A googol is 10100 or 1, followed by 100 zeroes.
In contrast, a googolplex is 10googol or 10(10100) or 1, followed by 10100 zeroes.
To write out googolplex, be prepared to invest some time. Also, be prepared for some serious deforestation:
- A book of 400 pages will hold 106 zeros, so you will need 1094 volumes to include all the zeros in a googolplex.
- If each volume weighed a quarter of a pound, your finished work would weigh about 2.204 x 1090 pounds. Compared to the earth’s paltry weight of 1.317 x 1025 pounds, you would need to find some spacious extraterrestrial real estate to house your library.
- In fact, that extra real estate would have to transcend our dimension, since the total number of atoms in the observable universe is 1078.
- The time investment should not be overlooked. Writing at the rate of 2 digits per second, it will take you 1.51 x 1092 years to complete the manuscript — roughly 1.1 x 1082 times longer than the estimated age of the universe, so be sure you get an advance on the publishing contract.
- Compare this time investment to that of writing smaller books about large numbers. To write your book about 1 million, it would take 5 days, 18 hours, 53 minutes, 20 seconds. A billion will take 15 years, 308 days, 9 hours, 41 minutes, 50 seconds. A mere googol will take 1.584 x 1090 centuries.
- Suppose you want to avail yourself of modern technology, and instead of writing your manuscript by hand, you use a computer. Counting at the rate of 7,834,000 numbers per second, your laptop computer can get to 10 million in 1.2 seconds, compared to the six weeks it would take to do it by hand. Using that same computer to tackle your googol (not googolplex, mind you) book, that cuts the time down to a paltry 4 x 1083 centuries — well beyond the estimated end of the world as we know it.
- Clearly, a faster computer is needed. If you could get your hands on a high-speed supercomputer that operates 100 times faster than your laptop, you can turn in your googol project in a mere 4 x 1081 centuries — still beyond the date on the expiration label of the sun.
Not to be discouraged, it is possible to see the realization of your project. Visit Googolplex Written Out to download in PDF form as many of the volumes as you wish. You may also purchase printed volumes, but please take note of the above-referenced space requirements — not to mention the fact that you may have to take on a few extra jobs to pay for your order.
Categories: Mathematics, Measurements, Numbers
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