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Topic: BIG NUMBERS #1
Replies: 19   Last Post: Feb 11, 2003 9:59 AM

 Messages: [ Previous | Next ]
 C. Stevens Posts: 25 Registered: 12/13/04
Re: BIG NUMBERS #1
Posted: Feb 4, 2003 1:09 PM

Dave:I read with great interest your post on BIG NUMBERS.I made a (curious) construction based on a similiar construction I saw concerning Graham's #.My little construction is based on Conway's chained arrows notation and the colossi 3->3->2->2->2

>>>>>>>>>>>>>>>>>>>>>>>>=3->3->2->2->2!
^
^
^ 1)27 { {1)27 {1)27 } }
^ 2)3^..1)..^3 { {2)3^..1)..^3 {2)3^..1)..^3 } }
^ . {.. { . { . } }
^ . { . { . { . }27 }
^ . { . { . { . } levels}
<<<........... { ..< .....levels < .....levels } }
\________________________________________________/ }
| }
. }
. }
. }
>>>>>>>>>>>>>>>>>>>>>>>>. }
^ }
^ }
^ 1)27 { {1)27 {1)27 } }
^ 2)3^..1)..^3 { {2)3^..1)..^3 {2)3^..1)..^3 } }
^ 3)3^..2)..^3 {.. {3)3^..2)..^3 {3)3^..2)..^3 } >3^27
^ . { . { . { . } } levels
^ . { . { . { . >27 }
^ . { . { . { . } levels}
<<<<.....BAYS { ..< ......levels < .....levels } }
{ { { } }
{ { { } }
\________________________________________________/ }
| }
>>>>>>>>>>>>>>>>>>>>>>>>| }
^ }
^ }
^ 1)27 { {1)27 {1)27 } }
^ 2)3^..1)..^3 { {2)3^..1)..^3 {2)3^..1)..^3 } }
^ 3)3^..2)..^3 {.. {3)3^..2)..^3 {3)3^..2)..^3 } }
^ . { . { . { . >27 }
^ . { . { . { . } levels}
^ . { . { . { . } }
<<<......Bays { ..< ......levels < ......levels} }
{ { { } }
\________________________________________________/ }
| }
27 bays }

Notes:Reads from right to left, bottom to top with the final amount of arrows top left. Why start with 27? I calculated this using Robert Munafo's c3(N):chain: function at http://home.earthlink.net/~mrob/pub/math/ln-notes1.html

The top of each "bay" should really read 1)27
2)3^..^3 with 1) arrows,in other words 27 arrows and so forth on down the bay vertically.

Thanks to Munafo's function above,I was able to make a rough estimate of 3->3->2->4 and worked from there. One thing about 3->3->2->2->2 is,three steps into the expansion,it changes into a 4-number notation similiar to 3->3->2->4 and I worked from there.
Having said all this,the construction above may very well be wrong.I would appreciate anyone posting if they find an error (or errors!).One thing for sure,3->3->2->2->2 is one "BIG NUMBER"!

Date Subject Author
4/8/02 Dave L. Renfro
4/8/02 Gerry Myerson
4/9/02 Harry J. Smith
4/9/02 Dik T. Winter
4/8/02 Gerry Myerson
4/9/02 Dave L. Renfro
4/8/02 Doug Magnoli
4/9/02 Rainer Rosenthal
4/9/02 Dave L. Renfro
4/9/02 Daniel Grubb
4/9/02 David C. Ullrich
4/9/02 Dave L. Renfro
4/9/02 Ioannis
4/9/02 don@cmtzone.net
4/9/02 David C. Ullrich
4/10/02 Mikko Haapanen
2/4/03 C. Stevens
2/4/03 C. Stevens
2/5/03 anonymous
2/11/03 anonymous