Size
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 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 zeros 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 0s, it could contain only 5.3×1087 zeros—far short of a googol of zeros. 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 googol 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, at 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 observable universe, giving about 7.1×10184 Planck spaces in the entire observable universe, so a googolplex is far larger than even the number of the smallest measurable spaces in the observable universe.
Read more about this topic: Googolplex
Famous quotes containing the word size:
“There are some persons we could not cut down to size without diminishing ourselves as well.”
—Jean Rostand (1894–1977)
“Our brains are no longer conditioned for reverence and awe. We cannot imagine a Second Coming that would not be cut down to size by the televised evening news, or a Last Judgment not subject to pages of holier-than-Thou second- guessing in The New York Review of Books.”
—John Updike (b. 1932)
“Beauty depends on size as well as symmetry. No very small animal can be beautiful, for looking at it takes so small a portion of time that the impression of it will be confused. Nor can any very large one, for a whole view of it cannot be had at once, and so there will be no unity and completeness.”
—Aristotle (384 B.C.–322 B.C.)