3 ms·
The minimum reasonable size of an "illegal number" is fairly comprehensively explored here [0] (tl;dr 128 bits) (You needn't be kept up at night by the thought
by dTal 6y ago
The minimum reasonable size of an "illegal number" is fairly comprehensively explored here [0] (tl;dr 128 bits)
(You needn't be kept up at night by the thought of accidentally publishing nuclear codes; as you say, the probability is 0 for all practical purposes, and the reluctance of government agents to dismiss it as a coincidence would be entirely reasonable)
[0] https://qntm.org/number https://qntm.org/number
- dane-pgp 6y agoI don't know about "reasonable", but much smaller numbers have, in practice, been banned in various contexts by legal authorities (tl;dr 2 to 11 bits). https://en.wikipedia.org/wiki/Illegal_number#Other_examples https://en.wikipedia.org/wiki/Illegal_number#Other_examples
- dTal 6y ago...I don't think it's quite fair to characterize the search term "4" as 2-bits of information, since it's possible to put any text in a search box, not just numbers. Although it's certainly not 128 bits either!
- ACS_Solver 6y agoThanks, that was an interesting read! It does of course raise interesting questions about a nefarious powerful government that wants to get rid of someone for "endangering national security". Taking the example of sensitive GPS coordinates, I can easily come up with an a way to encode a pair of coordinates (with 10m precision) in 5 bytes, or 40 bits. And that's no longer a number where probability is so much on your side. Unscrupulous government agents have a decent chance at finding those 5 bytes in the dump of your 1-terabyte drive! I guess the counterpoint here is, a government that wanted to put you behind bars by justifying it with 5 random bytes would have no problems with fabricating some much stronger evidence against you instead.