Paul Epstein

2020-07-19 08:41:30 UTC

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Permalinkhttps://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm

Paul

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Paul Epstein

2020-07-19 08:41:30 UTC

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Permalinkhttps://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm

Paul

c***@gmail.com

2020-07-19 17:35:45 UTC

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Permalinkhttps://en.wikipedia.org/wiki/Tim_Chow

Bradley K. Sherman

2020-07-19 17:55:11 UTC

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PermalinkSurprised he's got time for setting quizzes when he's claiming a weekly

stipend as a professional soccer player?

https://en.wikipedia.org/wiki/Tim_Chow

and was contributing sophisticated math proofs in 1998

(former cite)!

Seriously thanks to Tim for being the heartbeat of rgb,

and to Stick for dropping in with elliptical remarks to

keep Tim's sinus rhythm from decompenstating.

--bks

Yes, I've been reading too many Lancet C19 articles.

Peter

2020-07-20 11:12:13 UTC

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Permalinknumber.

Here's another question: how will the post novel coronavirus national

debt compare to G and M?

Paul Epstein

2020-07-20 11:37:36 UTC

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PermalinkI had not even heard of the Moser number, though I had heard of Graham's

number.

Here's another question: how will the post novel coronavirus national

debt compare to G and M?

they are) are not the way to go.

Busy beaver numbers are so large as to be non-computable and that's

only the first generation of non-computable numbers.

The definition of BusyBeaver(10) is [I hope]:

A deterministic finite state automaton S has 10 states and two

possible inputs -- 0 and 1.

A Turing tape is infinite in both directions with all squares initially 0,

and with a square designated as the starting square.

Assume that for each state and each input, S (deterministically) either

overwrites the current square with a 0 or overwrites it with a 1.

Similarly, depending on state and input, S either shifts one square to

the left or shifts one square to the right.

Similarly, depending on state and input, S either moves to a state or halts.

Assume also that S does halt eventually and that, after halting, at least

one 1 has been output and that all the 1s that have been written

are contiguous.

BusyBeaver(10) is the maximum number of 1s that are possible in the output.

Since the machines halt and since there are only a finite number of

possible such machines, BusyBeaver(10) must be well-defined.

If you go like, BusyBeaver(1000), BusyBeaver(a trillion)

BusyBeaver(a trillion trillion trillion trillion trillion) etc.

[with the purpose of revisiting being 5 to 7 years old] then you

will get bigger numbers than the Graham/Moser way.

Paul

Peter

2020-07-20 12:58:10 UTC

Reply

PermalinkI had not even heard of the Moser number, though I had heard of Graham's

number.

Here's another question: how will the post novel coronavirus national

debt compare to G and M?

they are) are not the way to go.

Busy beaver numbers are so large as to be non-computable and that's

I think they have been reintroduced in the UK. That is the unhappy

extent of my knowledge.

only the first generation of non-computable numbers.

A deterministic finite state automaton S has 10 states and two

possible inputs -- 0 and 1.

A Turing tape is infinite in both directions with all squares initially 0,

and with a square designated as the starting square.

Assume that for each state and each input, S (deterministically) either

overwrites the current square with a 0 or overwrites it with a 1.

Similarly, depending on state and input, S either shifts one square to

the left or shifts one square to the right.

Similarly, depending on state and input, S either moves to a state or halts.

Assume also that S does halt eventually and that, after halting, at least

one 1 has been output and that all the 1s that have been written

are contiguous.

BusyBeaver(10) is the maximum number of 1s that are possible in the output.

Since the machines halt and since there are only a finite number of

possible such machines, BusyBeaver(10) must be well-defined.

If you go like, BusyBeaver(1000), BusyBeaver(a trillion)

BusyBeaver(a trillion trillion trillion trillion trillion) etc.

[with the purpose of revisiting being 5 to 7 years old] then you

will get bigger numbers than the Graham/Moser way.

Paul

Paul Epstein

2020-07-20 13:12:13 UTC

Reply

PermalinkI had not even heard of the Moser number, though I had heard of Graham's

number.

Here's another question: how will the post novel coronavirus national

debt compare to G and M?

they are) are not the way to go.

Busy beaver numbers are so large as to be non-computable and that's

I think they have been reintroduced in the UK. That is the unhappy

extent of my knowledge.

by http://computation4cognitivescientists.weebly.com/uploads/6/2/8/3/6283774/rado-on_non-computable_functions.pdf which explains the issues well, and is the

seminal paper on the subject.

Paul

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