[DWJ] "Orthogonal" (orthogonally to T-shirt slogans)

Nicholas Jackson nicholas at makyo.org.uk
Mon Jun 7 05:10:35 EDT 2010


On 7 June 2010 00:22, Jameela Lares <Jameela.Lares at usm.edu> wrote:

> The best I can do with "orthogonal" is that it is "irrelevant" because "at
> right angles."


Yes, that's a good way of thinking of it.

In mathematics and physics some quantities have a direction associated with
them - they're called "vectors", whereas a directionless quantity is called
a "scalar".  For example, physicists make a distinction between speed (a
scalar quantity: "my car is travelling at 30mph") and velocity (a vector
quantity: "my car is travelling at 30mph in a north-easterly direction").

It often helps to break vector quantities into two or more (according to how
many dimensions the environment you're concerned with has) components -
especially if you're particularly interested in their relevance to specific
directions.

So if my car is travelling at 30mph in a north-easterly direction, then for
every mile I travel, I've moved a certain distance (actually about 0.7
miles, by application of Pythagoras' infamous theorem) northwards of my
original location and a certain amount (in this case also about 0.7 miles)
eastwards of my original location.  My velocity therefore has a northwards
component of about 21mph (= 0.7 x 30mph).

If, on the other hand, I'm travelling due east at 30mph, I'm not moving at
all in a northerly direction, so the north-south component of my velocity is
zero, and no matter how far or fast I drive, I'm not going to get any
further north than I already was.  In this case, we say that my velocity
(the speed and direction I'm travelling) is "orthogonal" to the north-south
direction - geometrically they are at right angles to each other.  My
velocity is, as you put it, irrelevant to any desire I might have to travel
further north than I currently am.

Analogously, if what I say in a particular discussion is not relevant to
whatever point I'm trying to make, then it doesn't get me any closer to (or,
for that matter, further away from) making that point.  (It should also,
ideally, have no effect on my ability to convince other people of that
point, but as politicians and advertising executives have discovered this
isn't always the case.)  In this context, the word "orthogonal" is
synonymous with "irrelevant" or "red herring".

I hope this makes some form of sense.

    nicholas


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