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Others already noted how shaky your assertion "Reality, in being geometrical, is infinitely informationally dense" is. Instead, let me throw out another extrem

by Radim 5y ago

Others already noted how shaky your assertion "Reality, in being geometrical, is infinitely informationally dense" is. Instead, let me throw out another extreme (but fun) view in the opposite direction: Finitism [0]. These guys not only reject the existence of the continuum; they reject all infinities altogether! In finitism, even discrete things exist only as finite objects (that is further constructable – Ultrafinitism [1]). So no infinite universe, no "set of all natural numbers", no "limits" and other ideals over infinite domains. Screw Platonism. Hello Wittgenstein (and Wolfram). I don't know how far that theory can be taken in a practical sense – most body of science is built on Platonism [2] – but I have to say finitism does appeal to my CS heart and my earthly experience. [0] https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Finitism [1] https://en.wikipedia.org/wiki/Ultrafinitism https://en.wikipedia.org/wiki/Ultrafinitism [2] https://en.wikipedia.org/wiki/Primitive_recursive_arithmetic https://en.wikipedia.org/wiki/Primitive_recursive_arithmetic

mjburgess 5y ago
My view is indeed the opposite. It seems trivial to me that reality has actual infinities as seen from a discrete pov. A trivial example: you can partition the environment into an infinite number of objects. And which partition scheme you choose is, in some sense, abitary. Eg., "object: the edge of the glass", "composite: edges of glasses on the table", etc. Reality admits an infinite number of such schemes, and also forcloses an infinite number (eg., if "pen"=pen, then "paper"!=pen). I dont think one can meaningfully speak "of reality", ie., provide a discrete linguistic/propositional account, which avoids these infinities. I also think there is no meta-scheme, so one cannot even order (in terms of fundamentality) which scheme is 'the really real' one. It's my view that the reason for this issue is that cognition is discrete but reality continuous. Since discrete aggregations arent enough, likewise "aggregative models of atoms" arent enough for chemistry. An aqueous solution, just like a society, is much more than merely the sum of the properties of its members. When we partition the world with a discrete scheme, we introduce "emergent properties" which are only the "leftovers from our reductive failure". The only problem infinity poses is to being realised by a discrete sequential process. That can never be actually infinite. But everything else can!
- bopbeepboop 5y ago
  The point is that number is large, but 0% of infinity. I’ll bet $1000 you can’t name more than 10^1000^1000 possibilities — a far cry from an actual infinity. Not that I disagree, but you’re using “infinity” in the sense of “a really large, unknowable so number” — when it’s actually infinitely larger than that. There’s an open question of whether reality is infinitely fine grained or finitely grained — and even if infinitely grained, how much so. (And more broadly, what the topology/geometry is.) Eg, can you have a particle at a Chaitan coordinate, or do they have to be computable? — classic Euclidean? — origami coordinates? Etc.

by Radim 5y ago

mjburgess 5y ago

My view is indeed the opposite. It seems trivial to me that reality has actual infinities as seen from a discrete pov. A trivial example: you can partition the environment into an infinite number of objects. And which partition scheme you choose is, in some sense, abitary. Eg., "object: the edge of the glass", "composite: edges of glasses on the table", etc. Reality admits an infinite number of such schemes, and also forcloses an infinite number (eg., if "pen"=pen, then "paper"!=pen). I dont think one can meaningfully speak "of reality", ie., provide a discrete linguistic/propositional account, which avoids these infinities. I also think there is no meta-scheme, so one cannot even order (in terms of fundamentality) which scheme is 'the really real' one. It's my view that the reason for this issue is that cognition is discrete but reality continuous. Since discrete aggregations arent enough, likewise "aggregative models of atoms" arent enough for chemistry. An aqueous solution, just like a society, is much more than merely the sum of the properties of its members. When we partition the world with a discrete scheme, we introduce "emergent properties" which are only the "leftovers from our reductive failure". The only problem infinity poses is to being realised by a discrete sequential process. That can never be actually infinite. But everything else can!

bopbeepboop 5y ago
The point is that number is large, but 0% of infinity. I’ll bet $1000 you can’t name more than 10^1000^1000 possibilities — a far cry from an actual infinity. Not that I disagree, but you’re using “infinity” in the sense of “a really large, unknowable so number” — when it’s actually infinitely larger than that. There’s an open question of whether reality is infinitely fine grained or finitely grained — and even if infinitely grained, how much so. (And more broadly, what the topology/geometry is.) Eg, can you have a particle at a Chaitan coordinate, or do they have to be computable? — classic Euclidean? — origami coordinates? Etc.