Saturday, November 15, 2014

Why do couples at Marine Drive sit equally spaced from one another?

An interesting observation made by @TheToothsayer when we recently visited Marine drive was that the couples that sit at the sea front, sit equidistant to one another, quite precisely equidistant that too and over large distances. This nonchalant observation has more interesting insights than what is prevalent on the first look.
Photo courtesy: Kunal Bhatia - www.mindlessmumbai.com
Two odd things – firstly, there is no clear coordinator imposing that they should be sitting at a certain distance from one another and secondly, there seems to be no conscious effort to do this coordination. It just happens, it happens every single day.

How this formation happens is perhaps not too difficult to imagine if we piece this together in the chronology of the couples arriving at Marine Drive. Much like the XKCD Urinal Protocal Situation, we can postulate 3 basic rules that a logical couple would follow to find themselves a spot at the sea front -

  1. The couples like privacy [citation experience needed] and they will optimize their distance from other couple such that they will maximize the minimum distance they have from any other couple.
  2. There is a distance after which increasing the minimum distance from the next couple has no added value. Simpler way to state this is that a couple once a certain distance away from the next couple will just choose that spot because it’s not worth walking further.
  3. Similarly, there is a distance that is the minimum acceptable distance from the next couple, that a couple can tolerate. This means that if the maximum minimum distance from any couple is less than this distance, then the couple will choose to wait for a spot over squeezing themselves awkwardly between the other couples.

Based on these the situation pans out to be something like this –


What is remarkable here is that all the 3 rules were for each individual couple and there was no coordinating agent that ensured that an equidistant pattern was formed. This is a purely self-organized pattern, which is a social trait of human beings. In fact, it would be safe to say that if there had been an established authority that made couples sit equidistant, then there would be resistance and it would not work with the smoothness it does naturally.

There is one situation when this logic does break down. When two neighbouring couples leave at the same time, where would the arriving couple choose their spot?


If the 3 logical rules are to be followed, then position A is the logical choice but Position B and C would keep the couples equidistant. I asked 30 random people on the train I am on right now, which position they would choose (I told them what I was doing after they chose). 27 out of the 30 chose position B. I would have chosen Position A because I would like to think I like logic over symmetry; however that is probably my frame of mind when writing this. Nature loves symmetry and it is clearly manifested in the human mind.

And THAT is why couples at Marine Drive are equidistant to one another.

Edit: This article has resulted in an overnight Phd into co-operative behaviour in the natural world – Seems like this is not only a human trait; interestingly here is a picture of ants self-organizing into equidistant pattern around their food.




Also surprisingly, Cognitive Biology is way simpler to make sense of over Photometry.


4 comments:

  1. Well written! I liked the illustrations!

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  2. There is another case. In the first scenario where two couples are already there, suppose the third couple approach not from their middle but from the left or right. In that case they won't generally cross a couple - but stop at a certain distance from the leftmost (or rightmost) couple. To explain the symmetry in that situation one may say that the distance in rule 2 is universal, that is to say it is the same for every couple. But this seems unlikely, so it's probably better to add another rule : If there is a certain distance that has been chosen by the existing couples, the new joiners will also choose that distance.

    In general, symmetry and optimization go hand in hand. For example, the shape that minimizes surface area for a fixed volume (i.e if you were to make a bag that would hold a certain amount of stuff what shape would you make it if you wanted to use the minimum amount of cloth in making the bag) is also the most symmetric - the sphere. This is why water bubbles are spherical actually :)

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    1. Yes, you are correct! Optimization usually leads to symmetry and it was really nice to see this happen live. However, if you notice the illustrations closely you will see that the sea front in this case extends to infinity on both sides since this is an ideal case. Which means that a couple coming from the right or left is for all practical purposes equivalent to the one that comes from the middle. Infinity works in funny ways ;p

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