Mathematics

2011-04-25T15:21:00.000-07:00

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2010-04-25T07:27:00.000-07:00

Math Goes to the Movies

ScienceDaily (Apr. 14, 2010) — Whether it's an exploding fireball in "Star Wars: Episode 3," a swirling maelstrom in "Pirates of the Caribbean: At World's End," or beguiling rats turning out gourmet food in "Ratatouille," computer-generated effects have opened a whole new world of enchantment in cinema. All such effects are ultimately grounded in mathematics, which provides a critical translation from the physical world to computer simulations.

Mathematics provides the language for expressing physical phenomena and their interactions, often in the form of partial differential equations. These equations are usually too complex to be solved exactly, so mathematicians have developed numerical methods and algorithms that can be implemented on computers to obtain approximate solutions. The kinds of approximations needed to, for example, simulate a firestorm, were in the past computationally intractable. With faster computing equipment and more-efficient architectures, such simulations are feasible today -- and they drive many of the most spectacular feats in the visual effects industry.

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(Image credit: labspaces.net)

2010-03-31T23:27:00.000-07:00

Math finds code in ancient Scottish symbols

In the northern British Isles, the Celtic tribes known as the Picts coexisted for centuries alongside literate cultures such as the Romans, the Irish and the Anglo-Saxons.

"They were the odd society out, in that they didn't leave any written record," says Rob Lee of the University of Exeter in England, save for some mysterious-looking sets of symbols on stones and jewels. In a paper published March 31 online in Proceedings of the Royal Society A, Lee and his coworkers now claim that the symbols are written language. Perhaps the Picts were not illiterate after all.

Lee's team attacked the problem with math. Written languages are distinguishable from random sequences of symbols because they contain some statistical predictability. The typical example is that, in the English language, a "q" is nearly certain to be followed by a "u"; and a "w" is much more likely to be followed by an "h" than, say, by an "s" or a "t".

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2010-03-20T14:25:00.000-07:00

Algebra in Wonderland

SINCE “Alice’s Adventures in Wonderland” was published, in 1865, scholars have noted how its characters are based on real people in the life of its author, Charles Dodgson, who wrote under the name Lewis Carroll...

But Alice’s adventures with the Caterpillar, the Mad Hatter, the Cheshire Cat and so on have often been assumed to be based purely on wild imagination. Just fantastical tales for children — and, as such, ideal material for the fanciful movie director Tim Burton, whose “Alice in Wonderland” opened on Friday.

Yet Dodgson most likely had real models for the strange happenings in Wonderland, too. He was a tutor in mathematics at Christ Church, Oxford, and Alice’s search for a beautiful garden can be neatly interpreted as a mishmash of satire directed at the advances taking place in Dodgson’s field.

In the mid-19th century, mathematics was rapidly blossoming into what it is today: a finely honed language for describing the conceptual relations between things. Dodgson found the radical new math illogical and lacking in intellectual rigor. In “Alice,” he attacked some of the new ideas as nonsense — using a technique familiar from Euclid’s proofs, reductio ad absurdum, where the validity of an idea is tested by taking its premises to their logical extreme.

Mathematics

Experiment indicates that infants recognize apparent errors in subtraction.

Much ado about nothing: First a placeholder and then a full-fledged number, zero had many inventors

A self-taught programming prodigy joins the ranks of technology buffs applying digital systems to the ultimate analogue puzzle