Q&A: What Is the Difference Between a Random Sequence and an Ordered One
What Is the Difference Between a Random Sequence and an Ordered One
Question
The well-known parable of the monkeys is very familiar to me: monkeys typing on a keyboard are extremely unlikely to produce a word with meaning. From this we see that ordered, meaningful things are not the product of chance, when chance is only a tiny fraction of the range of possibilities.
I would like to understand:
Suppose I were to ask in advance that the monkeys’ typing produce a sequence of letters with no meaning whatsoever, for example: hbe’atbenṭaṭtkakhlḥa’imka’go’akhga
The probability of getting that is also extremely small, and almost impossible even after years of typing.
So too, any random combination that came out—if we had asked in advance for that exact combination to come out—would have had almost no chance.
And yet it does come out.
So what, then, is the difference between a random sequence, which indeed happens, and an ordered sequence?
Answer
The probability of getting 6 a thousand times in a row when rolling a die is the same as the probability of getting any one specific sequence. But this is a special sequence compared to all the others, whereas any other sequence is not. The conclusion depends on the specialness, and not only on the absolute probability.