[asimpletune]

The little story about the alien at the beginning was interesting. It might be a way of rephrasing information theory as a limit on “measure-ability”.

I remember in high school physics realizing that an in-elastic rod would not be possible, because it would allow faster than light communication. There’s probably something to that effect that already exists that I don’t know about regarding information theory, and how you can’t store more information than is allowed by converting the problem into one of measurement rather than compression.

It might even say something about how small matter is allowed to be.

If you increase the number of sticks the alien is allowed to have, then his task becomes significantly easier. So the question could be rephrased as “what are the fewest sticks the alien could use to complete his task of encoding n bits representing m books”.

Fewer sticks than that would violate this law of measurement (I don’t know if that actually exists but it seems like it) and more than that is wasteful.

At any rate, for each bit of information you’re required to measure with one order of magnitude of precision better, so it’s clearly impossible.

[snarkconjecture]

You're on the right track, especially with the last sentence.

If reality had an infinite amount of detail (i.e. matter could be arbitrarily small), we could make storage media as dense as we liked by encoding ones and zeros as the presence or absence of tiny bits of matter.

The alien's stick is a version of this, albeit an exponentially inefficient one restricted to codewords of the form 1111...0000.

In practice, if atoms are about N orders of magnitude smaller than macroscopic objects, we can fit (very roughly) 10^N bits of information in an object, and the alien's method can only fit, as you said, roughly N bits.

Of course, existing storage methods are somewhere in between, because 1 gram of storage media can hold way more than 23 bits but way less than 10^23.

(I'm handwaving past some important distinctions, like the distinction between the size of atoms and the level of detail in the physical world. In classical Newtonian physics, things can be made of particles but the particles can have perfectly continuous positions, so that there's still no ultimate limit on measurement detail. Quantum physics changes this -- although this gets complicated because of the holographic principle; many physicists think the ultimate information limit grows like the 2/3 power of volume, instead of linearly...)

[fl0ki]

> many physicists think the ultimate information limit grows like the 2/3 power of volume, instead of linearly

I may have misunderstood and I'm clearly not up to speed on the literature, but even at an intuitive level, wouldn't this violate other principles?

If this is how information entropy scaled, either we could "work around" it by having more but smaller storage entities adding to the same volume, which violates this theory directly because then when would it ever actually apply; or it somehow enforces the limit over any given volume regardless, and therefore the entire universe's volume (which isn't even finite?) somehow sets and tracks a global limit because anything smaller would be a workaround. Neither makes sense to me.

Now if we're saying that the simulation running our universe has limitations that make this true in practice in some sense that we can measure but can't work around, I will need an explanation as to why we're not totally freaking out right now. There's navel gazing philosophy and then there's shit like this which could mean we discover a wrongwarp to the end credits within this century.