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Can you store a googolplex digitally? 
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#1
Oct1612, 02:16 PM

P: 15

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.



#2
Oct1612, 02:34 PM

P: 834

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.



#3
Oct1612, 03:32 PM

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P: 22,243

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



#4
Oct1612, 03:37 PM

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P: 11,625

Can you store a googolplex digitally?
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 


#5
Oct1612, 03:38 PM

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P: 22,243

Heh, me too.



#6
Oct1612, 03:47 PM

P: 15

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.



#7
Oct1612, 03:51 PM

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P: 22,243

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.



#8
Oct1612, 04:04 PM

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P: 11,602

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 ;). 


#9
Oct1612, 04:51 PM

P: 15

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*. 


#10
Oct1612, 06:44 PM

P: 390

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 tradeoff, ha.
http://en.wikipedia.org/wiki/IEEE_754 


#11
Oct1612, 06:45 PM

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P: 641




#12
Oct1712, 09:04 AM

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P: 11,602

The observable universe? Not even close. With ~10^{80} atoms, the number of photons is larger by many orders of magnitude. However, "many orders of magnitude" change that to ~10^{90}, ~10^{100} or maybe even ~10^{150} photons. You think that there are 10^{150} photons for every photon in my upper estimate? Then we would have 10^{300} photons. As you can see, the exponent grows slowly even with extremely high estimates  it will not reach 100.....0 (100 zeros). 


#13
Oct1712, 11:34 AM

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#14
Dec1812, 04:21 AM

Sci Advisor
P: 1,132

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 10^{10100}.
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 2^{n} such distances, amounting to a maximum of 100 * 2^{n} bits, which would be hard or impossible to reach depending on the value being stored, and quite an optimization problem. With 2^{265} particles in the universe, this would yield at best 100 * 2^{2265}  huge, but not as large as 10^{10100}. 


#15
Dec1812, 09:03 AM

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You cannot get exponential memory with n particles, those 2^{n} 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. 


#16
Dec1812, 02:14 PM

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P: 1,132

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. 


#17
Dec1812, 02:46 PM

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P: 11,602

2^{100} planck lengths are some micrometers, 2^{200} planck lengths are similar to the size of the accessible universe.



#18
Dec1812, 03:02 PM

Sci Advisor
P: 1,132

Here's an example  please check my math, I'm on my phone.
Given 2^265 (approx 10^80) particles in the universe, suppose we split the particles into groups of three. Each three particles store three distances  these values are independent, given that there are 3 dimensions. Let each distance encode 100 bits, as a low estimate. Each three particles has 2^300 possible states. Let each group of three particles correspond to a digit, in base 2^300 encoding, a really long alphabet. We can store (2^265)/3 such digits  approx 2^260. The result would be the enormous value of (2^300)^(2^260). 


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