The Garden of Cosmic Speculation

This wonderful garden in Dumfries, Scotlandd is open to the public only one day a year. I’d love to visit it; but until I do there’s an online gallery of images: The Garden of Cosmic Speculation by Charles Jencks.

Proposed proof for P not equal to NP is probably wrong

Scott Aaronson, on his Shtetl-Optimized blog, points out Eight signs that a proposed P≠NP proof is wrong.

As of this writing, Vinay Deolalikar still hasn’t retracted his P≠NP claim, but a clear consensus has emerged that the proof, as it stands, is fatally flawed. The first reason is that we’re not going to separate k-SAT from much easier problems purely by looking at the structure of the solution space:

Scott’s next article is the useful P vs NP for dummies.

The short answer is: the biggest unsolved problem of theoretical computer science, and one of the deepest questions ever asked by human beings!

Computability problem solved!

There’s big news in the computer computation world. Mark Chu-Carroll reports that mathematicians at HP research think their proof solves the classic problem of computational complexity.

Fractals—gotta love ’em!

Fractal flames make leaf patterns

Speaking only for myself, and not being a mathematician, I love fractals for their beauty and intricacy. I don’t understand them. I understand that they are repeating patterns that get smaller and smaller and for some, anyway, go on doing so infinitely.

As a child I recognized that the beauty of nature embraced both randomness and pattern. Although I did not know the term, in many cases, that pattern was fractal. The branches of a maple tree and the veins in a maple leaf diverge at the same angle, about 41.5 degrees of a circle. Small twigs, large boughs, and veins in the leaf thus harmonize.

The fractal that made the news was the Mandelbrot curve, which maps how quickly a series goes to infinity, or its limit. It is infinitely fine: you can keep expanding the curve and going further into it, finding repeated patterns, and never reach the end. Programmers have given us the tools to generate and display them. But there are other types of fractals. There are fractal flames, waves, and something the author calls gnarls.

Gnarl?

One site where you can enjoy them is UltraGnosis Fractal Art. You can order calendars with images of fractal leaves. They’re very appealing to the nature-lover in me.

Powers of ten—the Great Gate

This video is set to music: The Great Gate at Kiev from Pictures at an Exhibition by Mussorgski, played by Isao Tomita.

What are the odds?

Creationists, or anti-evolutionists, are fond of declaring that the odds against evolution or of abiogenesis are great, so great as to make it almost impossible. Some say that the odds of the simplest organism forming “by chance” are 1 in 10^340,000,000. Of course, to get those numbers they have to ignore the facts about how chemical changes occur or how evolution occurs and assume that everything happens at once, like an egg smash played in reverse.

However, scientists can play the numbers game, too. Doug Theobald has used phylogenetic software to calculate the odds that a group of proteins occurring in all life originated independently. You can read about it on Pharyngula.

…take a small set of known, conserved proteins that are shared in all organisms, not restricting ourselves to one kingdom or one phylum, but grabbing them all. In this paper, that data set consists of 23 proteins from 12 taxa in the Big Three domains: Bacteria, Archaea, and Eukarya. Then set up many different models to explain the relationships of these species. … And the winner is…common ancestry, with one branching tree!

Theobald distills it down to just the odds that bacteria have an independent origin from Archaea and eukaryotes:

But, based on the new analysis, the odds of that are “just astronomically enormous,” he said. “The number’s so big, it’s kind of silly to say it”–1 in 10 to the 2,680th power, or 10 followed by 2,680 zeros.

One in 10²⁶⁸⁰…

Swine flu deaths re-estimated, triple

The U.S. Center for Disease Control has revised its estimates of deaths caused by swine flu, using a more accurate method.

The CDC has updated its swine flu estimates with calculations by epidemiologists. They take detailed records from 62 counties and extrapolate them to the country as a whole. These figures include deaths such as pneumonia caused by the flu. The previous figures counted only laboratory-confirmed cases or “pure” swine flu deaths caused by fever, respiratory distress, and drowning in one’s own lung secretions.

With the new estimates, the number of deaths in the U.S. attributed to swine flu has thus tripled to 3900 people, including 540 children. This is the same method used to count deaths from the usual seasonal flu.

The CDC estimated that:

* 8 million children up to age 17 were stricken by swine flu; 36,000 were hospitalized and 540 died.

* 12 million adults ages 18 to 64 were infected; 53,000 were hospitalized and 2,900 died.

* 2 million people 65 or older were infected; 9,000 were hospitalized and 440 died. In a normal flu season, 90% of deaths occur in those over 65.

The new estimates do not include infections and deaths since Oct. 17, a period in which swine flu has been circulating at its highest rate.

Science papers online

Here’s a boost to research: more than half a million science papers online at arXiv. Their content description lists these subjects:

• Physics
• Mathematics
• Computer Science
• Quantitative Biology
• Quantitative Finance
• Statistics

In other words, these are papers that deal with mathematics and with quantifying results.

It’s one of the ways in which the Web makes science much more accessible to us.

Hat tip to Blake Stacey at Science After Sunclipse.