4 ms·

Taking the same idea further, there are plenty of (possibly) illegal numbers that don't even have to be prime, just because an ASCII-encoded string of text can

Taking the same idea further, there are plenty of (possibly) illegal numbers that don't even have to be prime, just because an ASCII-encoded string of text can be represented as a number. A pair of GPS coordinates with five decimal precision, written like 7.63941, -122.12825 is just 19 ASCII characters. So in ~400 characters you could have 20 such pairs. 400 ASCII characters being 400 bytes or 3200 bits, they can be represented by a number that's < 2^3200. What if the 20 pairs of coordinates are current locations of US nuclear submarines? That would make the ~900 digit number very dangerous from the US military's point of view. 400 characters is surely also enough for many other bits of highly classified information. Several names of CIA agents under non-official cover in China. A concise description of the purpose and capabilities of the X-37 spacecraft. The top item on the President's Daily Brief for today. It raises some interesting questions about the legality of numbers, and what would happen to someone publishing one. What if I'm writing an article that happens to contain the nuclear-submarine-coordinates-encoding number? What if I'm writing about a debugging problem and I show a memory dump that happens to contain it? The actual probability of that happening is of course zero, but something tells me that anyone who did publish such a number would suddenly find themselves in the company of government agents very willing to overlook that person's rights.

dTal 5y 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 5y ago
  I 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 5y 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 5y ago
  Thanks, 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.
uuidgen 5y ago
But those numbers without context are just that - numbers. It's the context that makes it information. GPS coordinates by itself are the same, they're just numbers, but by attaching meaning to them you may make them dangerous or illegal to publish. And sometimes enough meaning is "don't let anyone know it" - the rest can be gathered from the context and other data.

dTal 5y 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 5y ago
I 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 5y 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 5y ago
Thanks, 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.

uuidgen 5y ago

But those numbers without context are just that - numbers. It's the context that makes it information. GPS coordinates by itself are the same, they're just numbers, but by attaching meaning to them you may make them dangerous or illegal to publish. And sometimes enough meaning is "don't let anyone know it" - the rest can be gathered from the context and other data.