# Can a random sequence produce an ordered output

• rasp
In summary: The sequence "666666666666" is just as likely to appear as the sequence "216361426113". If you then force these 12 tosses to be a bernouli trial and do many iid bernouli trials, then they are still equivalent in probability.

#### rasp

Is it possible for order to arrive out of disorder on a macro scale? Contrary to the 2nd law? Specifically, is it scientifically acceptable to believe that the random mutation of genetic material, which was itself produced by the random coupling of molecules has resulted, over the extended course of time decaying periods into an ordered, rational, information bearing life form? I post this here as some might feel the question is not scientific enough in other forums. However, I would appreciate a scientific response.

My post should have said, can a random input produce a sustainable (thereby reproducible) ordered output.

Yes. An "ordered" sequence is just as likely as any specific "disordered" sequence in a truly random process. For example, if you toss a die a huge number of times the sequence "666666666666" is just as likely to appear as the sequence "216361426113". Furthermore, if you toss the die an infinite number of times, every possible sequence will occur an infinite number of times.
However, I don't believe there is much information contained there.
A lot of this depends on your precise definitions though.

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hutchphd
rasp said:
Specifically, is it scientifically acceptable to believe that the random mutation of genetic material, which was itself produced by the random coupling of molecules has resulted, over the extended course of time decaying periods into an ordered, rational, information bearing life form?

That's not how it works, you are ignoring selection. While random mutations do occur and their effects are random, only some of them are viable and will survive, most are rejected (their bearers die). So the better analogy is "is it possible that if we get random numbers on the input side but then choose only fours, we will get 444444444 as the output sequence" - and the answer is, obviously, yes.

russ_watters and BillTre
DaveE said:
if you toss the die an infinite number of times, [with probability 1] every possible [finite] sequence will occur an infinite number of times
Closed a couple of loopholes for you.

DaveE
DaveE said:
Yes. An "ordered" sequence is just as likely as any specific "disordered" sequence in a truly random process. For example, if you toss a die a huge number of times the sequence "666666666666" is just as likely to appear as the sequence "216361426113". Furthermore, if you toss the die an infinite number of times, every possible sequence will occur an infinite number of times.
However, I don't believe there is much information contained there.
A lot of this depends on your precise definitions though.
Yes. I think you are on to something. For although 66666 might appear to be ordered we can’t know for sure the next number in the sequence will be another 6, unless we understand the information in the algorithm that produced the results. No info in the input, means no info in the output. Means random produces random.

Borek said:
That's not how it works, you are ignoring selection. While random mutations do occur and their effects are random, only some of them are viable and will survive, most are rejected (their bearers die). So the better analogy is "is it possible that if we get random numbers on the input side but then choose only fours, we will get 444444444 as the output sequence" - and the answer is, obviously, yes.
So I think you are saying that selection is the algorithm that works on the random mutations to produce information carrying results. Then these random mutations would have to perculate up through the genome to a level in which they are be expressed to the environment. Is that how it works?

More or less. Mutations that don't express themselves are ignored - that happens quite often, as a lot of the genome (if memory serves me well in Eucaryotes only) doesn't code anything (google "non-coding DNA" or "junk DNA").

DaveE said:
For example, if you toss a die a huge number of times the sequence "666666666666" is just as likely to appear as the sequence "216361426113".
Unfortunately this is widely believed and contradicts results from renewal theory.

I had written up a bunch of math but since this is General Discussion forum I removed it.

That said if you toss a die exactly 12 times the sequence sequence "666666666666" is just as likely to appear as the sequence "216361426113". If you then force these 12 tosses to be a bernouli trial and do many iid bernouli trials, then they are still equivalent in probability.

But if you don't enforce compartmentalization -- e.g. if instead you literally toss a die a bunch of times and note the toss number of when you first see a desired pattern, then the way overlaps work renders the statement made, false.

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DaveE
StoneTemplePython said:
Unfortunately this is widely believed and contradicts results from renewal theory.

I had written up a bunch of math but since this is General Discussion forum I removed it.

That said if you toss a die exactly 12 times the sequence sequence "666666666666" is just as likely to appear as the sequence "216361426113". If you then force these 12 tosses to be a bernouli trial and do many iid bernouli trials, then they are still equivalent in probability.

But if you don't enforce compartmentalization -- e.g. if instead you literally toss a die a bunch of times and note the toss number of when you first see a desired pattern, then the way overlaps work renders the statement made, false.
Yes. Kind of obvious, now that you pointed it out!