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188 Are the Androids Dreaming Yet?

I know you’re looking for the difference but you won’t find one, as I did not have time to write the numbers out in full. The 10^20000th digit is different, but even if I took the whole age of the universe and counted as fast as possible I would not reach this digit. Any number greater than, 10^120/10^-43 digits cannot be distinguished from another in the age of the observable universe. Real numbers are in practice subject to an uncertainty principle. Some mathematicians even wonder whether they really exist. But, they do exist in our minds and our thought experiments. In my view, any model of the Universe that ignores them is likely to be wrong.

Random Numbers
Which of the following numbers is random?

1111111111111111
34289460370124001
49293741762343083

THINK ABOUT YOUR ANSWER THEN READ ON

Each of the numbers could be random. There is no reason any set of 10 digits is more likely than another, but it feels very unlikely that if I tried to generate a random number I would get 15 consecutive digits. What a human means by random is a jumbled up number: one with varying digits that have no real pattern. An American mathematician, George Chaitin has been able to explain this by saying that a random number is uncompressible. This means there is no way to describe the number more efficiently than writing it out in full. A string of ones can be compressed. “Write a million 1s” takes only 18 characters, yet accurately describes a number that is a million digits long. By contrast 8988376132 can’t be compressed very much at all, its information is just a jumble. There are many interesting numbers around. Some numbers are Hamlet; some numbers are pi. One interesting number is the following: 17733173332032037377. It is the genetic sequence for the virus smallpox, or at least the first 20 digits. Copies of the full sequence sit under lock and key in the Pasteur Institute in France and the CDC in Atlanta. This number is a candidate for an ‘evil’ number. You might think there are many numbers that could represent smallpox because there are

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