The conclusion being that you basically need the same amount of data to represent the address of your data as the data itself, so it's not really effective at compression, just a fun thought experiment.
The cool part of this in modern times is that LLMs are basically a form of lossy compression that actually achieves the gist of what these tools fail at. Although it is lossy, and requires a massive substrate. This is related to the idea of AI/LLMs being a form of language compression.
Reinventing Entropy Compression is Intelligence Part 1
3blue1brown https://youtu.be/l6DKRf-fAAM?is=ne73FCJ7ErXhzZ-v
Some of that is also the domain. It's less that science is an extreme form of compression, and more that natural phenomenon are highly compressible. They're a small number of kinds of interactions repeated a bajillion times. How many equations does it take to explain electricity (ignoring equations that are derivatives of ones already included)? I think it's less than 5.
On some level, you could probably reduce all of the Standard Model down to models of atoms, their motion, and the basic subatomic particles (the non-quantum ones). That would explain almost everything that happens on Earth in a very short form, though few people would be able to go from that to explaining how lightning works.
(Then it depends on your concern: "Aagh, the aunt fell!" // "Oh yes, that'd be Newton")
This is totally lost on me.
Appears to be lossy then ;)
(Sorry, you have to admit that was too easy to not say)
Laws (scientific, philosophical etc.) as compression represent the common side of classes of events - an abstraction of said events, stripping the irrelevant - irrelevant to some perspective, or irrelevant in a potential Procuste's bed. So, laws are compression, but a so extremely lossful compression that the loss can be relevant.
Brutally, "there may be more to the story of the fall of an elderly than just gravitation" - also in the sense that there are details behind the event.
Laws are compression - yes, with caveats.
On a more scientific, epistemological side: Einstein extended Newton covering more exceptions (reducing the abstraction - reducing the loss).
Back of the envelope calculation for storing valid 4-grams (sequences of four words) is around 10 billion x 14 bits per word = 17 gb for all 10 billion. There are LLMs 100x smaller which can write coherent prose.
GPT-2 for instance achieves roughly 1 bit per byte, so it can be used to compress (english) text 8-fold. Modern models are likely much better.
Almost like the other Borges work where “the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire”.