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How math relates to the physical world is not at all clear. Like yes 2 apples clearly makes sense, but non physical quantities like 10^241 of anything start to

by meroes 3y ago

How math relates to the physical world is not at all clear. Like yes 2 apples clearly makes sense, but non physical quantities like 10^241 of anything start to break down the relationship. It’s not the abstraction that gets me usually, it’s the lack of an explicit relationship between math and physics. I’m sorry but personally I am not satisfied by what I learned in my math and math/science classes on this. It started for me day 1 of high school physics and I’m now graduating in 1 month in undergrad applied mathematics. I felt reinforced when I read that Plato clearly delineated the two “realms”. I was hopeful a single math teacher would discuss this idea for one lesson, but it never happened. Plato was a champion of math who recognized the division. I’m not one of those disbelievers in complex numbers or anything like that, but if some model formulates precise physical scenarios, we should be able to have ample cross-over language. Even the explanation for why honeycombs have six sides: there is always some kind of fumble from going from the mathematical reason to the physical reason. It’s the paradigmatic example of mathematical explanations for physical phenomena, and between two heavily studied fields, and yet we fumble it continually. What is it about the mathematical hexagon which determines the physical honeycomb? These questions are at the height of philosophy of mathematics, e.g. Mark Colyvan, yet are still disputed and we act like it’s all so obvious. I get it works, but don’t tell me it’s not mysterious, because 6 years in now I’m not at all satisfied and have little confidence it will be mentioned in future math/science classes.

kriops 3y ago
Can you elaborate on why you describe 10^241 as non-physical? Just because it's too large to describe anything physical? Anyhow, Aristotle had another take on the problem of universals, and taking his view that every concept abstract or otherwise can only exist as part of our physical world (I'm not a philosopher, and there are variations on both themes that different people subscribe to), then your supposition would be nonsense in itself. Stated as a question: What is your reasoning for preferring a Plato-like model of the world vs. a Aristotle-like one? (If it needs to be said: This is not a gotcha or anything - your opinion intrigued me, and I'm curious as to your reasoning)
- gbjw 3y ago
  Well, based on a quick Google, there are approximately 10^186 Planck-length volumes in the known universe. So 10^241 is not physical in the sense that there is no way to 'realize' a set of 10^241 things. Another related notion is that there is no way to 'realize' an irrational 'number' -- sqrt(2) can be defined but we can never draw a length of sqrt(2).
  - anon291 3y ago
    It really depends what you consider 'real'. It is actually pretty straightforward to realize a representation of 10^241 (you just did). Why does that make it any less real than the digit 2, which represents two things, but is actually just itself one thing. > Another related notion is that there is no way to 'realize' an irrational 'number' -- sqrt(2) can be defined but we can never draw a length of sqrt(2). Again, it's unclear what anyone means by things like 'sqrt(2)'. Why is drawing a thing of length sqrt(2) any different than drawing a thing of length 1? If I draw a thing of length 1 and say it's a line of length 1, then why is that different than my drawing the same line, claiming its length is sort(2) and then pointing out that it's actually now impossible to mark where 1 would appear along its length?
    - gbjw 3y ago
      > It really depends what you consider 'real'. It is actually pretty straightforward to realize a representation of 10^241 (you just did). Why does that make it any less real than the digit 2, which represents two things, but is actually just itself one thing. One is a map, and the other is the territory. Both 'real' in some sense but a map without the territory feels less 'grounded' (pun?). > Again, it's unclear what anyone means by things like 'sqrt(2)'. Why is drawing a thing of length sqrt(2) any different than drawing a thing of length 1? If I draw a thing of length 1 and say it's a line of length 1, then why is that different than my drawing the same line, claiming its length is sort(2) and then pointing out that it's actually now impossible to mark where 1 would appear along its length? Perhaps a more precise way to describe the situation is that one can define one or the other as a base 'unit' but you can never get one from the other (they are 'incommensurate', as the greeks would say). Irrational numbers can be defined but not 'realized' (or 'constructed') in the same way that the rationals can.

by meroes 3y ago

kriops 3y ago

Can you elaborate on why you describe 10^241 as non-physical? Just because it's too large to describe anything physical? Anyhow, Aristotle had another take on the problem of universals, and taking his view that every concept abstract or otherwise can only exist as part of our physical world (I'm not a philosopher, and there are variations on both themes that different people subscribe to), then your supposition would be nonsense in itself. Stated as a question: What is your reasoning for preferring a Plato-like model of the world vs. a Aristotle-like one? (If it needs to be said: This is not a gotcha or anything - your opinion intrigued me, and I'm curious as to your reasoning)

gbjw 3y ago
Well, based on a quick Google, there are approximately 10^186 Planck-length volumes in the known universe. So 10^241 is not physical in the sense that there is no way to 'realize' a set of 10^241 things. Another related notion is that there is no way to 'realize' an irrational 'number' -- sqrt(2) can be defined but we can never draw a length of sqrt(2).
- anon291 3y ago
  It really depends what you consider 'real'. It is actually pretty straightforward to realize a representation of 10^241 (you just did). Why does that make it any less real than the digit 2, which represents two things, but is actually just itself one thing. > Another related notion is that there is no way to 'realize' an irrational 'number' -- sqrt(2) can be defined but we can never draw a length of sqrt(2). Again, it's unclear what anyone means by things like 'sqrt(2)'. Why is drawing a thing of length sqrt(2) any different than drawing a thing of length 1? If I draw a thing of length 1 and say it's a line of length 1, then why is that different than my drawing the same line, claiming its length is sort(2) and then pointing out that it's actually now impossible to mark where 1 would appear along its length?
  - gbjw 3y ago
    > It really depends what you consider 'real'. It is actually pretty straightforward to realize a representation of 10^241 (you just did). Why does that make it any less real than the digit 2, which represents two things, but is actually just itself one thing. One is a map, and the other is the territory. Both 'real' in some sense but a map without the territory feels less 'grounded' (pun?). > Again, it's unclear what anyone means by things like 'sqrt(2)'. Why is drawing a thing of length sqrt(2) any different than drawing a thing of length 1? If I draw a thing of length 1 and say it's a line of length 1, then why is that different than my drawing the same line, claiming its length is sort(2) and then pointing out that it's actually now impossible to mark where 1 would appear along its length? Perhaps a more precise way to describe the situation is that one can define one or the other as a base 'unit' but you can never get one from the other (they are 'incommensurate', as the greeks would say). Irrational numbers can be defined but not 'realized' (or 'constructed') in the same way that the rationals can.