Markos Moulitsas is the founder and publisher of DailyKos, the world's largest political blog. He travels quite a bit and is dependent on his laptop and the internet. So I read his first experience with the iPad with a great deal of interest. Go read it (like they need the traffic; on a quiet Sunday night they are running 35,000 visits an hour!). Bottom line: overwhelmingly positive for someone who has a few, routine but critical functions handled by email and Microsoft Office level programs. I've already written about my own plans to get one later in the year, after the kinks are worked out. It cost a tenth what my original Apple II+ costs in 1981 dollars but has 333,000 times as much memory, a color screen and is connected to the internet. Technology has obviously made strides in 30 years. How long can this last? Judging from an article in Nature this week, a long time. I'm not a solid state physicist, so I'll go with the New York Times description of the paper:
The devices, known as memristors, or memory resistors, were conceived in 1971 by Leon O. Chua, an electrical engineer at the University of California, Berkeley, but they were not put into effect until 2008 at the H.P. lab here.They are simpler than today’s semiconducting transistors, can store information even in the absence of an electrical current and, according to a report in Nature, can be used for both data processing and storage applications.
[snip]
The devices, known as memristors, or memory resistors, were conceived in 1971 by Leon O. Chua, an electrical engineer at the University of California, Berkeley, but they were not put into effect until 2008 at the H.P. lab here. (John Markoff, New York Times)
So I might get an iPad, but it's just a temporary device, because if this stuff comes along in as short as a 3 year window as HP is predicting I can't even imagine what things will look like, even in the very near future. We were approaching some size barriers for current technologies and all of a sudden they are gone. Grid computing is achieving unparalleled power by harnessing the simultaneous workings of computers distributed over the internet. What if we could have the same power on our desktop?
Probably the first fruits wouldn't be in computation, though, high density and very fast storage for portable devices like the iPad. That's a reasonable guess but there will likely be applications and developments that are not just unforeseen but perhaps even unimaginable at this moment. The iPad is a kind of computing device that few people -- if anyone -- imagined in 1981 when I bought my first personal computer. Yes, people talked about very powerful personal computers, but the kind of interaction between people and machine and between people using the machines was not appreciated, nor do I think, could have been. I feel confident in predicting that in 10 years the iPad will seem quaint and primitive. But that's all I feel confident in predicting.
I don't think most people are aware of the dramatic revolution we are living through, comparable in significance to the invention of the printing press in 1450. It will be for a future historian to make sense of it. I wonder in what form that judgment will be communicated to others. Meanwhile I'll still get an iPad, even knowing I'll be replacing it with something else in 3 to 5 years.
Quite likely something containing a stack of memristors.
- Log in to post comments
Some of the technical barriers may continue to fall, but there was a mathematician on NPR the other day talking about some unsolved math problems, one of which had profound implications for the future of encryption and therefore for the entire internet. It may have had something to do with properties of prime numbers; in any case, if the solution of the problem turns out one way, online banking and e-commerce could collapse. I am hoping that some commentator can supply some insight here.
Ed @ #1: It sounds like you're talking about RSA, a public key encryption algorithm. Prime numbers are used in key generation.
Ed: The issue is that, for classical computers, there is no known algorithm for factoring numbers in an amount of time that rises slower than exponentially with the number of digits in the number. IOW, whatever factor by which the difficulty increases when you go from, say, 64 bits to 128 bits is approximately the same factor by which difficulty increases when you go from 128 bits to 192 bits, and so on. Thus the security depends on the fact that, while it is relatively easy to construct a number which is the product of two prime numbers, the bad guys will not have the time or resources to extract the prime factors from the larger number.
The issue is that while no such classical algorithm is known to exist, it has never been proven that no such algorithm exists (nor that such an algorithm does exist). If such an algorithm were ever found, it would make decryption quite a bit easier, and as you say, e-commerce would collapse.
There is a twist here: given the existence of a quantum computer, there is an algorithm that will factor a number in less than exponential time (the Schor algorithm). Don't panic yet, because nobody can yet construct a quantum computer with sufficient capacity for the job--the Schor algorithm has been implemented to demonstrate that 15 = 3 * 5, but that was on a state-of-the-art toy system, and there are still several engineering hurdles that have to be overcome before anyone can make a quantum computer that will decrypt your encrypted transmissions. And even if they do succeed, quantum computers provide a truly secure encryption mechanism, in the sense that if anybody were listening in, the message would be destroyed.
Many thanks! That sounds about like what I heard while half asleep. The NPR story had to do with the Millennium Prize for the Poincare conjecture and other famous problems. The existence or non-existence of the algorithm you mention seemed to be one of the unsolved problems under discussion. Guess we can all continue to purchase sex toys securely online for the time being.
I can prove that every even prime is the sum of two odd numbers, and that is about the limit of my command of number theory.
Ed:
Yeah, I know what you mean. I can prove that, too. But I didn't have room to put the proof on the blog.
I think that Bertrand Russell and Alfred North Whitehead proved it in just under 200 pages.
There is no such thing as an even prime except for 2 itself. Every other even number is factored by 2 and some other number. That's the definition of 'prime' - no factors other than itself and 1.
Gray: Didn't read Ed's remark correctly. I assumed he was joking about every even number (>2) being the sum of 2 primes, the oldest unsolved problem in mathematics (aka Goldbach's conjecture). But the way it's written it isn't true, because 2 is not the sum of two primes (1 is not a prime number, a minor but crucial addition to your definition). It is true, of course, that every even number is the sum of two odd numbers and as noted, apparently true (but so far unproved) that every even number greater than 2 is the sum of two primes, but his statement is plainly false.
But all I said was that 1 is an odd number, and the proof that every even prime is the sum of two odd numbers should not be too difficult. Actually, I ripped this joke off of Douglas Hofstadter, who mentioned it in Godel Escher Bach; it has been over 25 years since I read it, but it is on page 551, together with the statement that there is no solution in positive integers to the equation a to the n plus b to the n = c to the n for n=0. The latter was a joke involving Fermat's last theorem, which was still unsolved when GEB was written. ALso in GEB there is a reference to the only positive integer to occur nowhere in the continued decimal expansion of pi. That book was a real tour de force.
Ed: So you did. My apologies. I read it two prime numbers. 1 is clearly an odd number. And I thought you were joking but thought it was a different joke. Two wrongs stil make a wrong. That's oddk I know, but now we are even.
Wow, Ed, and I've had the book sitting on the shelves here unread. Thanks.
You are all presumably familiar, too, with the late Peggy Gordon's discovery of the group of two elements: one is the identity element, and so is the other.
Revere, check your Times quote. Not sure you intended to quote four different paragraphs from it, but what you did was quote the same two paragraphs twice.
Jeez. Thanks. The last minute grant details have distracted me. Deleted the repetition.
Right Paula. GEB is full of logical fun. I do not remember if it was in GEB, but there was an example of a term paper with âERRATAâ listed on page ii, whose sole entry reads âii. For ERRATA read ERRATUM.â
I recommend reading the dialogues first as a way of dipping into the book. They give you a sense of what the chapters are all about. The whole book is playful, but the dialogue about the stereo system as a metaphor for self-referential systems was very entertaining.
Thanks, Ed. In my plentiful free time. (Well, yes, there's some, but it's hard to remember, with three editing deadlines coming up.) Stereo dialogue etc. sounds just right.