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This dismissal seems to implicitly accept Cartesian dualism, maybe? There's not much difference between a human engaging in mathematical reasoning and say, a co

This dismissal seems to implicitly accept Cartesian dualism, maybe? There's not much difference between a human engaging in mathematical reasoning and say, a computer enumerating proofs. Mathematical reasoning is a form of computation. Computation comprises physically realizable processes that are equivalent in a certain way. It is this equivalence between computational (and hence physical) processes which allows us to talk about mathematics as something "outside" of the human mind which itself is only one sort of computational physical process. As far as mathematics is concerned, the human mind isn't privileged. So if mathematics doesn't exist outside of people's minds, it certainly doesn't exist within it either. But then what are we talking about? Computation is a finitary process, but its behavior is informed by infinity. Even if infinity doesn't "exist" in the sense that we could ever observe and comprehend it, we can see its shadow everywhere. > The ability to notice some inherent patterns of natural phenomena, such as the ratio of a circle's circumference to its diameter, does yield this ratio to be immortal, or any other inferred constant. I have to disagree. The fact that there are patterns to notice is a deep mystery of the world and prefigures mathematical truth. Things are different in some ways but the same in other ways. Trivial, but fundamental. The fact that we can find mathematics everywhere relies on this fact.

lngnmn 10y ago
Math, as the science of patterns, captures some patterns of what is. There is absolutely nothing extraordinary about it. There is some necessary order, which physicists and philosophers are truing to grasp, and the language of choice to describe physics is math. But it is only a systematized and logically structured observations of what is. What is a deep mystery for me, is that life, it seems, does not have the notion of counting at all, at least on the level of cell biology. It is uses "pure functional" molecular structures as "code and data" and message-passing as its "language", but this is quite another topic. This, BTW, is a hint to justify the principle that what cannot exist without an observer does not exist in principle. There is, obviously the notion of a distance, but not necessarily of space. There is notion of a process as a result of applied forces, but not necessarily of duration and time. Time is a derivative. Derivatives does not exist, physical phenomena do.

lngnmn 10y ago

Math, as the science of patterns, captures some patterns of what is. There is absolutely nothing extraordinary about it. There is some necessary order, which physicists and philosophers are truing to grasp, and the language of choice to describe physics is math. But it is only a systematized and logically structured observations of what is. What is a deep mystery for me, is that life, it seems, does not have the notion of counting at all, at least on the level of cell biology. It is uses "pure functional" molecular structures as "code and data" and message-passing as its "language", but this is quite another topic. This, BTW, is a hint to justify the principle that what cannot exist without an observer does not exist in principle. There is, obviously the notion of a distance, but not necessarily of space. There is notion of a process as a result of applied forces, but not necessarily of duration and time. Time is a derivative. Derivatives does not exist, physical phenomena do.