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But they might start with different axioms (e.g. non-euclidean), exploring in different directions, and perhaps discover truths new to us that affect our own ma

But they might start with different axioms (e.g. non-euclidean), exploring in different directions, and perhaps discover truths new to us that affect our own mathematics. By definition, this is hard to imagine; I mean, try to imagine a mathematics that isn't even based on numbers...!

srcreigh 4y ago
Numbers are just this strange paint that humans apply to some things. Real computers are not based on numbers, they are based on physics of the natural world, which we only model with numbers. There is no ontological confirmation that reality is numerical; we just have a small handful of experiences which indicate that it can be understood as such. This hits to the core question of whether math is real or fantasy. If we built a computer to calculate 1+1=2 and prints true for some millennium until one day when it suddenly prints false; what type of problem is that? Is math now wrong, or is it safe? what if one day 1+1 becomes meaningless to us? The computer prints 2 but suddenly it’s as static to us? This seems like a downgrade, but what if this is accompanied by direct knowledge or an upgraded type of model to understand reality? It’s not seen as 2, but the underlying natural mechanisms are perceived directly? Math is broken, it doesn’t even seem to exist, yet the world continues on and we perceive it in some new strange predictive certainty?
GoblinSlayer 4y ago
I think mathematics has problems with continuum, because it tries to describe our analog universe with digital paradigm.
- BlueTemplar 4y ago
  The claim that the universe is fundamentally analog is on a somewhat shaky ground in postmodern (quantum) physics, especially once you bring (discretized!) information into it, which has to happen quite "soon" if you want to deal with statistically emergent phenomena like temperature.
  - GoblinSlayer 4y ago
    They quantize because the underlying solution is a circular standing wave, which is stable if it consists of a whole number of periods. The wave itself is of course analog, quantization emerges through many hoops and provides stable states with certain potential well like any stable state, and can squiggle a little under perturbation or squiggle a lot under, say, Zeeman effect.
    - BlueTemplar 4y ago
      Can we really speak of the wave(let) "being" analog when it is impossible (according to our current understanding of physics) to see that experimentally ?
      - GoblinSlayer 4y ago
        The theory says it's analog and experiments so far agree with the theory. There are continuous phenomena too.

srcreigh 4y ago

Numbers are just this strange paint that humans apply to some things. Real computers are not based on numbers, they are based on physics of the natural world, which we only model with numbers. There is no ontological confirmation that reality is numerical; we just have a small handful of experiences which indicate that it can be understood as such. This hits to the core question of whether math is real or fantasy. If we built a computer to calculate 1+1=2 and prints true for some millennium until one day when it suddenly prints false; what type of problem is that? Is math now wrong, or is it safe? what if one day 1+1 becomes meaningless to us? The computer prints 2 but suddenly it’s as static to us? This seems like a downgrade, but what if this is accompanied by direct knowledge or an upgraded type of model to understand reality? It’s not seen as 2, but the underlying natural mechanisms are perceived directly? Math is broken, it doesn’t even seem to exist, yet the world continues on and we perceive it in some new strange predictive certainty?

GoblinSlayer 4y ago

I think mathematics has problems with continuum, because it tries to describe our analog universe with digital paradigm.

BlueTemplar 4y ago
The claim that the universe is fundamentally analog is on a somewhat shaky ground in postmodern (quantum) physics, especially once you bring (discretized!) information into it, which has to happen quite "soon" if you want to deal with statistically emergent phenomena like temperature.
- GoblinSlayer 4y ago
  They quantize because the underlying solution is a circular standing wave, which is stable if it consists of a whole number of periods. The wave itself is of course analog, quantization emerges through many hoops and provides stable states with certain potential well like any stable state, and can squiggle a little under perturbation or squiggle a lot under, say, Zeeman effect.
  - BlueTemplar 4y ago
    Can we really speak of the wave(let) "being" analog when it is impossible (according to our current understanding of physics) to see that experimentally ?
    - GoblinSlayer 4y ago
      The theory says it's analog and experiments so far agree with the theory. There are continuous phenomena too.