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What is the theoretical limit of information density?

58 pointsby lpageover 11 years ago

6 comments

Steuardover 11 years ago
The remarkable thing that this explanation doesn&#x27;t really explore in depth is that the maximum information (~entropy) contained in a region scales according to its boundary <i>area</i> rather than to its volume. That means that &quot;maximum information per unit volume&quot; drops precipitously with size.[1]<p>Just for example, this allows you to calculate an <i>ultimate</i> limit on Moore&#x27;s law of only ~800 years, for any possible computer functioning within the bounds of the observable universe. As sketched below[1], the observable universe can hold only about 10^123 bits of information. Processors currently contain about 10^9 transistors (each of which has to be doing computations with an independent bit of information to be useful), a factor of 10^114 less. If Moore&#x27;s law claims that this number doubles every 2 years, that means it grows by a factor of 10^3 every 20. And 20x(114&#x2F;3) is about 760 years. (A more detailed calculation carried out in a paper by Krauss and Starkman at <a href="http://arxiv.org/abs/astro-ph/0404510" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;astro-ph&#x2F;0404510</a> came up with a limit of about 600 years.) That&#x27;s almost frighteningly soon.<p>[1] As the link says, for a cubic centimeter (cc) of volume, the maximum entropy is about 10^66 bits. But if you consider a cubic meter instead, you find it can hold at most 10^70 bits, which comes out to 10^64 bits per cc! For a cubic kilometer you get 10^76 bits, which is only 10^61 bits per cc. If the solar system has radius ~10^13 m, it could hold at most 10^96 bits, or 10^51 bits&#x2F;cc. And the whole observable universe (with radius ~5x10^26 m) could hold at most 2.5x10^123 bits, or 10^38 bits&#x2F;cc. That&#x27;s remarkably less than the direct one cc calculation! This behavior is exceedingly non-intuitive, at least to me.
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drakaalover 11 years ago
You have a molecule. Something that will &quot;stay put&quot; probably written on a &quot;2d&quot; surface like Graphene.<p>Graphene is composed of lots of little hexagons. Each side of the hexagon can be broken and have an atom attached to it in &quot;3d&quot;.<p>You have 6 sides and the angle break can go &quot;up&quot; or &quot;down&quot;.<p>You can only use 3 sides however so that each hexagon has data and you can tell unique data.<p>This gives you 3 positions in 3 states, Up, down, or Flat. 0.142 nanometers per bond...<p>That&#x27;s 27 states per hex, and 190 hexes per nanometer... 36,100 hexes per square nanometer...<p>I&#x27;m sure I screwed up a calculation in there somewhere. But Based on current tech this is my answer to what is possible to write. Now Reading might be a bit harder at any speed... but hey this is all theory right?
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vinceguidryover 11 years ago
This assumes that all information is stored physically.<p>Let&#x27;s say you get a telegram. The telegram itself can contain maybe a couple of paragraphs of text. You might think the bandwidth of the channel is at most a kilobyte or so. But there&#x27;s plenty of other aspects that can raise the amount of information conveyed. Say you get one saying &quot;Short Dow.&quot; Just going by the content, you&#x27;d have no idea what it was saying. Is there a guy named Dow somewhere that&#x27;s short? But if you&#x27;re a stockbroker, all of a sudden there&#x27;s a whole lot more info there. When you allow for context, information density can approach infinity.
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dizzystarover 11 years ago
Can anyone put this in terms like 100<i></i>100 Petabytes or something? Or is the number so large that it really isn&#x27;t conceivable at this point?<p>I&#x27;ll admit that I don&#x27;t understand the problem completely, but isn&#x27;t this assuming the absolute maximum with little consideration of actual technology limits? How much does it change when we consider the limits of technology and our ability to store it on said technology?
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galaktorover 11 years ago
might be nitpicking a bit here, but &quot;information&quot; != &quot;data&quot;. It is hard to tell how little or much information I can extract from any amount of data. data + context = information
MildlySeriousover 11 years ago
So the theories here assume qubits are the smallest unit of storage. I&#x27;m not into physics, so how&#x27;s the evidence they are really the smallest units possible to store information as? After all, atoms were said to be the smallest thing at some point.
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