Anarchopedia - User contributions [en]

googolplex

2006-03-05T13:23:59Z

Monkey:

A '''googolplex''' is the number 1010100 (or <math>{10}^\mbox{googol}</math>, or <math>{10}^\mbox{10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}</math>), that is, 1 followed by a [[googol]] (10100) [[0 (number)|zeroes]]. The term googol was coined by [[Milton Sirotta]], nephew of [[mathematician]] [[Edward Kasner]]. Googolplex was coined by Kasner to define an especially large number by extension from his nephew's idea.

A googol is greater than the number of [[elementary particle]]s in the [[known universe]], which has been variously estimated from 1072 up to 1087. Since this is less than the number of zeroes in a googolplex, it would not be possible to write down or store a googolplex in [[decimal notation]], even if all the matter in the known universe were converted into paper and ink or disk drives.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. [[Tex|TeX]] 1pt font is .3514598mm per digit, which means it would take about <math>3.5*10^{96} </math> meters to write in one point font. The known [[universe]] is estimated at <math> 7.4*10^{26} </math> meters in [[diameter]], which means the distance to write the digits would be about <math>4.7*10^{69} </math> times the diameter of the known universe. The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around <math>1.1*10^{82}</math> times the [[age of the universe]] to write down a googolplex.

Even then, the magnitude of the googolplex is not as large as some of the specially defined extraordinarily [[large number]]s, such as those using [[Knuth's up-arrow notation]] or [[Steinhaus-Moser notation]]. Even more simply, one can name numbers larger than a googolplex with fewer symbols, for example,
:<math>9^{9^{9^{9^{9^9}}}}
</math>,
which is much larger.

'''Googolplex''' is often considered a '''cardinal number''', which like any other number could represent quantity and not order.

== In popular culture ==

*Googolplex is the name of a [[movie theatre|multiplex cinema]] in the fictional town of [[Springfield (The Simpsons)|Springfield]] in the television series ''[[The Simpsons]]''.

*[[Google]] refers to their headquarters as the "[[Googleplex]]".

*In ''[[Back to the Future Part III]]'', googolplex was used by the "Doc" to describe his girlfriend, Clara Clayton:
:''Clara was one in a million. One in a billion. One in a googolplex!''

==See also==
*[[Googol]]
*[[Large_numbers#Standardized_system_of_writing_very_large_numbers|Standardized system of writing very large numbers]]
*[[Names of large numbers]]

== External links ==
* Known [[prime factor]]s of googolplex + n (0 <= n <= 999): http://www.alpertron.com.ar/GOOGOL.HTM
* Another Googolplex page: http://www.procrastinators.org/googolplex.html
* Includes [[C_programming_language|C code]] to count to Googolplex http://www.fpx.de/fp/Fun/Googolplex/

[[Category:Integers]]
[[Category:Large numbers]]

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googolplex

2006-03-05T13:23:46Z

Monkey:

A '''googolplex''' is the number 1010100 (or <math>{10}^\mbox{googol}</math>, or <math>{10}^\mbox{10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}</math>), that is, 1 followed by a [[googol]] (10100) [[0 (number)|zeroes]]. The term googol was coined by [[Milton Sirotta]], nephew of [[mathematician]] [[Edward Kasner]]. Googolplex was coined by Kasner to define an especially large number by extension from his nephew's idea.

A googol is greater than the number of [[elementary particle]]s in the [[known universe]], which has been variously estimated from 1072 up to 1087. Since this is less than the number of zeroes in a googolplex, it would not be possible to write down or store a googolplex in [[decimal notation]], even if all the matter in the known universe were converted into paper and ink or disk drives.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. [[Tex|TeX]] 1pt font is .3514598mm per digit, which means it would take about <math>3.5*10^{96} </math> meters to write in one point font. The known [[universe]] is estimated at <math> 7.4*10^{26} </math> meters in [[diameter]], which means the distance to write the digits would be about <math>4.7*10^{69} </math> times the diameter of the known universe. The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around <math>1.1*10^{82}</math> times the [[age of the universe]] to write down a googolplex.

Even then, the magnitude of the googolplex is not as large as some of the specially defined extraordinarily [[large number]]s, such as those using [[Knuth's up-arrow notation]] or [[Steinhaus-Moser notation]]. Even more simply, one can name numbers larger than a googolplex with fewer symbols, for example,
:<math>9^{9^{9^{9^{9^9}}}}
</math>,
which is much larger.

'''Googolplex''' is often considered a '''cardinal number''', which like any other number could represent quantity and not order.

== In popular culture ==

*Googolplex is the name of a [[movie theatre|multiplex cinema]] in the fictional town of [[Springfield (The Simpsons)|Springfield]] in the television series ''[[The Simpsons]]''.

*[[Google]] refers to their headquarters as the "[[Googleplex]]".

*In ''[[Back to the Future Part III]]'', googolplex was used by the "Doc" to describe his girlfriend, Clara Clayton:
:''Clara was one in a million. One in a billion. One in a googolplex!''

==See also==
*[[Googol]]
*[[Large_numbers#Standardized_system_of_writing_very_large_numbers|Standardized system of writing very large numbers]]
*[[Names of large numbers]]

== External links ==
* Known [[prime factor]]s of googolplex + n (0 <= n <= 999): http://www.alpertron.com.ar/GOOGOL.HTM
* Another Googolplex page: http://www.procrastinators.org/googolplex.html
* Includes [[C_programming_language|C code]] to count to Googolplex http://www.fpx.de/fp/Fun/Googolplex/

[[Category:Integers]]
[[Category:Large numbers]]

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[[fi:Googolplex]]
[[sv:Googolplex]]
[[de:Googolplex]]

googolplex

2006-03-05T13:23:24Z

Monkey:

A '''googolplex''' is the number 1010100</sup (or <math>{10}^\mbox{googol}</math>, or <math>{10}^\mbox{10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}</math>), that is, 1 followed by a [[googol]] (10100) [[0 (number)|zeroes]]. The term googol was coined by [[Milton Sirotta]], nephew of [[mathematician]] [[Edward Kasner]]. Googolplex was coined by Kasner to define an especially large number by extension from his nephew's idea.

A googol is greater than the number of [[elementary particle]]s in the [[known universe]], which has been variously estimated from 1072 up to 1087. Since this is less than the number of zeroes in a googolplex, it would not be possible to write down or store a googolplex in [[decimal notation]], even if all the matter in the known universe were converted into paper and ink or disk drives.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. [[Tex|TeX]] 1pt font is .3514598mm per digit, which means it would take about <math>3.5*10^{96} </math> meters to write in one point font. The known [[universe]] is estimated at <math> 7.4*10^{26} </math> meters in [[diameter]], which means the distance to write the digits would be about <math>4.7*10^{69} </math> times the diameter of the known universe. The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around <math>1.1*10^{82}</math> times the [[age of the universe]] to write down a googolplex.

Even then, the magnitude of the googolplex is not as large as some of the specially defined extraordinarily [[large number]]s, such as those using [[Knuth's up-arrow notation]] or [[Steinhaus-Moser notation]]. Even more simply, one can name numbers larger than a googolplex with fewer symbols, for example,
:<math>9^{9^{9^{9^{9^9}}}}
</math>,
which is much larger.

'''Googolplex''' is often considered a '''cardinal number''', which like any other number could represent quantity and not order.

== In popular culture ==

*Googolplex is the name of a [[movie theatre|multiplex cinema]] in the fictional town of [[Springfield (The Simpsons)|Springfield]] in the television series ''[[The Simpsons]]''.

*[[Google]] refers to their headquarters as the "[[Googleplex]]".

*In ''[[Back to the Future Part III]]'', googolplex was used by the "Doc" to describe his girlfriend, Clara Clayton:
:''Clara was one in a million. One in a billion. One in a googolplex!''

==See also==
*[[Googol]]
*[[Large_numbers#Standardized_system_of_writing_very_large_numbers|Standardized system of writing very large numbers]]
*[[Names of large numbers]]

== External links ==
* Known [[prime factor]]s of googolplex + n (0 <= n <= 999): http://www.alpertron.com.ar/GOOGOL.HTM
* Another Googolplex page: http://www.procrastinators.org/googolplex.html
* Includes [[C_programming_language|C code]] to count to Googolplex http://www.fpx.de/fp/Fun/Googolplex/

[[Category:Integers]]
[[Category:Large numbers]]

[[da:Googolplex]]
[[fr:Gogolplex]]
[[hu:Googolplex]]
[[nl:Googolplex]]
[[no:Googolplex]]
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[[fi:Googolplex]]
[[sv:Googolplex]]
[[de:Googolplex]]

boson

2006-03-05T13:18:38Z

Monkey:

:''This article is about the elementary particle. For the real-time strategy game, see ''[[Boson (game)]]'', or for the 1960s experimental musician, see ''[[Au, Boson]]''.''

'''Bosons''', named after [[Satyendra Nath Bose]], are particles which form [[identical particles|totally-symmetric composite quantum states]]. As a result, they obey [[Bose-Einstein statistics]]. The [[spin-statistics theorem]] states that bosons have integer [[spin (physics)|spin]]. Bosons are also the only particles which can occupy the same state as another.

All elementary particles are either bosons or [[fermion|fermions]].

[[Gauge boson]]s are [[particle physics|elementary]] particles which act as the carriers of the [[fundamental force]]s such as the W vector bosons of the [[Weak nuclear force|weak force]], the [[gluon]]s of the [[strong force]], the photons of the [[electromagnetic force]], and the [[graviton]] of the [[Gravity|gravitational force]].

Particles composed of a number of other particles (such as [[proton]]s or [[atomic nucleus|nuclei]]) can be either fermions or bosons, depending on their total spin. Hence, many nuclei are in fact bosons.

While fermions obey the [[Pauli exclusion principle]]: "''no more than one fermion can occupy a single quantum state''", there is no exclusion property for bosons, which are free to (and indeed, other things being equal, ''tend'' to) crowd into the same [[quantum state]].
This explains the spectrum of [[black-body]] radiation and the operation of [[laser]]s, the properties of [[superfluid]] [[Helium|helium-4]] and the possibility of bosons to form [[Bose-Einstein condensate]]s, a particular [[state of matter]].

It is important to note that [[Bose-Einstein condensation]] occurs only at ultralow temperature. There is nothing exotic about bosons otherwise. At any reasonable temperatures, both the boson and fermion particles behave as [[classical particles]], i.e. [[particle in a box]], and follow the [[Maxwell-Boltzmann Statistics]].

Examples of bosons:
* [[Helium-4]] atoms
* [[Sodium-23]] atoms
* Any nuclei with integer spins
* [[photon]]s, which mediate the electromagnetic force
* [[W and Z bosons]], which mediate the weak nuclear force
* [[gluon]]s
* [[Higgs boson]]s
* [[phonon]]s

== See also ==

* [[Bose gas]]
* [[Identical particles]]
* [[List of particles]]
* [[Parastatistics]]
* [[Tonks-Girardeau gas]]
* [[Superconductivity]]

== References ==

* Sakurai, J.J. (1994). ''Modern Quantum Mechanics'' (Revised Edition), pp 361-363. Addison-Wesley Publishing Company. ISBN 0-201-53929-2.

{{Elementary}}

[[Category:Boson]]
[[Category:Condensed matter physics]]
[[Category:Atomic physics]]

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