

Mathematical Theorem Suggests Humans Really Are Sheep - cwan
http://www.howwedrive.com/2010/03/30/mathematical-theorem-suggests-humans-really-are-sheep/

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rdtsc
I have noticed this while driving on interstates in a low traffic density
areas. Often there will be a group of cars maintaining a similar speed and
driving fairly close to each other. Sometime I notice cars following me,
sometimes I catch myself following others without deliberately thinking of it.

I could guess a couple of reasons why this happens:

1) Hiding from a speed radar behind other cars. I often see a group form if a
fast car passes a group of slower cars, some slower moving vehicle will speed
up and follow the leader matching its speed.

2) It is easier to drive if you focus on following something. It defers some
decisions (such as choice of speed, lane) to that car. Perhaps it takes less
mental energy to follow something than to drive on open road perhaps.

3) Humans are social mammals that like to follow a leader. Such quick groups
of leader+followers quickly appear and disappear while traveling on the road
just based basic mammal herding behavior.

2,3 might apply to crowds as well.

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go37pi
I can say with pretty strong confidence that its due to 1. On long trips this
situation can get pretty interesting if you end up finding groups of other
cars that are on the highway for similar amounts of time. You could say that
the group takes on a dynamic similar to a herd hiding from a predator.

The riskiest position for a car is the leader position and the last position,
as these are the easiest positions to get picked off by the police. Most
people want to go faster, but don't want to get caught. Often times you'll see
people alternate the leader position as a way to share the risk and
acknowledge that the other driver is taking greater risks by taking the leader
position.

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lmkg
That's not a "theorem" in the mathematical sense, that's a study. It's an
interesting one though, showing how humans perceive space and proximity and
suggesting it's biologically rooted since we share it with animals. I'd like
to see comparisons across cultures like US vs Japan, and across less herd-like
types of animals, like lions or something. And maybe one for fishes, because
they use a 3-D comparison. (Maybe I should ask for one with ponies by this
point.)

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roundsquare
Interesting. I'd like to get my hands on the data... the distribution looks
vaguely exponential.

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dododo
it looks more like it's gamma distributed to me: you could imagine the
generative process is something like a sum of exponentially distributed
decisions times.

~~~
roundsquare
Sorry, I'm not following. The graph shows the distribution of distances
between cars (and people and sheep). Each distance is, to some degree, an
individual decision made by a driver (the driver in the rear). How are you
imagining the generative process? I was imagining it as each person making a
single decision.

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dododo
each driver decides whether or not to increase the distance to the next car.
there are many such decisions that result in the total distance to the next
car: i think it's a constant adjustment rather than just one decision.

another view might be that an exponential distribution on distances would lend
(a lot of) support to zero distance: hopefully that's pretty rare.

~~~
roundsquare
Interesting... makes some sense.

 _another view might be that an exponential distribution on distances would
lend (a lot of) support to zero distance_

Well, I think that would be a case of sticking a bit too closely to the model.
Its likely that, even if the distribution is generally exponential, at very
short distances the decision process changes.

In fact, one would probably argue that the distribution would always change
based on how dense the traffic is.

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dododo
the gamma distribution is often used (for example, in neuroscience for spiking
rates for the refactory period) to capture the case where you do not wish to
give support to zero plus some short period after zero.

the exponential distribution is a kind of gamma distribution: Gamma(1,lambda)
= Exp(lambda)

