ARTS - Musical chess!

I thought this was rather neat. Jonathan W Stokes has been experimenting with ways of turning famous chess games into music. It's amusing to see how he does it and the results provide surprisingly good listening.

So how did he do it?

The process he chose is quite straightforward. He noticed that there are eight columns of squares on a chess board and also eight notes in a musical octave.

With some rather clever adjustments and using the values of the chess pieces to determine how long each note should be, he transcribed the chess notation into musical scores and then played them on a piano.

Here's my favourite - 'The Immortal Game' played in June 1851, and this is how it sounds on the piano.

Rather delightful!

The full details and a further two examples of the music are available on Jonathan's blog. And if you enjoyed Chess Music you might also like Jonathan's Fibonacci Music!

Wolfram Alpha

Wolfram Alpha is about to hit the streets (or at any rate, a computer screen near you). Created by Stephen Wolfram and his company, Wolfram Research, it will look superficially like a search engine but is fundamentally different in nature.

Like a search engine it comes with a text entry box where you can type in a query, like a search engine it goes away and thinks and then spits out results on a webpage. But what goes on behind the scenes and the nature of the returned webpage couldn't be more different.

Wolfram Alpha depends on two earlier developments from the same stable. Mathematica is software that enables mathematical manipulations to be entered, processed, and displayed on a computer, while NKS (which stands for 'A New Kind of Science') is an alternative to the normal tools used by scientists to model the way the universe works.

Using both of these innovative tools, Wolfram Alpha takes a free text query, decides what the user wants to know, looks up the relevant information in its enormous collection, processes the information to create an answer to the original query, and builds a webpage on the fly to display the response. The webpage may include text, images, graphs and charts etc. The end result is a tailored report that might have been written by an expert. Indeed, in many ways Wolfram Alpha is an expert!

Steven Wolfram is an extraordinary person. He is, frankly, a genius - one of a handful of truly great minds in our own time. He looks at things in new ways and comes up with fresh insights, testing them, proving them, and then publishing them. Here, in his own words, is how he's spent his life so far.

Major periods in my work have been:

• 1974-1980: particle physics and cosmology

• 1979-1981: developing SMP computer algebra system

• 1981-1986: cellular automata etc.

• 1986-1991: intensive Mathematica development

• 1991-2001: writing the book, 'A New Kind of Science'

(Wolfram Research, Inc. was founded in 1987; Mathematica 1.0 was released June 23, 1988; the company and successive versions of Mathematica continue to be major parts of my life.)

You can see right away that he is not a man in a hurry. He is not afraid to spend five years or more on a single project. Learn more about his background and work from Wikipedia.

Not everyone agrees with Wolfram's work on NKS, a range of reactions are included in the Wikipedia article on the book.

In the end, 'wait and see' may be the best advice for both Wolfram Alpha and NKS. As far as Alpha is concerned, we'll all get a chance to try it and draw our own conclusions when it's released. Hopefully that will be next month (May 2009).

Meanwhile you can watch video of Stephen Wolfram demonstrating the new technology at Harvard on 28th April.

For news about the new tool, take a look at the Wolfram Alpha Blog which will be updated regularly with further announcements and background information.

How many times?

How many times can you repeatedly fold a sheet of paper in half? It's widely accepted that about six or seven times is the maximum possible, and a quick experiment with a piece of writing paper, a sheet of newspaper, or any normal paper you can find around the home will prove that this is correct. Or will it? What does 'correct' mean? What does 'proof' mean?

A mathematician will tell you that however many times you do the experiment and find you can't fold the paper a seventh time, that is not proof. You cannot prove something to be impossible, only that something is possible. Folding a piece of paper six times and failing to fold it seven proves that six is possible, but not that seven is impossible.

Remarkably, someone has managed to fold a piece of paper twelve times! Was there something special about this piece of paper? Yes and no.

The paper was a long roll of toilet paper. The relevant attribute of this paper was not that it was especially thin (try folding a single sheet of toilet paper yourself) but that it was especially long.

Britney Gallivan, a high-school student from California, was not prepared to take 'no' for an answer. She began by developing some mathematics for paper folding, and this showed her that a piece of paper that is long enough can be folded many more times along its width than a shorter piece. Armed with this knowledge she did the experiment - and managed to fold it twelve times.

There are several lessons to be learned from this.

What seems to be impossible may, in fact, be perfectly possible if we go about it in the right way. Technology has shown this to be true over and over again. Here are a few things that were once thought to be completely impossible - travelling to the moon, ships made of iron, building a flying machine, sailing round the world, the earth moving, continents moving, orbiting a satellite.

Common sense often lets us down. It would be a wonderful thing to learn the value of not making assumptions or jumping to conclusions. But we are designed to assume and conclude, this serves us well most of the time and enables us to deal relatively simply with a very complex world.

Britney Gallivan's paper folding achievements are described online. I encourage everyone to read them, if mathematics is not your forte you can skip that part, but please understand that it was the mathematics that led her to a simple, elegant, but entirely unexpected conclusion. With hindsight it seems obvious, but nobody had thought of it before Britney. Clever young lady!