3 ms·

IDK, it seems easy to imagine an alien mathematics based only upon continuous values? There's nothing obviously universal about discretizing things.

naasking 4y ago
Firstly, the reals contain the integers, so there is an isomorphism as I said. Secondly, discretization absolutely is universal. It's literally in the laws of physics for one (particles are discrete, energy levels are discrete, etc.). For another, are you suggesting a physical alien species will have a continuous number of appendages, or organs, or that their population will somehow be continuous? I frankly don't see how you can possibly escape aliens capable of math developing a notion of basic counting.
- gmfawcett 4y ago
  Eh, you're not explaining universal truths here, you're just anthropomorphizing. Why must it have appendages, organs, or populations? Why presuppose that its conceptual model includes particles at all? What if a vast, hyper-continuous intelligence simply cannot comprehend the concept of being discrete?
  - naasking 4y ago
    Firstly, those were just examples of commonly countable structures, even if they're not universal (which is debatable). Discretely countable structures are literally everywhere and fundamentally inescapable, which is why I mentioned physics. I didn't presuppose physics, the discrete structure of physical reality is directly observable, it's not some fiction we made up. Secondly, what we know must be bound by what we've observed. You can imagine any sort of being you like, but that doesn't make your imagined creature logically coherent or physically realizable. Any physically realizable intelligence must: a) Be differentiable from its environment: that means it must have some enclosing boundary separating an inside that's different than an outside. b) Have internal structure: intelligence by necessity is structured thought. Structured thought entails differentiable physical structure to hold structured thoughts. Such structure by itself is necessarily countable, being made of matter.

naasking 4y ago

Firstly, the reals contain the integers, so there is an isomorphism as I said. Secondly, discretization absolutely is universal. It's literally in the laws of physics for one (particles are discrete, energy levels are discrete, etc.). For another, are you suggesting a physical alien species will have a continuous number of appendages, or organs, or that their population will somehow be continuous? I frankly don't see how you can possibly escape aliens capable of math developing a notion of basic counting.

gmfawcett 4y ago
Eh, you're not explaining universal truths here, you're just anthropomorphizing. Why must it have appendages, organs, or populations? Why presuppose that its conceptual model includes particles at all? What if a vast, hyper-continuous intelligence simply cannot comprehend the concept of being discrete?
- naasking 4y ago
  Firstly, those were just examples of commonly countable structures, even if they're not universal (which is debatable). Discretely countable structures are literally everywhere and fundamentally inescapable, which is why I mentioned physics. I didn't presuppose physics, the discrete structure of physical reality is directly observable, it's not some fiction we made up. Secondly, what we know must be bound by what we've observed. You can imagine any sort of being you like, but that doesn't make your imagined creature logically coherent or physically realizable. Any physically realizable intelligence must: a) Be differentiable from its environment: that means it must have some enclosing boundary separating an inside that's different than an outside. b) Have internal structure: intelligence by necessity is structured thought. Structured thought entails differentiable physical structure to hold structured thoughts. Such structure by itself is necessarily countable, being made of matter.