May 20, 2006
Odd little mathematical dreams
A few weeks ago, I had a dream in which the following equation featured:
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
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