A. K. A. Loose Canon
Bah. "seeing the equations as relations" and "imbuing the symbols with a physical meaning" is fine. But how is it supposed to make Mathematics which pays attention to more than just that "horseshit"?
What is this crap?
AA, what you write here is rather horseshitical: Mathematics which pays attention to more than just that. What's "that"? Do you mean that there's more math than just that which is applicable to physics? In that case, you're right, but that math inapplicable to physics is the horseshit.
Bull. How about Number Theory?
Ans: Logic games for kids that can't handle the drama of a word problem.
On a slightly related tack, it struck me two days ago, after listening to a group theory lecture by one of the more notable physicists here, that: There are plenty of interesting examples of group homomorphisms in physics and geometry --- e.g. that SU(2) is the double cover of SO(3) --- but very few interesting examples group *isomorphisms*. On the other hand, in number theory, there are examples group isomorphisms (existing in virtue of general, but subtle, principles) which are difficult to compute or even write down concretely --- e.g. the fact that the multiplicative group of a finite field is cyclic *or* the existance of special cyclic subgroups of elliptic curves (again, taken over finite fields). Indeed modern cryptography relies of the fact/thesis that these isomorphism get more and more difficult to write down as your prime (or power a prime) increases. cheers,A. Leverkühn
This sort of chasm between existence and computability is a commonplace in analysis. For example, in PDE, even PDEs from physics, the existence and uniqueness of solutions can be obtained from general considerations, but actually computing a solution is impossible, even approximately to decent precision.This is even more hopeless than chaos, as that weak tea is about ODEs which are much easier geometrically and, thus in the imagination, to understand.
Strangely, according to some Grothendieckians I know, the difficulty in writing down the isomorphism (for all powers of a fixed prime say) for these special cyclic subgroups of elliptic curves, is an artifact of the geometry of the corresponding *complex* elliptic curve ... something to do with the Weil conjectures which relates the Beti number of a (complex) variety to the problem of counting points of the same variety, but taken over a finite field. Weak Tea ? Ha! You should try drinking what counts for coffee in west Yorkshire, or even worse, Manchester !cheers, A. Leverkühn
One needs not be a connoisseur or experimental physical chemist to distinguish sewage from Alpine spring water. I'll stay off the pom coffee as if it were sodomy, except for Caffè Nero in major airports there, which is analogous to sex with a babe, in comparison.
Those connections you are mentioning, Leverkühn, are fascinating. Of course, they are lost on Mr Rot, who'd rather see sparks flying out of a Tesla infernal machine, than to decipher the mysteries of the zeta function.
The $\zeta$-function is an analytic number theory character, at closest to your barren discipline, Tecs. Go stare gawking at a "$\partial$" for awhile, trying hard to banish the "6" from your mind. When you succeed, contact my advisor. He can help.
As for coffee, forget about the British, and even the Italians. The best coffee I had (at least as a kid) was on Ada Kaleh, a long-lost island in the middle of the Iron Gates. What a stupid thing to do to dam those spectacular gorges on the Danube, and submerge that island. You guys ever heard of it?
Memories of lost island:And what if the people refuse to move? someone asked, at a meeting of top Romanian and Yugoslav Communist officials, sometime in 1967. Ahmed Engur held his breath. He lived on the island of Ada Kaleh, and was now serving coffee round the long table in Turnu Severin where the officials had assembled to discuss the latest plans to build the Iron Gates dam and hydroelectric project. Plans which involved raising the level of the Danube by 30 metres to create a massive storage lake, 150 km long, and destroying not only the historic island of Ada Kaleh in mid-stream, but also numerous small towns and villages along the bank of the river on both the Serbian and the Romanian banks. Not to mention sites of great archaeological importance, and roads and monuments dating back to the time of the Romans.“Then let them run, or drown like rats”, said the Romanian Prime Minister.[..]“They promised us free electricity for life when they built the dam”, he laughs. “But it never arrived. There are still power-cuts sometimes in winter. And we heat the house with wood – it’s cheaper.”
The follies of dictators are greater.
Ada Kaleh. If Tecs is inviting us for coffee there, I think that I have understood his strategy for avoiding the tab on reading the link he provided above.
Tecs: turkish coffee --- sediment, cardamom, and all ?
Kühn: turkish coffee -- sodomy, rum, and the lash?
as in ... don't talk to me about naval tradition ? or are you just happy listening to the Pogues ;) cheers,A. Leverkuhn
Once upon a time, Herr Rott served in the kaiserliche und königliche Kriegsmarine. He was based at the Pula naval yard (the successor to the Colonia Pietas Iulia Pola Pollentia Herculanea), where he met Nicolae Tesla, and learned first hand what it means to welsh on a tab, and get all huffy about it:In 1885 Tesla claimed that he could redesign Edison's inefficient motor and generators, making an improvement in both service and economy. According to Tesla, Edison remarked "There's fifty thousand dollars in it for you—if you can do it". This has been noted as an odd statement from an Edison whose company was stingy with pay and did not have that sort of cash on hand. After months of work, Tesla finally finished the task and inquired about payment. Edison claimed he had been only joking and replied, "Tesla, you don't understand our American humor". Edison offered a US$10 a week raise over Tesla's US$18 per week salary, but Tesla refused it and immediately resigned.
Those suga-pula are not too sharp at the business game, eh?
Tesla got conned by Edison, that's right.
Edison was one Funny guy.
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