Turing's topological proof that every written alphabet is finite (2010)
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Re: Turing's topological proof that every written alphabet is finite (2010)
#2Interesting argument. This assumes that cognition must also be happening on a compact manifold which seems like a reasonable assumption but the conclusion is somewhat counterintuitive because it means there are only finitely many personality types and ways of thinking.
Re: Turing's topological proof that every written alphabet is finite (2010)
#3Just a reading note to myself: the key assumption is that there is a "resolving limit" \epsilon such that symbols that are "closer and smaller" than \epsilon are indistinguishable. The implicit assumption there is that you can resize symbols while keeping them the same.
Re: Turing's topological proof that every written alphabet is finite (2010)
#4It is even easier to just say, given a fixed area of paper, and a finite printing resolution, there is a finite number of symbols possible?
Say you have a 1 in by 1 in area of paper and a printing resolution of 300 DPI then there are 300*300 total dots. If the printer is monochrome and each dot is either black or white then there are 2^(300^2) possible symbols.
Re: Turing's topological proof that every written alphabet is finite (2010)
#5Interesting argument. This assumes that cognition must also be happening on a compact manifold which seems like a reasonable assumption but the conclusion is somewhat counterintuitive because it means there are only finitely many personality types and ways of thinking.
That's how the math works out in general unless you think some kind of soul exists.
Re: Turing's topological proof that every written alphabet is finite (2010)
#6Interesting argument. This assumes that cognition must also be happening on a compact manifold which seems like a reasonable assumption but the conclusion is somewhat counterintuitive because it means there are only finitely many personality types and ways of thinking.
Is that counterintuitive? There's a finite number of electrons in a human brain (which fits in a space of size 1m^3), and information takes time to propagate across any distance, and humans die before 150 years; this all gestures at there being not only finitely many personality types and ways of thinking, but finitely many human mind states.
Re: Turing's topological proof that every written alphabet is finite (2010)
#7Turing's argument says "conditionally compact" but the article talks only about "compact". They are not the same; "conditionally compact" means every sequence has a Cauchy subsequence, while (sequentially) compact means every sequence has a convergent subsequence. If the metric space Turing mentions is complete, then I guess they're the same. Is that obvious?
Re: Turing's topological proof that every written alphabet is finite (2010)
#8Interesting argument. This assumes that cognition must also be happening on a compact manifold which seems like a reasonable assumption but the conclusion is somewhat counterintuitive because it means there are only finitely many personality types and ways of thinking.
Is that counterintuitive? There's a finite number of electrons in a human brain (which fits in a space of size 1m^3), and information takes time to propagate across any distance, and humans die before 150 years; this all gestures at there being not only finitely many personality types and ways of thinking, but finitely many human mind states .
I guess that means reincarnation is real.
Re: Turing's topological proof that every written alphabet is finite (2010)
#9It is even easier to just say, given a fixed area of paper, and a finite printing resolution, there is a finite number of symbols possible? Say you have a 1 in by 1 in area of paper and a printing resolution of 300 DPI then there are 300*300 total dots. If the printer is monochrome and each dot is either black or white then there are 2^(300^2) possible symbols.
Next week on Show HN: I made a fractal font with unlimited scaling
Re: Turing's topological proof that every written alphabet is finite (2010)
#10Interesting argument. This assumes that cognition must also be happening on a compact manifold which seems like a reasonable assumption but the conclusion is somewhat counterintuitive because it means there are only finitely many personality types and ways of thinking.
That's how the math works out in general unless you think some kind of soul exists.
It all follows from compactness so if the cognitive manifold is not compact then the conclusion is not true.