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In high school, my math teacher once asked us to write down a random string of zeroes and ones, similar to what they did in the study to measure "cognitive func

by twiss 9y ago

In high school, my math teacher once asked us to write down a random string of zeroes and ones, similar to what they did in the study to measure "cognitive functioning". He then asked us to count the number of times we alternated between 0 and 1. He told us that while most people try to have about a 50% split between 0 and 1, many alternate too often (0101101 instead of 0100011). Maybe there are other tests that one could learn to improve one's randomness, or at least write down a random string faster (they also measured speed). In the introduction, they cite that "the complexity of a subject-produced pseudorandom sequence (…) is surprisingly resistant to practice effects". However, is it also resistant to teaching effects?

trevyn 9y ago
This is a great question. What are the speed requirements? https://www.quora.com/Is-it-possible-for-a-human-to-generate-a-truly-random-sequence-mentally https://www.quora.com/Is-it-possible-for-a-human-to-generate... You could probably come up with a reasonably good, fast mental PRNG algorithm, and practice that.
- Someone 9y ago
  Pick a phrase (name, address, phone number would do), discard white space, and convert the upper two bits to binary. Example: "Pick a phrase" would become 00 01 11 11 01 00 00 10 01 11 01... That's certainly not random, but unlikely to be detectable for shorter sequences. (Edit: it probably is a fun exercise to write a program that decodes this code that reaches >75% (lossy) compression)
  - averagewall 9y ago
    That would hurt you on speed. It's much faster to just pull numbers out of your head as fast as you can write them down. That should be protection against using an algorithm. Even if you do have a fast algorithm, it would still get slower as you age, so you could use it to compare yourself at different ages. The test might also be scored using randomness tests that would pick up the repeated use of the same algorithm, like the one you described. Distribution of letters and their (ASCII?) bits won't be perfectly random. You could also hand code exceptions for known algorithms as you discover them. That's what interests me. Monitoring your own cognitive ability as you age for early detection and tracking of neurodegenerative diseases. For this, you need a test that's resistant to practice.
    - Someone 9y ago
      "It's much faster to just pull numbers out of your head" I don't doubt that, but the context was to generate reasonably good (in the sense of "looks like independent samples from a 50/50 distribution") sequences. Humans are notoriously bad at that (example: in the first 9 bits, one would expect four consecutive zeroes or ones. Try finding someone who produces that when 'just pulling numbers out f their head as fast as you can write them down'). I think this will be significantly better (as indicated above: for shorter sequences), even though it lumps a, e, i, n and r to the bit pattern '01'. It also can be quite fast, even if you do it by memorizing the mapping from letter to 1..26 doing 'mod 4', and conversion to two binary digits.
BlackFly 9y ago
There are a whole bunch of test for true white noise: http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html For those who don't want to visit the link, some of the more intuitive examples: * Ratio of zeros to ones (and in subsets) * Longest string of zeros/ longest string of ones (and in subsets) * Frequency of ngrams (00, 01, 10, 11, 000, 001, ...) * Maximum cumulative sum (treating it like +1 -1)
Houshalter 9y ago
You can test and refine your randomness ability here: http://www.loper-os.org/bad-at-entropy/manmach.html http://www.loper-os.org/bad-at-entropy/manmach.html

by twiss 9y ago

trevyn 9y ago

This is a great question. What are the speed requirements? https://www.quora.com/Is-it-possible-for-a-human-to-generate-a-truly-random-sequence-mentally https://www.quora.com/Is-it-possible-for-a-human-to-generate... You could probably come up with a reasonably good, fast mental PRNG algorithm, and practice that.

Someone 9y ago
Pick a phrase (name, address, phone number would do), discard white space, and convert the upper two bits to binary. Example: "Pick a phrase" would become 00 01 11 11 01 00 00 10 01 11 01... That's certainly not random, but unlikely to be detectable for shorter sequences. (Edit: it probably is a fun exercise to write a program that decodes this code that reaches >75% (lossy) compression)
- averagewall 9y ago
  That would hurt you on speed. It's much faster to just pull numbers out of your head as fast as you can write them down. That should be protection against using an algorithm. Even if you do have a fast algorithm, it would still get slower as you age, so you could use it to compare yourself at different ages. The test might also be scored using randomness tests that would pick up the repeated use of the same algorithm, like the one you described. Distribution of letters and their (ASCII?) bits won't be perfectly random. You could also hand code exceptions for known algorithms as you discover them. That's what interests me. Monitoring your own cognitive ability as you age for early detection and tracking of neurodegenerative diseases. For this, you need a test that's resistant to practice.
  - Someone 9y ago
    "It's much faster to just pull numbers out of your head" I don't doubt that, but the context was to generate reasonably good (in the sense of "looks like independent samples from a 50/50 distribution") sequences. Humans are notoriously bad at that (example: in the first 9 bits, one would expect four consecutive zeroes or ones. Try finding someone who produces that when 'just pulling numbers out f their head as fast as you can write them down'). I think this will be significantly better (as indicated above: for shorter sequences), even though it lumps a, e, i, n and r to the bit pattern '01'. It also can be quite fast, even if you do it by memorizing the mapping from letter to 1..26 doing 'mod 4', and conversion to two binary digits.

BlackFly 9y ago

There are a whole bunch of test for true white noise: http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html For those who don't want to visit the link, some of the more intuitive examples: * Ratio of zeros to ones (and in subsets) * Longest string of zeros/ longest string of ones (and in subsets) * Frequency of ngrams (00, 01, 10, 11, 000, 001, ...) * Maximum cumulative sum (treating it like +1 -1)

Houshalter 9y ago

You can test and refine your randomness ability here: http://www.loper-os.org/bad-at-entropy/manmach.html http://www.loper-os.org/bad-at-entropy/manmach.html