In fact, I'll assert here (entirely without proof for now ;) that time itself is a side-effect of computational cognition: http://www.wolframalpha.com/input/?i=e%5E%28i*pi%29+%2B1 (the mother of all equations and not subject to time or any evolutionary process).
G is the result of a measurement. It is different than Pi, because it will not fall out of the language itself. You can derive Pi without ever picking up a circular object, but you cannot find G without measuring the interactions of objects. Like G, time is a result of measurement. That said, I am actually willing to entertain that time and cognition might be inextricably linked in the same way that green and eyesight might be inextricably linked. Of course 500nm EM wavelengths probably existed before eyes and a brain that could detect them, but the notion of green did not. Time might be similar. Time might be a transformation of a physical characteristic into one that is useful for cognition (In this case, it'd be related to entropy, I suppose). The physical reality that underpins time probably existed before cognition, but time itself as experience might be a product of our brains.
I did skim above (and the other one below) and will get back to you, but in the interim just lets get some definitions straight: Define what "cognition" means to you. What is the most fundamental act of cognition, in your conception?]
Define what "cognition" means to you. My first stab would be something like: 'localized reflection-based intent'. That is, a place that patterns in a way that is representative of external patterns, which results in the genesis of unique patterns (confined to and defined by the limits of that place) which result in a change of the environment immediately about that place. I think I fell in! :D What is the most fundamental act of cognition, in your conception? In that sense, I'd say it would be: A mass moving under its own power in a manner that didn't reflect the mechanism of motion. p.s. I like my second answer better.
You mean the separation between the patterns? The problem I have here, and what lead me to movement, was reflection, and/or cause and effect. What is not a ripple in the pond? I'll admit that 'movement that doesn't reflect the mechanism of motion' probably falls short, but the 'doesn't reflect the mechanism of motion' is a partition of sorts. Maybe just one that isn't inclusive enough. See what I mean about a rabbit hole? But you said 'cleaving', and that suggests to me action. As if cognition is (or is the result of) the action of separation between the two patterns, making the external and the internal? How could that be defined? What makes my brain not a pond? :) My actions don't look like the effect of a pebble drop, but where does the disengagement occur? Or does it? Could it be a sufficiently obscuring complexity that depends on not just the perceived actor, but the observer? Is cognition in the eye of the beholder?
I simply assert the act of partitioning is the most fundamental cognitive action. [Related: is one a prime or composite ..] You mentioned "patterns" and I am simply saying "let's build one". Flip it and look at it another way (tool centric): I propose having a semantic cleaver in our tool-kit as being of primary importance to taking cognitive action.
- A substrate of some kind is assumed.
But is it? This is something that I simply have to question. In fact, if I have any religion whatsoever, it's probably my refusal to concede that it works that way, :) -that there is anything that is not bootstrapped. I think that instead of defining existence, we should simply see if we can define context, and then the boundaries of context. It's my gut feeling that in the nature of these boundaries, we have answers to our question. This is also the seed of the many worlds interpretation, IMO. But, not simply just that. Although I dislike the 'many worlds' interpretation, I don't disagree with the motivation behind it. I guess this might be why (off the cuff here): Cognition is a context. Instead of delineating between the pattern and the perceived, maybe there is more fruit to be found looking at the nature of that context as it relates to others. What are the boundaries of a cognitive scenario? Rather than define it from within, maybe we can define it from without. In that sense, yes cognition is a reflection. But, if we are to compare it to other reflections that we don't consider to be cognitive scenarios, we'd find that the cognitive reflection is always incomplete. Maybe cognition isn't something remarkably greater than, but something remarkably less than. Maybe cognition is the gift of imperfect reflection? And what is gained by that imperfection, is space that must be filled. And what is it filled with? -The only thing available, other imperfect reflections. This is something that feels unique and free to me.reality as a text that is read by a reader.
Indeed, that is the bone of our contention, is it not? A rather negative way of looking at thing, and that superfluous negation of the reality of The One ... ;) Or to be more precise, e^ipi is the temporal realm of phase spaces which without one is but naught ... [1 as they say is not a prime, nor a composite. It is primordial.] > Time [is] a side [effect] of entropy. http://mathworld.wolfram.com/Entropy.html -- you're gonna have a hard time @b_b disentangling entropy (defined axiomatically by "state") from "time" ...
As to the e^ipi=-1. I prefer it that way, because that is its reality. The expression e^it loses its meaning (its rotation in phase space) if a constant is arbitrarily is added to it. I think its more beautiful to let it evolve with time and notice that it falls on -1 at precisely pi.
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]