Don’t miss** BBC Radio 4’s In Our Time program on Negative Numbers. You listen at the website to this proramme until Thursday morning, when they replace it with the next one.
Here’s the blurb for the programme, which I stole from their website (I hope they don’t mind):
In 1759 the British mathematician Francis Maseres wrote that negative numbers “darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple”. Because of their dark and mysterious nature, Maseres concluded that negative numbers did not exist, as did his contemporary, William Friend. However, other mathematicians were braver. They took a leap into the unknown and decided that negative numbers could be used during calculations, as long as they had disappeared upon reaching the solution.
The history of negative numbers is one of stops and starts. The trailblazers were the Chinese who by 100 BC were able to solve simultaneous equations involving negative numbers. The Ancient Greeks rejected negative numbers as absurd, by 600 AD, the Indians had written the rules for the multiplication of negative numbers and 400 years later, Arabic mathematicians realised the importance of negative debt. But it wasn’t until the Renaissance that European mathematicians finally began to accept and use these perplexing numbers.
Why were negative numbers considered with such suspicion? Why were they such an abstract concept? And how did they finally get accepted?
The contributors on the programme are: Ian Stewart (Professor of Mathematics at the University of Warwick), Colva Roney-Dougal (Lecturer in Pure Mathematics at the University of St Andrews), and Raymond Flood (Lecturer in Computing Studies and Mathematics at Kellogg College, Oxford).
I’ve not heard it yet, but I’ve been reliably informed that it was pretty good…. They even chat a bit about imaginary numbers too. Enjoy!
-cvj
**Thanks Ed Copeland!
March 13th, 2006 at 2:50 pm
I’ve not heard it yet, but I’ve been reliably informed that it was pretty good…. They even chat a bit about imaginary numbers too. Enjoy!
Odd question:
When did imaginary numbers come into general use? In a conversation at a faculty happy hour last week, somebody made the claim that there hadn’t been a really significant advance in practical mathematics since Newton and Leibniz invented the calculus, and we were trying to come up with counter-examples (of which there were many. It wasn’t a terribly accurate statement, to say the least, but it made for some fun geeky conversation…)
March 14th, 2006 at 10:52 am
There is a great Calvin & Hobbes on imaginary numbers.
March 15th, 2006 at 12:50 am
This talk is a must, it is only available online for 7 days, so it will dissapear this thursday,really amazing clarity, the really interesting thing for me, was the square root of minus -1, for a non-mathemagician like me it was at first quite mindbending, but very fruitful in the context of complex plane numberlines!
March 15th, 2006 at 10:37 am
According to Wikipedia,
But I would say that Euler has a lot to answer for in terms of making imaginary numbers useful, which he did in the mid-18th century. Whoever made the claim of no significant progress in mathematics since the invention of the calculus clearly never studied complex analysis.
March 15th, 2006 at 7:24 pm
You’re much better off subscribing to the In Our Time podcast than trying to grab the file each week and worrying about the 7 day window.
http://downloads.bbc.co.uk/rmhttp/downloadtrial/radio4/inourtime/rss.xml
March 16th, 2006 at 1:05 pm
This episode and others are available in the ‘In Our Time’ archives.
March 16th, 2006 at 3:22 pm
Heaviside (of the Step Function) had a role to play in promoting the use of complex numbers, I believe (using them for analysis of electric circuits). He was also something of a nutter, as a matter of interest.
March 16th, 2006 at 3:31 pm
I’m a bit dubious at talk of whether negative, or complex, numbers ‘exist’ or not. It’s like inviting a beachball out for a game of golf. It doesn’t make any sense. It seems to me that you can’t say much more than that negative numbers, say, are useful in solving problems, at least not unless you could show that our chosen axiomatic mathematical system (which consistently allows for such entities) was the only one that would be useful in describing the universe (or perhaps would be ‘most useful’) and I’m not aware that anyone’s parametrised possible mathematical systems in order to make such a statement. But then, I’m not a platonist when it comes to mathematics: I do accept that we make ‘discoveries’ in mathematics, but I don’t think that those ‘discoveries’ exist independent of the creation of the axiomatic system by humankind (and, who knows, maybe alienkind) or, at least, I don’t feel that way, or see any reason to assume that mathematics exists independent of thought.