Solid and convincing defense of the expression for the Ur-equation. I agree that that trumps aesthetic/abstract consideration. (plus 1) We will not be able to find agreement regarding the gist of this matter. Your thoughts are sound as always given the axiomatic ground of reality. The very notion of "reversible process" betrays the prejudice of the arrow of time. I consider the idea of the arrow of time as the most fundamental superstition of the sentient. The situation is the same for the notion of the primacy of particle/energy vs information. I hold that information is more fundamental but /will/ grant that given current understanding such views are more accurately categorized as mysticism rather than scientific. Regarding the latter methodology, however, I could bring attention to the paradoxes of quantum mechanics and outline the sketch of the essential framework that does away with at least one such paradox -- wave/particle duality per 2-slit -- IFF one is ready to accept the notion of total system coherence (-∞<= t <= +∞) [1] without any recourse to mystic notions: http://upload.wikimedia.org/wikipedia/commons/1/1f/Feynmann_... [1][edit: read trans-taneous]
>I consider the idea of the arrow of time as the most fundamental superstition of the sentient. I am interested in this statement. I would like to hear an elaboration, or be pointed to a reference on this topic (genuinely so; I'm not being sarcastic in any way). The arrow of time is taken by many, myself included, to be among the fundamental inescapable realities of nature. The trudging forward of time is the reason Lorentz, in all his genius, gave us his transforms, then searched for where his error might lie so that he could abandon the transformation of time. There's a reason Einstein didn't win the Nobel Prize for Special Relativity. He didn't really give us any new theory. He merely (and this is obviously a very superficial account of a very revolutionary idea) said, "Lorentz was right; time does transform, so let's reinterpret physics with this in mind". It was a superstition to think that time absolute, and the physicists and mathematicians of the late 19th c. had all the evidence they needed but couldn't see the forest for the trees (Lorentz, and Michelson and Morely most notably). This is why I am interested to know why you believe that the arrow of time is superstition.
> I am interested to know why you believe that the arrow of time is superstition. There is telltale evidence in both Number and Quantum Mechanics. The necessary work regarding latter has already been done, but most physicists reject the thought out of hand because of the said superstition. Surely, information flows from both past and future and the fact of wave function collapse is witness to it. Even when some, such as Roger Penrose, do consider it, they are circumspect for obvious reasons. At some point, God Willing, the task of an elaboration of the nature of the former may be accomplished, or at least a measure of progress made, should yours truly become sufficiently motivated. For now consider (the fanciful notion that) the patterns of standing waves of the bounded electron are faithfully represented by "mere" Natural numbers. And would it interest you to know that the phenomena of the incidence, too, can be shown in what is to date asserted as the "chaotic" and "mysterious" Prime Numbers? While I maintain my own personal confidence in the veracity of this matter -- based on above and certain experiences -- it would surprise me should an attempt at conveying inner perception, regardless of heroic effort to touch the asymptote that forever bars one from communicating in full, would suffice to convince you and cause you to abandon your firm faith in the construct. Certainly, if global the construct rents itself asunder in places to maintain the facade of completion -- here I refer to the singularities -- then what chance do I, a mere mortal, have to succeed in rendering the matter in full in objective form? I don't see any reason why we should have less confidence
in this kind of perception, i.e., in mathematical intuition,
than in the sense perception, which induces us to build up
physical theories and to expect that future sense perceptions
will agree with them, and, moreover, to believe that a
question not decidable now has meaning and may be decided
in the future. The set-theoretical paradoxes are hardly any
more troublesome for mathematicians than deceptions of the
senses are for the physicist. […] Evidently the "given"
underlying mathematics is closely related to the abstract
elements contained in our empirical ideas. It by no means
follows, however, that the data of this second kind, because
they can not be associated with actions of certain things
upon our sense organs, are something subjective, as Kant
asserted. Rather, they, too, may represent an aspect of
objective reality, but as opposed to the sensations, their
presence in us may be due to another kind of relationship
between ourselves and reality.
[Kurt Gödel, What is Cantor's Continuum Problem?]
How the world is, is completely indifferent for what
is higher.
God does not reveal himself in the world.
...
Whereof one cannot speak, thereof one must be silent.
[Ludwig Wittgenstein - Tractatus Logico-Philosophicus]