[Ben.F.Rayfield]

Why is 0101010 more likely to be followed by 1 than 0?

Why is 00100100100 more likely to be followed by 1 than 0?

Why are the first 30 binary digits of 1/e more likely to be followed by digit 31, digit 32, and so on? Why not any random bits?

Where do these arbitrary rules come from? But they're not arbitrary.

What is likely to follow 1?

What is likely to follow 11?

What is likely to follow 111?

Seeing a pattern? 1 is most likely to come next, but how can we define that in the same way as why the digits of pi are likely to continue?

Why are the primes listed out in binary, back to back, more likely to continue that way than any random bits?

Theres a disconnect here, between short bit strings like 11 or 00 and when we start to say its the digits of pi instead of just some random bits. But aren't the first n digits of pi exactly the chance (1/2)^n to occur? No they're not. If we see a pattern it is likely to continue. Pi is not an arbitrary pattern, and if it does not occur in randomness, then where are all these circles coming from in physics?

I've read various places that http://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_inductive_inference "solomonoff induction" may be related to these kind of things but is impractical to calculate for small inputs.

Instead of that impractical path, maybe we should have a wiki where people, or AIs if they were smart enough, would list all the bit strings of a certain length as most probable first (like those listed above), with some reason like "digits of 1/e". When all such bit strings are debated by many and sorted consistently by how likely they are to occur in an intelligent message (instead of all possible integers), we might find a way to apply it to wave data (1 for vibrate up, 0 for vibrate down, etc) and search SETI's old data based on the wiki generated intelligence detector, but that is unlikely to work without looking deeply recursively and all kinds of rotations and translations that we're really not capable of without a black hole computer. But maybe we'd find something small repeated in the field.

http://en.wikipedia.org/wiki/Rule_110 combined with http://en.wikipedia.org/wiki/Boltzmann_machine is about as close as we can get for now, something like that.

[8pla.net]

Ones and zeros are symbols which follow no meaning, except by the convention in which they are used.

[Don Patrick]

Didn't science already figure out how to make computers recognise patterns? Pattern recognition is not applicable to short input simply because the repetition in "11" or "111" is too infrequent to be a probable pattern. For all we know it could be the first three pixels of an image and the fourth could be something completely different.

[Art]

There are 10 kinds of people in the world...

Those who understand binary, and those who don't!

[Ben.F.Rayfield]

Ones and zeros are symbols which follow no meaning, except by the convention in which they are used.

They have only the meaning that they are different symbols in some sequence, but theres lots of meaning in that.

Didn't science already figure out how to make computers recognise patterns?

We're good at finding patterns in many examples of values of the same variables, especially bit or scalar variables, but when the variables become parts of a language it becomes a Turing Complete problem (capable of general computing) and exceeds the flexibility of our best algorithms in many cases where parts of the language (written in 1s and 0s, for example) mean to look ahead some amount that depends on other things, and it can get harder without limit from there, unless its programmed to look for specific kinds of patterns.

For all we know it could be the first three pixels of an image and the fourth could be something completely different.

It could be, but the question is statistical. What is it most likely to be?

[Don Patrick]

Hmm... If it were statistical then 111 would be followed by another 1, but 00100100100 would most likely be followed by a 0 because statistically there is a greater occurrance of zeros than ones. I think it's a pattern question, and a pattern requires at least one status change and two recurrances as far as my smarts go.

But ehm, statistically predicting the next word in a sentence is an AI technique that has been in use for quite some time already in Natural language Processing and speech recognition.

[ivan.moony]

There are 10 kinds of people in the world...

Those who understand binary, and those who don't!

hehe, got this one 

[Carl2]

  When dealing with random number generators in computers I've often heard that the generators often generate 1 particular number more often.  In number theory ( I'd like to change this to flipping a coin, heads and tails ) each flip has a 50 50 chance of being either heads or tails, therfore after getting 4 heads in a row the next flip you have a 50% chande of getting another head.  In reality I can flip a coin and get 8 heads in a row, doing this more often probably more. So in the subject statement you should have a 50% chance of having a 1.  Heard people had a hard time trying to understand infinity when it was frist intoduced.