6 ms·

Mathematical Theorem Suggests Humans Really Are Sheep

6 points by cwan 17y ago

lmkg 17y ago
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.)
rdtsc 17y ago
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.
- go37pi 17y ago
  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.
roundsquare 17y ago
Interesting. I'd like to get my hands on the data... the distribution looks vaguely exponential.
- dododo 17y ago
  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 17y ago
    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.
    - dododo 17y ago
      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 17y ago
        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.
        17y ago

6 points by cwan 17y ago

lmkg 17y ago

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.)

rdtsc 17y ago

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.

go37pi 17y ago
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.

roundsquare 17y ago

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

dododo 17y ago
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 17y ago
  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.
  - dododo 17y ago
    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 17y ago
      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.
      - 17y ago