When using a language whose alphabet is finite — including maths — no general infinite systems may be fully characterized.

Lao Tzu opens his “The Classic Book of the Way and its Power” (the “Tao Teh Ching”) with:

“The way that can be spoken is not the real Way. The name that can be named is not the real Name.

About 2,600 years later, a scientific argument explains why this is true.

The paper, “Limits to Maths” — available here (*) — compels rethinking the work of Cantor, Godel, Russell, Turing and many, many others, by compelling the rethinking of the consistency of number (as accepted by current orthodoxy).  What emerges is a nuanced aspect of the scientific worldview in which any scientific mathematical model has a horizon of validity (based on infinitary limits) outside of which the model can no longer be valid.

reed.burkhart@gmail.com

(*) if affordability is an issue, please email me and we can work something out.  Btw, this paper was researched over several years’ spare time (adding up to many thousands of hours study!).

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4 Comments

  1. Craig

     /  June 15, 2012

    My browser is having trouble reading your paper on Scribd.

    Reply
  2. Hi Craig. Please send me an email (reed.burkhart@gmail.com), and I will be pleased to reply to you with a copy of the paper in pdf format (Adobe Acrobat). Thank you for your interest.

    Reply
  3. Ezra Abrahamy

     /  June 19, 2012

    I have not read your paper but with your quotation from Lao Tzu i believe that I understand your take. Simply put, if we consider that Math is a language and as such an extraction from the human mind in trying to describe ‘what ever it is’, then Math is but a filter like any other form of human thinking or communication.

    Reply
    • Yes. And there is an irrefutable scientific basis (the detailed proofs in my paper) for claiming that a vocabulary based on a finite number of symbols or letters will require infinite-length words (or numbers) if it would claim to be able to describe with consistency an infinitary thing (or number).

      Like the number PI, whose digits are an infinite sequence, the infinite-length nature of PI is inevitable because it has an infinitary quality that is not otherwise able to be represented by humans with full consistency.

      The current, orthodox, math and scientific viewpoint is that it is not only o.k., but requisite to exclude traditional numbers of infinite-length to the left of the decimal point, while it is considered acceptable to admit traditional numbers like PI that are of infinite-length to the right of the decimal point.

      This seems possibly to stem from a desire to have “finitary decidability”, yet why should we be able to decide something with finite vocabulary if the thing has infinite complexity? Anthropomorphizing logic (by which I mean conforming logic to what humans can argue with finitary decidability) leaves beyond consistent discussion the full representation of any infinitary phenomena.

      We actually do fine with PI without full representation of its infinitary nature, because getting just a few digits provides practical computational utility (we get close enough to the answer). But other cases of finitary UNdecidability crop up for which there is no acceptable approximation (whenever the finitary undecidability involves infinite extents of numbers to the left of the decimal point).

      Thank you, Ezra, for grasping and sharing the essence of the conclusion of my paper so succinctly.

      It seems important to emphasize that this conclusion is not merely an assertion, but that the conclusion is actually proved with specificity of argument in my paper. Hopefully this error (and correction) at the foundations of maths and human logic can be spread broadly — and soon — so that the work of scientists may no longer rest on an over-stepping of what is possible to state with consistency in maths!

      Reply

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