I am currently attending a workshop at the American Institute of Mathematics and am very busy indeed, so I am afraid that your answer will not get the full and in-depth response which it merits. My apologies.
I think that your raise some excellent points. While I am very receptive to the evolutionary approach - and while I think that it can be extended to provide a definition of mathematical beauty in terms of maximum fecundity - it leaves me thinking "and yet, and yet . . .". It simply does not, to my mind, address the thorny issue of why completely abstracted mathematical ideas should turn out to be so central to our understanding of the physical universe.
You are correct to point out that we have no notion of what an incomprehensible universe would be like. This does not answer the question of why our universe is comprehensible and, as far as I can see, does not even "dissolve" the question or render it a "pseudo-question. (I like the notion of "dissolve" vs solve, by the way!)
I don't understand what you mean by nature "giving reality" to mathematical notions. This seems to avoid the question.
I am only afraid of embracing theological baggage to the extent of claiming that it answers beyond doubt the question before us. I am quite happy to load that baggage onto my life-train for other reasons, reasons which tend to subjectively exclude a Spinozan pantheism. I do agree with you that the potentiality for intelligence evidenced by our existence is an awe-inspiring aspect of the universe.
Hi, Anonymous, and thanks for a great comment.
I am currently attending a workshop at the American Institute of Mathematics and am very busy indeed, so I am afraid that your answer will not get the full and in-depth response which it merits. My apologies.
I think that your raise some excellent points. While I am very receptive to the evolutionary approach - and while I think that it can be extended to provide a definition of mathematical beauty in terms of maximum fecundity - it leaves me thinking "and yet, and yet . . .". It simply does not, to my mind, address the thorny issue of why completely abstracted mathematical ideas should turn out to be so central to our understanding of the physical universe.
You are correct to point out that we have no notion of what an incomprehensible universe would be like. This does not answer the question of why our universe is comprehensible and, as far as I can see, does not even "dissolve" the question or render it a "pseudo-question. (I like the notion of "dissolve" vs solve, by the way!)
I don't understand what you mean by nature "giving reality" to mathematical notions. This seems to avoid the question.
I am only afraid of embracing theological baggage to the extent of claiming that it answers beyond doubt the question before us. I am quite happy to load that baggage onto my life-train for other reasons, reasons which tend to subjectively exclude a Spinozan pantheism. I do agree with you that the potentiality for intelligence evidenced by our existence is an awe-inspiring aspect of the universe.