josh's clients aren't stupid, they're smart [LWN.net]

josh's clients aren't stupid, they're smart

Posted May 9, 2011 7:55 UTC (Mon) by cmccabe (guest, #60281)
In reply to: josh's clients aren't stupid, they're smart by tialaramex
Parent article: Scale Fail (part 1)

Just for fun, here's a puzzle.

Are these digits random or not? And if not, what is the pattern?
69804177583220909702029165734725158290463091035903784297757265172087724

to post comments

josh's clients aren't stupid, they're smart

Posted May 9, 2011 16:02 UTC (Mon) by dskoll (subscriber, #1630) [Link] (10 responses)

Of course those digits are random. So are these digits:

1111111111111111111111111111111111111111111111111111111111111111

(In other words: Your question is meaningless.)

josh's clients aren't stupid, they're smart

Posted May 10, 2011 6:17 UTC (Tue) by cmccabe (guest, #60281) [Link] (8 responses)

I'm just asking if there is an interesting pattern in the digits or not. That question isn't meaningless.

josh's clients aren't stupid, they're smart

Posted May 10, 2011 10:45 UTC (Tue) by dskoll (subscriber, #1630) [Link] (7 responses)

Of course it's meaningless. There's no such thing as a set of digits that are "random" or "non-random". You can take a sequence generator and run some statistical tests, but that doesn't prove anything. You can test a sequence of digits for compressibility, but that also doesn't prove anything. The digits in the decimal expansion of pi pass all kinds of statistical tests for randomness, but they are assuredly not "random".

As for a pattern, given a finite sequence of digits, you can construct any pattern you like. I could construct a degree-71 polynomial that fits the 71 digits you posted and say "Yes, that's the generator!"

josh's clients aren't stupid, they're smart

Posted May 10, 2011 14:20 UTC (Tue) by bronson (subscriber, #4806) [Link] (3 responses)

Wow. Did you miss the "just for fun" in cmccabe's original post? You must be a riot at parties.

josh's clients aren't stupid, they're smart

Posted May 12, 2011 1:33 UTC (Thu) by dskoll (subscriber, #1630) [Link] (2 responses)

Well, at the parties I go to, people don't usually open the conversation with "69804177583220909702029165734725158290463091035903784297757265172087724".

josh's clients aren't stupid, they're smart

Posted May 12, 2011 4:43 UTC (Thu) by bronson (subscriber, #4806) [Link] (1 responses)

That doesn't explain why why you feel a need to shout someone down here. Must everybody conform to your narrow idea of fun?

josh's clients aren't stupid, they're smart

Posted May 12, 2011 16:12 UTC (Thu) by dskoll (subscriber, #1630) [Link]

Chill out.

josh's clients aren't stupid, they're smart

Posted May 10, 2011 19:05 UTC (Tue) by cmccabe (guest, #60281) [Link] (2 responses)

> I could construct a degree-71 polynomial that fits the 71 digits you
> posted and say "Yes, that's the generator!"

That would be a pattern, but not an interesting one.

josh's clients aren't stupid, they're smart

Posted May 10, 2011 19:07 UTC (Tue) by cmccabe (guest, #60281) [Link]

Sorry, what I meant to say was, that polynomial would not represent a pattern in the sequence itself.

A non-interesting pattern would be something like the observation "this is a number!" or the observation that all digits from 0 to 9 occur.

josh's clients aren't stupid, they're smart

Posted May 12, 2011 11:39 UTC (Thu) by etienne (guest, #25256) [Link]

A more interesting pattern in PI would be this one:
http://kasmana.people.cofc.edu/MATHFICT/mf55-spoiler.html

josh's clients aren't stupid, they're smart

Posted May 19, 2011 11:03 UTC (Thu) by yeti-dn (guest, #46560) [Link]

Please go and learn about Kolmogorov complexity. The question is meaningful but your post, I am afraid, is not.

Just answering so I don't miss the answer

Posted May 10, 2011 21:25 UTC (Tue) by man_ls (guest, #15091) [Link] (1 responses)

It looks pretty random, but there are too few repeated consecutive digits: only three 77 and one 22. I give up, what is the pattern?

Just answering so I don't miss the answer

Posted May 10, 2011 23:05 UTC (Tue) by neilbrown (subscriber, #359) [Link]

71 digits, which is prime so grouping them is unlikely to help.

If you consider just the first 4 digits (0,1,2,3), then even digits occur 10 times each, odd digits 5 time each. However this pattern does not continue (4 and 8 also occur 5 times, but are even).

The longest gap between repeats is 24 between 2 '8's.
'6' and '4' see gaps of 23.

'6' is the least frequent digit, 7 is the most frequent (3 times as frequent)

Taken as a decimal integer the factors less than 100 are
2,2,3,3,23,23

Yet the whole number is not a perfect square.

My conclusion is that this is probably the "least uninteresting number" - very interesting....

josh's clients aren't stupid, they're smart

Posted May 11, 2011 6:00 UTC (Wed) by cmccabe (guest, #60281) [Link] (5 responses)

It's digits 99768 through 99838 from the base 10 decimal expansion of pi.

Every digit is completely predetermined, but it's pretty hard to spot if you don't know what you're looking for!

josh's clients aren't stupid, they're smart

Posted May 11, 2011 8:07 UTC (Wed) by ballombe (subscriber, #9523) [Link]

The only thing that is remarkable is that Google did not find it.

josh's clients aren't stupid, they're smart

Posted May 11, 2011 16:56 UTC (Wed) by tialaramex (subscriber, #21167) [Link] (2 responses)

So in other words the answer was "No" ?

We suspect (as far as I remember no-one has proved) that all possible sequences of digits occur in Pi. Assuming this is so, the fact that a particular sequence occurs in Pi is not interesting at all.

josh's clients aren't stupid, they're smart

Posted May 11, 2011 20:08 UTC (Wed) by cmccabe (guest, #60281) [Link] (1 responses)

Even if all possible sequences of digits occur in Pi, the fact that a particular sequence occurs at a particular position can be "interesting". If nothing else, it would make for a pretty strange compression algorithm (although probably not a practical one for most input data, given how large the indices are likely to be.)

josh's clients aren't stupid, they're smart

Posted May 12, 2011 8:27 UTC (Thu) by ekj (guest, #1524) [Link]

On the average, the index of where in pi a certain sequence occurs, is as long as the sequence itself, thus the average savings of this compression-scheme is zero.

josh's clients aren't stupid, they're smart

Posted May 12, 2011 16:56 UTC (Thu) by fuhchee (guest, #40059) [Link]

I'm still missing the "fun" part.

What Do These Digits Mean?

Posted May 19, 2011 12:35 UTC (Thu) by ldo (guest, #40946) [Link] (1 responses)

#!/usr/bin/python

import sys

charset = ' Wadefhlnost'
modulo = 13
s = 13682311570832829480888979137834570837851469148689544502986
num = iter(range(2, 9999))
while s != 1 :
        n = num.next()
        if s % n == 0 :
                sys.stdout.write("%s" % charset[(n - 1) % modulo])
                s /= n
        #end if
#end while
sys.stdout.write("\n")

What Do These Digits Mean?

Posted May 26, 2011 12:20 UTC (Thu) by net_benji (subscriber, #75195) [Link]

All 23 prime factors of s are of order 1, I think that's the gist of it.
http://www.wolframalpha.com/input/?i=factor+1368231157083...

Here are more working combinations:
charset = "hetfn adlsoW"
s = 7062883793966047784250125868403644804557392731274644684033611
charset = "tslofWe dnha"
s = 1029201132023087388381452825147240668180384494509643451351
...
and here's a different one, just for the fun of it:
charset = "wfyonirvmD s?ecutdpah"
modulo = 23
s = 79 * 211 * 241 * 463 * 487 * 499 * 563 * 571 * 673 * 787 * 911 * 977 * 991 * 1039 * 1249 * 1483 * 1489 * 1493 * 1601 * 1621 * 1697 * 1699 * 1889 * 2243 * 2311 * 2347 * 2459 * 2521 * 2719 * 2909 * 2953 * 3119 * 3271 * 3323 * 3359 * 3533 * 3733 * 3947 * 3967 * 4057 * 4177 * 4283 * 4289 * 4597 * 4651 * 4733 * 4933 * 4969 * 5021 * 5087 * 5261 * 5281 * 5347 * 5399 * 5449 * 5557 * 5641 * 5711 * 5807 * 5869 * 5981 * 6353 * 6359 * 6389 * 6569 * 6701 * 6791 * 6823 * 6983 * 7187 * 7309 * 7321 * 7481 * 7529 * 7673 * 7873 * 7901 * 8017

The source for the generator is there: https://github.com/benthaman/lwn-digits/blob/master/encod...

Hope Jon won't mind posting this nonsense here ;)