

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 xaxis (the real equivalent),
inductance by the positive yaxis (the imaginary equivalent), and capacitance
the negative yaxis (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 xaxis?). 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 nontransparent
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.

