Monday, January 07, 2013

monday article roundup: among other things (A) absolute zero isn't absolute, and (B) check when maths is bogus or not.

so i read a lot of internet news, as you can tell from the sidebar of links, on the right-hand side of this webpage. some of the articles are worth sharing, especially for those of you who find this blog entertaining [1].

the thing is, i'm starting to collect more and more articles about maths and universities and education and technology and whatnot. (i could swear that reporting about maths is on the rise.) so my new habit will be to collect the top 5 (or fewer) articles over one week and post them on mondays.
(i'll make exceptions for articles that i'll write long opinions about though, such as the online education trend.)
this will probably shrink the number of visitors to this blog. then again, i never planned for it to be popular. in fact, i'm delighted to know that this blog doesn't appear in the first 10 pages when you google me (provided that you know my name, which shouldn't be hard to find out) [2].

anyways, without further ado ..

temperature, version 2.0

i should have known that temperature wouldn't have such an easy definition as average kinetic energy; apparently it's only true for ideal gases. i guess i've been working with ellιptic and parabοlic ρde for too long, where one typically minimises the Dirichlet energy $$f \mapsto \int_\Omega |\nabla f|^2 \,dx$$ without thinking too hard about whether it fits reality or not.

apparently the modern definition is sufficiently general so that quantum gases can actually achieve lower-than-absolute-zero "temperatures." in other words, there are examples which show that the classical definition is strictly stronger than the modern one.
Here’s the new definition that they came up with. Temperature measures the willingness of an object to give up energy. Actually, I lied. This isn’t how they really define temperature, because physicists speak math, not english. They define it as $\frac{1}{T} = \frac{dS}{dE}$ which says, in words, that the temperature is inversely proportional to the slope of the entropy $S$ vs. energy $E$ curve.

there's more: apparently particle physics exhibits a lot of pathologies:
Could you really have an object that gets colder as you give it energy?

This really happens, when you have a bunch of particles that attract each other. Stars are held together by gravity, and they behave in just this way. As a star loses energy, its temperature rises. Give a star energy, and you’re actually cooling it down. Black holes also behave in this odd way – the more energy you feed them, the bigger they get, and yet, the colder they get.
evidently: to model the temperature of stars and galaxies, don't minimise the previous Dirιchlet integral! (-;

maths sounds hard, impresses people

more and more, i think of mathematics as a language. it's not quite latin, of course; in some cases, however, like latin it has the power to unduly impress the less savvy.
At random, one of the two abstracts received an additional sentence, the one above with the math equation, which he pulled from an unrelated paper in psychology. The study's 200 participants all had master's or doctoral degrees. Those with degrees in math, science or technology rated the abstract with the tacked-on sentence as slightly lower-quality than the other. But participants with degrees in humanities, social science or other fields preferred the one with the bogus math, with some rating it much more highly on a scale of 0 to 100.

lastly, a matter of semantics

i hadn't thought about the difference in meaning, as discussed in the passage below. it is important, however, to note that there is a difference between the notions.
[C]oercion involves the use of (or the threat of) force.

Where I disagree — and where this gets slightly murky — is that I don’t think you need to fully understand something (at least at a conscious level) to be persuaded to act. That assumes persuasion is rational. I think you are persuaded by appeals to the irrational — emotions, psychology, and imagination.

Understanding something (e.g., what smoking does to the human body) largely comes from facts or arguments that appeal to intellect. When I get you to do something based on facts and reason I’m convincing you to act, which is different from persuading you to act.
this is a fine taxonomy and all .. so what would be an overarching term for all three?

induce might work, but it also applies to non-human situations (such as induced reactions in chemistry). in fact, after quickly looking up the word persuade, i'm not convinced [2] that there is a clear indication of irrationality in its definition. maybe i need a new dictionary, but it sounds like to convince simply means to persuade rationally.

so i would find fault with the linear ordering of ..
Persuading > Convincing > Coercion
.. and would prefer a venn diagram or perhaps, in $\LaTeX$ rendering, $${\rm convince} \subsetneq {\rm persuade} \subsetneq {\rm induce} \supsetneq {\rm coerce}$$ $${\rm persuasion} \cap {\rm coercion} = \emptyset$$ lastly, sometimes i wonder if i really convince audiences in my talks to accept these ideas, rather than just persuading them to trust me (and not show them the technical details) ..

[1] sometimes i'm surprised people keep visiting. i mean, it's mostly my complaints about the life of the academic mathematician. i guess the sort of person who would run a search for the right $\LaTeX$ code for that weaκ-star cοnvergence arrow has a pretty good chance as enjoy the same things that i might. q-:

[2] that said, i'd like to keep it that way.

[3] pun intended. (-:

No comments: