When you make that PR, you do not transfer any of youtube-dl to github. Their repo already has those objects.
So all you have done is pushed a repo containing a specific hash, which is now a TOS violation, in that specific case at least. I wrote "Certain commit hashes are rapidly heading toward being illegal" because of that specificity.
(I wonder when illegal transcendental numbers will become a thing.)
Git commit hashes are indeed deterministic, though it depends on the inputs.
From StackOverflow [0]:
Git uses the following information to generate the sha-1:
* The source tree of the commit (which unravels to all the subtrees and blobs)
* The parent commit sha1
* The author info (with timestamp)
* The committer info (right, those are different!, also with timestamp)
* The commit message
$ git rev-parse HEAD
78d66a4f169fec9cb9b3252f7a22bb020e967cd2
$ git log HEAD
commit 78d66a4f169fec9cb9b3252f7a22bb020e967cd2 (HEAD -> master)
Author: XXXX
Date: Mon Nov 2 20:44:04 2020 -0500
temp2
$ git reset --soft HEAD\^
$ GIT_COMMITTER_DATE='Mon Nov 2 20:44:04 2020 -0500' GIT_AUTHOR_DATE='Mon Nov 2 20:44:04 2020 -0500' git commit -m temp2
[master 78d66a4] temp2
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 b
$ git rev-parse HEAD
78d66a4f169fec9cb9b3252f7a22bb020e967cd2Except it's not.
You can post the numbers alone, without including information (directly or by reference) to the application about which information is banned, all you want.
You need to somehow include information on how to use the number, which is arguably easier to pull off, but still doesn't make it legal, just harder to find out.
1. Someone somewhere creates a numbered list of primes (so 1=1,2=2,3=3,4=5,5=7,6=11,7=13,8=17, etc etc) 2. You refer to "the [N]th prime" with a vastly smaller number, and people could fetch it from the list of primes. 3. They could theoretically ban the number N?
Fun fact, there are a _LOT_ of prime numbers. There are about 10^22 prime numbers smaller than 10^24, so about every 100th number is prime. The ratio decreases the higher you go of course. The vastly smaller number is actually just a few bits smaller :)
Edit: except for this one, I guess. This one wasn't about DRM, but rather just a locked down device. TI sent bogus DMCA notices for that one, but as far as I can tell there is no solid legal theory under which those primes were illegal, and nobody ever got sued, so we can file this one under "manufacturer upset they no longer control their users' devices throws a legally meaningless fit".
https://en.m.wikipedia.org/wiki/Texas_Instruments_signing_ke...
But the first popular 'illegal prime' was a gzipped code that would defeat the DRM of DVDs. See https://en.wikipedia.org/wiki/Illegal_prime
There is a great classic essay describing this called "What color are your bits?"
https://ansuz.sooke.bc.ca/entry/23
tl;dr yes. An illegal number multiplied by two is illegal. Randomly generating that number is not. The illegality is not strictly a property of the number itself, but it's color.
Therefore all numbers are illegal.
You can't just dodge color by mutating the number via mathematical operations, color doesn't work like that. You can only get rid of the taint by using a fresh number without taint.
If there's an illegal number X and I give you a number Y with the intention that you obtain X from it by some transform then Y is also illegal because I "tainted" it when I did the original transformation from X.
If I just need Y (or X) for some operation that's not related to the "illegality" then those numbers are not illegal.
The essay that droffel linked to explains this very well.
Two thoughts:
1. This appears to show a complete disregard for basic mathematics...
and
2. Do lawyers ever wonder why people make jokes about them?
The number itself isn't illegal, because it can come from any number of contexts. What's illegal is wilfully working towards generating that number while knowing its purpose as a key. It's just the principle of Mens Rea at work.
Another idea is to generate a random number and multiply it with an illegal prime. If the illegal prime is a sufficiently large number; we can extract the original illegal prime with very high confidence by just finding its prime factors and picking the shortest one.
Used to be illegal to have it in US and other countries, don't know status now
It's actually even cooler: store this prime in base-2 and interpret it as a gzip file, and it'll gunzip to a full working DeCSS (DVD decrypter) source code in C :-)
If you’re going to restrict “publishing” to binary fixed point, arguably 1/3 is unpublishable.
The integers are a subset of the rationals, which are a subset of the algebraic numbers, which are a subset of the computable numbers, which (most mathematicians would accept) are a subset of the reals.
There are lots of subtleties about this. In fact Scott Aaronson just started a series that is in some sense about some of those subtleties, which I hope to be able to understand some day!
Hmm... are you saying that, for example, pi is the one-step sequence of operations of dividing a circle's circumference by its diameter? But first, you have to get both those values...
In practice, speaking informally, people talk about programs that may run forever all the time.
People have developed lots of theory around those as well. Of specific interest here would be the class of programs that provably only runs for a finite time before it produces the next bit of output.
You need that latter class of programs to talk about producing digits of pi, or running the main loop of an OS.
See also https://en.wikipedia.org/wiki/Total_functional_programming
That captures all of the transcendentals we care about. The remainder (to be fair, almost all of them) aren't computable at all, even in principle.
Given an arbitrary stopping point x, you have approximately x / log x primes between 1 and x.
In other words, for a file of length n, you have to try about O(n) slight variations to find a prime number.
"The Trinity Hall Prime - Numberphile" https://www.youtube.com/watch?v=fQQ8IiTWHhg
"The Emerging Art of Drawing in Prime Numbers" https://www.popularmechanics.com/science/math/a28649996/the-...
When framed this way, so many laws become ridiculous. Copyright is about establishing a monopoly on numbers. It's illegal for normal people to know certain numbers because they represent classified information. People go to jail because of numbers stored in their hard drives.
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!”)
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.
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.
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.
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?
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.)
But this will, in time, generate every copyrighted material.
So finding a variant of one offending digital file that's also a prime is a rather straightforward process.
What fascinates me more is all the illegal bits people put into the bitcoin block chain; and how bitcoin people deal with that.
Especially since you can make random looking strings illegal after the fact:
I have an illegal file A. I produce a random binary file R of the same size as A. I publish (R xor A) and R in two different venues, both mathematically-perfectly random files on their own. But together, they produce illegal file A.
Are you aware of any specific instances where the presence of youtube-dl hashes in other repos have been found by github and used as the grounds for disciplinary action? That would be noteworthy indeed.