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Tell me more about the difference between "potential infinity" and "actual infinity". Recursive functions in computer programming, or fractals in maths, are in

Tell me more about the difference between "potential infinity" and "actual infinity". Recursive functions in computer programming, or fractals in maths, are infinite but can be described. Each small part looks like the whole, but the whole can never be fully known within a finite universe. Is that "potential" or "actual" infinity? I've been thinking a lot about infinity this past week, mostly because of Conway's lectures. I'm trying to figure out whether the following logic makes sense. - Assuming that the universe is finite -> Infinity cannot be approximated with finite numbers (MIP* = RE) [1] -> Numbers cannot have infinite strings of digits -> The future can never be perfectly preordained (Gisin) [2] -> Free will exists (Conway) [3] This is not a proof that free will exists! But I think this is a consistency proof that free will is finite. Now you're telling me that there's another kind of infinity, and I want to know what that means for this thought. [1] https://www.quantamagazine.org/landmark-computer-science-proof-cascades-through-physics-and-math-20200304/ https://www.quantamagazine.org/landmark-computer-science-pro... [2] https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ https://www.quantamagazine.org/does-time-really-flow-new-clu... [3] https://www.youtube.com/watch?v=tmx2tpcdKZY&feature=youtu.be&t=712 https://www.youtube.com/watch?v=tmx2tpcdKZY&feature=youtu.be...

gowld 7y ago
The video timestamp you linked does not say "free will exists". Is says "humans has free will implies element particles have free will".
- peterburkimsher 7y ago
  His definition of free will is quite limited. He only suggests that free will is limited to a "free" choice between options within one's power. Conway said that there either is determinism or free will. If the future can be perfectly preordained (Gisin) due to infinite possibilities, then there is no free will. But if there are finite options, I think that there is "free will" for particles and people to choose between those options. https://youtu.be/tmx2tpcdKZY?t=1074 https://youtu.be/tmx2tpcdKZY?t=1074 https://en.wikipedia.org/wiki/Free_will_theorem https://en.wikipedia.org/wiki/Free_will_theorem
TheOtherHobbes 7y ago
Free will is a philosophical concept which is essentially dualist. It's an attempt to reconcile two subjective experiences - the feeling of making a decision, and the fact that sometimes we can't predict the actions of others - with universal determinism. There's no reason why universal determinism and free will need to be related. So trying to "prove" free will with math makes as much sense as "proving" free will with weather forecasting. Even if that weren't true you still can't get to Conway's Step 3, because "free will" could just be statistical noise, and not willed in any sense at all.
- coldtea 7y ago
  >Free will is a philosophical concept which is essentially dualist. Is it though? I came to the conclusion that one could consider free will the self-realization of a person in space-time -- in other words, free will is the only and only choice one can make (at each decision they face), that they make because of who they are thus far. In that sense, "free will" is the same as the "person" (or the person's essense) -- and would it make sense for it to be any other way? Randomness wouldn't be free will, and having a second entity (e.g. a soul in dualism) do the decision making just moves the question and degree upwards (from "how the person has free will?" to "how the person's soul has free will?") If a person faced with a choice A or B could go either way, then I wouldn't call that really free will (even though for some reason that's what most people have in mind when talking about the subject). Either a person is a concrete personality/being and that manifests through its choices (which means that when faced with the A or B dillema they can only chose one or the other based on who they are), or they have some degree of randomness in their decision making (which makes them less of a person in my eyes -- randomness is not tied to our person, it is, as the name reveals, random). When some people say "free will" they actually mean "free (independent) from the person". But that's not a will then -- a will denotes something being tied to a person (a person is their will).
- otabdeveloper4 7y ago
  You're conflating different kinds of randomness here. A coin flip and a hand of cards are both random, but obviously cards are 'more random'. This can be quantified - 'more random' is information complexity, or information entropy. (Two names for the same thing.) If free will exists, then it must necessarily be a singularity of infinite information complexity, which is the same thing as a singularity of infinite randomness.
miscPerson 7y ago
Potential infinities are just saying, you don’t have an infinity in your hand — you just have a recipe for arbitrarily large numbers (or arbitrary accuracy on real numbers, etc). Eg, the “natural numbers” are a recipe to make as many as you want (by taking the successor of the last one) but not an actual (as in existing) infinite collection — the only ones which exist are the ones you construct, and the “potential infinity” refers to the fact that you can always make a new one.
Koshkin 7y ago
"Actual infinity" is merely an abstraction, not unlike many others. It is very useful. Abstract thinking is part of what separates humans from (other) animals.
ShamelessC 7y ago
While there is technically no proof, there is a lot of evidence that the universe is infinite. In particular it's curvature is flat within the margin of measurement error which implies an infinite universe outside the observable universe.

gowld 7y ago

The video timestamp you linked does not say "free will exists". Is says "humans has free will implies element particles have free will".

peterburkimsher 7y ago
His definition of free will is quite limited. He only suggests that free will is limited to a "free" choice between options within one's power. Conway said that there either is determinism or free will. If the future can be perfectly preordained (Gisin) due to infinite possibilities, then there is no free will. But if there are finite options, I think that there is "free will" for particles and people to choose between those options. https://youtu.be/tmx2tpcdKZY?t=1074 https://youtu.be/tmx2tpcdKZY?t=1074 https://en.wikipedia.org/wiki/Free_will_theorem https://en.wikipedia.org/wiki/Free_will_theorem

TheOtherHobbes 7y ago

Free will is a philosophical concept which is essentially dualist. It's an attempt to reconcile two subjective experiences - the feeling of making a decision, and the fact that sometimes we can't predict the actions of others - with universal determinism. There's no reason why universal determinism and free will need to be related. So trying to "prove" free will with math makes as much sense as "proving" free will with weather forecasting. Even if that weren't true you still can't get to Conway's Step 3, because "free will" could just be statistical noise, and not willed in any sense at all.

coldtea 7y ago
>Free will is a philosophical concept which is essentially dualist. Is it though? I came to the conclusion that one could consider free will the self-realization of a person in space-time -- in other words, free will is the only and only choice one can make (at each decision they face), that they make because of who they are thus far. In that sense, "free will" is the same as the "person" (or the person's essense) -- and would it make sense for it to be any other way? Randomness wouldn't be free will, and having a second entity (e.g. a soul in dualism) do the decision making just moves the question and degree upwards (from "how the person has free will?" to "how the person's soul has free will?") If a person faced with a choice A or B could go either way, then I wouldn't call that really free will (even though for some reason that's what most people have in mind when talking about the subject). Either a person is a concrete personality/being and that manifests through its choices (which means that when faced with the A or B dillema they can only chose one or the other based on who they are), or they have some degree of randomness in their decision making (which makes them less of a person in my eyes -- randomness is not tied to our person, it is, as the name reveals, random). When some people say "free will" they actually mean "free (independent) from the person". But that's not a will then -- a will denotes something being tied to a person (a person is their will).
otabdeveloper4 7y ago
You're conflating different kinds of randomness here. A coin flip and a hand of cards are both random, but obviously cards are 'more random'. This can be quantified - 'more random' is information complexity, or information entropy. (Two names for the same thing.) If free will exists, then it must necessarily be a singularity of infinite information complexity, which is the same thing as a singularity of infinite randomness.

miscPerson 7y ago

Potential infinities are just saying, you don’t have an infinity in your hand — you just have a recipe for arbitrarily large numbers (or arbitrary accuracy on real numbers, etc). Eg, the “natural numbers” are a recipe to make as many as you want (by taking the successor of the last one) but not an actual (as in existing) infinite collection — the only ones which exist are the ones you construct, and the “potential infinity” refers to the fact that you can always make a new one.

Koshkin 7y ago

"Actual infinity" is merely an abstraction, not unlike many others. It is very useful. Abstract thinking is part of what separates humans from (other) animals.

ShamelessC 7y ago

While there is technically no proof, there is a lot of evidence that the universe is infinite. In particular it's curvature is flat within the margin of measurement error which implies an infinite universe outside the observable universe.