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Posted to rec.audio.high-end
chung
 
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Default 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.


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  #2   Report Post  
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Mike Gilmour
 
Posts: n/a
Default 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. ;-)



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  #3   Report Post  
Posted to rec.audio.high-end
chung
 
Posts: n/a
Default 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


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  #4   Report Post  
Posted to rec.audio.high-end
Mike Gilmour
 
Posts: n/a
Default 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





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Posted to rec.audio.high-end
MC
 
Posts: n/a
Default 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   Report Post  
Posted to rec.audio.high-end
Billy Shears
 
Posts: n/a
Default 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.


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chung
 
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Default 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.


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  #8   Report Post  
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Billy Shears
 
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Default Abel Prize awarded to Norwegian mathematican

PS: Carleson is Swedish, not Norwegian. Abel was Norwegian.
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