Can you store a googleplex digitally?

lovenugget

will someone please enlighten me on whether this is possible? I'm debating a friend on whether it is, but i'm starting to reconsider my position. to be more specific, i want to know if you can store (10^(10^100)) in a text file on a hard drive that would fit inside the universe. also, whats that in bytes (lol). thanks.

Muphrid

We estimate the number of atoms in the known universe to be about ##10^{80}##, which is far short of a googol, let alone a googolplex. So even if you could use every atom in the universe as a bit, you wouldn't get close to all the digits necessary.

russ_watters

Do you mean just the number or actually that many pieces of data? Because the number already appears in this thread...

jtbell

When I saw the thread title I first thought you were asking about Google's headquarters.

http://www.time.com/time/photogaller...947844,00.html

russ_watters

Heh, me too.

lovenugget

you're right. good answer. what if i asked instead if you could record all of the zeros of a googleplex? i understand the number of zeros is far less.

russ_watters

You cannot write the number out, but since it is a simple number, the sci notation is just as good. I'd declare yourself the winner. I'll pm you the address to mail my commission check.

mfb

In base 10, this would require a 10^100 bytes of storage: No, you cannot, at least not in the classical way. You can use compression, of course - and there are compression systems which can do this with a conventional hard disk.

In an arbitrary base: In base googoloplex, your number is 10. Easy to store in conventional ways.

Googleplex is something different, as you can see from the images ;).

lovenugget

oh sorry about the error in the title. it's correctly spelled as you all have. thanks for the responses. i still wonder though, is there a googolplex photons in the universe? there has to be... or else i'm still underestimating the true size of the how large a number it is.

EDIT

there's not.

*head explodes*.

Kholdstare

actually russ the precision has to be sacrificed when someone tries to save such big number. IEEE 754 floating point standard is good example here. In fact you can save a very large number with a bad precision for a minimum number of bits. The more you add bits into it the precision improves (and also you can use the same memory to store even larger number with even worse precision). Talking about trade-off, ha.

http://en.wikipedia.org/wiki/IEEE_754

Dembadon

Time for a new integer data type! Tinyints just aren't cuttin' the mustard anymore.

mfb

The whole universe? It might be infinite, in this case: Sure
The observable universe? Not even close. With ~10⁸⁰ atoms, the number of photons is larger by many orders of magnitude. However, "many orders of magnitude" change that to ~10⁹⁰, ~10¹⁰⁰ or maybe even ~10¹⁵⁰ photons.
You think that there are 10¹⁵⁰ photons for every photon in my upper estimate? Then we would have 10³⁰⁰ photons.
As you can see, the exponent grows slowly even with extremely high estimates - it will not reach 100.....0 (100 zeros).

russ_watters

What I was getting at when I said it is a simple number is that with only 1 sig fig, there is no precision to be sacrificed by storing it in some variation of sci notation.

-Job-

It may be possible to store such a large value within the Universe, though it's likely to be at least a computationally difficult problem and we would possibly have to give up the ability to store any given string of 10¹⁰¹⁰⁰.

Given any two particles, there is a value implicitly stored that corresponds to their distance, in three dimensions, measured in some unit. If we measure at the Planck length, that's approximately 100 (?) bits per distance.

Given n particles, you can potentially store 2ⁿ such distances, amounting to a maximum of 100 * 2ⁿ bits, which would be hard or impossible to reach depending on the value being stored, and quite an optimization problem.

With 2²⁶⁵ particles in the universe, this would yield at best 100 * 2²²⁶⁵ - huge, but not as large as 10¹⁰¹⁰⁰.

mfb

You cannot get exponential memory with n particles, those 2ⁿ distances are not independent. Neglecting quantum mechanics, you can fully describe all via their coordinates - 3 per particle in space, 6 if you include their momentum. With ~100 bits per coordinate (roughly 1m^3 of space), 10^30 particles would give ~10^34 bits of storage. If you use the whole accessible universe, you get 200 bits per coordinate and ~10^80 particles, for a total capacity of ~10^84 bits.
Quantum mechanics does not allow that precision, so it gets even worse.

-Job-

That's right, as I pointed out only some strings may be encoded to make maximum use of the 2ⁿ values and it becomes a large optimization problem.

The point is there's substantially more storage capacity in the universe than the number of particles. Given two strings, we can encode a number of bits corresponding to the length of the universe measured in Planck units - I haven' t computed this value but it's greater than 100 bits.

mfb

2¹⁰⁰ planck lengths are some micrometers, 2²⁰⁰ planck lengths are similar to the size of the accessible universe.


It is not substantially. While 10^80 and 10^84 differ by a factor of 10000, this is a small factor compared to the overall size of the numbers.