Slashdot Mirror
Mathematician Solves a Big One After 140 Years
TaeKwonDood notes that ScientificBlogging.com has just written about a development in applied math that was published last year. "The Schwarz-Christoffel transformation is an elegant application of conformal mapping to make complex problems faster to solve. But it didn't do well with irregular geometries or holes, so it simplified too much for a lot of modern-day mechanical engineering applications. 140 years after Schwarz and Christoffel's work, a professor at Imperial College London has generalized the equation. MatLab users rejoice!"
That guy must be pretty old
It always amazes me how applicable math becomes hundreds of years after it's written. Think if Maxwell's equations, Newton's equations, Einstein's equations. Fluid Dynamics equations were probably pioneered well before they were applied to human machines. Modern-day aircraft would not operate without their understanding. Where the math goes, human technology will probably soon follow.
of course pilots don't need to know the math behind why their plane works. I sure hope the designers of the planes knew their math! Without them the planes wouldn't work.
I give credit to all the bran I've been eating lately.
The article is available at the author's website.
As far as I can tell, the original result provided a conformal map from a disk onto a polygon. Prof. Crowdy extended this result to provide a map from a disk with circular holes poked in it onto a domain with polygonal holes. Why is it useful? I am sure someone in the applied camp would know.
Read the paper. This is not the first S-C formula for multiply connected regions. The claimed "key result" is a formula for a case where a formula is already known. More work will be needed to a adapt the MATLAB technology from singly- and doubly-connected regions to multiply connected regions.
This paper seems to be part of ongoing work by a small community and is probably useful, but it's not a major mathematical breakthrough -- more of an incremental step. Small technical improvements in one field of mathematics shouldn't make up a slashdot story. Just because someone put "140 year old" in the press release doesn't mean it's really important. A math story belongs on /. when a big result is announced -- on the level of Poincare's Conjecture, or the Modularity Theorem.
I knew I could have scored better if there were no time limit!
Miss, I'd like 140 years to finish my paper!
These posts express my own personal views, not those of my employer
As a consultant for several large companies, I'd always done my work on
Windows. Recently however, a top online investment firm asked us to do
some work using Linux. The concept of having access to source code was
very appealing to us, as we'd be able to modify the kernel to meet our
exacting standards which we're unable to do with Microsoft's products.
Although we met several technical challenges along the way
(specifically, Linux's lack of Token Ring support and the fact that we
were unable to defrag its ext2 file system), all in all the process
went smoothly. Everyone was very pleased with Linux, and we were
considering using it for a great deal of future internal projects.
So you can imagine our suprise when we were informed by a lawyer that
we would be required to publish our source code for others to use. It
was brought to our attention that Linux is copyrighted under something
called the GPL, or the Gnu Protective License. Part of this license
states that any changes to the kernel are to be made freely available.
Unfortunately for us, this meant that the great deal of time and money
we spent "touching up" Linux to work for this investment firm would
now be available at no cost to our competitors.
Furthermore, after reviewing this GPL our lawyers advised us that any
products compiled with GPL'ed tools - such as gcc - would also have to
its source code released. This was simply unacceptable.
Although we had planned for no one outside of this company to ever
use, let alone see the source code, we were now put in a difficult
position. We could either give away our hard work, or come up with
another solution. Although it was tough to do, there really was no
option: We had to rewrite the code, from scratch, for Windows 2000.
I think the biggest thing keeping Linux from being truly competitive
with Microsoft is this GPL. Its draconian requirements virtually
guarentee that no business will ever be able to use it. After my
experience with Linux, I won't be recommending it to any of my
associates. I may reconsider if Linux switches its license to
something a little more fair, such as Microsoft's "Shared Source".
Until then its attempts to socialize the software market will insure
it remains only a bit player.
Thank you for your time.
"And verily in that day, it came to pass that the doctors rattled their canes and rejoiced." (Old Matth 3:14)
-Aegis Runestone-
1738. With bernoulli and newton, quite a few things could be explained.
http://mysite.du.edu/~jcalvert/tech/fluids/bernoul.htm
Backups are for wimps. Real men post their data in comments and have slashdot mirror it
Based on these notes, placed on a public web server by one of Princeton's greatest mathematical minds, where would humans go?
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
first contact with the medical engineering?
You couldn't have tomography without computer assistance, true, but you have lots of people going around with radiation burns from improperly calibrated X-ray equipment.
MSBPodcast.com The opinions expressed here are my own. If you don't like 'em... Think up your own stuff.
Why, are they selling Sudafed in bulk again?
But a symbol isn't a shape, it's an idea.
Math has two distinct aspects.
First there is math as is relates to physics principles. 1 + 1 must equal 2. In a classical wphysics world there is no getting around that. Arithmetic, Pi, e and a few others are discoverable math principles.
But, second is how we as human beings understand math, this is invented. There is no fundamental reason why calculus is as it was developed. Caculus represents our understanding of math and is an invention of convinience.
Remember, all math COULD be done with basic arithmetic....I just wouldn't want to do it by hand.
We only understand gravity because we observe it by falling on our diapered butts as babies. Therefore gravity becomes part of our logic.
Heavier than air flight was impossible (our logic told us), until proven otherwise and we had to modify our logic.
Going faster than 60mph, then 100mph, then sound would certainly kill people, until it was done.
Our logic tells us the world is flat, etc etc.
Stuff like quantum mechanics still completely baffles us, except for those few who have been able to modify their logic to actually understand it.
Engineering is the art of compromise.