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Is math real? The answer has major practical and philosophical implications

3 points by hsnewman 3y ago

injb 3y ago
I lean towards the "we invented it" camp. I used to assume that most phenomena in the physical world were approximations of mathematical perfection, which I think is the Platonic view (but I'm not sure). But then I had a different thought: what if it's the other way around? Take the famous Zeno's paradox about motion being impossible. The argument is basically that there's an infinite amount of space between any 2 points. So you can't travel from one point to another without traversing an infinite amount of space. Most people now say that Zeno's reasoning was wrong logically. But I don't think so. I think his mistake was his assumption that continuous motion is the right model. After that, his reasoning is fine. In other words, if it is possible to move from one point to another, then this refutes continuous space. Motion is inconsistent with continuous space. Platonic continuity is the illusion. The discrete is not an approximation for a true, continuous underlying reality: it's exactly the other way around. Continuity is the flawed, approximate model that our brains have come up with to model a discrete underlying reality. Why should our brains have developed this way? I can only guess that nature found this the most efficient thing that worked well enough. I'm sure many smarter people before me have thought of this and figured out what it would mean for physics so I'm probably wrong. But it certainly helped me to see the other side of the argument and I've never been able to see the Platonic view as anything but naïve since this occurred to me.
- DemocracyFTW2 3y ago
  Discontinuity rather than continuity as the fundamental principle of spacetime would certainly align nicely with the experience that whenever the maths yields infinity, the corresponding physics become meaningless. It also meshes with the impossibility of moving a mass by an infinitesimal distance and the inherent lower limit of energy needed to record one bit of information... so, yeah.
- nh23423fefe 3y ago
  I wouldn't say invented. I would say discovered. To me, math is just a particular kind of symbol game. All the math that ever could exist already does and you could just enumerate formulas mechanically. What humans do is provide interpretations of the formula. I think Platonism is incoherent because most phenomena aren't approximations. Consider 'tree' or 'electron' which fail in different ways. An ideal tree is incoherent, tree is a fuzzy label not a category of objects. Every electron is identical and so the idea of there being a platonic electron makes no sense. I'm resisting your rejection of continuity but I can't quite articulate why to myself, it's something to do with 1 to 1 correspondences of possible measurements I think. Imagine some process which results in a particle moving in some direction. Moving from point to point is analogous to emitting some particle in any direction. And then you could imagine a sphere of detectors of any size. Saying that space is discontinuous is like saying "when the sphere is large enough its not possible to trigger 2 adjacent detectors because angles are not continuous" This seems false to me.
bell-cot 3y ago
For me, the big problem with most philosophical questions like this ("Is math real?") is that they seem like cheap emotional click-bait spun around some poorly-defined word and/or concept. Dear Philosophers: Why can't you ever own up to the only real issue being that fully defining X is neither intuitive nor trivial?

3 points by hsnewman 3y ago

injb 3y ago

I lean towards the "we invented it" camp. I used to assume that most phenomena in the physical world were approximations of mathematical perfection, which I think is the Platonic view (but I'm not sure). But then I had a different thought: what if it's the other way around? Take the famous Zeno's paradox about motion being impossible. The argument is basically that there's an infinite amount of space between any 2 points. So you can't travel from one point to another without traversing an infinite amount of space. Most people now say that Zeno's reasoning was wrong logically. But I don't think so. I think his mistake was his assumption that continuous motion is the right model. After that, his reasoning is fine. In other words, if it is possible to move from one point to another, then this refutes continuous space. Motion is inconsistent with continuous space. Platonic continuity is the illusion. The discrete is not an approximation for a true, continuous underlying reality: it's exactly the other way around. Continuity is the flawed, approximate model that our brains have come up with to model a discrete underlying reality. Why should our brains have developed this way? I can only guess that nature found this the most efficient thing that worked well enough. I'm sure many smarter people before me have thought of this and figured out what it would mean for physics so I'm probably wrong. But it certainly helped me to see the other side of the argument and I've never been able to see the Platonic view as anything but naïve since this occurred to me.

DemocracyFTW2 3y ago
Discontinuity rather than continuity as the fundamental principle of spacetime would certainly align nicely with the experience that whenever the maths yields infinity, the corresponding physics become meaningless. It also meshes with the impossibility of moving a mass by an infinitesimal distance and the inherent lower limit of energy needed to record one bit of information... so, yeah.
nh23423fefe 3y ago
I wouldn't say invented. I would say discovered. To me, math is just a particular kind of symbol game. All the math that ever could exist already does and you could just enumerate formulas mechanically. What humans do is provide interpretations of the formula. I think Platonism is incoherent because most phenomena aren't approximations. Consider 'tree' or 'electron' which fail in different ways. An ideal tree is incoherent, tree is a fuzzy label not a category of objects. Every electron is identical and so the idea of there being a platonic electron makes no sense. I'm resisting your rejection of continuity but I can't quite articulate why to myself, it's something to do with 1 to 1 correspondences of possible measurements I think. Imagine some process which results in a particle moving in some direction. Moving from point to point is analogous to emitting some particle in any direction. And then you could imagine a sphere of detectors of any size. Saying that space is discontinuous is like saying "when the sphere is large enough its not possible to trigger 2 adjacent detectors because angles are not continuous" This seems false to me.

bell-cot 3y ago

For me, the big problem with most philosophical questions like this ("Is math real?") is that they seem like cheap emotional click-bait spun around some poorly-defined word and/or concept. Dear Philosophers: Why can't you ever own up to the only real issue being that fully defining X is neither intuitive nor trivial?