Let me start with PIZINE. I just noticed that the posts to that mag will appear every month the mag is out, and perhaps with editing. So it's not really a forum. It's more of a letters to the editor. You are likely to find this forum more responsive.
You appear to be learned, certainly more learned than I in the foundations of math. I am at most an applied mathematician. So as Harvey put it recently, I have to find meaning in math. For a pure mathematician, the math alone is sufficient.
But I am more of a physicist than a mathematician. I have not found god in math, but I see a glimmer of god in physics and even more in astronomy.
Regarding Cantor, I was just quoting from the PIZINE site. I personally do not think much of infinity (pun intended). I have read about Godel's theorem and that of his successor (Chapin?) who claims math is random with only islands of rationality. I did not know about the twin prime problem. And I confess to never thinking much about tautology, ontology, epistemology- Harvey is more the guy to think in these terms, if I may talk for him. Some other posters should be just ignored, as you will soon find out for yourself. Learned types are not respected here by some posters.
So I do not see god in math. I think that math is remarkable, but suspect that most of the godhead is subject to math, rather than the creator of math. My view is actually anthropic. If math were not so remarkable, we would not exist to wonder about it. The real wonder is that we can wonder.
So let me try to address your comments and questions in their order:
"I agree that there certainly seems to be something ‘divine’ about the apparent truth and beauty of mathematics."
As above I see it as anthropic
"I myself am an agnostic who is still struggling to reconcile my faith in science with my very human --and in my case, very compelling-- need to find meaning"
I look more to physics for meaning. I, however, find the greatest meaning in reincarnation and the evolution of the soul, including the possibility that we may in some sense be immortal and constantly progressing towards an ideal that is nominally referred to as god.
I have found physics reasons to think that the supernatural and reincarnation may exist, as described in a Dark Matter Model of Consciousness, which I published at the Arizona Quantum Mind 2003 conference (Email me at email@example.com for a copy)
I agree that science requires faith as most of us must rely on the honesty of publications and the experimentalists that verify theories. I have become less faithful as I learn more about the assumptions that go into even verified theories. It seems that drastically differing assumptions can yield the same equations. So we cannot trust that these assumptions are reflective of a reality.
For example, Feymann’s QED, which uses backward time traveling positrons to interact with electrons. The alternate interpretations of quantum theory imply drastically differing realities. Yet they all agree with experiment because the final equations are the same. As a result, one is tempted to adopt a Platonic view of physics where the equations somehow exist in nature, but perhaps none of the building blocks of the equations like waves and particles. Perhaps Cantor is on the right track.
”Yaniru, I have a question for you: If you see God in mathematics, then I assume that you are a Platonist? (Sorry for the philosophical jargon... do you believe that mathematics exists "out there" independently of us? ). Or, do you instead believe that mathematics is an abstraction of human consciousness? ”
Well, at this point I see Plato in physics more than god in math. I think math is real, like Plato did, rather than being n abstraction of consciousness. But that does not mean god exists, (e.g., meaning a supernatural, invisible intelligence, with perhaps multiple levels of abstraction and perhaps the capability to communicate intelligently to physical intelligences). The math, I believe, makes god a possibility, provided a medium exists in which the intelligence can exist, which is as well invisible and supernatural.
”, mathematics is indeed a mirror to nature,. “ Only at low energy- low energy physics, it does seem to guide biological growth, but not evolution. However, math seems to fail us in developing high energy physical theory.
”But on the other hand, our brains are the best "pattern detectors" in existence, far better than any computer. Are these patterns actually all around us? Or are we just very good at imposing/ detecting patterns where ever we look for them? “
I think the patterns exist in nature, provided we do not look too closely. Then they are replaced by other patterns and finally by a seeming chaos. Perhaps string physics or loop quantum theory will provide fundamental patterns of existence. But I am not confident that they will, because the foundations of physics seem ambiguous as explained above.
It may be that our physical world is governed by equations rather than physics. In quantum mechanics it does seem that information is more dominant than matter.
So when I was young. I used to think that the answer to god questions lay in microscopic physics. Now I suspect it is more in macroscopic mathematics. So I am getting to be more of a Platonist. Glad that you pointed that out.
My faith in the existence of a supernatural medium is based on physics. But my faith in something like a god or fate that seems to control my life with an uncanny set of coincidences is based on the patterns that I read into those experiences. So my godlike faith may be an abstraction of my consciousness. It certainly is an abstraction of my conscious experiences. Perhaps if I could imagine physics mechanisms by which a supernatural intelligence could control coincidence, my faith would then be based on physics. But for now, my faith is empirical, based on personal, subjective experience.
“If you came to find your faith by avenues other than by asking questions like these, then I won't burden you with feeling an obligation to provide me with any sort of an answer”
Yes and no. My faith came from different avenues. It started with the possibility of OBE- out of body experience, which meant that a supernatural medium must exist. Then it got reinforced by coincidence and conscious experience. But nonetheless in addressing your questions, I have learned about myself. One cannot ask more of a forum, or a poster.
To elaborate on the title of this post, I see intelligence being made possible by math and physics- in short by nature. I see the intelligence of god as one that understands nature sufficiently to guide biological life including humanity. It is possible that some very abstract form of god had a hand in creating this nature, perhaps over a great many generations of universes, which seem to be born and grow old. But once created, the god in all its levels of abstraction, interacts with the universe subject to its laws, but perhaps knows how to bend them. So bottomline our human existence is like practice for being a god.
Richard aka yanniru