« Beer! Part 2 | Main | From the horse's mouth »

May 20, 2006

Odd little mathematical dreams

A few weeks ago, I had a dream in which the following equation featured:

1

H
=
1-
H

2

I don't normally dream about mathematics. Scrub that. I've never dreamt about mathematics. But I remember this equation very clearly. The next day, I asked J (who is appropriately mathematically educated) if it's a well known equation. No, she said. The 'H' normally represents a Hamiltonian. She rewrote the equation in a more normal quadratic form, thus:

H2 - 2H + 2 = 0

and fairly quickly showed me that there are no real roots to this equation, the two imaginary roots being:

1+i and 1-i

This is fairly bizarre. It's probably the second simplest quadratic equation you could write with imaginary roots, after:

H2 + 1 = 0

(which has roots of i and -i).

Later on, after doing some googling, I found this post at the math forum at Drexel University. The author, Howard Engel, makes note of these two equations - and furthermore notes Hamilton's use of "ordered number pairs" to represent complex numbers.

I don't set much store by this, but obviously some part of my brain is more receptive than I thought when I encounter mathematics.

Thanks, by the way, to the very useful Stef's HTML equation generator for the math rendering!

Posted by daen at May 20, 2006 10:37 PM

Comments

Post a comment

Thanks for signing in, . Now you can comment. (sign out)

(If you haven't left a comment here before, you may need to be approved by the site owner before your comment will appear. Until then, it won't appear on the entry. Thanks for waiting.)


Remember me?