All computer files are sequences of bits. All sequences of bits are integers. All integers already exist in the infinite set of natural numbers. I can even calculate how big those numbers are given their bit count.
digits(bits) = ceil(bits * log10(2))
digits(32) = 10
digits(64) = 20
digits(128) = 39
digits(256) = 78
digits(512) = 155
digits(1024) = 309
digits(20 KiB) = 49,321
digits(2 GiB) = 5,171,655,946
Of course this is silly, but interesting nonetheless. And we routinely speak about such high-dimensional spaces in research and engineering. Or we can imagine optimization as traversing a pre-existing search space. It may be structured as a graph or perhaps a Euclidean space. And in that space we can imagine a loss surface, that sits there in peace all along, with its global minimum somewhere. And instead of "constructing" a solution, we are simply hiking in this space and trying to spot that valley. But this is a bit fictional. We never physically "instantiate" this surface. It's an imagined abstraction. In reality we just have a vector and some rules as to how we change that vector. But we can imagine those changes to be movements in an imagined space.
It's like the idea that the sculptor doesn't create the sculpture, the sculpture was there all along, he just had to remove the superfluous matter to reveal what was already there (i.e. the atoms belonging to the final sculpture).
The most interesting thing is kind of on the border, between these absurdly large spaces and the more manageable ones that are feasible to enumerate.
Another similar mindblow thing was when I forgot the password to a file that I encrypted. It's a fascinating thing that the bit pattern on the disk is functionally random now, and cracking it would take longer than the age of the universe. But if only I knew the password, it would only take just a second. There is a definite sequence of keystrokes I can execute to bring the universe in a state where the content will appear on my screen, it's so close, yet it's so-so far if you don't remember the password. Just a little difference in your brain state and it flips from trivial to hopeless.
PS, if you like thinking about such things, I recommend Meta-Math by Gregory Chaitin, it's very fun (providing an address VS constructing the thing is basically the gist of algorithmic information theory).
> It's like the idea that the sculptor doesn't create the sculpture, the sculpture was there all along, he just had to remove the superfluous matter to reveal what was already there (i.e. the atoms belonging to the final sculpture).
I understand this argument but I have far more trouble applying this logic to real things. I'm not sure the same logic applies once the information is instantiated in the real world as a physical object. I haven't thought very deeply about it. I think the true sculpture exists only in the ideal world and the real world object is merely an approximation of it.
> Of course this is silly
It's an existential issue for me. At some point it became a political issue. I became a copyright abolitionist because of this insight. Copyright is logically reducible to monopolistic ownership of numbers. The sheer absurdity of it led me to reject the very idea of intellectual property as delusional nonsense.
The legal system is rather the spiritual successor of the original "system" where a wise Solomon-like elder would adjugate the issue based on their best judgment and intuition and customs, ideally seeking peace and social satisfaction and future harmony. Codified law channels this into some more pre-shaped form, but the fuel of the legal system is still the human judgment and common sense at the core. Often the law basically just prompts and nudges the judgment of the jurors or judge to a certain direction, but it can't account for all corner cases. The nerd mind asks ok ok but what if X, where do you draw the sharp line between X and Y? It doesn't matter. If it comes up, a court will decide it based on all available common sense and the implicit values of the culture.
In the cases where someone seemingly gets away with "rules-lawyering", then it's not purely their genius logic-brain that wins, but there is some kind of slanted playing field that's not really available to you. Of course the line between "annoying rules-lawyering based on literal interpretation of technicalities that obviously nobody intended to be interpreted so" and something that was not anticipated initially but does fit within the rules. This decision itself is based on judgment and intuition. In life, sometimes coming up with a "technically works" thing is rewarded and lauded (math proofs, pathological counterexamples, cracking an encryption library via side-channel attacks), other times you get an eye-roll and that's obviously cheating and wasn't meant (e.g. courts of law and fun at parties).
Intellectual property is just rent seeking by established corporations as well as protection against competition so that others can't enter the market. The days where they protected individual creators and inventors are long gone.
It's basically creating value out of nowhere in lieu of resources that are truly valuable, but inconvenient to trade directly. But then like a metrics that got corrupted (I forgot the name of the law for that), there are other that are trying to game the system (and succeeding) so that they can maximize their share.
At our university lab we've been working on this for 25 years. Building a search engine is the easy part. Keeping a federated server with a billion users running is unsolved. Creating a fully -serverless- decentralised search engine is possible, you also need self-funding economy. Seems we're one of the few labs worldwide to still make actual operational prototypes of this stuff. More shameless self promotion:
"SwarmSearch: Decentralized Search Engine with Self-Funding Economy" [0]
Really handy to have s search engine to search this webpage with 45,671,926,166,590,716,193,865,151,022,383,844,364,247,891,968 pages and the rest of the web (no spyware, no tracking).
See also https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achi...
The claim is that humans are not "creators" but generators, very much in the random number generator sense. We are interesting number generators.
This kind of imposing or order is an act of lowering the entropy of the sample in a very specific way, parties that know the 'key' to the sample will be able to experience the sample in a way that parties without the key would not, to them the sample is still boring or random. Your reduction of the act of creation to picking a particular number is belying the fact that absolutely nobody that creates something is picking that number: the number is a carrier, it is not the ideas embedded in it. You could translate that novel (or textbook, or sound or video or any other medium) into other media, descriptive, literal or you could even completely transform it. And there would still be a relationship to the original creation, hence the concept of a 'derived work', which for your numbers example would utterly fail: you could not take that number outside of knowing its meaning and come up with any of these derivations without having the key to decode it.
This kind of reductive reasoning is not helpful, it merely attempts to flatten a whole pile of some of the most accomplished and positive contributions by humanity to the generation of interesting numbers. And it is so much more than that.
Besides all this, any kind of attempt to digitize an actual work of art, rather than just a simple text is going to be a lossy process. You are never going to be able to replicate the original to the point that you have created something that is equal. You may be able to get close but it won't be the same thing. More so for sculptures than for two dimensional art, less so for for instance audio where the replication gear is getting really good. But generation loss is a thing and if you re-create and re-digitize then after a surprisingly low number of such generations you will end up with noise.
Authors, sculptors, painters, even programmers and other creative people are so much more than interesting number generators, even if their works can be encoded or approximated numerically. That's flipping the encoding analogy on its head, the map really isn't the territory.
And that’s without me asking you to define “real”, which would be another rabbit hole.