Random Interesting Fact! - The Googolplex!

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Points2Shop Forums » Off-Topic » Random Interesting Fact! - The Googolplex!
Created: 2011-08-22 09:46:38
lacrimosaangel
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reply date: 2011-08-22 09:46:38 last edited on: 2011-08-22 09:46:58


(I find this fascinating so decided to share! -Taken from wikipedia)

In 1938, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term googol, then proposed the further term googolplex to be "one, followed by writing zeroes until you get tired". Kasner decided to adopt a more formal definition "because different people get tired at different times and it would never do to have Carnera be a better mathematician than Dr. Einstein, simply because he had more endurance and could write for longer". It thus became standardized to 10googol.


In the PBS science program Cosmos: A Personal Voyage, Episode 9: "The Lives of the Stars", astronomer and television personality Carl Sagan estimated that writing a googolplex in numerals (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than the known universe provides.
An average book of 60 cubic inches can be printed with 5×105 zeroes (5 characters per word, 10 words per line, 25 lines per page, 400 pages), or 8.3×103 '0's per cubic inch. The observable (i.e. past light cone) universe contains 6×1083 cubic inches (4/3 × π × (14×109 light years in inches)3).
This math implies that if the universe is stuffed with paper printed with '0's, it could contain only 5.3×1087 '0's—far short of a googol of '0's. In fact there are only about 2.5×1089 elementary particles in the observable universe so even if one were to use an elementary particle to represent each digit, one would run out of particles well before reaching a googolplex of digits.
Consider printing the digits of a googolplex in unreadable, one-point font (0.353 mm per digit). It would take about 3.5×1096 metres to write a googolplex in one-point font. The observable universe is estimated to be 8.80×1026 meters, or 93 billion light-years, in diameter, so the distance required to write the necessary zeroes is 4.0×1069 times as long as the estimated 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 about 1.51×1092 years, which is about 1.1×1082 times the age of the universe, to write a googolplex.
A Planck space has a volume of a Planck length cubed, which is the smallest measurable volume, which is approximately 4.222×10−105 m3 = 4.222×10−99 cm3. Thus 2.5 cm3 contain about a googol Planck spaces. There are only about 3×1080 cubic metres in the observed universe, making the number of Planck spaces in the universe to be about 7.1×10184 quantum spaces in the observed universe, so a googolplex is far larger than even the number of the smallest spaces in the observed universe.
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sk555
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reply date: 2011-08-24 11:44:18


lol wut....it just so happens I had to research Google today for some work, and came across this research...great find lac
lacrimosaangel
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reply date: 2011-08-24 16:41:38


lol yeah ^_^ I don't even know why I looked, I just fancied reading something random, but this was kind of amazing :o that's a LOT of 0's!
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daus26
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reply date: 2011-08-26 00:47:56


Nothing too surprising here. I always thought googolplex is just another made up number that's pretty much useless because you can always make a bigger number after, thus the term infinite.

What I find interesting is that our known universe can't handle such number, which baffles me a bit. I do believe the universe is a finite space, but it is ever growing in a scale that we can't imagine.
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