[Fun thing to do; Advice to NASA; Disproof of calculus] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

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Fun thing to do; Advice to NASA; Disproof of calculus

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Posted by: Steve Zimmerman

Fun thing to do--

Juxtapose the data of my previous post ("Four Layers of Equals") with the following exercise from K. Godel's "On Formally Undecidable Propositions of _Principia Mathematica_ and Other Related Systems":

[I'm using ".=." for the three-stroke equivalence sign. Also, "A[1]" should be read "A sub 1", etc.]

"36. A - Ax(x) .=. A[1] - Ax(x) V A[2] - Ax(x) V A[3] - Ax(x) V A[4] - Ax(x)"

And along these lines of fun things to do, a surprisingly fecund method of doing theoretical mathematics is found by doing them according to Sigmund Freud's method of dream analysis (!), to be found in _The Interpretation of Dreams_; that is, the method of non-critical free-association.

You only need a gift for mathematics, a taste for pure mathematics, and doing well in 1 or 2 algebra courses before you can use this method with great enjoyment.

However, calculus may have destroyed your ability to use this method, forcing as it does the linking of mentation with volition to such a pronounced degree.

I mean, with all that calculus, how come the NASA engineers can't even know what's going on with the pieces falling off the space shuttle?

Answer: Because calculus deals with the concepts of "slope" and "area" as its fundamental atomic primitives.

Then, because the engineers forget that calculus is fundamentally limited to finding slopes and areas, and because they mistakenly believe it is of much wider applicability than it is, they assume that it is telling them much more than it is in fact even capable of telling them.

My advice to these engineers: Give NKS a good college try :-).

Furthermore, from the standpoint of pure mathematics, calculus can be _very_ easily disproven from its very foundations.

For if x and delta x are two independent points--and how could they not be, since delta x means "a change in x"?--then logically you should be able to take the limit of x as it approaches delta x:

lim x as x->delta x.

But trying to do so exposes the fundamental inconsistency of the very idea of "limit."

For as you try to take the limit of x as it approaches delta x, you are unable to, because as soon as you try to, x _is_ delta x, which violates the consistency of the fact that logically, x and delta x must be two different points.

Thus, when looked at algebraically, not graphically, calculus is invalid.

But then why does calculus _use_ algebra so much?

That's _another_ inconsistency of calculus. It most certainly has no right to use something that proves its falsehood(!)

From a practical standpoint, of course, calculus may be useful--as useful as however useful finding slopes and areas is--no more useful.

Thus the fundamental limitation of those who insist on obsessing on pragmatism, pragmatism and more pragmatism: their hyper-focus on the pragmatic is a form of tunnel vision which denies entry to theory, and this denial drastically limits the scope and breadth of the tools that they are able to use, which, paradoxically, makes them impractical people(!)

Thank you to Stephen Wolfram for giving science a grand fresh start :-).




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