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#1
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Abel Prize awarded to Norwegian mathematican
http://www.guardian.co.uk/internatio...738394,00.html
Excerpts: "A £500,000 prize that is considered the "Nobel" for mathematics has gone to an 80-year-old Swedish academic whose work on the complexities of soundwaves has subsequently been used in the electronic components of iPods." "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." "In the 1960s Carleson showed that any sound, no matter how complicated, can be represented as a series of sine waves. "That translates in the real world as the idea that any sound can be reproduced using the sound of a tuning fork," said a University of Oxford mathematician, Marcus du Sautoy. "The sound of a lion roaring can be broken down into just simple tuning forks."" "In an iPod, tunes stored electronically as complex waves are split into their different components when played." "For years people didn't understand the complexities of it," said Prof du Sautoy. "In recent years they've realised how amazing Carleson's work was." Hopefully, this explains why frequency response measurements, and testing with test tones, are so important in audio. -- |
#2
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Abel Prize awarded to Norwegian mathematican
"chung" wrote in message
... http://www.guardian.co.uk/internatio...738394,00.html Excerpts: "A £500,000 prize that is considered the "Nobel" for mathematics has gone to an 80-year-old Swedish academic whose work on the complexities of soundwaves has subsequently been used in the electronic components of iPods." "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." "In the 1960s Carleson showed that any sound, no matter how complicated, can be represented as a series of sine waves. "du Sautoy. "The sound of a lion roaring can be broken down into just simple tuning forks."" Looks like Fourier Analysis to me. Tuning forks for sine waves..(jumpers for goalposts?).maybe Marcus du Sautoy (nice name) is using tuning forks as dumbing down the tabloids. "That translates in the real world as the idea that any sound can be reproduced using the sound of a tuning fork," Really? One tuning fork, that's amazing ;-) "In an iPod, tunes stored electronically as complex waves are split into their different components when played." "For years people didn't understand the complexities of it," said Prof du Sautoy. Really (is this an April fools joke, no it can't be or the scientist would be named 'Loof Lirpa' "In recent years they've realised how amazing Carleson's work was." With Fourier spinning in his grave... Hopefully, this explains why frequency response measurements, and testing with test tones, are so important in audio. Well, knock me over with a coconut I would never have guessed. ;-) -- |
#3
Posted to rec.audio.high-end
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Abel Prize awarded to Norwegian mathematican
Mike Gilmour wrote:
"chung" wrote in message=20 ... =20 http://www.guardian.co.uk/internatio...738394,00.html Excerpts: "A =A3500,000 prize that is considered the "Nobel" for mathematics has = gone=20 to an 80-year-old Swedish academic whose work on the complexities of=20 soundwaves has subsequently been used in the electronic components of=20 iPods." "Prof Carleson's major contributions have come in two fields - the firs= t=20 has subsequently been used in the components of sound systems and the=20 second helps to predict how markets and weather systems respond to=20 change." "In the 1960s Carleson showed that any sound, no matter how complicated= ,=20 can be represented as a series of sine waves. "du Sautoy. "The sound of= a=20 lion roaring can be broken down into just simple tuning forks."" =20 =20 =20 =20 Looks like Fourier Analysis to me. Tuning forks for sine waves..(jumper= s for=20 goalposts?).maybe Marcus du Sautoy (nice name) is using tuning forks as= =20 dumbing down the tabloids. "That translates in the real world as the idea that any sound can be=20 reproduced using the sound of a tuning fork," Really? One tuning fork,=20 that's amazing ;-) Perhaps you want to read more about Carleson's work: http://www.abelprisen.no/en/prisvinn.../building.html "In 1966 Carleson published a paper that explained why. All finite=20 graphs of the general type considered by mathematicians could be=20 captured by adding up the heights of sine waves of appropriate=20 frequencies. The proof was tough and involved showing why, when you add=20 up the infinitely many numbers that came out of Fourier's analysis, the=20 answer didn't spiral off to infinity but honed in on the graph you were=20 trying to capture. The ideas in the proof were so tough that it is only=20 in recent decades that mathematicians have appreciated how influential=20 these ideas really are. Fourier's problem however is still open for=20 higher dimensional graphs and represents a major goal for mathematicians=20 in this area." You can read a little bit more he http://en.wikipedia.org/wiki/Lennart_Carleson rest snipped -- |
#4
Posted to rec.audio.high-end
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Abel Prize awarded to Norwegian mathematican
"chung" wrote in message
... Mike Gilmour wrote: "chung" wrote in message ... http://www.guardian.co.uk/internatio...738394,00.html Excerpts: "A £500,000 prize that is considered the "Nobel" for mathematics has gone to an 80-year-old Swedish academic whose work on the complexities of soundwaves has subsequently been used in the electronic components of iPods." "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." "In the 1960s Carleson showed that any sound, no matter how complicated, can be represented as a series of sine waves. "du Sautoy. "The sound of a lion roaring can be broken down into just simple tuning forks."" Looks like Fourier Analysis to me. Tuning forks for sine waves..(jumpers for goalposts?).maybe Marcus du Sautoy (nice name) is using tuning forks as dumbing down the tabloids. "That translates in the real world as the idea that any sound can be reproduced using the sound of a tuning fork," Really? One tuning fork, that's amazing ;-) Perhaps you want to read more about Carleson's work: http://www.abelprisen.no/en/prisvinn.../building.html "In 1966 Carleson published a paper that explained why. All finite graphs of the general type considered by mathematicians could be captured by adding up the heights of sine waves of appropriate frequencies. The proof was tough and involved showing why, when you add up the infinitely many numbers that came out of Fourier's analysis, the answer didn't spiral off to infinity but honed in on the graph you were trying to capture. The ideas in the proof were so tough that it is only in recent decades that mathematicians have appreciated how influential these ideas really are. Fourier's problem however is still open for higher dimensional graphs and represents a major goal for mathematicians in this area." You can read a little bit more he http://en.wikipedia.org/wiki/Lennart_Carleson rest snipped Thats better, thanks. The Guardian was poor journalism, the clip above would have served it a lot better, the Guardian dumbed it down, hence the header "Prize for mathematician who paved the way for Ipod" I'm not denigrating his work only remarking on this particular type of tabloid journalism. Mike -- |
#5
Posted to rec.audio.high-end
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Abel Prize awarded to Norwegian mathematican
Ah. It sounds as if Carleson dealt with infinite Fourier series of
finite-length waves, while the earlier theory was finite Fourier series of infinitely long waves. That point was missing from the original article. -- |
#6
Posted to rec.audio.high-end
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Abel Prize awarded to Norwegian mathematican
In article ,
"Mike Gilmour" wrote: "chung" wrote in message ... Mike Gilmour wrote: "chung" wrote in message ... http://www.guardian.co.uk/internatio...738394,00.html Excerpts: "A £500,000 prize that is considered the "Nobel" for mathematics has gone to an 80-year-old Swedish academic whose work on the complexities of soundwaves has subsequently been used in the electronic components of iPods." "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." "In the 1960s Carleson showed that any sound, no matter how complicated, can be represented as a series of sine waves. "du Sautoy. "The sound of a lion roaring can be broken down into just simple tuning forks."" Looks like Fourier Analysis to me. Tuning forks for sine waves..(jumpers for goalposts?).maybe Marcus du Sautoy (nice name) is using tuning forks as dumbing down the tabloids. "That translates in the real world as the idea that any sound can be reproduced using the sound of a tuning fork," Really? One tuning fork, that's amazing ;-) Perhaps you want to read more about Carleson's work: http://www.abelprisen.no/en/prisvinn.../building.html "In 1966 Carleson published a paper that explained why. All finite graphs of the general type considered by mathematicians could be captured by adding up the heights of sine waves of appropriate frequencies. The proof was tough and involved showing why, when you add up the infinitely many numbers that came out of Fourier's analysis, the answer didn't spiral off to infinity but honed in on the graph you were trying to capture. The ideas in the proof were so tough that it is only in recent decades that mathematicians have appreciated how influential these ideas really are. Fourier's problem however is still open for higher dimensional graphs and represents a major goal for mathematicians in this area." You can read a little bit more he http://en.wikipedia.org/wiki/Lennart_Carleson rest snipped Thats better, thanks. The Guardian was poor journalism, the clip above would have served it a lot better, the Guardian dumbed it down, hence the header "Prize for mathematician who paved the way for Ipod" I'm not denigrating his work only remarking on this particular type of tabloid journalism. Yes, but note that "the components of sound systems" and the like are not mentioned at these other sites. That's because none of Carleson's work figures into these real world applications. None. Zippity doo-dah. Carleson proved the Lusin Conjectu The Fourier series of a square-integrable (Lebesgue measurable) function converges to the function "almost everywhere". That is of zero use in electrical engineering. Also I would have to say that even www.abelprisen.no gives a sort of dumbed down version of Careleson's work. It states "But could every finite graph of a general type be captured by Fourier's analysis? It was not clear that there might not be some pathological graphs that were beyond the scope of Fourier's theory. As generations of mathematicians battled with the ideas, the difficulty of the problem began to make mathematicians suspect that there might indeed be strange graphs that couldn't be built out of Fourier's sine waves. But no-one could find such a graph. ... In 1966 Carleson published a paper that explained why. All finite graphs of the general type considered by mathematicians could be captured by adding up the heights of sine waves of appropriate frequencies." Well, no. Not every "finite graph of a general type" can be captured in this manner. Kolmogorov (the father of modern mathematical probability theory) gave an example of an integrable function whose Fourier series diverges *everywhere*. Thus if f merely satisfies integral |f| oo, the Fourier series may be a disaster, but if f satisfies integral |f|^2 oo, then as Carleson proved, the Fourier series of f converges to f almost everywhere. Carleson is a genius and his proof of Lusin is amazing, but his work on Fourier series has had no impact whatsoever in the design of audio systems, and the iPod reference is just a joke. -- |
#7
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Abel Prize awarded to Norwegian mathematican
MC wrote:
Ah. It sounds as if Carleson dealt with infinite Fourier series of finite-length waves, while the earlier theory was finite Fourier series of infinitely long waves. That point was missing from the original article. You may want to check out this article: http://en.wikipedia.org/wiki/Converg...Fourier_series Good set of references on the subject. -- |
#8
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Abel Prize awarded to Norwegian mathematican
PS: Carleson is Swedish, not Norwegian. Abel was Norwegian.
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