Maybe. Numbers in real life — the domain of the legal system — tend to be either for counting or measuring.

Numbers that are huge and precise are data, information, something quite different.

The thing with illegal primes is that they are small enough to really feel like numbers rather than a concatenation of things forced to look like a number (“the shape of my bedroom is 201809!”)

What is the ontological status of "the smallest number which is outside the domain of the legal system in this sense"?

I don't think it exists because you can always copyright some piece of self-created digital art so that it hashes to the number (if the hash maps to enough bits to represent that number).

I think there is a biggest number though, and it should be higher than 64bit-1 because your processor would otherwise occasionally handle illegal numbers, thereby (probably) making it illegal as well.

My point is rather than if we agree that large-enough numbers can be data, then there is a number at which they start to be data, N say, then "all numbers greater than or equal to N are data" uses N not as data, but as "counting and measuring". So this distinction is self-contradictory, so incoherent.

You could just say "greater than N-1" to avoid this problem, so this doesn't seem like a very strong argument.

I think the better point to make is that the law will never actually produce a concrete N, preferring to leave itself vague so that it can criminalise things at a whim. This is what makes it a farce and why such notions need to be purged from the law.

How can you subtract 1 from data?

You don't. That was subtraction on a meta level. You name the largest non-data number instead of naming the smallest data "number".

the fact that you cannot identify the exact number of sand grains that make a collection into a heap of sand does not mean heaps of sand do not exist

At least in the case of sand you can give examples of numbers of grains that don't constitute a heap, and numbers that do. And numbers smaller than the former will be non-heaps and numbers larger than the latter will be heaps.

For natural numbers, the lawyers seem unable to do even that. Sure, they might want to name some of the "illegal primes" mentioned in this thread as examples, but what will they say about those numbers +1? They're gonna paint themselves into a corner of ridiculousness nomatter what.

N = 10^85

You’ll know it when you see it.

> Numbers in real life — the domain of the legal system — tend to be either for counting or measuring.

What does "in real life" mean? You and your brain presumably exist in real life. If you brain can construct any natural number, then do they not exist just as much as the ones that happen to appear as counts of rice or the price of beer?

I think any number whose information density is more than could be memorized becomes data, and no longer counts as a real life number.

One might stretch the definition to allow numbers that you could read on a postcard in one go to still count as numbers, but it’s a big stretch. If there’s a more understandable representation of the number — especially if there’s a more understandable representation — then it’s data and not a number.

Beyond a certain amount of information content numbers just become data. Certainly at the point where counting the number of digits is non trivial. (There are notations to make magnitude easier to see, but these purposefully delete information content.)

And you get into pretty absurd situations: Whatever the status quo on this matter is, I think we all agree that the integer 0 is in the public domain. And also the following algorithm: (0) let n = 0. (1) Increment n. (2) Go to (1).

But this will, in time, generate every copyrighted material.

Indeed. The only possible conclusion is that all copyrighted material already exists since all numbers already exist. Artists are just people who discover interesting and really big numbers through the convoluted process of "creation". After the number is found, all bets are off.