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Amen. Not a mathematician, but this perfectly articulates my thoughts on the subject. >the real world does not contain infinities I have no idea what "real wo

Amen. Not a mathematician, but this perfectly articulates my thoughts on the subject. >the real world does not contain infinities I have no idea what "real world" even means, but I'd say that infinity does not exist within anything that can be conceptualized.

thomasahle 9y ago
> infinity does not exist within anything that can be conceptualized. Yet math is consistently being conceptualized? Enabling clear thinking about concepts outside of the real world is the while point of math.
- Chris2048 9y ago
  > math is consistently being conceptualized What does this mean?
- placebo 9y ago
  >Yet math is consistently being conceptualized? Sure, how else could we capture it or convey it to others? The thing is that I don't see it as that different than conceptualizing things in the "real world". In the latter, conceptualization is done on input of the senses, while in math conceptualization is done on inputs from a higher level of abstraction. In both cases, something is defined and then manipulated for something useful. It's just that I believe that whatever is defined automatically becomes a finite concept otherwise it could not be grasped and manipulated, and a finite infinity seems problematic...
Tloewald 9y ago
When your hand moves, does it pass through an infinite or a finite number of positions at a finite or infinite points in time? Infinity need not be big.
- cobbzilla 9y ago
  Could one argue that the Planck length/time means the number of points in space/time in your example is finite?
- danharaj 9y ago
  Why does the continuum need to be made of points? Can you really show me a particular point in space?
  - deleted 9y ago
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DonbunEf7 9y ago
Quantum mechanics has several facets which correspond to path integrals, infinite-dimensional operators, and infinite series, sums, and products.
- deleted 9y ago
  [deleted]
- placebo 9y ago
  True - you don't even need to venture into quantum mechanics, the concept of infinity has been useful in practical science far before anyone dreamed of quantum mechanics - but there's a difference between a definition of what happens to a formula when a limit approaches infinity and claiming to somehow understand infinity as a concept. I mean when you deal with infinite-dimensional operators, infinite-series etc. does it matter what ordinal of infinity is used?
mcguire 9y ago
If you are going to play with the "real world", you are going to have to deal with continuous math; i.e. the real numbers at least. At which point you get to deal with infinity somehow.
- Viliam1234 9y ago
  I believe that potential infinity (i.e. the idea of intervals becoming ever smaller and smaller) will be sufficient to deal with the "real world". But the infinities described in the article are of a different kind. I don't think there will ever be a situation like: "According to the axiom of choice, this photon should go to the left, but according to the axiom of something else, this photon should go to the right." Or: "If there is such a cardinal X that mumbo-jumbo(X) is true, then the photon should go to the left, otherwise it should go to the right." Therefore, this part of math is just playing with words. An interesting game, especially if you can get paid for it, and it can provide indirect benefits such as greater insight into how to correctly play with words, but ultimately just a game with no correspondence to the "real world".

thomasahle 9y ago

> infinity does not exist within anything that can be conceptualized. Yet math is consistently being conceptualized? Enabling clear thinking about concepts outside of the real world is the while point of math.

Chris2048 9y ago
> math is consistently being conceptualized What does this mean?
placebo 9y ago
>Yet math is consistently being conceptualized? Sure, how else could we capture it or convey it to others? The thing is that I don't see it as that different than conceptualizing things in the "real world". In the latter, conceptualization is done on input of the senses, while in math conceptualization is done on inputs from a higher level of abstraction. In both cases, something is defined and then manipulated for something useful. It's just that I believe that whatever is defined automatically becomes a finite concept otherwise it could not be grasped and manipulated, and a finite infinity seems problematic...

Tloewald 9y ago

When your hand moves, does it pass through an infinite or a finite number of positions at a finite or infinite points in time? Infinity need not be big.

cobbzilla 9y ago
Could one argue that the Planck length/time means the number of points in space/time in your example is finite?
danharaj 9y ago
Why does the continuum need to be made of points? Can you really show me a particular point in space?
- deleted 9y ago
  [deleted]

DonbunEf7 9y ago

Quantum mechanics has several facets which correspond to path integrals, infinite-dimensional operators, and infinite series, sums, and products.

deleted 9y ago
[deleted]
placebo 9y ago
True - you don't even need to venture into quantum mechanics, the concept of infinity has been useful in practical science far before anyone dreamed of quantum mechanics - but there's a difference between a definition of what happens to a formula when a limit approaches infinity and claiming to somehow understand infinity as a concept. I mean when you deal with infinite-dimensional operators, infinite-series etc. does it matter what ordinal of infinity is used?

mcguire 9y ago

If you are going to play with the "real world", you are going to have to deal with continuous math; i.e. the real numbers at least. At which point you get to deal with infinity somehow.

Viliam1234 9y ago
I believe that potential infinity (i.e. the idea of intervals becoming ever smaller and smaller) will be sufficient to deal with the "real world". But the infinities described in the article are of a different kind. I don't think there will ever be a situation like: "According to the axiom of choice, this photon should go to the left, but according to the axiom of something else, this photon should go to the right." Or: "If there is such a cardinal X that mumbo-jumbo(X) is true, then the photon should go to the left, otherwise it should go to the right." Therefore, this part of math is just playing with words. An interesting game, especially if you can get paid for it, and it can provide indirect benefits such as greater insight into how to correctly play with words, but ultimately just a game with no correspondence to the "real world".