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Swedish Mathematician Lennart Carleson Wins Abel
William Robinson writes "Sci Tech is reporting that Swedish mathematician Lennart Carleson has won the Abel Prize on Thursday for proving a 19th century theorem on harmonic analysis. His theorems have been helpful in creating iPod. Prof Carleson's major contributions have come in two fields - the first has subsequently been used in the components of sound systems and the second helps to predict how markets and weather systems respond to change. One of Carleson's many triumphs was settling a conjecture that had remained unsolved for over 150 years. He showed that every continuous function (one with a connected graph) is equal to the sum of its Fourier series except perhaps at some negligible points."
Young people today. You tell them about a deep result in real analysis, and the only thing they're interested in is how it relates to their iPod. And get off my lawn.
Athletic Scholarships to universities make as much sense as academic scholarships to sports teams.
Wiki Article on the Breakthrough
"Sure there's porn and piracy on the Web but there's probably a downside too."
It would have been better if they had said "almost everywhere". That is, the set of points at which a Fourier series diverges has Lebesgue measure zero. There is a quasi-converse, due to the Israeli analyst Katznelson, which, given any set of Lebesgue measure zero -- let's call it Bill -- constructs a continuous function whose Fourier series diverges everywhere in Bill. For more info, see Tom Korner's excellent "Fourier Analysis".
Well they mean "almost everywhere", which has a very precise meaning. i.e. except at a set of measure zero (finite or countably infinite set of points.) Of course, that countable set could theoretically be the rationals, so I don't know whether I'd call it negligible.
Athletic Scholarships to universities make as much sense as academic scholarships to sports teams.
The result he proved is nice mathematics, but you don't need it for iPods or audio coding. First of all, for many engineering purposes, it only matters that it works, not that you can prove that it works theoretically. Secondly, audio coding is done over discretely sampled signals, and most of those theorems become simple linear algebra in that case.
No wireless. Less decimals than pi. Lame.
Yeah, it might be that the MPEG-4/AAC/H.264 algorithms are based in part on Fourier analysis, but I fail to understand how Carleson's theorems have been used in making the iPod. Cupertino is hardly knowledgable in the more esoteric realms of theoretical mathematics, and there is simply no need to incorporate such stuff in an mp4 player.
This is bad journalism, written by bad reporters who lack the most basic understanding of mathematics and engineering. He just thought it might be cool to clam in an iPod in the mess.
The iPod reference is completely misleading, as simple harmonic analysis is way bigger than just an iPod. It's merely talking about this guy proving that Fourier was basically right, validating harmonic analysis and expanding the horizons for signal processing. That's the biggie: signal processing, not the bloody iPod. The stupid article probably includes iPod just for the sake of hits.
Oh really? Search Wikipedia entries, the articles, all links - no mention of iPod except in those annoying side adverts. Why? Because it has nothing to do with it
Credit where credit is due, and none is due here.
If you want credit, how about: Shannon, Fourier and Huffman. Then there's all the folks involved in working out noise masking and all the oddities of human hearing that I don't have the names of.
I seriously need a "No iPod mentions whatsoever" checkbox for my slashdot profile to pull some more signal out of the slashdot article noise.
Incorrect. A set of measure zero can be uncountable. (cf the Cantor set)
Quid festinatio swallonis est aetherfuga inonusti?
Africus aut Europaeus?
This is sometimes mis-stated as 'you can draw the graph without taking your pen off the paper'.
That's not a mis-statement in the case of a real function of a real variable. It's not that informative, but definitely correct in the sense that a function (real etc.) is continuous iff the graph is path-connected (i.e. every two points on the graph can be connected by a continuous path (and by saying 'continuous path' I have of course made the definition self-referential and thus silly, but it is still true)).
The iPod reference got this story greenlighted on slashdot. Otherwise it might not have made it. If you want to guarantee acceptance, mention something bad about M$, something good about Linux, or anything about Apple (preferably good, but there is the odd flame article).
This advice was brought to you by someone with a 100% submission record. (ok, one of one ;-)