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Next try 10 million digits instead of 10 thousand. The Z-score cannot be interpreted so easily. It must be evaluated over all the different ways people have tr
by eesmith 2y ago
Next try 10 million digits instead of 10 thousand.
The Z-score cannot be interpreted so easily. It must be evaluated over all the different ways people have tried to test the digits for randomness.
"Since the advent of computers, a large number of digits of π have been available on which to perform statistical analysis. Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of π, and found them consistent with normality; for example, the frequencies of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found." - https://en.wikipedia.org/wiki/Pi https://en.wikipedia.org/wiki/Pi
- seccode 2y agoI don't think you're correct that the z-score is not being interpreted correctly. I haven't been able to find research demonstrating any non-randomness in pi, so without that we have nothing to compare it to.
- eesmith 2y agoIt's literally an xkcd, #882 https://xkcd.com/882/ https://xkcd.com/882/ There's a large literature of people looking for non-randomness in pi, and failing. If you try 50,000 different tests, with a z-score of 3.29 then 0.1% - 50 of them - will give false positives.
- thunderbong 2y agoMobile version https://m.xkcd.com/882/ https://m.xkcd.com/882/
- seccode 2y agoGetting higher z-scores now. But you could always just try running the code yourself
- seccode 2y agoI don't have the resources to try this unfortunately. I highly encourage somebody to try. But with more digits you may have to change the model.
- eesmith 2y agoYes, you do. You can download the digits at https://www.pilookup.com/download.html https://www.pilookup.com/download.html . You can generate models for different sized subsets. If it's really non-random, you should see the predictability stabilize as you get larger. Otherwise you risk being seen as yet another math crank.
- seccode 2y agoThe issue is not with getting the digits, the issue is with running a large model for larger digit ranges. I tried running with 10,000,000 digits and haven't gotten a prediction yet.
- seccode 2y agoAlso, I am testing different ranges of digits other than first 10,000, but the problem with other ranges is that the distribution of digits is highly imbalanced and the model is not showing statistical significance, but models have a harder time when the distribution of classes is not 50/50, so I think its not quite fair to evaluate the model on these ranges. So why do you think the first 10,000 digits are somewhat predictable?
- lifthrasiir 2y agoBecause "somewhat predictable" doesn't mean "non-random". In fact, almost all prefixes of algorithmically random bit sequences are somewhat predictable with an appropriate definition of "somewhat", because you can find and exploit an accidental bias from taking the prefix and any such bias translates to some predictability. (Another possibility is that, since pi itself is not really algorithmically random, the classifier was somehow able to learn how to partially compute pi! That's another pitfall you need to avoid even when you have a good understanding of information theory and statistics...)