Aren't you really just talking about the level of abstraction being applied? If there are infinite possibilities between zero and one, then it's just our way of relating to it that imposes the perception of a limitation.

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djsjajah 5 hours ago | parent | next [-]

No. You might be reading into it a little bit too much. My point was that finding three needs to be possible for you to find it. If you are looking on the interval 0-1, it is not possible. As other comments have kinda of suggested, you could map every integer to a real and find "three" but if you are going to do that, why not just look on an interval that actually contains the number?

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psychoslave 4 hours ago | parent [-]

It's unclear to me at least what you mean here. In term of what is logically possible, if we take for granted that all integer numbers and more are mappable from a subset of this interval, then we do have this number.

Now, on logistical level, the mapping procedure is not free, it does have a physical/energetic/mental cost to handle it, and a more trivial representation of integer has a lower cost on this regard.

But the simpler integer representation can represent less many situations. If all one need to deal with in a certain frame is covered by a simpler shipper representation, from an economical perspective it can be argued it worth the risk of hitting a point where the representation will be insufficient as the situation evolved with cases it can't handle.

My impression is that your underlying premises are conflating all of this distinguishable aspects. But of course my impression is limited by my own narrow representation of the world, no matter how open and curious I can be about learning from experiences it makes me go through.

	▲	djsjajah 3 hours ago \| parent \| next [-]
		I think you are overthinking it too. The task was to find three, not something that is equivalent to three. However you choose to represent it, it wouldn't be hard to come up with a different "three" that you won’t find within that representation. If you are changing the representation, why wouldn't you just change the interval that you are searching?
	▲	moi2388 3 hours ago \| parent \| prev [-]
		He means that 3 is not between 0 and 1, which it really isn’t.

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bryanrasmussen 2 hours ago | parent | prev | next [-]

there aren't infinite possibilities between 0 and 1; there is an infinite sequence, the possibilities of which are quite strictly bound.

on edit: maybe should say infinite set instead of infinite sequence.

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packetlost 6 hours ago | parent | prev | next [-]

Maybe you can theoretically encode arbitrary (but not infinite) information, but there are still discrete underlying states.

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fc417fc802 5 hours ago | parent [-]

> encode arbitrary (but not infinite) information

What leads you to claim that you can't encode infinite information given an infinite set to work with?

	▲	ben_w 2 hours ago \| parent \| next [-]
		I suspect a looseness with language; this often happens with maths done in natural language, and I may be guilty of it even when I try not to be. If spacetime is infinite in extent yet discrete at the Plank scale, it would be ℵ₀; the Hilbert space is real-valued and therefore (a vector of) ℵ₁. The Bekenstein bound, in practice, would do limit how much information can be actually encoded, even if all quantum states have an underlying real value and therefore even just one quantum value of one particle is ℵ₁ all by itself.
	▲	magimas 3 hours ago \| parent \| prev [-]
		reality does not have an infinite set though. Infinity is an abstraction that simplifies a lot of maths, it isn't real though.

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mathisfun123 6 hours ago | parent | prev [-]

Terrence Howard is that you?