general philosophy www

phantom parabolas

Saw this morning on TV1 Breakfast – not much (anything? maybe this??) about it on the net yet…

But according to TVNZ, “maths teacher Philip Lloyd, an Auckland man who has made a maths-changing discovery to do with parabolas.” (though the date of the above forum post is 2003, and the name is TJ Evert!!??  hmmm…)

Anyway, the discovery is cool – whether by TJ Evert in 2003 or by Philipo Lloyd more recently.  Apparently (if I’m wording this right – it’s been a while since algebra class!) equations with an ‘imaginary’ solutions for ‘x’  (([Dale refuses the philosophical tangent – no pun intended])) do not intersect the x axis.

The news is that a ‘phantom parabola’ can be plotted, which does intersect an imaginary x-‘plane’ (we always had to imagine the x & y axis’ did we not?).

The ‘ooh that’s a cool parallel with spirituality’ thought that I initially had may well be not much more than a play on the word ‘imaginary’, but hey…  Like the Flatland analogy (used by C.S. Lewis [unknowingly? i cannot remember] and Rob Bell), this would be another case of adding another dimension.  After all, we imagine real things all the time, don’t we?

So there it is.  I’ve sent TVNZ an email with the link above.  Will see if it’s relevant :)

One reply on “phantom parabolas”

William Rowan Hamilton (1805-1865) formalised the definiton of complex numbers, so he was probably the first person to make the connection to extra dimensions. In modern mathematics, we can introduce complex numbers in algebra as Hamilton did;

‘. . . as ordered pairs of real numbers. They form a commutative, 2-dimensional extension field C [complex] of the field R [real numbers]. There is an element i ∈ C with i2 + 1 = 0, and every complex number can be written uniquely in the form x + iy, with x, y ∈ R. Complex numbers can also be described elegantly as real 2 x 2 matrices …’
[Ebbinghaus et al.; Numbers, Springer-Verlag, 1991, p.65]

These matrices perform a vector rotation from the real line onto the complex plane.
(from an essay I wrote back in ~1998 as part of my B.Sc.)

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