5 ms·

Math works because reality works. Not the opposite. Reality is bigger than math. Math is just a tool that models reality.

kaffeemitsahne 9y ago
..and with one simple statement, HN user jcmoscon forever put an end to this age-old debate.
- Koshkin 9y ago
  Still, if you think about it, that statement is very deep (and is probably true).
- Avshalom 9y ago
  Well no, Samuel Johnson and a good sized rock put an end to it centuries ago, jcmoscon is just trying to remind people.
hackinthebochs 9y ago
On the contrary, reality works because reality cannot contain contradictions. But the set of possible structures without contradiction is a superset of what is physically realizable. And mathematics is just discovering and cataloging the set of structures without contradiction. So reality works because math works.
- kaiwen1 9y ago
  In _Road to Reality_, Roger Penrose has a diagram that illustrates the Platonic world of mathematics fully encompassing the physical world, and the physical world fully encompassing the mental world (since minds are physical), and the mental world fully encompassing the Platonic world of mathematics. Although each encompasses the other in its entirety, each depends only on a small part of its predecessor. Penrose says "...the Platonic world may be the most primitive of these three, since mathematics is a kind of necessity, virtually conjuring its very self into existence through logic alone."
- deleted 9y ago
  [deleted]
- jcmoscon 9y ago
  If in your math 2+2 does not give you 4 it's not reality that is wrong, but your math. >So reality works because math works. Reality is that the one that contains the structures not math. So what you said does not make sense.
  - hackinthebochs 9y ago
    >Reality is that the one that contains the structures not math But math contains all physically realizable structure, i.e. all structure that can represent some feature of reality. But also structure that cannot be realized in reality, e.g. sets too big to fit in reality. That one can deduce some logical structure from observing reality isn't the deciding factor here.
- jcmoscon 9y ago
  Also, Aristotle invented logic while studying cats (reality). That's what I am telling you: reality is amazing, not math!
  - deleted 9y ago
    [deleted]
- malkarouri 9y ago
  Why wouldn't reality contain contradictions?
  - jcmoscon 9y ago
    The contradictions is not in reality but in your ideology/agenda. Everybody has an agenda nowadays...
  - hackinthebochs 9y ago
    I mean in the logical sense. If reality could contain logical contradictions then that would mean reality isn't rule-based, which means unconstrained randomness, no information, no meaning, etc.
    - namelost 9y ago
      But the contradiction is in the mathematical model not reality. Even a totally random universe follows some kind of distribution, which can then be modelled (which is exactly what QM is).
      - hackinthebochs 9y ago
        >But the contradiction is in the mathematical model not reality So then you're saying reality can't have a logical contradiction? Seems like you're agreeing with the original statement. >Even a totally random universe follows some kind of distribution Which is just a kind of rule.
      - naasking 9y ago
        > But the contradiction is in the mathematical model not reality. He's assuming a mathematical model that faithfully represents reality, hence "reality can't contain contradictions". We're not going to one day find a contradiction and vanish in a puff of logic, the ultimate model of reality will be contradiction-free.

kaffeemitsahne 9y ago

..and with one simple statement, HN user jcmoscon forever put an end to this age-old debate.

Koshkin 9y ago
Still, if you think about it, that statement is very deep (and is probably true).
Avshalom 9y ago
Well no, Samuel Johnson and a good sized rock put an end to it centuries ago, jcmoscon is just trying to remind people.

hackinthebochs 9y ago

On the contrary, reality works because reality cannot contain contradictions. But the set of possible structures without contradiction is a superset of what is physically realizable. And mathematics is just discovering and cataloging the set of structures without contradiction. So reality works because math works.

kaiwen1 9y ago
In _Road to Reality_, Roger Penrose has a diagram that illustrates the Platonic world of mathematics fully encompassing the physical world, and the physical world fully encompassing the mental world (since minds are physical), and the mental world fully encompassing the Platonic world of mathematics. Although each encompasses the other in its entirety, each depends only on a small part of its predecessor. Penrose says "...the Platonic world may be the most primitive of these three, since mathematics is a kind of necessity, virtually conjuring its very self into existence through logic alone."
deleted 9y ago
[deleted]
jcmoscon 9y ago
If in your math 2+2 does not give you 4 it's not reality that is wrong, but your math. >So reality works because math works. Reality is that the one that contains the structures not math. So what you said does not make sense.
- hackinthebochs 9y ago
  >Reality is that the one that contains the structures not math But math contains all physically realizable structure, i.e. all structure that can represent some feature of reality. But also structure that cannot be realized in reality, e.g. sets too big to fit in reality. That one can deduce some logical structure from observing reality isn't the deciding factor here.
jcmoscon 9y ago
Also, Aristotle invented logic while studying cats (reality). That's what I am telling you: reality is amazing, not math!
- deleted 9y ago
  [deleted]
malkarouri 9y ago
Why wouldn't reality contain contradictions?
- jcmoscon 9y ago
  The contradictions is not in reality but in your ideology/agenda. Everybody has an agenda nowadays...
- hackinthebochs 9y ago
  I mean in the logical sense. If reality could contain logical contradictions then that would mean reality isn't rule-based, which means unconstrained randomness, no information, no meaning, etc.
  - namelost 9y ago
    But the contradiction is in the mathematical model not reality. Even a totally random universe follows some kind of distribution, which can then be modelled (which is exactly what QM is).
    - hackinthebochs 9y ago
      >But the contradiction is in the mathematical model not reality So then you're saying reality can't have a logical contradiction? Seems like you're agreeing with the original statement. >Even a totally random universe follows some kind of distribution Which is just a kind of rule.
    - naasking 9y ago
      > But the contradiction is in the mathematical model not reality. He's assuming a mathematical model that faithfully represents reality, hence "reality can't contain contradictions". We're not going to one day find a contradiction and vanish in a puff of logic, the ultimate model of reality will be contradiction-free.