Jonathan Bowers

POLYCHORA

Bowers is one of the participants in the Uniform Polychora Project , an attempt to name higher-dimensional Polychora , higher dimensional analogues of Uniform Polyhedra . He independently began his search for Polychora in 1990. Circa 1993, he invented his short names for the uniform polyhedra and polychora, which have come to be known as the Bowers Style Acronym s (or pet name). In 1997, he contacted others who are also interested in the subject, such as Magnus Wenninger , Vincent Matsko , and George Olshevsky .

ILLION GROUP

Bowers has also invented names for very large numbers that extend the -illion family in Names Of Large Numbers .

Megillion <math>10^{310^{3\ \mathrm{million} }+3}

10^{310^{310^6}+3}</math>

$\{a,b,1\} = a \{1\} b = a+b\;$

$\{a,b,2\} = a \{2\} b = a---b\;$

$\{a,b,3\} = a \{3\} b = a^b\;$

$\{a,b,4\} = a \{4\} b = \ ^{b}a$ ''a'' tetrated to ''b''.

$\{a,b,5\} = a \{5\} b = \ ^{\ ^{\ ^{\ ^a\cdot}\cdot}a}a$ - ''a'' pentated to ''b'' - ''a'' tetrated to itself ''b'' times.

GOOGOL, GIGGOL AND GAGGOL GROUPS

Jonathan Bowers defines the googol, giggol, and gaggol groups as being lower than the infinity scrapers. Here's a list of some numbers in these groups:

INFINITY SCRAPERS

Numbers higher than those in the Gaggol group are referred to by Jonathan Bowers as the infinity scrapers. These require four or more terms in the array notation to represent. An older notation represents four term arrays using multiple pairs of braces about the third term, thus extending the operator notation. Some of the rules for constructing these numbers include:

$\{a,b,c,2\} = a \{\{c\}\}b\;$

$\{a,2,1,2\} = a \{\{1\}\}2 = a \{a\}a\;$

$\{a,3,1,2\} = a \{\{1\}\}3 = a \{a \{a\}a\}a\;$

$\{a,b,1,2\} = a \{\{1\}\}b = a \{a\ldots\{a\}\ldots a\}a\;$ - ''a'' expanded to ''b''.

$\{a,b,2,2\} = a \{\{2\}\}b\;$ - ''a'' expanded to itself ''b'' times.

Here's a list of the names of those numbers that are infinity scrapers:
The following numbers require an extended array notation to define. These are defined recursively, using rules such as:
:

\left\langle\begin{matrix}a&b\2&\end{matrix}
ight
angle=\{a,a,\ldots,a\}

with ''a'' repeated ''b'' times.
:

\left\langle\begin{matrix}a&b\k&\end{matrix}
ight
angle=\left\langle\begin{matrix}a&a&\ldots&a\k-1\end{matrix}
ight
angle

with ''a'' repeated ''b'' times.
The last few numbers from the previous table are repeated to establish the notation.

SEE ALSO

Large Numbers

Names Of Large Numbers

Knuth's Up-arrow Notation

Conway Chained Arrow Notation

Uniform Polychoron

EXTERNAL LINKS

Jonathan's home page

illions

infinity scrapers

array notation

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Information About

Jonathan Bowers