Discussion:
He is primarily known (to me) as a backgammon quiz-maker but one of his maths results was referenced when I googled for large numbers
Add Reply
Paul Epstein
2020-07-19 08:41:30 UTC
Reply
Permalink
Just saw this by Tim Chow:
https://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm

Paul
c***@gmail.com
2020-07-19 17:35:45 UTC
Reply
Permalink
Post by Paul Epstein
https://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm
Paul
Surprised 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
Bradley K. Sherman
2020-07-19 17:55:11 UTC
Reply
Permalink
Post by c***@gmail.com
Post by Paul Epstein
https://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm
Surprised 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
How remarkable that Tim was born in 1994 (latter cite)
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
Reply
Permalink
Post by Paul Epstein
https://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm
Paul
I 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?
Paul Epstein
2020-07-20 11:37:36 UTC
Reply
Permalink
Post by Peter
Post by Paul Epstein
https://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm
Paul
I 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?
To define large numbers, Graham and Moser (great drinking buddies though
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
Permalink
Post by Paul Epstein
Post by Peter
Post by Paul Epstein
https://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm
Paul
I 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?
To define large numbers, Graham and Moser (great drinking buddies though
they are) are not the way to go.
Busy beaver numbers are so large as to be non-computable and that's
I came across BB in Boolos & Jeffery, but I had forgotten the details.
I think they have been reintroduced in the UK. That is the unhappy
extent of my knowledge.
Post by Paul Epstein
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
Permalink
Post by Peter
Post by Paul Epstein
Post by Peter
Post by Paul Epstein
https://www-users.cs.york.ac.uk/~susan/cyc/b/gmproof.htm
Paul
I 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?
To define large numbers, Graham and Moser (great drinking buddies though
they are) are not the way to go.
Busy beaver numbers are so large as to be non-computable and that's
I came across BB in Boolos & Jeffery, but I had forgotten the details.
I think they have been reintroduced in the UK. That is the unhappy
extent of my knowledge.
I can understand your grief. However, your unhappiness can be ameliorated
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

Loading...