The inventors of the RSA algorithm (Ron Rivest, Adi Shamir, and Len Adleman) were awarded the Turing Award on Monday. This was announced at the opening of the RSA conference. More information can be found in this article.
There are several misconceptions about DNA computers out there that I would like to clear up. The National Geographic article was written for a popular audience and has mistakes that most of you problably picked up (for example, the beautiful quote "fuzzy logic" problems... have many possible solutions rather than the either/or logic of binary computers). And I'm not even going to comment on the Guiness Book of World Records nonsense.
As many of you have pointed out, DNA computers are not going to replace conventional electronic computers. Len Adleman, the inventor of DNA computing, has said "Despite our successes, and those of others, in the absence of technical breakthroughs, optimism regarding the creation of a molecular computer capable of competing with electronic computers on classical computational problems is not warranted." The problem is partly the effort required to read the answer once the solution is available, and partly the effort required to perform the computation itself. Reading the answer from the first DNA computation took Adleman about a week, and reading the answer from his most recent DNA computation (the largest computation ever performed) took two weeks. The computation itself was very manpower intensive: thousands of precise moves were required of a human experimentor to get the necessary components in a test tube, but once they were all in, the computation itself happened virtually instantly.
Although I have only read the popular accounts of this experiment and not the actual results, this experiment seems to simply be using the ATP in DNA as the power source for the computation instead of external ATP. This is impressive, but it is not the "technical breakthrough" needed to propel DNA computing to the everyday world.
The claim of this computer working 100,000 times faster than a PC is probably true. But this speed comes from the parallelism inherint in DNA computation. When each computer is only 1 molecule in size, it is easy to have 10^10 computers in one tube. But if you do the math, this says that each individual molecule is 100,000 times slower than a PC. So it is equally true to say that my PC is 100,000 times faster than a DNA computer, its just that I can't afford millions of them. This also says that DNA computers are not good for computations that are serial in nature: the speed comes from the fact that DNA computers can run in parallel.
That being said, there may be specific applications for DNA computers in the future. Because of their parallelism, DNA computers are great at solving NP-complete problems (not fuzzy logic problems, as said in the article). This does not make them tractable, however. They run in linear time, but take exponential space. So instead of the problem that "solving this problem will take the age of the universe" you run into the problem "solving this problem will require the mass of the Earth in DNA".
I guess I have a better computer than I thought. All this time I thought I only had one burner, but it turns out that I have the equivelent of 10 burners! Sweet!
There are an infinite number of bases that you can write pi in a finite number of digits. You found one, base pi. There's also base sqrt(pi), base pi^2, etc. If you write pi in base pi^q where q is rational, its expansion will contain a finite number of digits.
There is such a thing as "complexity inherent in a system". In fact, computer scientists (the ones who work for universities, not the ones who build web pages) have been working on this for 30 years. Complexity theory is a very well defined, but not very well understood, discipline.
A good place to get started with complexity theory is the book Computational Complexity by Papadimitriou, if you're interested. The definitions of a "complex system" are given in this book, and they have nothing to do with analogies of our experience of being human. Complexity is a mathematical object.
By the way, one of the open problems in complexity theory is the famous P=NP problem, and if you solve it, you will win $1 million.
Those of you who are interested in the future of alternative computing, including quantum computing, might want to check out Caltech's Computing Beyond Silicon Summer School program. The top minds from around the world will present the latest information about quantum, molecular, and DNA computing.
The Gamma function is the extention of the factorial function onto the complex plane. Specifically, Gamma(n+1)=n!
The Gamma function is the integral from 0 to infinity of e^-t * t^(n-1) dt
Gamma(1) = 0! = 1
Re:An Infinite Random Irrational Number
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If Pi is infinitely long, non-repeating and random, then isn't the rule that any such number must contain all finite numbers... eventually?
Not necessarily. Consider pi, written base 10. Now replace every occurrence of the digit 7 with the digit 2. The resulting number is still infinitely long, non-repeating, and random (but I suppose this depends on what your definition of random is). It doesn't contain any finite number that contains a 7 and thus doesn't contain all finite numbers.
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The inventors of the RSA algorithm (Ron Rivest, Adi Shamir, and Len Adleman) were awarded the Turing Award on Monday. This was announced at the opening of the RSA conference. More information can be found in this article.
As many of you have pointed out, DNA computers are not going to replace conventional electronic computers. Len Adleman, the inventor of DNA computing, has said "Despite our successes, and those of others, in the absence of technical breakthroughs, optimism regarding the creation of a molecular computer capable of competing with electronic computers on classical computational problems is not warranted." The problem is partly the effort required to read the answer once the solution is available, and partly the effort required to perform the computation itself. Reading the answer from the first DNA computation took Adleman about a week, and reading the answer from his most recent DNA computation (the largest computation ever performed) took two weeks. The computation itself was very manpower intensive: thousands of precise moves were required of a human experimentor to get the necessary components in a test tube, but once they were all in, the computation itself happened virtually instantly.
Although I have only read the popular accounts of this experiment and not the actual results, this experiment seems to simply be using the ATP in DNA as the power source for the computation instead of external ATP. This is impressive, but it is not the "technical breakthrough" needed to propel DNA computing to the everyday world.
The claim of this computer working 100,000 times faster than a PC is probably true. But this speed comes from the parallelism inherint in DNA computation. When each computer is only 1 molecule in size, it is easy to have 10^10 computers in one tube. But if you do the math, this says that each individual molecule is 100,000 times slower than a PC. So it is equally true to say that my PC is 100,000 times faster than a DNA computer, its just that I can't afford millions of them. This also says that DNA computers are not good for computations that are serial in nature: the speed comes from the fact that DNA computers can run in parallel.
That being said, there may be specific applications for DNA computers in the future. Because of their parallelism, DNA computers are great at solving NP-complete problems (not fuzzy logic problems, as said in the article). This does not make them tractable, however. They run in linear time, but take exponential space. So instead of the problem that "solving this problem will take the age of the universe" you run into the problem "solving this problem will require the mass of the Earth in DNA".
I guess I have a better computer than I thought. All this time I thought I only had one burner, but it turns out that I have the equivelent of 10 burners! Sweet!
There are an infinite number of bases that you can write pi in a finite number of digits. You found one, base pi. There's also base sqrt(pi), base pi^2, etc. If you write pi in base pi^q where q is rational, its expansion will contain a finite number of digits.
A good place to get started with complexity theory is the book Computational Complexity by Papadimitriou, if you're interested. The definitions of a "complex system" are given in this book, and they have nothing to do with analogies of our experience of being human. Complexity is a mathematical object.
By the way, one of the open problems in complexity theory is the famous P=NP problem, and if you solve it, you will win $1 million.
Those of you who are interested in the future of alternative computing, including quantum computing, might want to check out Caltech's Computing Beyond Silicon Summer School program. The top minds from around the world will present the latest information about quantum, molecular, and DNA computing.
Can you give references? I'd like to know more about this.
The Gamma function is the extention of the factorial function onto the complex plane. Specifically, Gamma(n+1)=n!
The Gamma function is the integral from 0 to infinity of e^-t * t^(n-1) dt
Gamma(1) = 0! = 1
Not necessarily. Consider pi, written base 10. Now replace every occurrence of the digit 7 with the digit 2. The resulting number is still infinitely long, non-repeating, and random (but I suppose this depends on what your definition of random is). It doesn't contain any finite number that contains a 7 and thus doesn't contain all finite numbers.
I'm pretty sure no one would have heard a sonic boom from an object (of any size) going 100 to 200 mph.