Skewe's Number

[Lee Rudolph]

pfl...@MCS.COM (Patrick J. Fleury) writes:

> According to my copy of _Fundamentals of Mathematics_ (Behnke,
>Bachmann, Fladt, Suss editors, MIT Press), Volume III, page 488,
>the approximate value is --- drum roll, please ---
>
> 10^(10^(10^34))
>
>According to the book, this is "definitely the largest number that has ever
>played a role in science."
>
> Nice little discussion there of what the number is, too.

Miserably outdated.

In his paper ``A reimbedding algorithm for Casson handles'' (based
on his Notre Dame thesis), \^Zarko Bi\^zaca estimates ``the number of
kinks in the core of the embedded tower $T^1_7$'' produced by
applying his algorithm to construct a ``7 level Casson tower
inside an arbitrary 6 level tower'', in terms of an integer x
determined by the input 6 level tower. His estimate, for x = 1,
is

10^(10^(10^(10^(10^7))))

--and I daresay that 4-dimensional topology, in aid of which
Bi\^zaca determined this number, is closer to ``science'' than
whatever result in number theory Skewes was interested in.

I am quoting ``Bi\^zaca's Number'' from the preprint, by the way; I
believe the paper has now appeared in the Journal of Differential
Geometry, and maybe the estimate has been improved a bit.

Lee Rudolph
Dept. of Mathematics
Clark University, Worcester, Mass.

[Jarle Brinchmann]

In article <Cs26A...@umassd.edu>, rud...@cis.umassd.edu (Lee Rudolph) writes:
|> pfl...@MCS.COM (Patrick J. Fleury) writes:
|>
|> > According to my copy of _Fundamentals of Mathematics_ (Behnke,
|> >Bachmann, Fladt, Suss editors, MIT Press), Volume III, page 488,
|> >the approximate value is --- drum roll, please ---
|> >
|> > 10^(10^(10^34))
|> >
|> >According to the book, this is "definitely the largest number that has ever
|> >played a role in science."

|> Miserably outdated.
|>
|> In his paper ``A reimbedding algorithm for Casson handles'' (based
|> on his Notre Dame thesis), \^Zarko Bi\^zaca estimates ``the number of
|> kinks in the core of the embedded tower $T^1_7$'' produced by
|> applying his algorithm to construct a ``7 level Casson tower
|> inside an arbitrary 6 level tower'', in terms of an integer x
|> determined by the input 6 level tower. His estimate, for x = 1,
|> is
|>
|> 10^(10^(10^(10^(10^7))))
|>

Sorry for being completely ignorant on these issues, but I was under the
impression that the so-called Graham's number was the largest number to
play a role in mathematics, is this correct or am I misunderstanding
something here?

Jarle.

---------------------------------------------------------------------
Nuke the Whales ! | Jarle Brinchmann,
| Email: Jarle.Br...@astro.uio.no
International Krill Union. | or : jar...@astro.uio.no

[Jay Shorten]

In article <Cs26A...@umassd.edu> rud...@cis.umassd.edu (Lee Rudolph) writes:

>In his paper ``A reimbedding algorithm for Casson handles'' (based
>on his Notre Dame thesis), \^Zarko Bi\^zaca estimates ``the number of
>kinks in the core of the embedded tower $T^1_7$'' produced by
>applying his algorithm to construct a ``7 level Casson tower
>inside an arbitrary 6 level tower'', in terms of an integer x
>determined by the input 6 level tower. His estimate, for x = 1,
>is

> 10^(10^(10^(10^(10^7))))

I don't understand what this represents. What is a "Casson tower"?
Jay Shorten
jsho...@julian.uwo.ca
Graduate School of Library and Information Science
University of Western Ontario