A mathematical look at interpersonal interaction

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This article: <http://www.brainpickings.org/2015/02/18/hannah-fry-the-mathematics-of-love/> is an interesting, and very plausible, attempt to model the sequence of interactions between two parties.

It is conceived of in terms of a pair of linked responses.  Let's look at it from the point of view of an interacting couple, H for husband, and W for wife, though no stereotypes have been applied, so the analysis is absolutely gender-neutral.  (In fact, they claim that the analysis applies even to the relationship between two nations.)

Suppose the husband has just said something, H(t) at time t, to which the wife replied with W(t).  Here H(t) and W(t) are not actually what they said, but the degree of positivity of the remark.

The husband next responds with H(t+1), to which the wife responds with W(t+1), and so on.  These sorts of things are well studied in mathematics, and the author quotes a pair of theoretical equations that define H(t+1) and W(t+1) in terms of the earlier H(t) and W(t).  The interesting question is what makes the sequence of remarks ---the conversation--- head upwards in tone, versus what makes it head downwards, into a spiral of negativity?

There is another interesting observation that I don't quite understand (because I did not read it carefully enough): that if you're looking for an assistant, for instance, and you're considering 100 applicants, the recipe is
(1) Reject the first 37 applicants.
(2) Accept the next applicant who is better than any of the ones you have seen.

If you only plan to consider 10, you would reject the first 3.7 applicants, and so on.

Happy reading!!!