Randomness: Difference between revisions
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When we say 'random', people have different specific senses. | When we say 'random', people have different specific senses. | ||
The main one is probably ''' | |||
The main one is probably '''unpredictable'''. | |||
Sequences that have effects but no cause, if you will. | Sequences that have effects but no cause, if you will. | ||
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This is arguably the mathematical or philosophical view. | This is arguably the mathematical or philosophical view. | ||
Another is '''not like last time''' | |||
With a lot of choices, that's likely to happen. | |||
But | |||
Consider putting a playlist on random. If it picked a new song randomly each time, it might pick the same thing twice in a row. | |||
If it didn't, that would be a pattern and less ''technically'' random. | |||
But people will question it, plus it's not the functionality we wanted here. | |||
So music players tend to shuffle, or at the very least just keep a memory of the last few played songs. | |||
Consider picking eight numbers between 1 and 100 | |||
5,5,5,5,5,5,5,5 | |||
is exactly as likely as every other sequence of eight numbers. | |||
However, 99.999+% of the other 100 million don't look like a pattern to us, | |||
so our eyes draw past those as noise and we don't question them. | |||
But we do question this one. | |||
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Another is '''evenly spread''' | Another is '''evenly spread''' | ||
This is sort of implied from | This is sort of implied from 'unpredictable': if all outcomes weren't equally likely, | ||
that would be ''some'' sort of pattern, | that would be ''some'' sort of pattern. You wouldn't be able to guess the next output, | ||
but you would be able to guess which ones would appear more often. | |||
Unpredictable ''roughly'' implies evenly spread | Unpredictable ''roughly'' implies evenly spread. | ||
(this only goes in one direction: evenly spread does not mean random. Sometimes obvious, sometimes worth noting). | |||
There is such a thing as weighed randomness. | |||
Say, if you know the probability of an event has a gaussian probability, and/or gaussian error, | Say, if you know the probability of an event has a gaussian probability, and/or gaussian error, | ||
and you want to simulate that, then it is very useful to get random numbers that, when you make a histogram of them, | and you want to simulate that, then it is very useful to get random numbers that, when you make a histogram of them, | ||
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This is arguably the statistical view. | This is arguably the statistical view. | ||
In fact, you can do this not only with gaussian, but with any distribution. | |||
A [[probability mass function]] is basically already the input you want: a list of (probability, value) pairs. | |||
Do these distinctions really matter? | |||
Depending on the application, absolutely. | |||
Consider [[pseudo-random number generators]]. | Consider [[pseudo-random number generators]]. | ||
They give a very good spread (and, in a practical sense, give numbers very quickly), yet are fully deterministic. | They give a very good spread (and, in a practical sense, give numbers very quickly), yet are fully deterministic. | ||
In a practical sense it is not necessarily easy to learn from just observation where it is in that deterministic process. | |||
Yet once you do, you can fully predict what it will output next. And after that, etc. | |||
In e.g. testing some functions with some data, this is not at all an issue. It's fast, it did the testing. | |||
In e.g. cryptography, ''this is not good enough'' (depending a little on what you're doing). | In e.g. cryptography, ''this is not good enough'' (depending a little on what you're doing). | ||
Which is roughly why people make a big fuss of hardware based randomness. | Which is roughly why people make a big fuss of hardware-based randomness. | ||
It's not perfect, but it's a lot better | It's not perfect, but it's a lot better | ||
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