On Fermat, Fine Structure, and the Intellectual Bankruptcy of Science 1.1.4

Abstract¬†The world -under the sway of the religion called “science” is in a very sorry state. There is an accumulation of data, an accumulation that says nothing more nor less than that everything is running toward eternal death, but no one knows why. All science can do is can say is “that’s just the way it is”. This is due to the neglect by science of the basis and the reason for scientific laws/mathematical principles. Feynman described the scientific enterprise best when he analogized scientific inquiry to the study of a gigantic natural chess game where the scientist tries to work out what the rules of the game are. But if and when he or she is able to do this, the question remains as to why the rules are as they are. Science has it backwards. Once one knows the rules governing the empirically discernible rules -once one knows the deep rules- it is a relatively easy matter to work out what the shallow rules are and why, but it is impossible to discover the deep rules from the shallow ones, i.e. the scientific quest is a walk down the proverbial garden path. The shallow philosophy encapsulated by Feynman has given us proofs of Fermat’s Last Theorem, and the Poincare Conjecture, in the form of more or less incomprehensible and arbitrary numerical facts, and it has given us the Standard Model of Particle Physics in which all of the free parameters are set from experiment, i.e. science would have us believe that these values are arbitrarily chosen. Science presents us with a world whose evident, encroaching, and irreversible bleakness makes no sense…

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1. At school we are taught mathematics and other subjects as rule-following exercises.

2. Follow the rule according to which doing x results in y, do x, and you will always get y.

3. This teaching is then taken out of the childhood-classroom and applied in the world.

4. Scientists -the high priests of the most dominant religion of the day (the God of this religion is self and its goal is self-gratification) are obsessed by learning rules.

5. But although they know a little about the rules, they don’t know how and why the rules were made.

6. C.S. Lewis in “The Lion, The Witch, and the Wardrobe”, speaks of the “deep magic” on whose basis Narnia is what it is. Scientists don’t know the deep magic.

7. A scientist is like a man locked in a room with a set of rules in English explaining how to manipulate Chinese symbols to create the illusion that he understands Chinese (an illusion which is quick dispelled when the task is, not the manipulation of symbols, but the correlation of the rules governing the manipulation of symbols to the symbols).

9. A starting example of the intellectual bankruptcy of the scientific method is Andrew Wiles’ proof of Fermat’s Last Theorem. The right conclusion has been drawn -there can be no positive integer solutions to the equation x^n + y^n=z^n- but why is it the right conclusion?

10. As it stands, Wiles’ proof is a tortuously convoluted and blind exercise in the manipulation of symbols. It shows us nothing about reality, because as it stands the result seems arbitrary and quite trivial.

11. A second example is Grigori Perelman’s proof of the Geometrization (and thus the Poincare) Conjecture. Again the right conclusion has been drawn -the sphere is the simplest compact object in 4 dimensions- but why is this the right conclusion?

12. As written, Perelman’s result is an arbitrary, inexplicable, and trivial fact arrived at by blind rule-following, not worth 100, let alone1000000.

13. Let’s turn thirdly to the Standard Model of Particle Physics in which all of the masses of the particles, the strength of gravity, and all of the parameters of the theory are set from experiment.

14. But we need to know, not only THAT is the amplitude for a real electron to emit or absorb a real photon 1/137, but WHY this is the case.

15. Richard Feynman:

You might say the “hand of God” wrote that number, and “we don’t know how He pushed his pencil.” We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out, without putting it in secretly.

16. This is what happens when the extent of your knowledge is like the knowledge of a man who knows how to bake a cake by following the recipe, but doesn’t know how to create his own recipe, or what cakes are for.

17. And it is by this approach no more possible to work out why the rules are what they are and come to know the deep magic than it is possible for a dog to catch its own tail.

18. The deep answer to these questions concerns the distinction there is between continuous surfaces (infinite primes) and discontinuous surfaces (strictly finite primes).

19. Wiles’ argument for the truth of Fermat is that all elliptic curves are continuous in our sense (s = 1 as opposed to a positive real number other than 1), and so that the falsity of theorem implies that there is a discontinuous elliptic curve. The argument is successful because Fermat-unfriendly solutions of the theorem are associated to surfaces involving finite primes.

20. Poincare also concerns continuous (smooth) surfaces, and the claim is that a 3-sphere is simply connected, i.e. it is continuous in our sense.

21. If this were false, then -again- there would be a continuous surface associated to a finite number of primes.

22. The trick is that the basis of this distinction between the continuous and the discontinuous, between surfaces involving potentially infinite primes and those involving strictly finite primes is the basis of arithmetic continuity and therefore the basis of consciousness.

\hbar = the reduced Planck constant = \frac{6.66134}{10^{16}}


G = the Gibbs constant =\int_0^{\pi } \frac{x \sin }{x} \, dx

And let

e=the elementary charge
c=the speed of light in a vacuum
\epsilon _0=the electric constant
\mu _0 =the magnetic constant
R_K=the van Klitzing constant
Z_0=vacuum impedance

\alpha =\frac{1}{137.036}=\left(e^{2 \gamma } \left(e^{\frac{1}{12-1}-\zeta (12)}\right)^2-e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^1 \frac{1.00009}{1^{12}}-\int_1^1 \frac{1.00009}{1^{12}} \, dn\right)}\right){}^2\right){}^2

and so

\left(e^{2 \gamma } \left(e^{\frac{1}{12-1}-\zeta (12)}\right)^2-e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^1 \frac{1.00009}{1^{12}}-\int_1^1 \frac{1.00009}{1^{12}} \, dn\right)}\right){}^2\right){}^2=\frac{1}{\frac{\left(\frac{3 \pi }{2}\right)^3 G}{\sqrt{2}}}=\frac{1}{4 \pi \epsilon _0}=\frac{e^2}{c \hbar }=\frac{\left(e^2 c\right) \left(\pi \mu _0\right)}{4 \hbar }=\frac{e^2 k_e}{c \hbar }=\frac{c \mu _0}{2 R_K}=\frac{e^2 Z_0}{(4 \pi ) \hbar }

23. This analysis shows us that the constants of nature are not constant – they belong to one particular time in history, and one particular mode of consciousness, and that there are other times and other modes…

24. It also shows that the free parameters are not free – they have to conform to the dictates of the mathematical principles governing our world at all times and modes in virtue of which these times and modes are arithmetically continuous and therefore subject to the irreversible arrow of time.

25. Scientists are very concerned with ’empirical evidence’, they disbelieve in a super-intelligent alien creator because there is -they say- no empirical evidence such a thing exists.

26. But they forget that before it is possible to have any sensory experience whatsoever, and divide the world into units and measure it, there must be a very special relationship between the world (that is measured) and the mind (that measures it).

27. This relationship is deeper than the senses, and deeper than the integers -it is the “deep magic” of C.S. Lewis -but it is more real than what we call “real”.

28. Aslan in The Lion, the Witch, and the Wardrobe:

“There is a deep magic more powerful than us that rules over all of Narnia. It defines right and wrong, and governs all our destinies, yours and mine.”

29. There is an ideal distance between a representational painting and a viewer.

30. If the viewer stands too close or to too far from the painting, they will be unable to make out what it is a painting of.

31. Yet a coherent image emerges from the combination of these brush strokes surveyed from the appropriate distance.

32. The failure of science to see the truth of a transcendent creator is born of their obsession with rule-following: scientists fail to see that beneath the world of the rules of science there lies an abstract world that is not within the bounds of the rules, but without which the rules wouldn’t work. They work only because they have been so crafted.

33. And not until one acquaints oneself with the strictures of this invisible world -with the deep magic- is it possible to have anything more than a shallow understanding of the visible world. But understanding is not be found in the simplistic rule-following operations taught at school and that form the basis of the decadent, mindless, culture of science.



Adamson, A (2005), The Chronicles of Narnia: The Lion, The Witch, and the Wardrobe

Lewis, C (1950), The Lion, The Witch, and the Wardrobe

Feynman, R (1965), The Character of Physical Law

Feynman, R (1985), QED: The Strange Theory of Light and Matter

Perelman, G (2002), The entropy formula for the Ricci flow and its geometric applications

Wiles, A (1995), Modular elliptic curves and Fermat’s Last Theorem

Zhou, Z (2002), An observation on the relation between the fine structure constant and the Gibbs phenomenon in Fourier analysis