from the glacier

I was thinking today about the infinite density of the real numbers a la set theory. Then it occurred to me that Cantor has an elegant proof for the incompleteness of the density of real numbers - that I would like to show in a scaled down model. Suppose one thought that numbers could only be broken down into eighth's, and that was the smallest division of numbers allowable - and this covered all numbers. Then suppose you listed them in decimal notion between zero and one like this: (the boldface will become clear)

. 1 2 5 0 0 0 0
. 2 5 0 0 0 0 0
. 3 7 5 0 0 0 0
. 5 0 0 0 0 0 0
. 6 2 5 0 0 0 0
. 7 5 0 0 0 0 0
. 8 7 5 0 0 0 0

Take the decimal illustrated by the diagonal. Add any number to each of the digits (say 1 in this example). You get .2661111 - which is not on the chart. Now generalize. The modified diagonal number has the first digit different than the first number, the second digit different from the second number, the third digit different from etc etc etc. So even if we had very very small differences the diagonal number modified will always be different than any other number on the list.
What is the import of this? Probably nothing. But something analogous to this reasoning is used to show omega inconsistency in formalized mathematical systems. But more on this at another time.

I was thinking. . .
When we look at the theory of Relativity in comparison with classical physics in the relation of time to motion, gravity, space and so forth, we see the dissolution of the exact and eternal time arrow. Rather (possibly because it make equations look better) we now conceive of a "space-time" in four dimensions - not analogously to the three spatial dimensions, but even more closely tied. In fact, with a view toward different motions, one man's present is another man's past or future. There is no absolute time outside of motion. I, for one, was relieved, finding the study of Newton distasteful on a multitude of levels. But why does the Physicist make such a strange deal out of time? I quote:
In their search for this mysterious time-flux many scientists have become deeply confused. All physicists recognize that there is a past-future asymmetry in the universe, produced by the operation of the second law of thermodynamics. But when the basis of that law is carefully examined, the asymmetry seems to vanish.
I don't think it is very fruitful to examine this in any great detail, but Davies goes on to say that the asymmetry of time vanishes when you look at the particles that make up the universe. Each "thing" bouncing against others is perfectly reversible. And the whole of the (material) universe is just things bouncing against things. So it could just as soon go "forwards" as "backwards" - whatever forwards and backwards would then mean. But all the arguments for time dilation (muon decay rates at near light speed, relativity, et cetera) depend on motion. Why not simplify everything and define time as "the number of motion" (I think I seem to remember reading that somewhere) - which would have the happy side effect of having every distinct motion having a distinct time. Also, it would account for the asymmetry in the sense that motion is based on causality, which does not have perfect symmetry (as indicated by the second law of thermodynamics). Concordant with relativity, in agreement with muon decay rates, supported by entropy, and - here's the kicker -
SUPPORTED BY EXPERIENCE
No. There can be nothing in modern science that is supported by experience. I forgot, the whole purpose is to try and destroy common perception, so that the physicist can appear as the new priestly class, with revelations from on high, esoteric doctrines that clash with reasonableness for the sake of appearing as cognoscendi. Obfuscation breeds respect from the masses. Clarity brings contempt.
One associated digression: to be profound, just be confusing.

I was thinking about physics again.....

Why is the relationship between mathematics and physics so strong? Remember, where Plato taught had the sign "Let no one enter who does not first know Geometry". Examine (though bad examples of philosophers) Descartes, Leibnitz, Kant (in his own way), even in modern times Edmund Husserl, - all mathematicians. Even the Pricipia is a truncated title. Maybe it is because Physics is the science of nature, and dispuisti omnia secundum numerum, (something I can't remember - probably Latin for weight) et mensuram. How the world is created is according to mathematics. To describe it in intelligible human terms we must describe it mathematically. This leads to the question of why Physicists do not call themselves philosophers - a question I have often asked. Not to cut my meandering preface short, but I stumbled across another very interesting passage from a book, I would like to painstakingly type out and comment on. Without further ado, the reason I started writing this:

It has always amazed me that the members of the scientific community always base their branch of science as the queen. Paul Davies, for example, does so in "God and the New Physics". But every time a discipline speaks of more than its content - generalizing to say something about the universe or whatever - it falls into the trap of self reference. Statements about mathematics are themselves not mathematical, but meta-mathematical. A good example that most should be familiar with is the fifth postulate argument and the various attempts to "prove" it. Trying to reduce a fundamental axiom of plane geometry to a problem of geometry is confusing the meta- for the thing in question. All sorts of paradoxes and irrationality follows.

I think most paradoxes (parenthetically) resolve in some way to self-reference.

This sentence is false.

See? Clearly it is a problem of self-reference. Even if you look into particle physics the problems see to all arise from the same. Look at any Feynman diagram for the path of an isolated electron moving from point A to point B. At any time in the moving it can generate photons and "virtual photons" that stay or decay randomly, but those photons that stay can randomly degenerate into electron-positron (positron = anti-electron) pairs that combine to destroy each other and make new photons, which in turn either degenerate or form new matter/anti-matter pairs, which in turn - and magically the electron makes it to point B - now named a renormalized electron. Most Feynman diagrams are too complicated to even admit of mathematical calculation, but that is another digression. The relationship between the photon and the electron-positron pair, and the fluid movement back and forth between them forms a self-referential pair. If you can't speak of the electron moving without these other things coming to pass, which make up the moving electron, well, then.... then what? Perhaps particle physics has gone so far off base assuming the material reality of these things, and using these assumptions to prove other things that the self-reference contained therein is inherent in the flawed assumption of physical reality. Ouch. It really doesn't please me to say that.
But on the other hand, why don't they call the bulk of what is called physics philosophy, because they are plainly expanding beyond the horizon of pure experiment and observation. Slide out of the problem of meta-physics by turning it into metaphysics.
perhaps
I'd like to leave off with one slightly plagarized (with my own spin) thought:

Beitia's First Law of Physics:

Without true philosophy, physics will always resolve into contradictions, even if you take into account Beitia's first law of physics.

I was thinking about physics again... I find it interesting the reasoning that they use and the evidence that they have, and then the bizarre leaps from evidence to theory. For example, if you see that light is wavelike and can be shifted (like the Doppler effect of a passing train) depending on the motions, and everything in the heavens is shifted toward the red end of the spectrum, you can pretty safely conclude that everything is going away from everything else. I'm fine to this point. Turn time on its head, run the tape backwards, and everything is going toward everything else. This suggests that the universe had a beginning and so forth, called the "Big Bang Theory" - which the Church said in the fifties was a good theory in terms of revelation. I'm fine to this point as well. My problem comes at the other end of the tape.

Is the expansion of the various galaxies moving fast enough to escape the inevitable pull of gravitation? Is there a break point where it all comes tumbling back together? Although this would be a fiery and exciting end of the world, I just don't see it coming to pass that way. Plus, most of the Physicists who believe in the big crunch just think everything starts all over again, bang, crunch, bang, crunch . . . this kind of endless repetition I find personally distasteful, like watching an NBA game - back and forth.
I like the idea of heat-death. Thermodynamic equilibrium. Every closed system tends to thermodynamic equilibrium, from more usable energy to less, to a uniform temperature and pressure with no disturbances. In stars, this is done by nuclear reactions that change Hydrogen (and later, Helium) into stuff (I won't say "atoms") with much higher entropy - most notably iron. To avoid wasting any more time - basically, stars run out of fuel, burn out or explode. The entire universe approaches thermodynamic equilibrium where all matter is turned into energy and all energy degenerates into heat energy and there is a vast expanse of simply radiating heat glowing a barely above absolute zero (-273C).

I guess maybe how one looks at the end of the universe is probably based on how a person views the world - the essentially optimistic enternal return of the same - or we're all tending in a direction, but that direction is not good, kind of like a negative teleologist.
but, typically, I digress

I was thinking

while reading a lecture by Paul Dirac today (nobel physicist, 1933), at the abject absurdity of mathematical constructs of nature. . . He discusses in his first lecture on how a quantum theory would mathematically arise out of a classical dynamic theory of motion, in terms of atomism. But that theory in its mathematical formalism would have to agree in principle with (at least) Special Relativity. Remember from you books that relativity not only shows the motions to be relative, but also the times. So we have to re-formulate our equations with time and distance variables - at random - so that we do not have any particular time or distance bias. Again, remember at the end of Einstein's Relativity, Cartesian co-ordinates are replaced by Gaussian co-ordinate planes by non-intersecting curves of infinite fullness. . . remember also that relative to one's frame of reference the motion can be none at all, rectalinear, curvalinear, accelerated, all describing the same world-event.
I digress....
So anyway, Dirac sets about a series of strange analytical equation transformations to solve for these randomly picked time and distance functions. Again, to be concise (hardly) he takes an undefined normal motion equation, transforms it into a Lagrangian, then, with the use of "Poisson Brackets" transforms it into Hamiltonian equations, all the while showing there must be primary and secondary contraints on the equation - also undeciphered - all for the sake of

are you ready?
ARE
YOU
READY??
i doubt anyone's made it this far anyway



I quote:
When we have the Hamiltonian, we can apply a standard method which gives us a first approximation to a quantum theory, and if we a lucky we might be able to go on and get an accurate quantum theory.


You may now exhale. The wait is over. Nature - thus explained.
NO! WAIT! the mind reels. What standard method? Approximation - I go through all this formalistic mathematical bullshit for a fucking approximation - of fucking things I can't see, or sense or anything else? Oh, I get it. I go through mathematical rigmarole for the sake of saying that a particle is everywhere in its "energy level" at the same time until I "look" at it. Oh, nonesense for the sake of - nonsense.
Before we ask the question of whether a Hamiltonian (Hamiltonian what? - Dirac never says) can approximate a quantum theory we need to ask the question
why is it necessary to believe in a Hamiltonian

(who the fuck is Hamilton?)


I will study more, and, sadly, update as necessary
thus spake Beitiathustra