"...Not only does DNA store information at a density per unit volume exceeding any other known medium, it can achieve one quarter of the maximum information density allowed by the laws of physics..."
Hmm... That number 1/4 of the Bekenstein bound seems suspicious. A quick search gives:
"A gram of dry DNA is about one cubic centimeter, so the radius is 0.0062 meters. So, the best DNA storage can do with those dimensions is 5.610^15 bits. A Bekenstein-bound storage device with those dimensions would store about 1.610^38 bits."
That's 10^22 difference. Not 1/4. That's more like it ... A Bekenstein bound is Plank-level. Around 8mb per something like a volume of an electron. And DNA uses chemical level. Configurations of atoms.
Agreed. The interesting thing about DNA is not its raw storage capabilities, but with how it interacts with itself and its environment to expose and withdraw certain portions of itself for protein synthesis.
It's self extracting code, so maybe the unpacked density is close to 1/4? That's a wild guess unlikely to be true, IMHO - can't tell without sources from the author.
I think `trhway above has it right. A 2.1 dimensional fractal would be very much like a bumpy sheet in 3-space. A 2.9 dimensional fractal would be a fairly convoluted crumpled sheet. [0]
You'd be amazed how much of the fractal stuff is practical. You don't need to deal with infinities before it becomes useful. For example, fractal antennas can filter for multiple frequencies well (instead of tuning for just one perfectly)[1]. On this topic, check out space-filling curve - it's pretty cool stuff, and the wiki page has a nice diagram of the Peano curve[2].
It's sort of like imaginary numbers. At first glance they seem like a very theoretical construct, but it soon becomes apparent they're everywhere. You can't hardly do any sort of electrical engineering with out them. Likewise with fractals (and the oft associated field of chaos).
EDIT: whoops, missed a reference. (And sorry they're all Wikipedia - there's a ton of great material on this stuff. Many books on chaos will talk about fractals extensively, but the best don't shy from the math!)
I don't think putting 'fractals' on the front of a discussion is very useful. A line segment is a fractal. A dot is a fractal. Everything can be a fractal in the right light. Of course they are useful -- but not usually just because they are fractals.
>A fractal drawn on a two-dimensional sheet of paper, for example, has a higher dimension—say, 2.1. This is a useful feature, allowing nature to pack some part of a fourth dimension into three-dimensional space.
if i remember correctly fractal can't have dimension higher than the space it is embedded in. It can have dimension higher than its local dimension though (that what makes it a fractal :) - a fractal drawn on a 2D plane using lines has local dimension of 1 while it's fractal dimension can be anything up to 2, yet can't be greater than 2. The same way with nervous system, blood arteries/veins - these are just 1D pipes locally, yet as fractals they get to 2.x thus achieving good density in 3D volume of the body with amount/size much less than just a regular network of pipes would do.
In all the sensible dimensions, if X is included in Y then dim(X) <= dim(Y). I'm tempted to write that this holds in every possible dimension, but I think that there are no official criteria to classify something as a fractal dimension. Anyone can propose a new definition of a new fractal dimension, and if it does not have some minimal property it will be simply ignored. The problem is that the set of minimal properties is not well defined, it's more a mater of mathematical taste and usage adoption in the mathematical comunity.
More technical details:
For example, a nice property is that the dimension is countably additive. The Hausdorf dimension has this property, but the box counting dimension doesn't have this property. Should we eliminate the box counting dimension?
On the other hand it's easier to estimate the box counting dimension than the Hausdorf dimension. So, what definition is more useful?
This article takes a broad view of an interesting subject. You twits are arguing over the tiniest of minutiae and completely missing the big picture. Both the fractal dimension inaccuracy and the issue of information density within DNA are entirely irrelevant to the thesis being put forward. This is something I really dislike about hacker news.
Is the thesis that nature is so efficient that it is near the limit of what is physically possible?
I don't quite believe that thesis. While nature is vastly more efficient than our current technology in things like storage density of information and energy efficiency of computation, the arguments that it is near the limit of what is physically possible are flawed, as HNers are pointing out.
Will our technology ever reach the physical limits?
Does our technology advance by copying nature's examples?
Will our technology surpass nature along the way to the physical limits?
>Not only does DNA store information at a density per unit volume
I'm surprised the author didn't mention that the human DNA sequence is ~750 megabytes of data.[1] And that 750MB is replicated billions (or trillions) of times across all living cells of the body. A sort of living organism RAID redundancy.
I found the lack of citations in this article to be both disappointing and suspicious. When you conclude "we will need a vastly different approach to science in order to understand the higher-order, emergent capabilities of nature’s self-organizing structures", I feel like more evidence is required. Though the author did mention some exciting ideas and research, she left it to the audience to follow up on where she might have gotten them from.
14 comments
[ 3.2 ms ] story [ 34.0 ms ] threadHmm... That number 1/4 of the Bekenstein bound seems suspicious. A quick search gives:
http://www.forbes.com/sites/quora/2013/05/22/can-data-storag...
"A gram of dry DNA is about one cubic centimeter, so the radius is 0.0062 meters. So, the best DNA storage can do with those dimensions is 5.610^15 bits. A Bekenstein-bound storage device with those dimensions would store about 1.610^38 bits."
That's 10^22 difference. Not 1/4. That's more like it ... A Bekenstein bound is Plank-level. Around 8mb per something like a volume of an electron. And DNA uses chemical level. Configurations of atoms.
Is that true? Could one make CPU on a 2D chip surface in a fractal pattern and use that for faster computation? Or fancy supercomputer topologies?
I always thought fractal dimension was more of an abstract concept, not actually practical. Sounds awesome though.
You'd be amazed how much of the fractal stuff is practical. You don't need to deal with infinities before it becomes useful. For example, fractal antennas can filter for multiple frequencies well (instead of tuning for just one perfectly)[1]. On this topic, check out space-filling curve - it's pretty cool stuff, and the wiki page has a nice diagram of the Peano curve[2].
It's sort of like imaginary numbers. At first glance they seem like a very theoretical construct, but it soon becomes apparent they're everywhere. You can't hardly do any sort of electrical engineering with out them. Likewise with fractals (and the oft associated field of chaos).
[0] http://en.wikipedia.org/wiki/Fractal_dimension#Introduction See paragraph 3. It makes intuitive sense as you see a 1-dimensional line fill the space of a 2-dimensional plane.
[1] http://en.wikipedia.org/wiki/Fractal_antenna
[2] http://en.wikipedia.org/wiki/Space-filling_curve
EDIT: whoops, missed a reference. (And sorry they're all Wikipedia - there's a ton of great material on this stuff. Many books on chaos will talk about fractals extensively, but the best don't shy from the math!)
It's too much woo.
if i remember correctly fractal can't have dimension higher than the space it is embedded in. It can have dimension higher than its local dimension though (that what makes it a fractal :) - a fractal drawn on a 2D plane using lines has local dimension of 1 while it's fractal dimension can be anything up to 2, yet can't be greater than 2. The same way with nervous system, blood arteries/veins - these are just 1D pipes locally, yet as fractals they get to 2.x thus achieving good density in 3D volume of the body with amount/size much less than just a regular network of pipes would do.
Long version: There are a lot of definitions of fractal dimension (http://en.wikipedia.org/wiki/Hausdorff_dimension , http://en.wikipedia.org/wiki/Minkowski%E2%80%93Bouligand_dim... , ...) but they are not equivalent.
In all the sensible dimensions, if X is included in Y then dim(X) <= dim(Y). I'm tempted to write that this holds in every possible dimension, but I think that there are no official criteria to classify something as a fractal dimension. Anyone can propose a new definition of a new fractal dimension, and if it does not have some minimal property it will be simply ignored. The problem is that the set of minimal properties is not well defined, it's more a mater of mathematical taste and usage adoption in the mathematical comunity.
More technical details:
For example, a nice property is that the dimension is countably additive. The Hausdorf dimension has this property, but the box counting dimension doesn't have this property. Should we eliminate the box counting dimension?
On the other hand it's easier to estimate the box counting dimension than the Hausdorf dimension. So, what definition is more useful?
http://tirania.org/blog/archive/2011/Feb-17.html
I don't quite believe that thesis. While nature is vastly more efficient than our current technology in things like storage density of information and energy efficiency of computation, the arguments that it is near the limit of what is physically possible are flawed, as HNers are pointing out.
Will our technology ever reach the physical limits?
Does our technology advance by copying nature's examples?
Will our technology surpass nature along the way to the physical limits?
I'm surprised the author didn't mention that the human DNA sequence is ~750 megabytes of data.[1] And that 750MB is replicated billions (or trillions) of times across all living cells of the body. A sort of living organism RAID redundancy.
[1]http://newsroom.ucr.edu/1776