Universe Word Problem: How big is "10^10^123 power"?

jbgoody

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Oct 23, 2020
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10^(10^123). Use the example 10^(10^6) to get an idea. 10^(10^6)= 10 followed by 1 million (10^6) zeroes. Not just 6 zeroes, but 1 million zeroes.

This is an good explanation of the Penrose entropy conclusion:
Teleological Argument and Entropy
QUESTION: Teleological Argument and Entropy

ANSWER:


The term “entropy” describes the degree of thermodynamic “disorder” in a closed system like the universe. “Maximum entropy” would describe the “heat death” of the universe (which is the state it is slowly gravitating towards). Amazingly, our universe was at its “minimum entropy” at the very beginning, which begs the question “how did it get so orderly?” Looking just at the initial entropy conditions, what is the likelihood of a universe supportive of life coming into existence by coincidence? One in billions of billions? Or trillions of trillions of trillions? Or more?

Roger Penrose, a famous British mathematician and a close friend of Stephen Hawking, wondered about this question and tried to calculate the probability of the initial entropy conditions of the Big Bang.

According to Penrose, the odds against such an occurrence were on the order of 10 to the power of 10123 to 1.

It is hard even to imagine what this number means. In math, the value 10123 means 1 followed by 123 zeros. (This is, by the way, more than the total number of atoms [1079] believed to exist in the whole universe.) But Penrose's answer is vastly more than this: It requires 1 followed by 10123 zeros.

Or consider: 103 means 1,000, a thousand. 10 to the 103 power is a number that has 1 followed by 1000 zeros. If there are six zeros, it's called a million; if nine, a billion; if twelve, a trillion and so on. There is not even a name for a number that has 1 followed by 10123 zeros.

Teleological Argument – Practical Impossibility
In practical terms, in probability theory, odds of less than 1 in 1050 equals "zero probability". Penrose's number is more than trillion trillion trillion times less than that. In short, Penrose's number tells us that the “accidental" or "coincidental" creation of our universe is an impossibility.

Concerning this mind-boggling number Roger Penrose comments:

"This now tells how precise the Creator's aim must have been, namely to an accuracy of one part in 10 to the 10123rd power. This is an extraordinary figure. One could not possibly even write the number down in full in the ordinary denary notation: it would be 1 followed by 10123 successive 0's." Even if we were to write a 0 on each separate proton and on each separate neutron in the entire universe- and we could throw in all the other particles for good measure- we would fall far short of writing down the figure needed.1

It takes far more “faith” to believe that this happened by chance than to believe that it was instigated by an incredibly powerful mind. The latter inference does not require blind faith!

It’s important to recognize that we're not talking about a single unlikely event here. We’re talking about hitting the jackpot over and over again, nailing extremely unlikely, mutually complementary parameters of constants and quantities, far past the point where chance could account for it.

NOTES
Compliments of Steve J. Williams. Rendered with permission from the book, The Skeptics’ Guide to Eternal Bliss (2nd ed), Steve J. Williams, Lulu Press, 2009. All rights reserved in the original.

1 (References: Roger Penrose, The Emperor's New Mind, 1989; Michael Denton, Nature's Destiny, The New York: The Free Press, 1998, p. 9)
 

HallsofIvy

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Jan 27, 2012
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You can't talk about probability "a posteriori". Suppose that a person is asked to choose a number from 1 to 1000000 "at random" (every number being "equally" likely. It is easy to see that the probability of choosing any one number is \(\displaystyle \frac{1}{1000000}= 0.000001\).

Okay so I close my eyes and pick a number: 325902. Aha, the probability of my choosing that number was 0.000001! Did a miracle happen?
 
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