vttoth — May 28th, 2010
This Homer Simpson is one smart fellow. While he was trying to compete with Edison as an inventor, he accidentally managed to discover the mass of the Higgs boson, disprove Fermat’s theorem, discover that we live in a closed universe, and he was doing a bit of topology, too.
His Higgs mass estimate is a tad off, though. Whether or not the Higgs exists, the jury is still out, but its mass is definitely not around 775 GeV.
Categories: Mathematics, Physics, Television |
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vttoth — May 14th, 2010
The long-awaited successor to the classic “Handbook of Mathematical Functions” by Abramowitz and Stegun has finally been released: its online version is available courtesy of the US National Institute of Standards and Technology. (It is yet another one of those often under-appreciated contributions of Uncle Sam to the world.)
Categories: Mathematics, Programming |
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vttoth — May 14th, 2010
I was watching the noontime local CTV news today. At around 12:39 (!), in three consecutive reports, the number 39 popped up. First, a report about a youth who is charged with vandalizing 39 tombstones. This report mentioned the number 39 several times, which is probably why I noticed that in the next report, one about the recent terrorism-related arrests in the US, footage shown in the background included the front door of a house bearing the number 39. At this time, I began paying attention. The next report was about Ottawa tourism advertisements in American newspapers; it didn’t seem likely that the number 39 would pop up there until the official being interviewed answered a question about funding and mentioned their 39 member hotels. That’s when I told my wife that this is getting a tad creepy.
The other day, I was watching a Stargate Universe episode in which one of the protagonists was reliving a part of his life while his brain was connected to an alien computer, and a particular number kept popping up as a clue. That number was 46, the number of chromosomes in a human cell. So that’s what makes 46 special. But what about 39?
Or perhaps all this was just a clever form of subliminal advertising for a Web site called The 39 Clues, which happens to be the first hit on Google when one searches for “39″?
Categories: Mathematics, Television |
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vttoth — March 22nd, 2010
Imagine solving one of the most profound outstanding problems in mathematics. Imagine living in poverty, in a cockroach-infested apartment in St. Petersburg, Russia. Imagine being awarded one of the world’s most prestigious prizes in science, the Millennium Prize of the Clay Mathematics Institute, which, incidentally, also comes with a cool $1,000,000.
And imagine turning it down. Which is precisely what reclusive Russian mathematician Grigory Perelman apparently did.
I don’t know what to think. Was it a matter of principle for him? Perhaps. But then, he could have indicated in advance that he wouldn’t accept the award, just as he refused to accept the Fields Medal a few years earlier. Why did he keep the world in suspense? Was it posturing? Or is he, hmmm, how can I put this politely, one fry short of a happy meal, to use a favorite phrase of mine from the television series Stargate SG-1?
Categories: Mathematics |
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vttoth — March 16th, 2010
An interesting anniversary today: 25 years ago, on March 15, 1985, the first ever .com domain name was registered, symbolics.com. The company, in addition to building their own brand of “Lisp Machine” computers, also happened to be selling the commercial version of the MACSYMA computer algebra software. The same software that, in the form of its open-source version, Maxima, continues to evolve thanks to a devoted team of developers… of which I happen to be one.
Alas, Symbolics is no longer, at least not the original company. A privately held company by the same name which obtained much of Symbolics’ assets still sells licenses of the old MACSYMA code.
Categories: Computer Algebra, Internet |
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vttoth — December 29th, 2009
There is a fascinating book published by the RAND Corporation, available at Amazon for a mere 81 US dollars. I am tempted to buy it. It must be a fascinating read. Readers’ comments at Amazon are certainly encouraging; while the book has some minor flaws, despite the lack of serious proofreading it is guaranteed not to contain any errors, and it helped at least one reader get to meet the woman who eventually became his wife.
Categories: Books, Mathematics |
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vttoth — August 15th, 2009
I’m watching Cubers on the CBC, a documentary about the revival of interest in Rubik’s Cube, and a recent Rubik’s Cube solvers’ competition. What can I say… it takes me back.
I wouldn’t stand a chance competing in this crowd, but I did win the world’s first (as far as I know) Rubik’s Cube competition, held in Budapest in 1980. I completed my cube in 55 seconds, which wasn’t a very good time by my standards then (I often managed to solve the cube in well under 30 seconds) but it was enough to win.
These days, world class competitors solve the cube in 15 seconds or less. In addition to manual dexterity, such spectacular performances also require memorizing a large number of moves. And then I am not even going to mention the blindfold competitions, involving not just the “standard” 3×3×3 cube but the larger, 4×4×4 and 5×5×5 versions… such skills are hard to comprehend.
I can still solve my (3×3×3) cube without trouble (so long as I am allowed to use my eyes), but I only remember a relatively modest number of moves, which means that my solution is far from efficient. In other words… I am rusty. And my cube is sticky. Literally, it feels sticky on the outside (is the plastic decomposing?) and it’s a bit hard to turn. Still, on the third try, I managed to solve it in a minute an 45 seconds. Not bad, considering that I haven’t touched the thing in years.
Categories: Mathematics |
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vttoth — June 24th, 2009
I found this gem of a sentence on the Web site of the Embassy of the Islamic Republic of Iran here in Ottawa:
“The Islamic Republic of Iran will register acts of all these states whose records are filled with support for terrorism, pro-colonialist policies for colonizing the oppressed nations, support for the despotic regimes, arming some with weapons of mass destruction and support for anarchy in all parts of the world as disdainful behavior and stipulates that they can not cast doubt on the excellent democratic election held recently in the Islamic Republic of Iran by no means advising them to change their miscalculated approach vis-à-vis the developments having taken place in Iran because designers of the chess game are closely monitoring their behavior and calculating them in the future relations.”
This sentence reminds me of Soviet-era propaganda leaflets. I wonder if the Islamic Republic of Iran has hired propagandists from the former Soviet Union who were left unemployed after 1991.
Anyhow, what exactly are they saying here? Something is wrong with this sentence. They say that,
The Islamic Republic of Iran
- will register, as disdainful behavior,
- acts of all these states whose records are filled with
- support for terrorism,
- pro-colonialist policies for colonizing the oppressed nations,
- support for the despotic regimes, arming some with weapons of mass destruction and
- support for anarchy in all parts of the world
and
- stipulates that they can not cast doubt on the excellent democratic election held recently in the Islamic Republic of Iran
by no means advising them to change their miscalculated approach vis-à-vis the developments having taken place in Iran
because
designers of the chess game are closely monitoring their behavior and calculating them in the future relations.
Hmmm… they seem to be telling us that despite all the bad things they say about our disdainful behavior, they are NOT advising us to change our miscalculated approach. The reason for this surprising advice has to do with the designers of the game of chess. Okay, I know that chess may have arrived in Europe from India by way of Persia, but what do the long dead inventors of one of the world’s most popular games have to do with the reelection of Ahmedinejad?
Maybe they are trying to confuse us intentionally, in order to deflect our attention away from a study that suggests that the election was seriously rigged. They really shouldn’t bother. This study says that the election was likely rigged because the final two digits of provincial results show unlikely statistics. But unlikely is not the same as impossible, and unless they can quantify how much more likely this outcome is in a rigged election, the study means nothing; after all, 1-2-3-4-5-6 is as likely to win in a random 6/49 lottery draw as any other number combination, and if they pick these numbers next week, it does not prove fraud by the lottery corporation. For that claim, one would also have to quantify the increased likelihood that a fraudulent draw is more likely to produce the 1-2-3-4-5-6 result when compared to a truly random draw.
Categories: Mathematics, Politics |
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vttoth — June 8th, 2009
Some moderately interesting Maxima examples.
First, this is how we can prove that the covariant derivative of the metric vanishes (but only if the metric is symmetric!)
load(itensor);
imetric(g);
ishow(covdiff(g([],[i,j]),k))$
%,ichr2$
ishow(contract(canform(contract(canform(rename(expand(%)))))))$
ishow(covdiff(g([i,j],[]),k))$
%,ichr2$
ishow(canform(contract(rename(expand(%)))))$
decsym(g,2,0,[sym(all)],[]);
decsym(g,0,2,[],[sym(all)]);
ishow(covdiff(g([],[i,j]),k))$
%,ichr2$
ishow(contract(canform(contract(canform(rename(expand(%)))))))$
ishow(covdiff(g([i,j],[]),k))$
%,ichr2$
ishow(canform(contract(rename(expand(%)))))$
Next, the equation of motion for a perfect fluid:
load(itensor);
imetric(g);
decsym(g,2,0,[sym(all)],[]);
decsym(g,0,2,[],[sym(all)]);
defcon(v,v,u);
components(u([],[]),1);
components(T([],[i,j]),(rho([],[])+p([],[]))*v([],[i])*v([],[j])
-p([],[])*g([],[i,j]));
ishow(covdiff(T([],[i,j]),i))$
ishow(canform(%))$
ishow(canform(rename(contract(expand(%)))))$
%,ichr2$
canform(%)$
ishow(canform(rename(contract(expand(%)))))$
Finally, the equation of motion in the spherically symmetric, static case:
load(ctensor);
load(itensor);
K:J([i],[])=covdiff(T([i],[j]),j);
E:ic_convert(K);
ct_coords:[t,r,u,v];
lg:ident(4);
lg[1,1]:B;
lg[2,2]:-A;
lg[3,3]:-r^2;
lg[4,4]:-r^2*sin(u)^2;
depends([A,B,T,rho,p],[r]);
derivabbrev:true;
cmetric();
christof(mcs);
J:[0,0,0,0];
ev(E);
T:ident(4);
T[1,1]:rho;
T[2,2]:T[3,3]:T[4,4]:p;
J,ev;
These examples are probably not profound enough to include with Maxima, but are useful to remember.
Categories: Mathematics, Physics |
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vttoth — May 21st, 2009
I heard on CBC Newsnet that according the US hurricane center, there is a 50% likelihood that this year will be an average year, hurricane-wise.
I am still pondering whether or not this statement had any information content.
Categories: Mathematics, Weather and Climate |
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