So what does “gone wild” mean? Your paragraph about this is not very charitable to the pure mathematician.
Say that mathematics is about generating compressed models of the world. How do we generate these models? Surely we will want to study (compress) our most powerful compression heurestics. Is that not what pure math is?
I agree I was too brief there. The original motivation for math was to help figure out the physical world. At some point (multiple points, really, starting with Euclid), perfecting the tools for their own sake became just as much of a motivation. This is not a judgement but an observation. Yes, sometimes “pure math” yields unexpected benefits, but this is more of a coincidence then the reason people do it (despite what the grant applications might say).
Say that mathematics is about generating compressed models of the world. How do we generate these models? Surely we will want to study (compress) our most powerful compression heuristics. Is that not what pure math is?
The main reason is pure curiosity without any care for eventual applicability to understanding the physical world. Pretending otherwise would be disingenuous.
Theoretical physics is not very different in that regard. To quote Feynman
Physics is like sex: sure, it may give some practical results, but that’s not why we do it.
I guess I always took the phrase “unreasonable effectiveness” to refer to the “coincidence” you mention in your reply. I’m not really sure you’ve gone far toward explaining this coincidence in your article. Just what is it that you think mathematicians have “pure curiousity” about? What does it mean to “perfect a tool for its own sake” and why do those perfections sometimes wind up having practical further use. As a pure mathematician, I never think about applying a tool to the real world, but I do think I’m working towards a very compressed understanding of tool making.
I guess I always took the phrase “unreasonable effectiveness” to refer to the “coincidence” you mention in your reply.
Unreasonable effectiveness tends to refer to the observation that the same mathematical tools, like, say, mathematical analysis, end up useful for modeling very disparate phenomena. In a more basic form it is “why do mathematical ideas help us understand the world so well?”. The answer suggested in the OP is that the question is a tautology: math is a meta-model build by human minds, not a collection of some abstract objects which humans discover in their pursuit of better models of the world. The JPEG analogy is that asking why math is unreasonably effective in constructing disparate (lossy) models is like asking why the JPEG algorithm is unreasonably effective in lossy compression of disparate images.
The “coincidence” part referred to something else: that pursuing math research for its own sake may occasionally work out ot be useful for modeling the physical world, number theory and encryption being the standard example.
As a pure mathematician, I never think about applying a tool to the real world, but I do think I’m working towards a very compressed understanding of tool making.
When I talk to someone who works in pure math, they usually describe the motivation for what they do in almost artistic terms, not caring whether what they do can be useful for anything, so “tool making” does not seem like the right term.
So what does “gone wild” mean? Your paragraph about this is not very charitable to the pure mathematician.
Say that mathematics is about generating compressed models of the world. How do we generate these models? Surely we will want to study (compress) our most powerful compression heurestics. Is that not what pure math is?
I agree I was too brief there. The original motivation for math was to help figure out the physical world. At some point (multiple points, really, starting with Euclid), perfecting the tools for their own sake became just as much of a motivation. This is not a judgement but an observation. Yes, sometimes “pure math” yields unexpected benefits, but this is more of a coincidence then the reason people do it (despite what the grant applications might say).
The main reason is pure curiosity without any care for eventual applicability to understanding the physical world. Pretending otherwise would be disingenuous.
Theoretical physics is not very different in that regard. To quote Feynman
I guess I always took the phrase “unreasonable effectiveness” to refer to the “coincidence” you mention in your reply. I’m not really sure you’ve gone far toward explaining this coincidence in your article. Just what is it that you think mathematicians have “pure curiousity” about? What does it mean to “perfect a tool for its own sake” and why do those perfections sometimes wind up having practical further use. As a pure mathematician, I never think about applying a tool to the real world, but I do think I’m working towards a very compressed understanding of tool making.
Unreasonable effectiveness tends to refer to the observation that the same mathematical tools, like, say, mathematical analysis, end up useful for modeling very disparate phenomena. In a more basic form it is “why do mathematical ideas help us understand the world so well?”. The answer suggested in the OP is that the question is a tautology: math is a meta-model build by human minds, not a collection of some abstract objects which humans discover in their pursuit of better models of the world. The JPEG analogy is that asking why math is unreasonably effective in constructing disparate (lossy) models is like asking why the JPEG algorithm is unreasonably effective in lossy compression of disparate images.
The “coincidence” part referred to something else: that pursuing math research for its own sake may occasionally work out ot be useful for modeling the physical world, number theory and encryption being the standard example.
When I talk to someone who works in pure math, they usually describe the motivation for what they do in almost artistic terms, not caring whether what they do can be useful for anything, so “tool making” does not seem like the right term.