Comments by "Taxtro" (@MrCmon113) on "Busy Beaver Turing Machines - Computerphile" video.

  1. Seegal Galguntijak You don't need a genius for that. Here BB(n). There is your mathematical formula. Thing is that you can write formulas for anything, but that doesn't make them computable. What you are looking for is an algorithm and because algorithms are just as powerful as TMs, you cannot construct a computable function growing faster than BB by definition.
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  2. He means the number that is printed on the tape, not the number of possible TMs (the one he showed the formula for).
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  3. It's fun. Welcome to mathematics.
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  4. That's the same as a finite tape.
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  5. No. The brain being a physical object is why it's not a Turing machine, which are conceptual entities. Further you are confusing computability of a problem with computability of an INSTANCE of a problem. It might be trivially easy to see whether a TM halts on an input, but you cannot formulate an algorithm that always tells you whether any TM halts with any input.
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  6. Yeah, dunno why he says cards. States is much more obvious.
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