There is a finite amount of information in the Universe

Theory: The amount of information in the universe is finite.

Assumption: There is a finite amount of mass/energy (hereafter called "stuff") in the universe.

Groundwork. First, we must examine information theory, and specifically the concept of entropy. For this analysis, we will accept the definition of entropy to be synonymous with information.

Example. Papa and Momma have a biological son, Joe, 15, and a biological daughter, Elenka, 12. The following is the "information" encoding in this sentence:
  • Joe is Papa's and Momma's son.
  • Joe is 15 years old.
  • Elenka is Papa's and Momma's daughter.
  • Elenka is 12 years old.
That's it. There are a much larger (potentially infinite) number of statements we could make; however, none of these have new information.
  • Joe is male (This is encoded in Joe being a son).
  • Elenka is younger than Joe (This is encoded in their ages).
  • Momma is older than 15 (This is encoded in the biological mother relationship).
Got it so far?

Given that there is a finite amount of stuff in the universe, if there are a finite number of states the stuff can exist in, there is a finite amount of information in the universe.

But wait! Space is infinite! The universe is unbounded! Of course. However, there is a finite amount of stuff in the universe. Being finite, it can only occupy a finite amount of space. One piece of information: any space unoccupied by stuff is empty accounts for the remainder of infinite space.

Sure, that sounds like handwaving, but it isn't. The number 1 has an implicit infinite number of zeros preceding it, but they do not encode any information. Neither does empty space.

Okay, now we come to the hard part. If we accept the lemma "there are a finite number of states the stuff can exist in," we're done, but that would be cheating. First, we must accept that stuff is not infinitely divisible. If, in fact, there are basic units of stuff (quarks, photons, tachyons, et al), each of these units has some simple state:

I'm not a physicist, nor will I ever be. However, I will take on good authority the truth of this fact. If so, then,

There is a finite amount of information in the universe


To respond to Stealth Munchkin:

SM purports that the infinite series of natural numbers, by their mere existence, represent an infinite amount of information. Not so. If one attempted to label each number in a non-trivial fashion, one might generate more information. The fact that 762 is the number after 761 in radix 10 is trivial. There is no information involved.

If, however, one were to attempt to create a piece of information for every number, where would you store it? Every brain, every piece of silicon, every wavicle would be full, and you'd still only have encoded a finite amount of information.

Ah... nodes based on catbox arguments, don'tcha just love 'em?

There's a basic flaw in cordelia's writeup. While thereis probably only a finite amount of 'stuff' in the universe, information does not have to relate to matter or energy.

Example - the whole numbers. There are infinitely many (Aleph Null) of these numbers. Each one of those numbers is a unit of information, and nontrivial information at that, since for example its primality might be hard to determine.

If one were to make a node on Everything for every single integer, then one could create an interesting writeup on every single number - an infinite amount of them. And that would still leave an infinite amount of numbers that hadn't been noded.

So in fact, there is an infinite amount of information in the universe - but only a finite amount of it is data pertaining to actual physical events - everything else is abstract information.

Another point cordelia fails to deal with - while matter may be indivisible (and I've seen no proof that it is, although like her I am not a physicist), is time? If not, one could easily say that any particle that exists for a finite length of time has been in an infinite amount of states...

m_turner points out the last sentence may be flawed - see Planck time and Planck space.

In response to what I think is the point of cordelia's response the total amount of information that can be encoded in the universe is not the same as the total amount of information that exists in the universe - I think. And surely every number is a piece of information?

Cordelia changed her response. I would argue that we weren't talking about non-trivial information, necessarily...

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