User:Salix alba/Jonathan Bowers

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Jonathan Bowers (November 27, 1969) is an amateur mathematician known for his work on polychora (higher-dimensional analogues of polyhedra), and on the representation of very large numbers. He sometimes refers to himself as Hedrondude or Dimension dude.

Contents 1 Polychora 2 Illion group 3 Very large numbers 4 Googol, giggol and gaggol groups 5 Infinity scrapers 6 See also 7 External links

[edit] 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 acronyms (or pet name). In 1997, he contacted others who are also interested in the subject, such as Magnus Wenninger, Vincent Matsko, and George Olshevsky.

[edit] Illion group

Bowers has also invented names for very large numbers that extend the -illion family in names of large numbers.

Name	Short scale value
Million	106, not coined by Bowers.
Deciliion	1033, not coined by Bowers.
Vigintillion	1063, not coined by Bowers.
Trigintillion	1093, not coined by Bowers.
Googol	10100, not coined by Bowers.
Quadragintillion	10123
Quinquagintillion	10153
Sexagintillion	10183
Septuagintillion	10213
Octogintillion	10243
Nonagintillion	10273
Centillion	10303, not coined by Bowers.
Cenuntillion	10306
Duocentillion	10309
Centretillion	10312
Ducentillion	10603
Trecentillion	10903
Quadringentillion	101203
Quingentillion	101503
Sescentillion	101803
Septingentillion	102103
Octingentillion	102403
Nongentillion	102703
Millillion
Platillion	106000
Myrillion	1030003
Micrillion
Nanillion
Picillion
Femtillion
Attillion
Zeptillion
Yoctillion
Xonillion
Vecillion
Mecillion
Duecillion
Trecillion
Tetrecillion
Pentecillion
Hexecillion
Heptecillion
Octecillion
Ennecillion
Icosillion
Triacontillion
Googolplex	, not coined by Bowers.
Tetracontillion
Pentacontillion
Hexacontillion
Heptacontillion
Octacontillion
Ennacontillion
Hectillion
Killillion
Megillion
Gigillion
Terillion
Petillion
Exillion
Zettillion
Yottillion
Xennillion
Vekillion
Mekillion
Duekillion
Trekillion
Tetrekillion
Pentekillion
Hexekillion
Heptekillion
Octekillion
Ennekillion
Twentillion
Triatwentillion
Icterillion	10^(3x10^(3x10^72) +3)
Icpetillion	10^(3x10^(3x10^75) +3)
Ikectillion	10^(3x10^(3x10^78) +3)
Iczetillion	10^(3x10^(3x10^81) +3)
Ikyotillion	10^(3x10^(3x10^84) +3)
Icxenillion	10^(3x10^(3x10^87) +3)
Thirtillion
Googolduplex or Googolplexian	, not coined by Bowers.
Fortillion
Fiftillion
Sixtillion
Seventillion
Eightillion
Nintillion
Hundrillion
Botillion	10^(3x10^(3x10^600) +3)
Trotillion	10^(3x10^(3x10^900) +3)
Totillion	10^(3x10^(3x10^1200) +3)
Potillion	10^(3x10^(3x10^1500) +3)
Exotillion	10^(3x10^(3x10^1800) +3)
Zotillion	10^(3x10^(3x10^2100) +3)
Yootillion	10^(3x10^(3x10^2400) +3)
Notillion	10^(3x10^(3x10^2700) +3)
Thousillion
Dalillion	10^(3x10^(3x10^6000) +3)
Tralillion	10^(3x10^(3x10^9000) +3)
Talillion	10^(3x10^(3x10^12,000) +3)
Palillion	10^(3x10^(3x10^15,000) +3)
Exalillion	10^(3x10^(3x10^18,000) +3)
Zalillion	10^(3x10^(3x10^21,000) +3)
Yalillion	10^(3x10^(3x10^24,000) +3)
Nalillion	10^(3x10^(3x10^27,000) +3)
Manillion	10^(3*10^ (3*10^30,000) +3)
Lakhillion	10^(3*10^ (3*10^300,000) +3)
Mejillion	10^(3x10^(3x10^3,000,000) +3)
Crorillion	10^(3*10^ (3*10^30,000,000) +3)
Awkillion	10^(3*10^ (3*10^300,000,000) +3)
Gijillion	10^(3x10^(3x10^3,000,000,000) +3)
Bentrizillion	10^(6*10^(6*10^(6*10^6billion)))
Astillion	10^(3x10^(3x10^3trillion) +3)
Lunillion	10^(3x10^(3x10^3quadrillion) +3)
Fermillion	10^(3x10^(3x10^3quintillion) +3)
Jovillion	10^(3x10^(3x10^3sextillion) +3)
Solillion	10^(3x10^(3x10^3septillion) +3)
Betillion	10^(3x10^(3x10^3octillion) +3)
Glocillion	10^(3x10^(3x10^3nonillion) +3)
Gaxillion	10^(3x10^(3x10^3decillion) +3)
Supillion	10^(3x10^(3x10^3undecillion) +3)
Versillion	10^(3x10^(3x10^3duodecillion) +3)
Multillion	10^(3x10^(3x10^3tredecillion) +3)
Googoltriplex	10^10^10^10^100
Googolquadriplex	10^10^10^10^10^100
Googolquinplex	10^10^10^10^10^10^100
Googolsexplex	10^10^10^10^10^10^10^100
Googolseptaplex	10^10^10^10^10^10^10^10^100
Googoloctaplex	10^10^10^10^10^10^10^10^10^100
Googolnonaplex	10^10^10^10^10^10^10^10^10^10^100
Googoldecaplex	10^10^10^10^10^10^10^10^10^10^10^100

[edit] Very large numbers

Bowers has proposed a series of names (including giggol, gaggol, geegol, goggol, tridecal, tetratri, dutritri, xappol, dimendecal, gongulus, trimentri, goppatoth, golapulus, golapulusplex, golapulusplux, big boowa and guapamonga) for extremely Large numbers, which he terms infinity scrapers (a pun on skyscraper), many of which are so large that they can only be expressed using a special set of extended mathematical notations which he has devised.

These notations are very similar to the hyper operators and Conway chained arrow notation, and rely on the tetration operator , and its higher order analogues: pentation, sexation, heptation. Some examples are:

• 
• 
• 
• a tetrated to b.
• - a pentated to b - a tetrated to itself b times.

[edit] 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:

[edit] 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 expanded to b.
• - a expanded to itself b times.

Here's a list of the names of those numbers that are infinity scrapers:

Name	Value
Googol	10^100: "roughly" 10 tetrated to 2 = 10^10
Googolplex	10^10^100: roughly 10 tetrated to 3 = 10^(10^10)
Googolduplex or Googolplexian	10^10^10^100: roughly 10 tetrated to 4
Googoltriplex	10^10^10^10^100: roughly 10 tetrated to 5
Googolquadriplex	10^10^10^10^10^100: roughly 10 tetrated to 6
Googolquinplex	10^10^10^10^10^10^100: roughly 10 tetrated to 7
Giggol	{10,100,4} = 10 {4} 100: 10 tetrated to 100
Mega	roughly 10 tetrated to 258
Giggolplex	10 {4} giggol: 10 tetrated to giggol
Tripent	{5,5,5} = 5 {5} 5 = 5 {4} 5 {4} 5 {4} 5 {4} 5: 5 pentated to 5
Megaston	roughly 10 pentated to 11
Gaggol	{10,100,5} = 10 {5} 100: 10 pentated to 100
Gaggolplex	10 {5} gaggol = 10 {5} 10 {5} 100: 10 pentated to gaggol
Geegol	{10,100,6}=10 {6} 100
Geegolplex	{10,geegol, 6}
Trisept	{7,7,7} = 7 {7} 7 (7 heptated to 7)
Gigol	{10,100,7}
Gigolplex	{10,gigol,7}
Goggol	{10,100,8}
Goggolplex	{10,goggol,8}
Gagol	{10,100,9}
Gagolplex	{10,gagol,9} + De pi waarde met de zwaveldioxide nitraat fosfaat bepaling Delta Q wortel in het kwardraad!
Loempia	Chinees voedsel
Oempaloempia +1=	Te veel
Name	Value
Tridecal	{10,10,10} = 10 {10} 10 = 10 decated to 10
Boogol	{10,10,100} = 10 {100} 10
Moser's number	...
Boogolplex	{10,10,boogol}
Graham's number	roughly {3, 64, 1, 2}
Corporal	{10,100,1,2}
Corporalplex	{10,corporal,1,2}
Grand Tridecal	{10,10,10,2}
Biggol	{10,10,100,2}
Biggolplex	{10,10,biggol,2}
Baggol	{10,10,100,3},
Baggolplex	{10,10,baggol,3}
Beegol	{10,10,100,4}
Beegolplex	{10,10,beegol,4}
Bigol	{10,10,100,5}
Boggol	{10,10,100,6}
Bagol	{10,10,100,7}
Supertet	{4,4,4,4}
Tetratri	{3,3,3,3}
General	{10,10,10,10}
Generalplex	{10,10,10,general}
Troogol	{10,10,10,100}
Troogolplex	{10,10,10,troogol}
Triggol	{10,10,10,100,2}
Triggolplex	{10,10,10,triggol,2}
Pentatri	{3,3,3,3,3}.
Traggol	{10,10,10,100,3}
Traggolplex	{10,10,10,traggol,3}.
Treegol	{10,10,10,100,4}
Superpent	{5,5,5,5,5}
Trigol	{10,10,10,100,5}
Troggol	{10,10,10,100,6}
Tragol	{10,10,10,100,7}
Tragol	{10,10,10,100,7}
Pentadecal	{10,10,10,10,10}
Pentadecalplex	{10,10,10,10,pentadecal}
Quadroogol	{10,10,10,10,100}
Quadroogolplex	{10,10,10,10,quadroogol}
Quadriggol	{10,10,10,10,100,2}
Quadriggolplex	{10,10,10,10,quadriggol,2}
Hexatri	{3,3,3,3,3,3}.
Quadraggol	{10,10,10,10,100,3}
Quadreegol	{10,10,10,10,100,4}
Quadrigol	{10,10,10,10,100,5}
Quadroggol	{10,10,10,10,100,6}
Quadragol	{10,10,10,10,100,7}
Superhex	{6,6,6,6,6,6}.
Quintoogol	{10,10,10,10,10,100}
Quintoogolplex	{10,10,10,10,10,quintoogol}
Pentatri	{3,3,3,3,3}
Hexatri	{3,3,3,3,3,3}
Hexadecal	{10,10,10,10,10,10}
Hexadecalplex	{10,10,10,10,10,hexadecal}
Quintaggol	{10,10,10,10,10,100,3}
Quinteegol	{10,10,10,10,10,100,4}
Quintigol	{10,10,10,10,10,100,5}
Heptatri	{3,3,3,3,3,3,3}
Supersept	{7,7,7,7,7,7,7}
Heptadecal	{10,10,10,10,10,10,10}
Octadecal	{10,10,10,10,10,10,10,10}
Ennadecal	{10,10,10,10,10,10,10,10,10}
Superoct	{8,8,8,8,8,8,8,8}
Superenn	{9,9,9,9,9,9,9,9,9}
Sextoogol	{10,10,10,10,10,10,100}
Septoogol	{10,10,10,10,10,10,10,100}
Octoogol	{10,10,10,10,10,10,10,10,100}
Iteral	{10,10,10,10,10,10,10,10,10,10}
Ultatri	{3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Iteralplex	{10,10,10,10,10,10,...........,10,10,10} (iteral 10's)
Goobol	{10,100 (1) 2} = {10,10,10,.....,10} - has 100 10's.
Dupertri	{3,tritri (1) 2}.
Iteralplex)	{10,iteral (1) 2}
Goobolplex	{10,goobol (1) 2} and truperdecal = {10,duperdecal (1) 2}
Truperdecal	{10,duperdecal (1) 2}
Quadruperdecal	{10,truperdecal (1) 2}
Gibbol	{10,100,2 (1) 2}
Latri	{3,3,3 (1) 2}
Gabbol	{10,100,3 (1) 2}
Geebol	{10,100,4 (1) 2}
Gibol	{10,100,5 (1) 2}
Gobbol	{10,100,6 (1) 2}
Gabol	{10,100,7 (1) 2}
Boobol	{10,10,100,1 (1) 2} where n goes from 1 to 7
Bibbol	{10,10,100,2 (1) 2}
Babbol	{10,10,100,3 (1) 2}
Beebol	{10,10,100,4 (1) 2}
Bibol	{10,10,100,5 (1) 2}
Bobbol	{10,10,100,6 (1) 2}
Babol	{10,10,100,7 (1) 2}
Troobol	{10,10,10,100,1 (1) 2}
Tribbol	{10,10,10,100,2 (1) 2}
Treebol	{10,10,10,100,3 (1) 2}
Tribol	{10,10,10,100,5 (1) 2}
Trobbol	{10,10,10,100,6 (1) 2}
Trabol	{10,10,10,100,7 (1) 2}
Quadroobol	{10,10,10,10,100,1 (1) 2}
Quadribbol	{10,10,10,10,100,2 (1) 2}
Quadrabbol	{10,10,10,10,100,3 (1) 2}
Quadreebol	{10,10,10,10,100,4 (1) 2}
Quadribol	{10,10,10,10,100,5 (1) 2}
Quadrobbol	{10,10,10,10,100,6 (1) 2}
Quadrabol	{10,10,10,10,100,7 (1) 2}
Quintoobol	{10,10,10,10,10,100,1 (1) 2}
Quintibbol	{10,10,10,10,10,100,2 (1) 2}
Quintabbol	{10,10,10,10,10,100,3 (1) 2}
Quinteebol	{10,10,10,10,10,100,4 (1) 2}
Quintibol	{10,10,10,10,10,100,5 (1) 2}
Quintobbol	{10,10,10,10,10,100,6 (1) 2}
Quintabol	{10,10,10,10,10,100,7 (1) 2}
Gootrol	{10,100 (1) 3}
Bootrol	{10,10,100 (1) 3}
trootrol	{10,10,10,100 (1) 3}
quadrootrol	{10,10,10,10,100 (1) 3}.
Gooquadrol	{10,100 (1) 4}
Booquadrol	{10,10,100 (1) 4}
Gitrol	{10,100,2 (1) 3}
Gatrol	{10,100,3 (1) 3}
Geetrol	{10,100,4 (1) 3}
Gietrol	{10,100,5 (1) 3}
Gotrol	{10,100,6 (1) 3}
Gaitrol	{10,100,7 (1) 3}
Quadreequadrol	{10,10,10,10,100 (1) 4}
Gooquintol	{10,100 (1) 5}

The following numbers require an extended array notation to define. These are defined recursively, using rules such as:

with a repeated b times.

with a repeated b times.

The last few numbers from the previous table are repeated to establish the notation.

Name	Value
Emperal
Emperalplex
Gossol	{10,10 (1) 100
Gossolplex	{10,10 (1) gossol}
Gissol	{10,10 (1) 100,2}
Gassol	{10,10 (1) 100,3}
Geesol	{10,10 (1) 100,4}
Gussol	{10,10 (1) 100,5}
Hyperal
Hyperalplex
Mossol	{10,10 (1) 10,100}
Mossolplex	{10,10 (1) 10,mossol}
Missol	{10,10 (1) 10,100,2}
Massol	{10,10 (1) 10,100,3}
Meesol	{10,10 (1) 10,100,4}
Mussol	{10,10 (1) 10,100,5}
Bossol	{10,10 (1) 10,10,100,1}
Bissol	{10,10 (1) 10,10,100,2}
Bassol	{10,10 (1) 10,10,100,3}
Beesol	{10,10 (1) 10,10,100,4}
Bussol	{10,10 (1) 10,10,100,5}
Trossol	{10,10 (1) 10,10,10,100,1}
Trissol	{10,10 (1) 10,10,10,100,2}
Trassol	{10,10 (1) 10,10,10,100,3}
Treesol	{10,10 (1) 10,10,10,100,4}
Trussol	{10,10 (1) 10,10,10,100,5}
Diteral	{10,10 (1)(1) 2} = {10,10,10,10,10,10,10,10,10,10 (1) 10,10,10,10,10,10,10,10,10,10}
Diteralplex	Diteralplex = {10,diteral (1)(1) 2} = {10,10,......,10 (1) 10,10,......,10} - diteral 10's in each row.
Dubol	{10,100 (1)(1) 2}
Dutrol	{10,100 (1)(1) 3}
Duquadrol	{10,100 (1)(1) 4}
Admiral	{10,10 (1)(1) 10}
Dossol	{10,10 (1)(1) 100}
Dossolplex = {10,10 (1)(1) dossol}.
Dutritri
Dutridecal
Xappol	10 by 10 array of 10's
Xappolplex	xappol by xappol array of 10's
Grand xappol	{10,10 (2) 3}
Dimentri	3 x 3 x 3 array of 3's
Colossal	10 x 10 x 10 array of 10's
Colossalplex	colossal x colossal x colossal array of 10's
Terossol	10^4 & 10 = {10,10 (4) 2} - which is a 10 by 10 by 10 by 10 tesseract of tens.
Terossolplex	terossol^4 & 10
Petossol	a size 10 penteract of tens - a 10^5 array of tens that is.
Petossolplex	a size petossol penteract of tens.
Ectossol	the value of a size 10 hexeract (six dimensional cube) of tens.
Ectossolplex	an ectossol size hexeract of tens.
Zettossol	10^n & 10 = {10,10 (7) 2}
Yottossol	10^n & 10 = {10,10 (8) 2}
Xennossol	10^n & 10 = {10,10 (9) 2}
Dimendecal	10x10x10x10x10x10x10x10x10x10 array of 10's
Gongulus	100 dimensional array of 10's (10^100 array that is)
Gongulusplex	gongulus dimensional array of 10's (10^gongulus array)
Gingulus	{10,100 (0,2) 2} = 100^100 array of D's where D is a 100^100 array of 10's
Trilatri	{3,3 (0,3) 2} = {A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A} where A represents "3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3" - this is a size 3 - x^3x array of 3's.
Gangulus	{10,100 (0,3) 2}
Gowngulus	{10,100 (0,5) 2}
Gungulus	{10,100 (0,6) 2} - which is a size 100 - x^6x array of 10's.
Bongulus	{10,100 (0,0,1) 2)
Bingulus	{10,100 (0,0,2) 2)
Bangulus	{10,100 (0,0,1) 3)
Dulatri	(3^3)^2 array of 3's
Trimentri	3^(3^3) array of 3's
Trongulus	{10,100 (0,0,0,1) 2}
Quadrongulus	{10,100 (0,0,0,0,1) 2}
Goplexulus	{10,100 (0,0,0,.......,0,0,1) 2} - where there are 100 0's - this is a size 100 - x^x^100 array of 10's
Goduplexulus	{10,100 ((100)1) 2} which is a size 100 - x^x^x^100 array of 10's - following is another trimensional array example: {3,3 (4,2 (1) 6,7 (1) 7,8 (2) 7,8,5) 2} - the (4,2 (1) 6....8,5) represents separations between two x^(4+2x+ (6+7x)x^x + (7+8x)x^2x + (7+8x+5x^2)x^x^2) structures.
Goppatoth	10 tetrated to 100 array of 10's
Goppatothplex	{10,goppatoth,4} array of 10's
Gotriplexulus	{10,100 ((0,0,0,....,0,0,1)1) 2 - with 100 0's - this is a size 100 - x^x^x^x^100 array of 10's.
Triakulus	{3,3,3} & 3 = 3^^^3 array of 3's
Kungulus	{10,100,3} & 10 = 10^^^100 array of tens.
Kungulusplex	{10,kungulus,3) & 10 = 10^^^kungulus array of tens.
Quadrunculus	{10,100,4} & 10 = 10^^^^100 array of tens
Tridecatrix	{10,10,10} & 10 = 3 & 10 & 10 = 10^^^^^^^^^^10 array of tens
Humongulus	{10,10,100} & 10 = 10^^^^^^^^^^^^`````^^^^10 (100 ^'s) array of tens.
Tridecatrix	{10,10,10} array of 10's
Golapulus	a "10^100 array of 10's" array of 10's.
Golapulusplex	a * "10^100 array of tens" array of tens* array of tens.
Golapulusplux	X{10,100,3},golapulusX
Big boowa	X3, {X3,dutritriX, 2} X
Great big boowa	X3,3,3X
Grand boowa	{3,3,big boowa / 2}
Super gongulus	a 10^100 exploded array of 10's (within X X that is!!)
Wompogulus	10^10 "100th level" exploded array of 10's
Wompogulusplex	10^10 "wompogulusth level" exploded array of 10's!!
Guapamonga	10^100 array of B's within "# #"
Guapamongaplex	10^100 array of B's within guapamonga-level "# #"
Big hoss	{100,100 //////.......///// 2} - with 100 /'s.
Great big hoss	{big hoss, big hoss /////.......///// 2} - with big hoss /'s
Meameamealokkapoowa	{Not Defined Yet}
Meameamealokkapoowa Oompa	{Not Defined Yet}
Oompaloompa candy	Oompaloempa's OWNDEN DIKKK!
Loempiauilenfilet3bier	Altijd 1 meer dan het aantal scherpe komkommerschijfjes sap in Bens cola
sambalfiletamercanenzureharing	Die verdwijnen altijd in sanders aars dus je hebt der geen fuck aan

[edit] See also

• Large numbers
• Names of large numbers
• Knuth's up-arrow notation
• Conway chained arrow notation
• Uniform polychoron

[edit] External links

• Jonathan's home page
• illions
• infinity scrapers
• array notation
• Robert Munafo's Large Numbers page, pages 3 and 4 discuss Bowers work.

Nick je hébt gewoon een natte anus waar ik aan wil likken! :)