Re: Largest number in 32 characters contest


Dave L. Renfro wrote:
Michal wrote:

I am interested, I looked it up on Wikipedia and
I don't understand it, can you please explain a
bit?As I mentioned busy beavers I assume that
it is larger than them so why there is everywhere
written that they are the fastest growing function?
I assume that you are a lot more experienced in
maths than I so I think that Howard ordinal must
be unimaginably more large than BB numbers.

Even if I was doing BB (99) BB(99) times would be
it still smaller than that?

I have no idea how quickly the BB function overtakes
(in a significant way) some of the ordinal-indexed
functions I've brought up in other posts, but for
sufficiently large inputs the BB function definitely
wins. For very lowest levels, operations such as ^,
[...]

Concerning the Big Number Bakeoff contest with computer
code in the C language, I can imagine it would be
a real headache to translate the winning program
into a two-symbol Turing machine with as many states as
needed. I think programming in assembler or an assembler-like
language would be easier than programming an equivalent
Turing machine.

For two symbols and six states, the amazing record of Marxen and Buntrock
was recently improved by Terry and Shawn Ligocki:
< http://www.logique.jussieu.fr/~michel/ha.html#tm62 >

Pascal Michel writes:

Sigma(6,2) > 4.6 x 10^1439

Cf.:
< http://www.logique.jussieu.fr/~michel/bbc.html >

or if 2 symbols is assumed, BB(6) > 4.6 * 10^1439 .
By comparison, BB(5) >=4098.

David Bernier




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