David Thompson
Subscribe

Categories

Blog powered by Typepad

« Smart Resizing | Main | A Fear of Seeming »

August 31, 2007

Comments

EBD

"One (snake-venom)compound in particular is a pain killer many times more effective than morphine."

In other words, it will either it will kill you instantly or cause you to involuntarily launch, as they lower you down, into a note-perfect, seemingly-eternal impersonation of Peter Allen singing "When My Baby Smiles At Me I Go to Rio", replete with air-piano hand gestures.

If you gotta go on doctor's orders, fine. But it's highly unenjoyable for the bereaved.

David

Sorry, I’m still reeling from the idea of a drug-induced air piano rendition of ‘I Go to Rio.’

Lordy, look what I found. Hugh “Wolverine” Jackman going to Rio, bigstyle.

http://www.youtube.com/watch?v=jXstcQh5ngI

EBD

To hell with Jackman -- he doesn't even go to Glasgow without protection. *Peter Allen* does directly to Rio -- "Aussie style", as you will surely never regret to remind your Australian friends -- and by the end of this simple pop piece you will understand what eternity means.

For you to draw sa parallel between Hugh Jackman and Peter Allen, well that's like comparing George Kennedy to Carmen Miranda. And you're better than that.

Enjoy:

http://youtube.com/watch?v=Kgq1g-2cQ54&mode=related&search=

TDK

There's another interesting TD article in the Times today:

http://www.timesonline.co.uk/tol/comment/columnists/guest_contributors/article2358028.ece

David

TDK,

Thanks for that.

Dr.Dawg

Help! I thought pi was a constant--the transcendental number that is the ratio between a circle's diameter and its circumference. What am I missing here?

Vitruvius

According to the release notes for the pi program: "This program calculates the value of pi for circles, spheres and hyper-spheres by brute force mechanisms, so you can experimentally verify that pi is same in 2d, 3d, and even 4d".

The source code for the program - http://tinyurl.com/2jun9r - says that it calculates the area of a circle with radius r, the volume of a sphere with radius r, and the enclosure of a hypersphere of radius r, and in each cases uses the formulas for same to factor out the r and arrive at pi.

One other thing to keep in mind is that it is only the case that pi is a constant transcendental number that is the ratio of a circle's circumference to its diameter *in Euclidean geometry*. In non-Euclidean geometry, the ratio of a circle's circumference to its diameter does not equal pi.

Vitruvius

Ok, I've had the time to work through the links, and once again, thanks, David. Great stuff. Both Dalrymple and "The Diversity Nation" are excellent, and I love "What to do on a date".

I would like to recommend this link to a Japanese test in which a full-size six-story building was destructively tested on a huge earthquake-simulating shake table: http://tinyurl.com/37agxa

The excitement of the narrator is, I agree, enough, but my point is more than that. Here we see a canonical example of a case where the value of the result is sufficiently high to warrant the cost of the exercise. It's a classic case of axiology: what's your value function? Unfortunately, too many people with excellent sales skills are peddling fraudulent value functions.

Also, the SeaPhantom from Maritime Flight Dynamics reminded me a bit of the famous Russian Ekranoplan - http://tinyurl.com/2jhqb3 - a more recent scaled-down work-horse version of which I recently discovered in the Russian Be-200 amphibian plane - http://tinyurl.com/yqboa6

Of course, ground-effect airships are not everyone's cup of tea, so if you prefer hydrofoils, I can recommend the Brossard trimaran - http://tinyurl.com/33b6ym - or the late lamented HMCS Bras d'Or - http://tinyurl.com/2okzth

By the way, in the set of archived things I have stored in the basement, the cardinality of which is approaching infinity, I have a copy of the U.S. Navy's 1950-era research book on hydrofoils, from back in the late '70s when I was considering adding hydrofoils to my Tornado the "Seagoon" - http://tinyurl.com/2wskws - which I purchased from the '77 Canadian Olympic trials team after they were finished experimenting with it.

She was a wonderful device for the tinkering empiricist: 27 controlling line-ends on only a six meter boat. I never did race her though, I always preferred taking her out in bad storms and surviving to beating the clock on a nice day.

Vitruvius

I think I should also note that if we're going to invoke Frank, then I think we should pay due tribute to his classic individualist essay: http://tinyurl.com/ypxy47

Vitruvius

For EBD, here - http://tinyurl.com/27bwyp - is Carmen Miranda in the only surviving footage from the classic 1939 film "O Que É Que A Baiana Tem?", and here she is with Benny Goodman in the 1934 movie "The Gang's All Here" - http://tinyurl.com/22v2lk

Clearly, as in the case of D.A. Selby in Earl Stanley Gardner's early works, Jackman doesn't "hold a candle" compared to Miranda, as EBD notes.

David

Hm. I quite like the earthquake machine. I may have to acquire one for Operation Overlord. Those orphans will rue the day they crossed me.

Dr.Dawg

Thank you, Vitruvius. I hadn't gathered the method from the website I was directed to, but that's probably just me. I'm aware, however, that pi is a value derived from Euclidean geometry.

What I find odd about all this, though, is the notion that pure mathematics is something to be established by experiment. The value of pi is not, in my view at least, a hypothesis to be verified by testing. There is much more I could write here--my father was a mathematician, and we had long conversations about this sort of thing--but I'm put in mind of an argument I once heard about Galileo's proof that objects of different weights dropped from the same height reach the ground at the same time. But here, the results of an experiment are established beforehand by simple logic.

The commenter said that Galileo had figured this out in the following manner: Suppose heavier objects fall faster. Then, by attaching a light object to a heavy one, the speed of the heavy one should be retarded. But, in fact, one has just constructed an even heavier object, so the conjoined two should fall even faster. This all being contradictory, all objects dropped at the same height must reach the ground at the same time.

I've always been unhappy with this--physics being established a priori by a logical construction--but now we have someone industriously seeking to establish by brute force that pi really is the same for circles, spheres and hyperspheres. Of course it is, by definition. I'm obviously missing something.

Thanks again. Math is not, frankly, my strong suit, although I have some training in the sciences.

Vitruvius

You are correct, Dr. Dawg, pi is a mathematical constant that exists by definition; it is not a physical constant that exists by measurement. On the one hand, you can consider the pi program to just be some gear-head kids like I was/am having fun.

On the other hand, the referenced pi program is a "computer model" of pi. It divides up a simulation of n-space into small unit sub-spaces and counts them. The more spaces there are, the smaller they are, the more precise the count is, and in the infinitesimal limit: bang, you've got calculus. Approximations like the pi program are called numerical analysis.

In my opinion, the best way to think about computer models is that they are a demonstration of rule-predicted behaviour. To the degree that their predictions are accurate, and then precise, they are useful or at least interesting; to the degree they are not, they are not.

Galileo's argument reminds me of Holmes' comment to Watson that (if I may paraphrase) once you've eliminated all the things that aren't true, the one you're left with is the truth. I think I would have to agree with that.

Of course, a problem arises when we can't determine the truth value of every proposition. That's when we call in Perry Mason ;-)

But seriously, the Thin Man put it another way here recently when he noted that Venn diagrams are a poor approximation for chaotic human network behaviour. The inventor of the *stored program* digital computer, and the fetch-execute cycle now known as the Von Neumann architecture, who was indeed a top-notch mathematician in his own right, said: "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is".

Meanwhile, it remains the case that mathematics and empiricism are the most significant improvements we humans have come up with since we figured out language and music. In that light, you may be interested in my "Top Ten Human Accomplishments" list, in which I cheat and list 32 accomplishments (for some value of accomplishment):

* We're individual warm-blooded vertebrate scavenging omnivores.
* We're bipedal and have arms with hands with opposed thumbs.
(Not having a prehensile tail is one of our notable mistakes.)
* We have a massive forebrain, neurologically speaking.
* We figured out speech, writing, music, dance, and art.
* We figured out fire, machines, and electricity.
* We figured out reason, logic, mathematics, and science.
* We figured out the rule of law, property, the separation of church and state, and democracy.
* We figured out responsibility, trust, and fraud.
* We figured out the concepts of fundamental freedoms and negative rights
(though we currently suffer a trendy free-loading thereupon).
* We walked on the moon and returned safely to Earth.

Dr.Dawg

"I cheat and list 32 accomplishments (for some value of accomplishment)"

That reminds me of the statement I read somewhere that "2+2=5 for very large values of two." :) I don't disagree with your list, though, although it is partial.

It's the relation between mathematics and the empirical that fascinates me, as an admitted layman in the philosophy of science. My old man used to say that mathematics was discovered, but I have some difficulty with that. At the same time, there is clearly a relation between what we know as mathematics (including logic) and our phenomenal observations. I just wish I knew what it was.

Thanks for explaining what the pi folks were up to. I leave you with a short poem that allows one to memorize pi to 14 decimal places:

How I want a drink
Alcoholic, of course,
After the heavy lectures
Involving quantum mechanics.

Have a good weekend.

Vitruvius

All lists are partial, for multiple values of partial ;-)

A mathematician, scientist, and engineer were each asked: "Suppose we define a horse's tail to be a leg. How many legs does a horse have?" The mathematician answered "5"; the scientist "1"; and the engineer said "But you can't do that!"

So while I don't agree that 2 + 2 = 5 for very large values of 2, because very large values of 2 don't exist (only 2-sized values of 2 exist), I do agree with Stephen Hawking when he noted that "Eternity is a very long time, especially towards the end".

I would venture to say that the relationship between mathematics and the empirical is that mathematics is a discovered *and* invented abstract model of the empirical that happens to have the interesting property that properly applied it works in practice. Of course, I'm a pragmatic amystic phenomenological nondeterministic mechanist, so what would you expect?

I leave you with a short poem that I just crafted in relation to a matter that over the last couple centuries mathematicians have tended to agree is the most beautiful thing in mathematics: Euler's identity - http://tinyurl.com/b7fln

e to the power
of pi times
the square root
of minus one
plus one
equals zero

And so, as the sun sets slowly in the west, to the strains of Don Ho singing "Hawaii Calls", I too wish y'all a good weekend.

Vitruvius

I s'pose it should be mentioned that it is not clear whether or not Carmen Miranda can hold a candle to Grace Jones:

Slave to the Rhythm
http://www.youtube.com/watch?v=bj4xWuM86GE

I've seen that face before
http://www.youtube.com/watch?v=zZRTbjpFCF4

La Vie En Rose
http://www.youtube.com/watch?v=modA9aa_ihA

Grace Jones with Pavarotti
http://video.google.ca/videoplay?docid=1309793878152354620

Vitruvius

Alas, it has just come to my attention that Mr. Lucianio Pavarotti is no longer with us. He was a classic gentleman. Here are a few of his aphorisms:

* Learning music by reading about it is like making love by mail.

* One of the very nicest things about life is the way we must regularly stop whatever it is we are doing and devote our attention to eating.

* The rivalry is with ourself. I try to be better than is possible. I fight against myself, not against the other.

The comments to this entry are closed.

Blogroll