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Jun 27, 1994, 9:46:52 AM6/27/94

to

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Miserably outdated.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.

Jun 27, 1994, 1:08:26 PM6/27/94

to

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 Miserably outdated.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))))

|>

|>

|> 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

Jun 27, 1994, 3:21:58 PM6/27/94

to

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

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