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Text, Bytes and Videotape


January 2003

Understanding bits and bytes

With 8 bits, we have 28= 256 possibilities (each bit can be zero or one, and the possibilities multiply together). We call 8 bits a byte. The very common ASCII system makes each letter of the alphabet, both capital and small (plus punctuation and some other symbols) correspond to a number from 0 to 255 (for example a=97, b= 98 and so on), so one letter can be expressed with one byte.

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Editorial

  • Information overload - how mathematicians are helping us all to make sense of the vast amount of information now available to us
  • Sum problems - can you be good at mathematics without being good at arithmetic?
  • Readers' corner - Meet Mandy, the cuddly Mandelbrot set!
Review

'1089 and all that'

Since the phenomenal success of "The little book of calm", publishers have been falling over themselves to produce "little books" of everything else, presumably in the hope that the essential ingredient was the littleness, rather than the calmness. Although, at 5 inches by 7¼, "1089 and all that" makes a rather big little book, and its content couldn't be further from the banalities of "The little book of calm", there is something of a "little book of mathematics" about it, with its short chapters and personal narrative.
Review

'Mathematics: a Very Short Introduction'

One of Oxford University Press's series of "Short Introductions", this book is a rigorous and challenging description, by one of the greatest pure mathematicians alive (Timothy Gowers is Rouse Ball Professor of Mathematics at the University of Cambridge, and a Fields Medal recipient), of what mathematics is. Perhaps too challenging, in fact - on page 23 we are introduced to an axiomatisation of number systems, and things only get tougher. Clearly, as one of a highly intellectual series, the book is intended to stretch its readers' abilities to the utmost.
Review

'How to dunk a doughnut'

Paul Erdös is reported to have said "A mathematician is a machine for turning coffee into theorems". We may never know if he appreciated the mathematics behind the perfect dunk of a biscuit into said coffee, but we can all begin to understand the ubiquity of maths in our lives, thanks to Len Fisher's delightful book. The subtitle is "The science of everyday life", though pretty much all the content is maths with the equations (mostly) taken out. Perhaps Professor Fisher was advised that sales would suffer if they weren't, but anyone interested in the applications of mathematics to the real world will find plenty to amuse and educate.
Review

'Reckoning with risk'

Gerd Gigerenzer is not a mathematician or statistician per se, but primarily a psychologist, working across disciplines to understand how human beings make decisions in the face of uncertainty. What he offers here is nothing less than a prescription for how to think, how to choose, and how to live, when the information on which we base our decisions is necessarily incomplete and flawed. For example - how worried should you be if you have a positive mammogram as part of a screening programme for breast cancer, or a positive HIV test despite the fact that you are in a low-risk group?
Article

Newton and the kissing problem

In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.
Article

Text, Bytes and Videotape

How can a 3 hour long film like the Lord of the Rings fit on a single DVD? Hw cn U rd txt msgs? How do MP3s make music files smaller, so they can be downloaded faster off the Internet? All these things rely on the mathematics of data compression.
Article

Dashing along

Currently, disabled computer users have a hard time inputting text, using laborious word-completion. Plus find out how this is changing, thanks to Dasher, a new open-source text-entry system based on arithmetic coding.