Dear Tejinder,
thank you also for your reply.
To make sense out of the supposed dichotomy of timeless mathematics and a world of time, one could well say that the very concept of time is timeless, in the sense that there is no static state of things. So, in this sense, there will always be some dynamics irresolvably linked with existence.
I guess when you speak of mathematics being timeless, you mean that the truths that are expressed by mathematics should be timeless, but the concrete arrangement of some mathematical relationships must not. I am not sure whether or not this is also true for you for a timeless consciousness.
But I am led to conclude that it must be in some way true, since if mathematics and the neural pathways in the brain turn out to be identical, then what we have is a dynamical conscious pattern (mind) that is only and only possible due to the fact that mathematics has a time-dependent part.
I think what you have done is to assume that a certain subset of mathematical truths are able to generate a dynamical process that is timeless exactly in the sense that it was, is and will forever take its dynamical course. A result of this dynamical course is a human self-aware mind. Although these lines of reasoning are somewhat coherent, I have a problem with them.
Since mathematics is defined as timeless truths and consciousness being possible at all within the framework of pure mathematics as also a timeless truth, nothing in the form or in the substance of a human brain or even in the whole evolution of brains seems to indicate that its mathematical grounding must result in exactly the architecture of brains as we know them.
Surely, it would be thinkable that in the infinite realms of mathematics, there exist other mathematical patterns that also have the dynamics to generate consciousness, on the basis of some other architecture of some clumb of matter than the brains as we know them. But either way, I would consider such identities of a certain clumb of matter with some mathematical pattern that is capable of self-awareness as either arbitrary or anthropic. Arbitrary for the case that one presupposes an infinite - and therefore somewhat infinitely powerful - realm of mathematics, or anthropic for the case one claims that consciousness is only and only possible within such clumbs of matter as we know them - namely human or animal brains.
In a very real and unequivocal sense, the terms 'law', 'thing', 'thing-law', 'law-time' and 'thing-time' are encodings that intertwine certain aspects and by decoding disentangle them again. In another real sense this is indeed an algorithmic process on the basis of an algorithm. Since the mind is aware of this fact, it may conclude that itself must entirely be the result of algorithms. But as I outlined in my own essay, such a conclusion does only close a circle, means it is consistent. If I look into the world, and especially into psychiatry, I see that the mind does not exclusively operate on the basis of consistency, but also can operate on the basis of inconsistent, irrational 'algorithms', even madness.
The big question is why mathematics should prefer consistency over inconsistency to facilitate minds at all and should be destined to do this in the form of brains. Making an analogy with the famous Boltzmann brain, such brains may well give one the impression of a lawless, chaotic, irrational external reality. So the big question for me is whether or not it is sufficient for a rational mind to notice that itself operates according to some stable rules to come to the conclusion that it is entirely based on algorithmic processes that are at the end pure mathematics (although in dynamical clothes). I suspect that this is only a kind of self-confirmation where a certain circle of reasoning is closed and additional reasons are excluded a posteriori.
Anyways, I highly appreachiate if you like to further engage in this discussion, since these are very important, yes, fundamental questions I think. Moreover, I would like to know how your approach differs from Max Tegmark's approach, the latter i consider as an hypothesis that intertwines many fundamental questions and therefore, albeit being highly controversial, deserves more discussion - and of course also critics.
Hope for your reply.
Stefan Weckbach