We live in a digital world of
0 and
1,
no and
yes,
off and
on, quantum mechanics, etc.: ways of representing "
information" (and "
randomness").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: If you turned every one of
1080 small particles in the known universe into super-computers, and ran them each trying
1,000,000,000 (
1 billion) combinations of zeros and ones for
15,000,000,000 years (
15 billion years), and never tried the same bit combination twice, the probability that you could match the above bit pattern is one in the following.
1,000,000,000,000,000,000,000,000,000,000,000
This is
1033. Obviously, obtaining even a small pattern requiring exact matching by random chance is not possible.
Note: The above bit pattern would represent about
85 characters (
6 bits per character) or about one line of text.
A
Boltzmann brain is named after Ludwig Boltzmann, whose ideas were being ridiculed. The counter-argument to Boltzmann's claims were as a thought experiment of statistical physics whereby, by random chance, a complete human brain with memories, etc., would arise from random statistical fluctuations with a higher probability than other events (e.g., the universe as we know it from the "
big bang").
Let us return to "
yes" and "
no" answers.
The entropy of giving a definitive "
yes" or "
no" answer to a given question can be plotted for the probability of the result of a choice.
"yes" is a definitive answer.
"no" is a definitive answer.
"maybe" is the "bottom" or "⊥" or "?" (missing) value that may have a probability associated with it.
Note that when the probability is
0.5, as in a flip of a fair coin, the entropy is
0.5.
