Tuesday, 11 August 2009

Modelling Men at a Urinal

Since we're keeping this quantitative how might you model where men choose to pee at a urinal?

There's basically a short range repulsion and a long range attraction - normalised such that the potential minimum is two thirds of the length of the room. This is a well known problem in physics as, for instance, atoms in a solid are attracted to each other at long range and repelled from each other when they stray to close.

I bet this generalises to how people fill up in any circumstance e.g. in a row of seats or in a lift. Having had a quick play on google it occurs to me that the people who design tube trains and alike should factor in these considerations if they want to most efficiently fill their vehicles when the density of people is at some medium to high value. Are there any other places where it would be a benefit to improve filling density?

A wild idea to generalise this further might be to consider how people fit their opinions in a spectrum of ideas. Again there's the attraction of peer pressure (you want your opinions to fit with the crowd) but the repulsive force of expressing one's individuality (you want to stand out as an intellectual pioneer). Most psychological versions of experiments to test this kind of phenomena show peer pressure dominating. I don't think this invalidates the idea, though, as the construction of the experiment means there is no benefit to standing out from the crowd. Creating an experiment that includes a repulsive term to get a more realistic effect is a trickier question. There has to be two benefits; one which is gained through a correct answer, the other which is gained through being different.

(as a related aside i wonder whether anyone's tested whether personal space is room dependent?)


  1. I once attended a talk at UCL where someone examined "peer pressure" and "leadership effect" in a flock of fish.

    There was a bunch of fish in a container. A fake predator - a toy fish - was immersed in water. Fish tried to escape.

    Then they got a fake fish to swim past the predator. And the flock of original fish still tried to escape.

    Once they increased the number of fake fish swimming past the fake predator to something like 3, the fish didn't bother escaping and just swam past.

    (re the aside. What did you mean by the "personal space". When two people (not a couple) are in the same room?)

  2. Regarding the point about choosing one's opinions and ideas.

    This might have an extra layer of complexity. Since deposits of previous opinions and experience will determine which peers we choose to talk to, and whose opinions to take into consideration - that will in general skew the result away from the one obtained by optimising over a random sample.

  3. agreed.

    i was thinking of a stripped down situation - something more akin to a psychological experiment than a real world decision.

  4. Regarding personal space: i was trying to decide at what person density this 'theory' would dominate.

    At low and high density it wouldn't be an issue; either there's plenty of room or everything is filled, respectively.

    But at some middle density, where the average volume of space per person is slightly less than the optimum personal space, there may be some odd effects. Kind of like a phase transition.

    Of course i didn't take personal space into account directly when considering the urinal model so i was wondering how to make the two consistent. If personal space was room dependent then the two would be consistent. I'm fairly certain that this isn't true but i wondered whether anyone had checked.

  5. A tangential remark re the psychological experiment mentioned above.

    An obvious point is that how one chooses to design the test will have a major effect on the results. What exactly is the space of opinions. How you measure how far off two opinions are. How subtle is the difference between an individual opinion and a cohort opinion. What personal stakes are involved in making choices - it's one thing to be choosing between red and green circles in an experiment, and another to hold an opinion that jeopardises some privilege of a social group to which one belongs - even if that opinion would perfectly balance out the peer pressure and individuality, etc.
    But, sure, these experiments are very stripped down versions of reality, but even as such have been enough to kick off neuro and behavioural economics fields. Not much of a surprise since classical econ is based on the assumption that humans are rational agents - that really kind of needed an update.

    I imagine an explosion of new models in economics, each cooking up a slightly different description of homo economicus, each one based on valid experimental data. Maybe it's already happening, people rewriting laws of consumer theory. I don't really know anything about this.


    To which extent makes sense to talk of choices as "biological" and innate to our nature?
    As opposed to us being taught some time in nursery & elementary school some of these traits.

    A personal example is from my high school days in Bosnia. I applied to some American funding agency to send me to the US for a semester. At the interview they asked me what I thought were ridiculous hypothetical questions - "if your boat crashed on an island, and there were 10 other people with you, how would you prepare for the night"? I think I said "I'd help with finding the wood and making a shelter". I was rejected.
    Much later I figured this particular agency was looking to fund "leaders" who will lead the Balkans into American values. I had no clue that standing out and leading was something someone at school wants you to do! If anything, in the Bosnian schools of the 90s, you better follow what the teacher says to the letter.

    My kind of obvious point being, that yes, a lot of things are taught and socially constructed and also the ones pertaining to choices of opinions. And hopefully the "objective scientific psychological experiments with proper control groups" performed on subjects living in Boston, MA are not generalised too easily to all humans as something coming out of our biology.

    Not that they shouldn't be done!

  6. Oh - I'm not saying I think I was rejected by the US funding body because of the clash of cultures! Maybe it was an entirely different matter, like looking dumb.

  7. That’s a really good point. I cannot agree more that all these psychological experiments are steered by biases of the designer, the same way as all the experiments that have ever been done.

    This is however still an excellent way if not the only to study human behaviour provided we are aware of this defect and the experimenters clarify how a particular conclusion may be applicable or make good attempts to demonstrate it applies to diverse groups.

    My view is that the ultimate goal of all these studies is to help devising the right incentives, which in many cases have to be quite specific, for instance to a social group, for it to be effective. So yes, I agree there certainly are biases and perhaps too much reductionism as well, but it will hopefully be self-correcting.

    On the note of your US application, did you find out who got the funding at the end? Probably some arrogant twat, leader they were looking for, no? ;P

  8. I think attraction and repulsion are an oversimplification for men at urinals. The two competing effects are:
    * not making the other chap feel like you're crowding him
    * not making the other chap feel like you're avoiding him

    If you like, both urges could be repulsive forces: you'd be repelled by each person already at a urinal, and by the outer boundary. That should deal with all cases.

  9. Mathematically a repulsion from a boundary and a long range attraction of the sort i talk about are the same thing. I think your way of phrasing it is clearer in this instance, but in physics we like conditions that aren't determined by the boundaries, i guess so that we can pretend they're at infinity.

  10. So you prefer not to deal with this instance? I would have thought the best method for a given problem was the best method for that given problem. And it is easy to construct an example where repulsion from a boundary is different from attraction to a point within the system because it's in a different direction (yes, that's where the "attractive" point is not on the line away from the other point's closest boundary point).

  11. It's not a matter of not dealing with it, what i suggest is actually a more physically appropriate theory. You say [brackets mine]:

    "I think attraction and repulsion are an oversimplification for men at urinals. The two competing effects are:
    * not making the other chap feel like you're crowding him [a repulsion]
    * not making the other chap feel like you're avoiding him [an attraction]"

    I presume that you were thinking that the "not making the other chap feel like you're avoiding him" could be modelled as a repulsion from the boundary. I agree that you could construct it like that, but it makes more intuitive sense to model it as an attraction.

    If you're interested in more detail you might want to look into the Lennard-Jones potential.

  12. The second one is not an attraction.

  13. It is.

    "not making the other chap feel like you're avoiding him" can only mean that you don't want to stand too far away from him i.e. an attraction.

    Remember that an attractive potential can be dominated by a repulsive potential at close range (as in Lennard-Jones) so it doesn't mean that the second person is going to end up standing right next to the first. The new person will stand at the point where the attraction and repulsion are balanced.

  14. It is an "attraction" whose parameters depend entirely on how far away the boundaries are from (you and) the other chap. Entirely. Algebraically, since the attractive/repulsive forces will work monotonically, the "non-crowding" force's equation would have the "attraction" component drop out, leaving only terms for the boundary.

  15. It's possible to construct an identical theory either way. Perhaps this will clarify:

    If the situation were that the walls stank [repulsion from a boundary] and people didn't want to crowd [repulsion from the people] then i'd construct the model the way you describe.

    Since the situation is that you don't want to crowd [repulsion] but also don't want to avoid [attraction] then it seems clearer to me to construct the model the way i suggest.

    Again, that isn't to say that you couldn't get the right results your way. I think that it's probably more difficult but that certainly doesn't make it wrong. It's just that my way isn't any less general and makes more intuitive physical sense, at least to me.

    Pedantic technical note
    I'm not sure that what you say about the algebra is correct, perhaps because I don't quite get which forces "attractive/repulsive forces" is referring to. If you still disagree could you explain this further?

  16. I've just twigged where the confusion might be. You are probably thinking of a one-row toilet, which means it has only one dimension. However, I am thinking of a more general solution with two dimensions, hence my reference above to "direction".

  17. A friend (and a summer student in my group - fresh talent in town) kindly pointed out to some related published results.