Google ad, via gmail: "Quantum Corporate Funding - Quantumfunding.com - Factoring For Contractors Direct Contractor Funding Source".
I was hoping it would be about quantum computers to do integer factoring, say using Shor's algorithm, but something seemed a bit off about the text; it had "quantum" and "factoring" in it, but also words like "funding" and "contractor".
"Factoring" in this context is apparently a banking service that involves selling your accounts receivable (i. e. money people owe your business) in exchange for a (slightly smaller) amount of cash, which you get now. Wikipedia has more. I'm not quite sure why it has that name.
But it wouldn't have surprised me to see somebody saying that they have invented a quantum computer large enough to do non-trivial factorization via a Google advertisement. I'm not saying they'd be right, but I've seen other mathematics/physics crackpottery delivered through that channel.
Showing posts with label quantum. Show all posts
Showing posts with label quantum. Show all posts
11 August 2008
26 September 2007
Parallel universes?
Recently it's been reported at Slashdot that a mathematical answer to the question of parallel universes exists.
(They used the word "mathematical", which should have been my first clue that I shouldn't be reading it. "Mathematical" means "I'm trying, and failing, to use math".)
Anyway, a bit of combing through the Slashdot comments turned up this article and this one from New Scientist. It seems reasonably clear that somewhere there is some work, and what this work purportedly shows is that the many-worlds interpretation of quantum mechanics is consistent. One of the articles I found said that the work was done by David Deutsch, David Wallace, and Simon Saunders, and was presented at a conference at the Perimeter Institute for Theoretical Physics; I think that the articles are referring to this talk by David Wallace, but they might be referring to a talk by Saunders at the same conference.
Basically, what the many-worlds theory says is that parallel universes are constantly branching off of ours whenever any sort of observation occurs, therefore causing the collapse of a wavefunction.
Of course, events like those are happening all the time. Where are these parallel universes? And I'm not even going to try to think about how many of them there are, because the number is obscenely ridiculous. How many wavefunctions are collapsing around you right now? And the whole structure is branching. Let's say that every second, somewhere in the universe, exactly one wavefunction collapses, and there are two possible pure states that it could collapse to. The universe is about 5 × 1017 seconds old, so the number of universes you'd need to make this work is two to that power. Occam is rolling over in his grave. Except maybe in the universe these people are in, Occam never existed.
Besides, we can't see these other universes. Isn't that convenient? Perhaps the two major interpretations of quantum mechanics -- the probabilistic interpretation and the many-worlds interpretation -- are just two different formalisms for understanding the same thing. It's easy to picture this giant combinatorial tree of universes; it's harder to picture superpositions.
You're offended by the idea that "God plays dice with the universe". So you call zillions of other universes into existence because you can't handle it? Einstein would be ashamed.
(Edited, 12:37 pm: today's Questionable Content refers to the many-worlds interpretation.
(They used the word "mathematical", which should have been my first clue that I shouldn't be reading it. "Mathematical" means "I'm trying, and failing, to use math".)
Anyway, a bit of combing through the Slashdot comments turned up this article and this one from New Scientist. It seems reasonably clear that somewhere there is some work, and what this work purportedly shows is that the many-worlds interpretation of quantum mechanics is consistent. One of the articles I found said that the work was done by David Deutsch, David Wallace, and Simon Saunders, and was presented at a conference at the Perimeter Institute for Theoretical Physics; I think that the articles are referring to this talk by David Wallace, but they might be referring to a talk by Saunders at the same conference.
Basically, what the many-worlds theory says is that parallel universes are constantly branching off of ours whenever any sort of observation occurs, therefore causing the collapse of a wavefunction.
Of course, events like those are happening all the time. Where are these parallel universes? And I'm not even going to try to think about how many of them there are, because the number is obscenely ridiculous. How many wavefunctions are collapsing around you right now? And the whole structure is branching. Let's say that every second, somewhere in the universe, exactly one wavefunction collapses, and there are two possible pure states that it could collapse to. The universe is about 5 × 1017 seconds old, so the number of universes you'd need to make this work is two to that power. Occam is rolling over in his grave. Except maybe in the universe these people are in, Occam never existed.
Besides, we can't see these other universes. Isn't that convenient? Perhaps the two major interpretations of quantum mechanics -- the probabilistic interpretation and the many-worlds interpretation -- are just two different formalisms for understanding the same thing. It's easy to picture this giant combinatorial tree of universes; it's harder to picture superpositions.
You're offended by the idea that "God plays dice with the universe". So you call zillions of other universes into existence because you can't handle it? Einstein would be ashamed.
(Edited, 12:37 pm: today's Questionable Content refers to the many-worlds interpretation.
27 August 2007
some links, primarily about the "social graph"
Brad Fitzgerald, formerly of livejournal, gives his Thoughts on the Social Graph. The social graph is, roughly, the graph whose vertices are individuals and whose edges connect pairs of people who know each other (for some definition of "know"); Fitzgerald advocates making the social graph a "community asset" that would be available to anyone who wanted it.
I see the term "social graph" is a bit misleading because it suggests that there is only one type of edge, i. e. one kind of way in which one can know other people. (Indeed, this is a perennial problem on a lot of social networking sites; there's often no way to indicate the difference between, say, a person that one met once at a party and one's spouse.) Fitzgerald acknowledges this:
The next step in the analysis of social networks might be to take into account the "strength" of relationships, as currently most social networking sites I know of don't acknowledge that I am more interested in some of my friends than others. Also, to what extent can the strength of relationships be guessed just from looking at the social graph without this strength information? A person who I know quite well is likely to be someone with whom I have many friends in common.
Also, the social graph is in some important ways directed (the link goes to Good Math, Bad Math); for example, if edges connect X to Y if X reads Y's LiveJournal. (It wouldn't surprise me to learn that Fitzgerald has this example in mind.) The somewhat addictive tool LJ Connect, which finds the shortest path between two individuals with LiveJournals via their friends, explicitly acknowledges this.
Finally, some shadowy figures seem to be aggregating the mathematics blogging community, and various other blogging communities as well. Their in-house mathematician gives yet another example of using the formula 1+2+...+n = n(n+1)/2.
And some links:
Paul Graham writes about Holding a program in one's head; a lot of his ideas seem to have obvious analogues to mathematical research, which isn't surprising, as programming and mathematics are quite similar. I'll probably have more to say about this later.
There is a graphical formalism for quantum mechanics, which its authors call "kindergarten quantum mechanics"; this is said to be a very considerable extension of Dirac's notation, and gives short derivations of deep results concerning teleportation, quantum mechanics, and so on. If this is true (I'm not familiar enough with the results concerned to say), it's a good example of what Graham has to say about choosing appropriate notation.
Vlorbik asks us to please lie more carefully. He writes:
In Nature's Casino, by Michael Lewis, from the New York Times, August 26, about the insurance market for catastrophic events.
I see the term "social graph" is a bit misleading because it suggests that there is only one type of edge, i. e. one kind of way in which one can know other people. (Indeed, this is a perennial problem on a lot of social networking sites; there's often no way to indicate the difference between, say, a person that one met once at a party and one's spouse.) Fitzgerald acknowledges this:
It's recognized that users don't always want to auto-sync their social networks. People use different sites in different ways, and a "friend" on one site has a very different meaning of a "friend" on another. The goal is to just provide sites and users the raw data, and they can use it to implement whatever policies they want.
The next step in the analysis of social networks might be to take into account the "strength" of relationships, as currently most social networking sites I know of don't acknowledge that I am more interested in some of my friends than others. Also, to what extent can the strength of relationships be guessed just from looking at the social graph without this strength information? A person who I know quite well is likely to be someone with whom I have many friends in common.
Also, the social graph is in some important ways directed (the link goes to Good Math, Bad Math); for example, if edges connect X to Y if X reads Y's LiveJournal. (It wouldn't surprise me to learn that Fitzgerald has this example in mind.) The somewhat addictive tool LJ Connect, which finds the shortest path between two individuals with LiveJournals via their friends, explicitly acknowledges this.
Finally, some shadowy figures seem to be aggregating the mathematics blogging community, and various other blogging communities as well. Their in-house mathematician gives yet another example of using the formula 1+2+...+n = n(n+1)/2.
And some links:
Paul Graham writes about Holding a program in one's head; a lot of his ideas seem to have obvious analogues to mathematical research, which isn't surprising, as programming and mathematics are quite similar. I'll probably have more to say about this later.
There is a graphical formalism for quantum mechanics, which its authors call "kindergarten quantum mechanics"; this is said to be a very considerable extension of Dirac's notation, and gives short derivations of deep results concerning teleportation, quantum mechanics, and so on. If this is true (I'm not familiar enough with the results concerned to say), it's a good example of what Graham has to say about choosing appropriate notation.
Vlorbik asks us to please lie more carefully. He writes:
We were supposed to test the claim that a certain population proportion was 10% against a sample proportion of 13%, based on n= 57 data points (at some stated confidence level that I’ve forgotten). But wait a minute. You can’t get 13% from a sample of 57 subjects: 7/57 ~ .122807 (i.e., 12%) and 8/57 ~ .14035 (i.e., 14%).This particular one isn't a big problem, but it's symptomatic of something more general -- that the "applications" problems in a lot of mathematics textbooks bear very little resemblance to reality, which only seems to frustrate the students. (Another complaint I have about such textbooks is that the calculus texts seem to assume the student is familiar with physics, which is often not a reasonable assumption to make, and so the instructor ends up teaching physics instead of calculus.)
In Nature's Casino, by Michael Lewis, from the New York Times, August 26, about the insurance market for catastrophic events.
21 June 2007
Quantum probability, and one and a half dead cat jokes
There exists such a thing as "quantum probability". Basically, it's like ordinary probability, except that instead of having probability density functions, you have wavefunctions. (Sometimes you have "discrete wavefunctions", which are wavefunctions that are concentrated on, say, the integers; I don't know if this is the right technical terminology. This doesn't seem to occur in actual quantum systems -- what with the world being continuous and all -- but that doesn't stop a mathematician!) These are annoying because wavefunctions are complex-valued and I can't keep nearly as many complex numbers straight in my head as real numbers. I'll probably have more to say about quantum probability in the future.
Anyway, I was walking down the street earlier today, lamenting this fact (after trying to do such computations in my head and failing) and I saw somebody wearing a T-shirt which said Schrodinger's cat is dead. I thought this was sad! Then after she walked past I saw that on the back of her shirt it said "Schrodinger's cat is not dead".
This joke's been done before, though. Griffiths' text on quantum mechanics has a picture of a live cat on the front and a dead cat on the back.
An ex of mine said that the only legitimate use of HTML's <blink> tag (which fortunately is used a lot less often than it was in, say, the late nineties) was the following:
Schrodinger's cat is NOT dead.
Anyway, I was walking down the street earlier today, lamenting this fact (after trying to do such computations in my head and failing) and I saw somebody wearing a T-shirt which said Schrodinger's cat is dead. I thought this was sad! Then after she walked past I saw that on the back of her shirt it said "Schrodinger's cat is not dead".
This joke's been done before, though. Griffiths' text on quantum mechanics has a picture of a live cat on the front and a dead cat on the back.
An ex of mine said that the only legitimate use of HTML's <blink> tag (which fortunately is used a lot less often than it was in, say, the late nineties) was the following:
Schrodinger's cat is NOT dead.
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