends you state.

So there are irrational numbers in the real world?

Quote from: John Davis on January 05, 2011, 01:19:54 PM

Quote from: Raist on December 27, 2010, 09:22:48 PM

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

If you now say that you only meant "there are no numbers in the world" then that is meaningless garble. A number is simply a representation of amount.

No, its not. Its an abstraction that can be used, among many other things, as a tool to the ends you state.

So there are irrational numbers in the real world?

No, I think you must have misread me, or perhaps I misstated.  No number exist in the physical world.  A number is an abstract mathematical object that sometimes relates to, and sometime doesn't, the physical world.

So, isn't there an abstract mathematical object called 'irrational number'?

Quote from: Raist on January 07, 2011, 01:26:53 PM

Quote from: John Davis on January 05, 2011, 01:19:54 PM

Quote from: Raist on December 27, 2010, 09:22:48 PM

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

If you now say that you only meant "there are no numbers in the world" then that is meaningless garble. A number is simply a representation of amount.

No, its not. Its an abstraction that can be used, among many other things, as a tool to the ends you state.

So there are irrational numbers in the real world?

No, I think you must have misread me, or perhaps I misstated.  No number exist in the physical world.  A number is an abstract mathematical object that sometimes relates to, and sometime doesn't, the physical world.

And irrational numbers don't relate to the physical world? I'd really like you to express the ratio of the radius of a real world circle to the circumference using only rational numbers.

Quote from: John Davis on January 07, 2011, 01:38:07 PM

Quote from: Raist on January 07, 2011, 01:26:53 PM

Quote from: John Davis on January 05, 2011, 01:19:54 PM

Quote from: Raist on December 27, 2010, 09:22:48 PM

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

If you now say that you only meant "there are no numbers in the world" then that is meaningless garble. A number is simply a representation of amount.

No, its not. Its an abstraction that can be used, among many other things, as a tool to the ends you state.

So there are irrational numbers in the real world?

No, I think you must have misread me, or perhaps I misstated.  No number exist in the physical world.  A number is an abstract mathematical object that sometimes relates to, and sometime doesn't, the physical world.

And irrational numbers don't relate to the physical world? I'd really like you to express the ratio of the radius of a real world circle to the circumference using only rational numbers.

There is no such thing as a real world circle.  Irrational numbers relate to the physical world in the same way normal numbers do - sometimes they do, and sometimes they don't.  In other words, by designed coincidence.

In otherwords, I hold math to exist for pure math;  not for application.  Any application is secondary to their nature, a nature which is simply axiomatically defined.

Quote from: Raist on January 08, 2011, 02:11:51 AM

Quote from: John Davis on January 07, 2011, 01:38:07 PM

Quote from: Raist on January 07, 2011, 01:26:53 PM

Quote from: John Davis on January 05, 2011, 01:19:54 PM

Quote from: Raist on December 27, 2010, 09:22:48 PM

Quote from: John Davis on November 24, 2010, 07:41:46 PM

Quote from: Ichimaru Gin :] on November 06, 2010, 04:11:58 PM

There is no such thing as an irrational number.

While levee may want you to believe that, his point falls flat.   In short: there is no such thing as a number in the physical world (where he was trying to apply said statement.)  As such its a meaningless statement.

Irrational numbers exist because we define them to exist.  Like everything else in math.

If you now say that you only meant "there are no numbers in the world" then that is meaningless garble. A number is simply a representation of amount.

No, its not. Its an abstraction that can be used, among many other things, as a tool to the ends you state.

So there are irrational numbers in the real world?

No, I think you must have misread me, or perhaps I misstated.  No number exist in the physical world.  A number is an abstract mathematical object that sometimes relates to, and sometime doesn't, the physical world.

And irrational numbers don't relate to the physical world? I'd really like you to express the ratio of the radius of a real world circle to the circumference using only rational numbers.

There is no such thing as a real world circle.  Irrational numbers relate to the physical world in the same way normal numbers do - sometimes they do, and sometimes they don't.  In other words, by designed coincidence.

In otherwords, I hold math to exist for pure math;  not for application.  Any application is secondary to their nature, a nature which is simply axiomatically defined.

Ok, then let us bring this full circle, how do irrational numbers not exist in any way that rational numbers do exist?

Ok. first proof is by induction,
it is wrong, because all it shows is that if taking pi to the nth digit as "pi", then "pi" is rational.
but induction works one step at a time, and only for FINITE steps. "pi" does not equal pi.
the reason why you can't take FINITE steps and make conclusions about the INFINTE steps, is because you have to worry about the TAIL of the number.


second proof is by physical constraints.
this is dumb because numbers don't only exist in the real world, but as abstract figures. So the proof relies on a certain set of possibilies which are more limited than the world of numbers, for example, the universe has no imaginary distances, but that doesn't mean imaginary numbers don't exist. ignoring this flaw, the proof is wrong, because it assumes that you can divide the world into countable pieces, where in reality, the distance between atoms have a degree of variation due to outside forces, so a 2 10-carbon chains might be of different length


Alternative algebra?
this system is not valid, because it has inherent paradoxes. If any realm of Mathematics was found to have a paradox, it would be flawed, but since none have been found in normal algebra, it is considered correct. You cannot start a proof via an incorrect statement. 2=/=1


Also:
"Since this page was published on the Internet sometime in November 1994 (it was available as my .plan file for a while before then), a few visitors have explained to me a supposed hole in my theorem concerning division by zero, or something else. If you are one of those people, then you can safely rest assured that that this page is a joke, and that the only reason I didn't respond to some of you was simply that I couldn't figure out what to say."

There is no such thing as a real world circle.  Irrational numbers relate to the physical world in the same way normal numbers do - sometimes they do, and sometimes they don't.  In other words, by designed coincidence.

In otherwords, I hold math to exist for pure math;  not for application.  Any application is secondary to their nature, a nature which is simply axiomatically defined.

If I understand, you are just pointing out that math is abstract and the physical world is real, and as such, applied math (math of  the physical world) is not perfect because we applied it/math is not inherent to the world.

But as I see it, the natural numbers actually come from the real world, like someone had one son and one daughter, so they needed to find a word for how many children they have.

addition came from combining or giving, while subtraction came from taking away. The point is, this type of math is just a way of keeping track of real processes. Here math is derived from reality, the man has two children. But I agree that many other math applications just happen to be useful, like with quadratics, its not like a programmer made the universe and decided things would fall without resistance at a quadratic rate vs time. But rather it just so happens that a lot of math is coincdentally useful (but not absolutely correct).

And why do you say that a circle doesn't exist? are you saying no circle is possibly perfect? because that is wrong, it could be that a certain fundamental particle is spherical, in which case you could take any cross section.

Quote from: John Davis on January 08, 2011, 07:03:21 AM

There is no such thing as a real world circle.  Irrational numbers relate to the physical world in the same way normal numbers do - sometimes they do, and sometimes they don't.  In other words, by designed coincidence.

In otherwords, I hold math to exist for pure math;  not for application.  Any application is secondary to their nature, a nature which is simply axiomatically defined.

If I understand, you are just pointing out that math is abstract and the physical world is real, and as such, applied math (math of  the physical world) is not perfect because we applied it/math is not inherent to the world.

But as I see it, the natural numbers actually come from the real world, like someone had one son and one daughter, so they needed to find a word for how many children they have.

addition came from combining or giving, while subtraction came from taking away. The point is, this type of math is just a way of keeping track of real processes. Here math is derived from reality, the man has two children. But I agree that many other math applications just happen to be useful, like with quadratics, its not like a programmer made the universe and decided things would fall without resistance at a quadratic rate vs time. But rather it just so happens that a lot of math is coincdentally useful (but not absolutely correct).

And why do you say that a circle doesn't exist? are you saying no circle is possibly perfect? because that is wrong, it could be that a certain fundamental particle is spherical, in which case you could take any cross section.

Its a bit more than "just pointing out" but yes.  Its an old phil of math debate.  Really old.  There are several schools;  Its basically the difference between the two extremes you talk of.  Are we discovering math or are we inventing it?  How does this discovery happen?  Is it empirical? etc etc.

Quote from: Thevoiceofreason on January 09, 2011, 02:49:08 PM

Quote from: John Davis on January 08, 2011, 07:03:21 AM

There is no such thing as a real world circle.  Irrational numbers relate to the physical world in the same way normal numbers do - sometimes they do, and sometimes they don't.  In other words, by designed coincidence.

In otherwords, I hold math to exist for pure math;  not for application.  Any application is secondary to their nature, a nature which is simply axiomatically defined.

If I understand, you are just pointing out that math is abstract and the physical world is real, and as such, applied math (math of  the physical world) is not perfect because we applied it/math is not inherent to the world.

But as I see it, the natural numbers actually come from the real world, like someone had one son and one daughter, so they needed to find a word for how many children they have.

addition came from combining or giving, while subtraction came from taking away. The point is, this type of math is just a way of keeping track of real processes. Here math is derived from reality, the man has two children. But I agree that many other math applications just happen to be useful, like with quadratics, its not like a programmer made the universe and decided things would fall without resistance at a quadratic rate vs time. But rather it just so happens that a lot of math is coincdentally useful (but not absolutely correct).

And why do you say that a circle doesn't exist? are you saying no circle is possibly perfect? because that is wrong, it could be that a certain fundamental particle is spherical, in which case you could take any cross section.

Its a bit more than "just pointing out" but yes.  Its an old phil of math debate.  Really old.  There are several schools;  Its basically the difference between the two extremes you talk of.  Are we discovering math or are we inventing it?  How does this discovery happen?  Is it empirical? etc etc.

So do fractions even exist then? How could you ever take exactly half of something? Negative numbers don't exist, unless you count debt as real.

Where do you draw the line?

Quote from: John Davis on January 10, 2011, 05:26:50 AM

Quote from: Thevoiceofreason on January 09, 2011, 02:49:08 PM

Quote from: John Davis on January 08, 2011, 07:03:21 AM

There is no such thing as a real world circle.  Irrational numbers relate to the physical world in the same way normal numbers do - sometimes they do, and sometimes they don't.  In other words, by designed coincidence.

In otherwords, I hold math to exist for pure math;  not for application.  Any application is secondary to their nature, a nature which is simply axiomatically defined.

If I understand, you are just pointing out that math is abstract and the physical world is real, and as such, applied math (math of  the physical world) is not perfect because we applied it/math is not inherent to the world.

But as I see it, the natural numbers actually come from the real world, like someone had one son and one daughter, so they needed to find a word for how many children they have.

addition came from combining or giving, while subtraction came from taking away. The point is, this type of math is just a way of keeping track of real processes. Here math is derived from reality, the man has two children. But I agree that many other math applications just happen to be useful, like with quadratics, its not like a programmer made the universe and decided things would fall without resistance at a quadratic rate vs time. But rather it just so happens that a lot of math is coincdentally useful (but not absolutely correct).

And why do you say that a circle doesn't exist? are you saying no circle is possibly perfect? because that is wrong, it could be that a certain fundamental particle is spherical, in which case you could take any cross section.

Its a bit more than "just pointing out" but yes.  Its an old phil of math debate.  Really old.  There are several schools;  Its basically the difference between the two extremes you talk of.  Are we discovering math or are we inventing it?  How does this discovery happen?  Is it empirical? etc etc.

So do fractions even exist then? How could you ever take exactly half of something? Negative numbers don't exist, unless you count debt as real.

Where do you draw the line?

I think he is defining existence in a specific way. You could define it to include abstractions, or limit it to the physical world. He is doing the latter

Its a question between Platonism or not.  If they exist only abstractly, but not really (as perhaps a platonist might hold they exist abstractly and in a more real sense) its different from existing in the physical world or existing only abstractly.

From what I understand, the claim being made that we are discussing is concerning whether irrational numbers exist any less than, for example, integers.