I've never understood the "number of the atoms in the universe" argument. The number of states the universe can be in doesn't seem to be equal to the number of atoms. For example, just two atoms could encode lots of numbers simply by using their distance. Quantum physics would affect it, but I mean in principle: we are not switching atoms on and off to encode state.
It’s 2^1729 digits, (vastly) more digits than there are atoms in the universe.
The vastly bit is kind of an understatement.
Each stable isotope is indistinguishable from every other carbon isotope. So, you can probably encode a few bits per atom assuming you can somehow read this data. However they are talking vastly larger numbers of digits here. Where there are only ~10^80 digits worth of atoms in the visible universe, but hey bump that to 10^90 it does not help.
Sure you might encode 10^6 or hell I will give you 10^100 bits of data per atom or something but that’s not even close to helpful. It’s still on the order of K atoms in the universe and you want to encode 10^400+ * K bits of data. So each atom needs to encode 10^400+ bits and remember each stable isotope is indistinguishable from every other atom of that stable isotope.
Yea, that specific number fits into 2 kilobytes of memory, but it’s so large it’s hard to compare it to anything.
Which is why I suggest comparing it to the number of bits required to encode the universe. If all you wanted was to store a single arbitrary number and could read write the universe you could do anything out to 2^(10^(80 * k)) where k is larger than 1 but I suspect below 100.
It's really just a phrase used nearly-rhetorically in order to convey the vast scope of a thing. Everyone understands that the number of atoms in the universe is a huge number, so it's a good benchmark.
When people use this phrase they're not trying to claim that the number of atoms in the universe is directly related to the problem at hand; they're just trying to convey scale.
It's not states, it's logarithmic of states (# of dimensions of finite size) . Think about writing down a number. One atom per digit is a pretty natural heuristic for the optimal spatial cost of information. Yes you can get clever, but there's no point, were already at astronomical levels of imprecision.
As I said, one atom per digit is not really natural. Just two atoms could encode an infinite number of numbers, by measuring their distance. Well except quantum physics might get in the way, not allowing us to measure with arbitrary precision. But that would be another argument.
Another argument would perhaps be the energy required to do the computation. Maybe that relates more directly to the number of atoms in the universe, via Einstein's equation?
> Well except quantum physics might get in the way,
This is a pretty huge well except. When people talk about information that can be stored in the universe this is exactly the limitation they have in mind.
It's just there for a reference, maybe a better one would be Kurzweil's ultimate laptop (made from the whole universe). But the interesting part is that I don't think the ultimate laptop takes into account interactions and state between atoms. AFAIR it assumes computation is done on every available dimension (like electron spin) but not on how atoms move and interact with each other. Intuitively it shouldn't make much difference though.
So what quantum value is it? Shouldn't the argument then at least say "the number is greater than the number of possible states of the universe", or something like that?
Doing computations with single atoms also doesn't sound very practical.
Measuring distances, I suppose there could be numerous ways, like measuring the gravity or electric pull (not sure what it is called in English). I think only Quantum theory says we can not measure to arbitrary precision, or at least if we do, there are other issue. Still, that would be another argument than simply pointing at the number of atoms.
