On Thu, 2012-07-19 at 19:30 -0500, Jimmy Hess wrote:
The ratio of the number of bits doesn't tell you anything about whether the number was random or not.
Sure it does. A ratio of 1s to 0s of a sufficient deviation, is a sufficient but not a necessarily condition, for establishing that a sequence of binary numbers shown almost certainly was not chosen randomly.
A *sequence*, yes. A single number in isolation, no. Whether the bits within a single value are distributed randomly or not is irrelevant. You seem to be confusing the randomness of a sequence of bits (i.e., within a particular prefix) with the randomness of a sequence of prefixes. You have the entire bit sequence of a particular prefix available to inspect, so you can make a call on the randomness of the bits, but you do NOT have the entire prefix sequence, so CANNOT make a call on the randomness of the prefix. You can say, for a sufficient number of bits, whether the bits are distributed randomly. Agreed. But given a specific bit, without knowing the other bits, you cannot tell whether that specific bit was chosen randomly. If my prefix generating algorithm is to choose 39 bits completely randomly but always set bit 7, you cannot tell that bit 7 has been set non-randomly by inspecting only one prefix, because in a certain number of genuinely random prefixes, bit 7 will be set anyway. Maybe the one you happen to be looking at is such a one. The same is true of any two bits, and any three bits - and so on, all the way out to 40 bits.
However, there _are_ many non-random strings that exist which a 'lazy' or broken ULA ID generator might pick, that can be very easily detected as non-random with sufficient confidence, to tell the user "Hey, sorry, you can't use that. Please generate a new ULA ID".
You can pick them against human criteria; you can't pick them against mathematical criteria unless you have the sequence as well as the value. All zeros is exactly as likely as insert-any-prefix-here. But: IANAS (I Am Not A Statistician :-) so I think I'll stop now. I am either flogging a dead horse or digging an embarrassing hole for myself :-) Regards, K. -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Karl Auer (kauer@biplane.com.au) http://www.biplane.com.au/kauer GPG fingerprint: AE1D 4868 6420 AD9A A698 5251 1699 7B78 4EEE 6017 Old fingerprint: DA41 51B1 1481 16E1 F7E2 B2E9 3007 14ED 5736 F687