Comments on: Negative Numbers in Our Time

By: Adam

Adam — Thu, 16 Mar 2006 20:31:19 +0000

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.

By: Adam

Adam — Thu, 16 Mar 2006 20:22:52 +0000

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.

By: Jase Rex

Jase Rex — Thu, 16 Mar 2006 18:05:12 +0000

This episode and others are available in the ‘In Our Time’ archives.

By: Maynard Handley

Maynard Handley — Thu, 16 Mar 2006 00:24:05 +0000

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

By: Kristin

Kristin — Wed, 15 Mar 2006 15:37:44 +0000

According to Wikipedia,

Imaginary numbers were defined in 1572 by Rafael Bombelli. At the time, such numbers were thought not to exist, much as zero and the negative numbers were sometimes regarded by some as fictitious or useless.

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.

By: Paul Valletta

Paul Valletta — Wed, 15 Mar 2006 05:50:08 +0000

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!

By: PK

PK — Tue, 14 Mar 2006 15:52:49 +0000

There is a great Calvin & Hobbes on imaginary numbers.

By: Chad Orzel

Chad Orzel — Mon, 13 Mar 2006 19:50:19 +0000

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…)