Mathematics in everyday life

Why are people getting better at everything?

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I had an interesting discussion with my barber the other day (yes, barber).
He is an avid runner, and we started talking about the dramatic improvements
in the track and field records over the last century. Let’s look at marathons.
The first few years can probably be discounted, but even if we start with 1913
the best time is 2:36:06 (Alex Ahlgren, Sweden). The world
record today is officially 2:03:59 (with Geoffrey Mutai finishing
the 2011 Boston Marathon in 2:03:02, not recognized as a
world record for reasons that are still unclear to me).
I know people who have beaten the 1913 world record. There must be hundreds,
if not thousands of runners who can do so nowadays.
There is nothing special about marathons, or running, or sports
for that matter. This is happening across disciplines – the NYT
recently had an article about how piano virtuosos are becoming more
and more common
.

What could be the reason for this? One possibility is better training
and preparation. I am certain that today people know much more about
the mechanics of running and playing the piano than at any time in
the past. However, my barber suggested another possibility:
Simply many more people today engage in these activities seriously.
A century ago it was only the privileged or lucky few who could afford
to spend the time necessary to develop their skills to a sufficient
level to compete at an international level. Today, athletes and
artists are recruited from a much wider base, and there are more resources
available to train them from an early age. Therefore the number of
exceptionally talented people identified early is much greater.
(BTW, this may also be why the Soviet Union was dominant in chess
during the last century – the number of amateur players was higher there
than anywhere else in the world. In part this was due to state support).
In mathematical terms, if you choose a sample from a distribution, then
the number of picks far from the mean increases with sample size.

I am sure that this is not the only, or even the dominant factor. I am
also not sure how one could test it. One could, for instance, check
whether the disciplines with the greatest increase
in participant number have seen the greatest improvements. However,
with increased interest in a discipline also come greater resources.
Better resources could lead to improvements in training, nutrition, etc.

However, I believe that there is something to the idea that increasing sample
size will increase the number of outliers that are chosen. And that brings
me to a worrisome trend: The defunding of public schools and the decrease
in grant money available to those who cannot afford college will decrease
the pool from which will come the scientific leaders and top innovators of
the next generation. I am afraid that many will simply not be able to develop
their talents. This could have a large impact on our entire society.

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