When I was young I had this idea that any hard drive can be compressed into 100 bytes.
The compressed data is a 4 dimensional vector, a component of the vector is a 25 byte floating point number, and represent the space-time coordinates of the hard drive. (For example my hard drive in 1994 marc 3 23:00:45.456 at a specific place in Budapest)
The extractor algorithm just have to simulate the universe from the big bang up until the given time, read the state of the atoms at the specified location, recognize the hard drive, and read the data from it. (Provided that the universe is deterministic, and what seems to be random in quantum mechanics can be simulated with a pseudorandom number generator.)
That's quite clever. Of course, only 2^800 hard drives can actually be represented in this way, but it would, by definition, be in principle capable of covering everything we would ever desire to place on a hard drive anywhere (during the relevant time period, in the relevant space, to the relevant resolution...).
One drawback (on top of astronomically slow extraction time...), is that this still requires us to go ahead and actually write the data in uncompressed form onto a hard drive somewhere. So storage space is still taken up at some point in the world, but at least we can erase and reuse that space as soon as we like, and transmit the data elsewhere with minuscule bandwidth.
Of course, all this really amounts to "Any data you are actually interested in presumably has a short description (e.g., something like 'A complete audio and video recording of every occurrence in Eurasia over the 10,000 years beginning with 6000 BC') and thus, in perfectly compressed form, you will never have any need for large numbers of bits". Or, put another way, "There can't be more than [some reasonably finite number] pieces of data you will ever actually be interested in in your very finite life, so as far as you're concerned, log_2([said number]) bits suffices for everything".
Even if all your assumptions hold, of course, you can still only represent 2^800 universes, and thus only 2^800 different file systems. That's probably sufficient for cases with infrequent read-write cycles, assuming that your floats tend to cover useful time-space coordinates (i.e. where and when a hard drive could plausibly reside). I'm not sure how "space-time coordinates" would work (where is the origin and what is the granularity?), so I don't know if it's likely.
That being said, I would be more concerned by the philosophical and practical consequences of such capability, namely the ability to read hard drives in normally inaccessible locations and hard drives in the future.
" That's probably sufficient for cases with infrequent read-write cycles, assuming that your floats tend to cover useful time-space coordinates (i.e. where and when a hard drive could plausibly reside). I'm not sure how "space-time coordinates" would work (where is the origin and what is the granularity?), so I don't know if it's likely."
Now I have calculated a little:
The age of the universe is 8 * 10^60 in planck time units:
So if the simulation is for example something like a cellural automaton with a planck-time (5.4 * 10^(-44) sec) step-size, than assuming we use fix-point numbers, 26 bytes suffice. (25 bytes are just not enough, 256^25 = 1.6 * 10^60)
Suprisingly the size of the universe is 5.4 * 10^61 in planck-length units:
For what it's worth, despite the common perception that the Planck length is the the grid-scale on which the world is quantized, or the smallest measurable distance, or various such things, the Planck length is not actually known to have any particular physical significance; it's just the length that falls out of combining various other constants of significance. It's not unreasonable to guess that it will eventually turn out to have some significance in itself, but if there is any, it is as of yet unknown.
Well, let's assume that the past is constantly changing. The path leading from the start to the universe to the writing of your 4D vector would also change and therefore your vector itself might change automatically with every change to space-time. Or would that still be called deterministic?
Not too much, just one thing: If we could simulate the universe then of course there would be a simulation in the simulation, etc... And maybe there is a fundamental yet undiscovered 'law of computation' that a sufficiently complex simulation can embed itself only on a slower timescale, so even if everything is deterministic, we even theoretically cannot calculate fast enough to calculate the future.
Embedding itself is one thing, but what about embedding a small portion of itself? Suppose the area to be simulated was merely the Solar System (with the rest faked), and the size of the computer far larger...
