Had a lot of fun with my stats students today.
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Which one is random?
(data sets are 100 numbers 1 to 6)listA=[2,3,5,1,2,2,4,2,4,5,2,3,3,4,5,6,4,2,6,2,2,1,3,4,5,5,6,3,3,6,1,4,2,1,4,5,2,2,3,3,3,5,6,3,2,4,5,5,1,1,1,6,1,4,3,5,5,3,1,1,1,6,1,4,6,6,3,6,6,2,4,4,4,5,1,5,6,2,6,1,1,2,4,2,2,3,4,4,5,6,1,3,3,3,5,4,6,5,1,6]
listB=[4,2,5,6,3,5,3,1,3,4,2,3,4,3,4,5,5,1,3,3,2,1,1,6,1,3,2,2,2,6,1,5,6,3,6,3,2,3,2,4,6,1,1,6,3,2,4,1,6,1,3,1,5,6,2,3,3,5,1,6,4,5,2,5,1,1,5,3,6,2,3,3,6,5,2,3,3,1,6,3,2,3,2,1,6,6,4,4,6,2,4,5,4,5,3,4,6,5,3,2]
Replacing a bad analysis where I forgot we are dealing with dice, not decimal digits.
The first has 23/99 runs of two matching digits and 5/98 runs of three.
The second has 12/99 and 1/98.
The expected mean fractions would be 1/6 and 1/36.
The latter series is a little closer to the expected values, but each of the two series is at some distance (on opposite sides) of the mean.
These are only a couple of the possible information signals that could be checked, but they seem prima facie to suggest the second is a slightly more plausibly random-adjacent series.
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Which one is random?
(data sets are 100 numbers 1 to 6)listA=[2,3,5,1,2,2,4,2,4,5,2,3,3,4,5,6,4,2,6,2,2,1,3,4,5,5,6,3,3,6,1,4,2,1,4,5,2,2,3,3,3,5,6,3,2,4,5,5,1,1,1,6,1,4,3,5,5,3,1,1,1,6,1,4,6,6,3,6,6,2,4,4,4,5,1,5,6,2,6,1,1,2,4,2,2,3,4,4,5,6,1,3,3,3,5,4,6,5,1,6]
listB=[4,2,5,6,3,5,3,1,3,4,2,3,4,3,4,5,5,1,3,3,2,1,1,6,1,3,2,2,2,6,1,5,6,3,6,3,2,3,2,4,6,1,1,6,3,2,4,1,6,1,3,1,5,6,2,3,3,5,1,6,4,5,2,5,1,1,5,3,6,2,3,3,6,5,2,3,3,1,6,3,2,3,2,1,6,6,4,4,6,2,4,5,4,5,3,4,6,5,3,2]
@futurebird Before I look at where the answer shows up, my guess would be that List A is random.
The odds of both dice being the same number when you roll 2 dice is 1/6 (36 possibilities, 6 desired results). For 3, that becomes 1/36. (6*6*6 possibilities, 6 desired).
What we have here is 98 consecutive possible places for a 3-of-a-kind to start. The odds that you would only draw the 1/36 chance ONCE (The 3 2's near the beginning of B) is something like....8%?
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@futurebird Before I look at where the answer shows up, my guess would be that List A is random.
The odds of both dice being the same number when you roll 2 dice is 1/6 (36 possibilities, 6 desired results). For 3, that becomes 1/36. (6*6*6 possibilities, 6 desired).
What we have here is 98 consecutive possible places for a 3-of-a-kind to start. The odds that you would only draw the 1/36 chance ONCE (The 3 2's near the beginning of B) is something like....8%?
@futurebird The point is, having it appear once is something like a 94% chance. Seeing a 3-of-a-kind appear more than once is very much expected in a random distribution.
But it's NOT what we EXPECT a random distribution to look like, from a human perspective. When people see things like that appear, they get nervous. If they're making a list to LOOK random, having 3 of the same number in a row starts to feel NOT random, like it's some kind of pattern, and so they won't do it much.
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The LLM is like a little box of computer horrors that we peer into from time to time.
I'm sorry but the whole interface is just so silly.
You ask for random numbers with sentences and it pretends to give them to you? What are we doooooing?
@futurebird the first time I had to go nuclear about LLM use in my department was when my boss was showing me her design for a major experiment where they were planting actual trees of different species in long term plots, and when I asked how did they randomise the distribution of species she said the post doc responsible for setting up the experiment had asked chatgpt to randomise it! (1/2)
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@futurebird the first time I had to go nuclear about LLM use in my department was when my boss was showing me her design for a major experiment where they were planting actual trees of different species in long term plots, and when I asked how did they randomise the distribution of species she said the post doc responsible for setting up the experiment had asked chatgpt to randomise it! (1/2)
@futurebird And that was about 2 years ago, when this kind of thing would probably be even worse. It took me half an hour to write code to generate the plots and some nice figures with the positions of every tree... I wonder how long they were fighting the chat box to get any kind of answer. Let alone the fact this experiment will be running for years to come. How can people be so careless? (2/2)
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@futurebird The point is, having it appear once is something like a 94% chance. Seeing a 3-of-a-kind appear more than once is very much expected in a random distribution.
But it's NOT what we EXPECT a random distribution to look like, from a human perspective. When people see things like that appear, they get nervous. If they're making a list to LOOK random, having 3 of the same number in a row starts to feel NOT random, like it's some kind of pattern, and so they won't do it much.
@futurebird Also somehow I was wrong. Either I did my calculation wrong or that 8% chance really slipped through and I picked the absolutely wrong metric to judge this.
Alternately, I didn't consider HOW the non-random list was made and just assumed it was just someone with a pencil picking numbers based purely on vibes, when there was just a different, non-random methodology.
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@futurebird And that was about 2 years ago, when this kind of thing would probably be even worse. It took me half an hour to write code to generate the plots and some nice figures with the positions of every tree... I wonder how long they were fighting the chat box to get any kind of answer. Let alone the fact this experiment will be running for years to come. How can people be so careless? (2/2)
@LeoRJorge @futurebird Over and over again, if you know what you're doing, the LLM-generated version of it is so bad that doing it from scratch is easier and faster. Only people who don't know what they're doing, and usually people who sneer at learning to do something, really want to use LLMs. They think it's a cheat-code against acquiring skills, but it just makes them look lazy and uncaring. That's the owner-class dream, of course.
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There is something very creepy about the way LLMs willy cheerfully give lists of "random" numbers. But they aren't random in frequency, and as my students pointed out "it's probably from some webpage about how to generate random numbers"
But even then, why is the frequency so unnaturally regular? Is that an artifact from mixing lists of real random numbers together?
Heh, it's xkcd 221 with more steps.
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@futurebird I know how to find the SD and I will use the php-stats library every day of the week and twice on Sunday. I would much rather be able to depend on well supported community code. (At least until it is all replaced by ai slop)
@ldpm @futurebird
AIUI, there's also that the formulas for mean and especially stdev that we learn in school don't work great with the way we represent floating point numbers in computers, with the way rounding works with those, and hopefully the stats library uses more obscure formulas that take care of that, what they call "numerical stability" -
There is something very creepy about the way LLMs willy cheerfully give lists of "random" numbers. But they aren't random in frequency, and as my students pointed out "it's probably from some webpage about how to generate random numbers"
But even then, why is the frequency so unnaturally regular? Is that an artifact from mixing lists of real random numbers together?
@futurebird @benroyce Noticed that a while ago, too. Found it interesting that they work a lot like humans (who are totally unable to create random numbers - there are even fraud detection systems basing on that human flaw).
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Which one is random?
(data sets are 100 numbers 1 to 6)listA=[2,3,5,1,2,2,4,2,4,5,2,3,3,4,5,6,4,2,6,2,2,1,3,4,5,5,6,3,3,6,1,4,2,1,4,5,2,2,3,3,3,5,6,3,2,4,5,5,1,1,1,6,1,4,3,5,5,3,1,1,1,6,1,4,6,6,3,6,6,2,4,4,4,5,1,5,6,2,6,1,1,2,4,2,2,3,4,4,5,6,1,3,3,3,5,4,6,5,1,6]
listB=[4,2,5,6,3,5,3,1,3,4,2,3,4,3,4,5,5,1,3,3,2,1,1,6,1,3,2,2,2,6,1,5,6,3,6,3,2,3,2,4,6,1,1,6,3,2,4,1,6,1,3,1,5,6,2,3,3,5,1,6,4,5,2,5,1,1,5,3,6,2,3,3,6,5,2,3,3,1,6,3,2,3,2,1,6,6,4,4,6,2,4,5,4,5,3,4,6,5,3,2]
@futurebird @Bumblefish Without any careful analysis, just winging it here, but the double occurrence of 1 6 1 4 in List A makes it sus to me. Especially since John Napier published his outline of logarithms in 1614. Coincidence? I think not!!
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ListA was created by making a list of 16 or 17 of each number. The Stdev **of the frequencies** is much lower than what you will find on random lists of similar size.
ListB was made by rolling dice.
@futurebird@sauropods.win @charette@mstdn.ca I hope you are proud of your students for getting it:)
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@futurebird @Bumblefish Heh, this reminds me of something from school where... Evan? Somebody. made a plot of outputs from the system's (pseudo-)random number generator and turns out there some _very visible_ patterns. Like, obvious visible stripes in the number selection density plot.
@moira @futurebird @Bumblefish RANDU!
That's a blast from the past (already obsolete by the time I started fiddling with computers many years ago).
I never used a system with RANDU installed, but I did discover that the PRNGs in old BASICs from the 1980s had the same basic flaw, and I found it in the nerdiest way possible: trying to draw artificial star charts with plausible distributions of star brightnesses, noticing there were some *really funky* patterns in the resulting "constellations", and eventually discovering they had the same mathematical properties that RANDU had (in some cases, worse).
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@moira @futurebird @Bumblefish RANDU!
That's a blast from the past (already obsolete by the time I started fiddling with computers many years ago).
I never used a system with RANDU installed, but I did discover that the PRNGs in old BASICs from the 1980s had the same basic flaw, and I found it in the nerdiest way possible: trying to draw artificial star charts with plausible distributions of star brightnesses, noticing there were some *really funky* patterns in the resulting "constellations", and eventually discovering they had the same mathematical properties that RANDU had (in some cases, worse).
@dpnash @futurebird @Bumblefish omg
that's it
tilted to the right instead of the left
that's what he found
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@dpnash @futurebird @Bumblefish omg
that's it
tilted to the right instead of the left
that's what he found
@dpnash @futurebird @Bumblefish (and this is also when we all got into rolling our own random() implementations. based on proper principles, of course, we weren't inventing any. but!)
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@dpnash @futurebird @Bumblefish (and this is also when we all got into rolling our own random() implementations. based on proper principles, of course, we weren't inventing any. but!)
@moira @futurebird @Bumblefish
Some months before I found the RNG patterns in the fake star charts (I was around 15 or so), I had the really bright idea of “hey, let’s take the RNG output for a chosen seed as a key stream for a cipher! That’ll be really hard to break, and it’ll only be about 10 lines of code!”
That was the first time I rolled my own crypto, and thanks to serendipitously strange-looking artificial star maps, it was also the last.
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@moira @futurebird @Bumblefish
Some months before I found the RNG patterns in the fake star charts (I was around 15 or so), I had the really bright idea of “hey, let’s take the RNG output for a chosen seed as a key stream for a cipher! That’ll be really hard to break, and it’ll only be about 10 lines of code!”
That was the first time I rolled my own crypto, and thanks to serendipitously strange-looking artificial star maps, it was also the last.
@dpnash @futurebird @Bumblefish o noes xD
S'funny, none of us ever got into cryptography, at least not that I remember. Way more interested in getting _finding_ things than _hiding_ things, I think
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@futurebird
things I would check are first the frequency of each number... they should be somewhat uniform but not TOO close to equal as all exactly equal is unlikely... next I'd look at the length of repeat sequences and compare to expected values.the actual definition of random sequences (Per Martin-Löf) is in terms of passing tests actually
@Bumblefish@dlakelan @futurebird @Bumblefish another thing to look for could be frequency of pairs of numbers. for an unbiased, independent dice, there should be about a 1/36 chance of each pair of numbers to appear.
unfortunately you'd quite a large number of randomly generated samples to get this chance exactly, but i guess you could do some fancy statistics to analyze these distributions and try to guess which one is "more random looking"
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@Bumblefish @futurebird (cryptographically-secure) hash functions are a textbook example of something that is not random (given the same input, it should always give the same output), but it's designed to look random (there should not be any way to get any amount of information about the input just from looking at/analyzing the output, even if you know how the function works)
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The LLM is like a little box of computer horrors that we peer into from time to time.
I'm sorry but the whole interface is just so silly.
You ask for random numbers with sentences and it pretends to give them to you? What are we doooooing?
@futurebird Well, LLMs are tools. Know their limitations. Know their power.
In your case:
"create 20 random numbers between 1 and 100 by developing a little python app and running it"
Some day, AIs will respond to any prompt in a perfect way and we humans will be in deep shit.
Edit: LOL mistral.ai answers this prompt by generating the random numbers and THEN SORTING THEM.
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