Sunday 20 January 2008

Signs of the Times (or of the Thames)

In 1887 Oscar Wilde wrote: `We have really everything in common with America nowadays except, of course, language'. Some say he may have been paraphrasing something by George B. Shaw. Whichever said it first, they were wrong; the British are different. I've been over here for a while, and I don't giggle anymore when I hear a seven-year-old ask his mom to buy him some new rubbers (erasers). I even know I'm not looking for footweae when I go to a boot sale (flea-market). But sometimes the British road signs just take me back to square one.

The sign above is an example. It is located in Greenwich near the loaction where they are restoring the Cutty Sark. You have to figure out what it means. It is not just that they use the same words to mean different stuff. They just have a different mind set. North of my home here in Stoke Ferry as I drove towards Kings Lynn there was a sign that read, "Cats Eyes removed ahead" Yikes!!!

A common road sign that I have yet to figure out has the warning, "Beware of oncoming traffic in center of road"???? If there is a problem with oncoming traffic in the center of the road, shouldn't this sign be turned the other way and say something like, "Get your Butt back in your own lane!" You see? The British just think differently.

Ok, one more example. I was in London to see the "Tut" exhibit last weekend (a bit disappointing, actually) and in King's Cross station I noticed this sign.

The sign is located on an electronic schedule that tells you the track on which trains depart. When the station is busiest, they apparently turn them off so people won't crowd around them.... YES, READ IT AGAIN... In the peak periods they remove information. People blindly wandering from track to track apparently are less likely to congregate in one place and create congestion... Ok, I don't really know why they have such a sign, or why they would do it.... My only explanation... The British ARE different.

Wednesday 9 January 2008

Mentos and Coke.... But Why?

Talking to my kids about Mentos and coke eruptions recently, and found this on a web site... this may be the ULTIMATE Mentos and coke performance on the net.

The kids always say wow... and then... WHY? Why does Mentos and Diet Coke make such an explosion, does it have to be diet coke?

The answer is.... well actually there are several possible answers and no one is sure exactly which is the dominant factor. There are some things we think we know, so here is what I think I understand about the eruptions now:

When they bottle pop, the expose the liquid to a highly pressurized Carbon Dioxide (C02) gas, that is what puts the "fizz" in soda pop. When the bottle is capped, the molecules of CO2 are trapped in the liquid and because of the surface tension, they can't expand. Now if you shake one up, and pop the lid, the shaking has broken the surface tension enough to let the molecules of CO2 start to expand and you get a blast all over the place, the expanding molecules take up more space, pushing out the soda pop. But if you open it gently, the surface tension is only mildly disturbed near the top of the bottle or can, and a few thousand molecules expand and rise to the surface or foam up in the bottle.

Two things seem to be the most important factors, surface tension, and the ability of the carbon dioxide molecules to get close together. If you drop salt, marbles, sugar, or most anything else into the pop, it will start to fizz. If the material has soap or fats that break down the surface tension of the liquid, you get more bubbles. And if the material has lots of corners and crevaces for the molecules of CO2 to hook onto, then you get more (bigger) bubbles. This idea is called nucleation If the surface is jagged or irregular, it encourages this nuclaeation, and more tiny molecules of gas expand.

Mentos is good in both aspects, the gum arabic and gelatins in the coating disolve and promote lowering of the surface tension in the liquid. In addition, the candy itself is covered with tiny little depressiions, sort of like a golf ball. They provide a prime source of nucleation sites. Add one more quality to help make a big eruption, the Mentos are heavy. Well heavy enough that they sink quickly to the bottom of the bottle. If they set at the top and expanded, there would be a rush of gas out of the bottle, but mostly invisible. At the bottom, the expansion of the gas is so quick that as they press outward, the cola can not get out of the way and so it is pushed right out the top and up into the sky.

Does it have to be diet. Some say diet is much better, maybe something in the artificial sweetener. Others claim the only difference is that the non-diet soda is a sticky mess to clean up, and there is really no difference in the pressure of the eruptions. Heat seams to make a difference, hot cola shoots higher than cold cola.

So what else might effect it? Go ahead, but a couple of liters of Diet Coke, and a couple of packages of Mentos and have a little experiment. Make a mess, have a ball... and if you learn something along the way... well, that's just the price you pay.

Sunday 6 January 2008

Christmas in Paris 2007

Trying to type on a French keyboard; yes Virginia; there is a difference!!!

Got to love a city where they have streets named for mathematicians.... this one is in the 17 th district near my apartment,,,,, visited the Eiffel Tower; The Louvre; Notre Dame; all the tourist sites, but near the Pantheon there is a little Gothic church, St. Etienne; that was Pascal's church, and where he is buried.

The Arts de Metiers Museum in Paris was a great visit; Pascal's Calculating machine, at nineteen??? What a mind!!! and Foucault's penulum could still be there watching; but the streets called; the food; the bakeries, Paris is a fest for the nose as well as the eyes. Walking; watching the people; and then sitting on a bench by the Eiffel Tower, listening to evey dilect known to man; watching children on a hand turned carousel..... Can life get better than this???

At the Louvre I got to stand close up and contemplate the Beautiful statue of Pascal by Pajou . They also have another of D'Alembert who was instrumental in the French measurement of the Paris Meridian.

I tried to get a close-up of the roulette or cycloid which he is considering.

One of my favorite stories about Pascal relates to the roulette . Pascal was a very devout man, and also a wonderful mathematician early in his life. When he was in his early teens he wrote one of the important papers on analytic geometry at 16 and invented the calculating machine shown below when he was only nineteen, and in truth, it was not significantly improved on until the first electronic calculator/computers. Later, along with his studies in pressure and physics, he helped to create the study of probability in his letters with Fermat (around 1554) .

But then, at about age 31, he had an accident when his horses ran into the river at the bridge at Neuilly (Paris). Miraculosly, he was saved when the harnesses broke and the horses fell into the river leaving the carrage, and an unharmed Pascal, on the bridge. Pascal took this as a sign that God was not pleased with the time and attention he gave to math and physics, and so he abandoned them entirely to devote himself to the study of Religion. It was during this time that he wrote most of the documents which would be gathered to create his Penses.

Then about three years later, so the story goes, Pascal developed an ulcer that caused him such discomfort he could find no rest at all (he always did have problems with insomnia). To occupy his mind, he turned his attention to an article on the cycloid, a question much in consideration in all of Europe at the time. As Pascal used the new calculus of indivisibles created by Cavalieri to solve the area under the curve his pain disappeared. He took this as a sign that God did not object to his study of math, and returned to consider the problem and others for the few remaining years of his life. He died at thirty-nine from cancer of the stomach that had spread to his brain.