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Increasing the clarity of the unclear clearly

(published 22 March 2011)

The light half.

Day 44. (already) A brief meeting with the boss. What a difference ten minutes makes. He has been reading the blog and is evidently appalled by the woeful lack of understanding and factual content therein; he specifically mentions the unclear “Clearly, this implies that...” which I referred to some weeks ago. It’s time for me to learn something. Only a few minutes later I leave the office with real comprehension about that formerly incomprehensible page turn (not least that the vertical lines either side of the letter r, the r representing the reflection coefficient, are the math shorthand for ‘the magnitude of’, so I can now at least write out the sentence in English rather than mathematics: Clearly this implies that the magnitude of the reflection coefficient is equal to one. (Why didn’t he just say that in the first place?)). But I’m also a little sad to have lost the infinitely intriguing imagined interpretation of imaginary numbers, having had them tied down to the mundane conceptual realities of axes on a graph (although as I write the understanding of why one would want to map the imaginary on the perpendicular axis to the real is again disappearing in a fog of misunderstanding, so that’s ok). Anyway, for the moment I don’t think it’s necessarily important to know the mathematician’s rationale for the perpendicularisation of real and imaginary, of import is that electronic engineers use the fact that real and imaginary numbers are plotted on the x- and y- axes (respectively) as an analogue for impedance in circuits. In capacitors the voltage and current are 90 degrees out of phase, and so these components (as well as the roles of resistors and inductors, the three collectively comprising impedance) can be mapped out on the axes (resistance is represented by the positive x-axis (the real equivalent), inductance by the positive y-axis (the imaginary equivalent), and capacitance the negative y-axis (imaginary equivalent). Bother, that seems to describe the roles of three of the four axes, but begs the question of what it is represented by the negative x-axis?). Anyway, it is evidently clear that by this means the overall impedance of a circuit can readily be calculated. You see?
As I write I am sitting on the train heading back home – again my reserved “window” seat was next to a piece of non-transparent train structure that largely obscures any view of the outside world, and someone else was already sitting in it anyway (having evidently also switched the seat tickets around to make it look like his!); but he is welcome to his falsely acquired sliver of view. It’s almost dark anyway, and I am now sitting at a forward facing window seat at a table, where I have spread out all over the place, and with relative acres of darkening glass next to me. I am riding high on the knowledge that I’ve acquired knowledge, and desperately trying to think of what to ask for the tutorial we have timetabled for next week; it seems that this art tomfoolery can remain obdurately obfuscated no longer.

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