The closer, the more similar.
There are 16 athletes here, all different.
Almost everyone interprets the problem as,
"How do I line 'em up?"
But a line can't do the job.
The athletes have both weight and height.
That's two different parameters of "size." A line is one dimensional (even if it curves about.)
problem requires two dimensions.
However, if we turn over a tile, we find a different athlete on the other side.
One one side is an athlete who is a beanpole or a bit wide in the middle,
on the other side is an athlete who is wide across the shoulders.
We have a third dimension!
These new athletes also require two dimensions
|Our runners teach something important:
the common, but usually unrecognized, errors of using comparatives and
superlatives. Comparatives and superlatives require that what we
are comparing can be put into a line that represents the measure we are
comparing by. If the thing we are measuring has more than a single
part (a single-component measure is called a scalar), then our line is ambiguous.
We can usually toss in a big dose of personal bias and claim we are making
valid measurements and valid comparisons.
That's a deception. Back in the 19th century, science discovered a whole family of errors of this kind and worked out a lot of math that can steer us down a whole family of correct paths. Today we know a lot of that math as "vector analysis" and "tensor analysis." These are ways to calculate with multi-component measures using concepts of multdimensional spaces. But very few people who today make many decisions about such matters are aware of such math. Nor are they aware of the kinds of errors they regularly make.
So when Richard Feynman declares--in The Feynman Lectures on Physics--"Since most of you are not going to become physicists, but are going into the real world...sooner or later you will need to use tensors" his truly deep, important, magical insight remains mere misty and mystical non-sense.
It actually has in it that profound magical sense which is found in special places -- places waiting for people to think deeper, and to think to look into them.
and keep in mind that arranging
colors is a lot like arranging runners.
The ways we looked at the problem in other years: HERE
Scope -- Relevance -- Math -- Logic -- Tensor
"You can find magic in places you never thought to look."
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