What has interested me lately is mathematical aporia like the three body problem. My question would be, as one who has really only theoretical understanding of mathematics--e.g. it functions as a language--is when this language breaks down and ceases to be able to circumscribe the very phenomena under investigation. Any thoughts on this?
Sorry for the late response, this is a rather difficult question. I generally tend to hold that mathematics aren't merely a tool which we created to be able to construct models which "represent" reality but rather that there is something fundamentally mathematical about the intelligibility of reality. I believe this because it flees from the paradigm Cartesian "representational" rationalism and doesn't reduce the intelligible order of the universe to something purely phenomenological. And this would in theory mean that no physical phenomena can't be mathematically circumscribed. But of course, in practice, this does seem to break down at times as you say. I am not very well-read on such mathematical aporia, admittedly but the three-body problem has captured my attention too, while I don't have the boldness of some physicists to claim we will never have an explanation for the three-body problem, it might be philosophically sound to consider the three-body problem as something of a physical antinomy. If we venture into using symbolic thinking in a Pageauvian sense and try to understand the greater cosmic scope of this problem, we could maybe say that the three-body problem is a symbolic natural reflection of the Divine Paradox of the Trinity, assigning a higher meaning to what seems to be an exception to a rule in physics. Just a few thoughts, I hope this gives you at the very least something interesting to think about!
What has interested me lately is mathematical aporia like the three body problem. My question would be, as one who has really only theoretical understanding of mathematics--e.g. it functions as a language--is when this language breaks down and ceases to be able to circumscribe the very phenomena under investigation. Any thoughts on this?
Sorry for the late response, this is a rather difficult question. I generally tend to hold that mathematics aren't merely a tool which we created to be able to construct models which "represent" reality but rather that there is something fundamentally mathematical about the intelligibility of reality. I believe this because it flees from the paradigm Cartesian "representational" rationalism and doesn't reduce the intelligible order of the universe to something purely phenomenological. And this would in theory mean that no physical phenomena can't be mathematically circumscribed. But of course, in practice, this does seem to break down at times as you say. I am not very well-read on such mathematical aporia, admittedly but the three-body problem has captured my attention too, while I don't have the boldness of some physicists to claim we will never have an explanation for the three-body problem, it might be philosophically sound to consider the three-body problem as something of a physical antinomy. If we venture into using symbolic thinking in a Pageauvian sense and try to understand the greater cosmic scope of this problem, we could maybe say that the three-body problem is a symbolic natural reflection of the Divine Paradox of the Trinity, assigning a higher meaning to what seems to be an exception to a rule in physics. Just a few thoughts, I hope this gives you at the very least something interesting to think about!