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A googolplex is the number 10^{googol}, i.e. 10^{(10100)}. The reciprocal of the googolplex is called googolminex.^{[1]}
In 1938, Edward Kasner's nine year old nephew, Milton Sirotta, coined the term googol, which is 10^{100}, 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".^{[2]} It thus became standardized to 10^{(10100)}.
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 standard form (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than is available in the known universe.
A typical book can be printed with 10^{6} zeros (around 400 pages with 50 lines per page and 50 zeros per line).^{[3]} Therefore it requires 10^{94} such books to print all zeros of googolplex. If each book has a size of 210 mm × 297 mm × 13 mm, the total volume of all the books is 8.1×10^{90} m^{3}, which is many orders of magnitude larger than the visible universe, which has a volume of 'only' 4×10^{80} m^{3}.^{[4]}
With only about 10^{80} ^{[5]} elementary particles in the observable universe, even if only one elementary particle is used to represent each digit, there are not enough particles to represent a googolplex.
Printing digits of a googolplex in one long line would be unreasonable, even in onepoint font (0.353 mm per digit). Writing a googolplex in that font would take about 3.53×10^{97} meters. The observable universe is estimated to be 8.80×10^{26} metres, or 93 billion lightyears, in diameter;^{[6]} the required line to write the necessary zeroes is therefore 4.0×10^{70} times as long as the observable universe.
Writing the number takes too long: if a person can write two digits per second, then writing a googolplex would take around about 1.51×10^{92} years, which is about 1.1×10^{82} times the age of the universe.^{[7]}
A Planck space has a volume of a Planck length cubed, which is the smallest measurable volume, at approximately 4.22×10^{−105} m^{3} = 4.22×10^{−99} cm^{3}.^{[8]} Therefore 2.4 cm^{3} contain about a googol Planck spaces. Only about 4×10^{80} cubic metres exist in the observable universe,^{[4]} giving about 9.5×10^{184} Planck spaces in the entire observable universe; therefore, the number googolplex is about times larger than even the number of the smallest measurable spaces in the observable universe. However, if one Planck space is used to represent each digit of a googolplex, a mere 2.4 cm^{3} of volume gives us enough Planck spaces for that task.
In pure mathematics, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as tetration, Knuth's uparrow notation, SteinhausMoser notation, or Conway chained arrow notation.
One googol is presumed to be greater than the number of hydrogen atoms in the observable universe, which has been variously estimated to be between 10^{79} and 10^{81}.^{[9]} A googol is also greater than the number of Planck times elapsed since the Big Bang, which is estimated at about 8×10^{60}.^{[10]} Thus in the physical world it is difficult to give examples of numbers that compare to the vastly greater googolplex. In analyzing quantum states and black holes, physicist Don Page writes that "determining experimentally whether or not information is lost down black holes of solar mass ... would require more than 10^{76.96} measurements to give a rough determination of the final density matrix after a black hole evaporates".^{[11]} The end of the Universe via Big Freeze without proton decay is expected to be around 10^{(1075)} years into the future, which is still short of a googolplex.
In a separate article, Page shows that the number of states in a black hole with a mass roughly equivalent to the Andromeda Galaxy is in the range of a googolplex.^{[7]}
If the entire volume of the observable universe (assumed ^{[4]} to be 4×10^{80} m^{3}) were packed solid with fine dust particles about 1.5 micrometres in size, then the number of different ways of ordering these particles (that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered) would be approximately one googolplex.^{[12]}
