Data Science vs Bimbo Math

Ms. FrySaint Valentine, that romantic and beautiful festivity for department stores also brings everybody to talk about love in all sort of contexts and TED, my favorite talk place (I will have to rethink about this), brought for the occasion complexity theorist Hannah Fry to talk about The Mathematics of Love. She summoned the almighty and powerful daemon of Mathematics in a quite entertaining talk to reveal us all mere mortals the secrets of Love…  Not really.

So many things to tell about this talk I do not know where to begin. But you know what, TED picking a math bimbo to sell books; I can understand. Turning Science into show business to make it appealing to the general public; I am for it.  Oversimplify complex subjects to make them accessible to everyone even if the oversimplification is not quite true; I can take that. Using all the previous to push people into taking life changing decisions based on sloppy science… Well, allow me to draw a line there Ms. Fry. Science is getting little by little a bad reputation and talks like these are one of the reasons why.

Anyway, long story short, ignore her love tips and specially #2, that one is really damaging. On my side, I will use Data Science and common sense to show that the best you can do is to marry / partner the person you are in love with when you are in love. And when it comes to use reason in the field of love, allow me please to quote Monsieur Blaise Pascal on this one

“The heart has its reasons of which reason knows nothing”

Let’s now kick some ass in the name of good science. Misses Fry present us with three “Mathematically Verifiable” tips to:

  1. Win at online dating: Show yourself the way your are.
  2. Pick the perfect partner: Choose whoever is better than the previous 37% you have previously dated.
  3. Avoid divorce: Don’t let small things go and continuously try to repair your relationship.

In this post I am particularly interested in the ridiculous tip #2, however, I would like to mention a few things about #1 and #3 as well.

  1. Show yourself the way you are?
    • Nice hair color Ms. Fry, indeed.
    • Also I imagine Ms. Fry follows her own advice and does not depilate, which lead us to infer that while wearing a bikini Ms. Fry looks like a ginger coconut tree… just guessing.
  2. Pick the perfect partner?
    • So let me get this straight, if your first candidate happens to be Angelina Jolie or Brad Pitt like, you just can’t profit from your loved ones expedience in life (parents, older friends, siblings… ) and you must ignore their advice and dump him / her for not being beyond the 37% threshold; all this in the name of Optimal Stopping Theory because there’s no other possible strategy that can do any better! Could it be that God / Nature gave us two hands so that we could double face palm before claims like Ms. Fry’s?
    • Oh, by the way, it seems to me you just did a uni-variate optimization (goodness of the candidate) but turns out that this problem is multidimensional; how much risk aversion to end up single you handled in your model? Not every person has the same risk aversion and turns out that the further you set the threshold the better the candidate IF you find one.
  3. Avoid divorce?
    • But that would give us another shot in the in the post 37% partner selection. Why should we avoid it? I mean, other than not to mess with the fantastic model of yours in tip #2, of course.
    • In fact, the perfect strategy would be to partner every single candidate and breakup with him/her for the next best so we guarantee thus the optimal choice at all times… Which is by the way what most people do, probably including you Ms. Fry.

Common sense is enough to disregard all Ms. Fry’s arguments but let’s check her model anyway, she says that tip #2 is based on Optimal Stopping Theory. I went through her book to see what premises exactly those calculations were considering but since the target audience is the general public nothing really technical was explained. Anyway, whatever assumptions she used in her model it comes down to the following advice as the “best strategy possible”:

“If you are destined to date twenty people, you should reject the first eight.”

Really Ms. Fry? Like, really? I imagine that the quality of the candidates must follow a statistical distribution, it cannot possibly be otherwise, let’s say a standard normal distribution for the sake of discussion. And let’s say that the first seven quality values for the candidates one to seven are:

1.60, -0.90, -1.45, 0.00, 0.13, 0.07, -1.25

Now let’s say that candidate eight has a quality of 1,000,000… You still abide to your 37%? Of course you do Ms. Fry! Because you just did the calculations considering an infinity of cases! So this freak failure cases even out in the long run but, you know what, the boy or girl losing his / her 1,000,000 quality partner in the name of your math should care very little about your infinity assumptions and more about the gigantic distance between candidate eight and the previous seven.

At this point I feel like beating a dead horse, really. So let’s do some simulations and call it a day.

Assumptions

Now let’s simulate the position in which the best candidate happens to appear assuming an average number of serious candidates in one’s life is five:

Mr Ms Right - lambda 5

Now, how do you like that, turns out that the 37% of Ms. Fry training contains the majority of best candidates!! Should we hurry?

But to be fair Ms. Fry’s statement “If you are destined to date twenty people, you should reject the first eight” seems to imply a uniform distribution among those exactly 20 dates. Of course this assumption is ridiculous; nobody knows how many serious candidates we are going to encounter, and that’s why her advice is not any less ridiculous.

However, for the sake of discussion, how would the histogram would look if we now consider someone who actually happens to have many relationships and consider as serious candidates every one and each of them? Let’s try with a average of 50.

Mr Ms Right - lambda 50

Wait a minute, now it stays pretty much uniform until we reach the 40 partners considered. Now the distribution is more alike to the one Ms. Fry uses for her calculations. So let’s say we just date so many people that we can consider as equally likely the position in which Mr./Ms. Right will appear… Is now the 37% the right threshold? Well, turns out the 37% is just as good as any other since you must set your risk aversion in the model to properly and realistically answer the question!

Let’s actually simulate Ms. Fry’s assumption of uniformity in the chance to find Mr. / Ms Right. Also, let’s plot the probability to find a partner vs the mean quality of the partner found. Here is the result:

Risk vs Quality

Oh Well!! Look at that! The Ms. Fry Magical 37% appears when both lines cross! So yeah, that might the optimal solution for the expected value of an infinity of trials… But in our life we only have one shot. Ms. Fry’s model guarantees a bit more of 60% chance to find a partner but if you lower that probability to 40% the quality of the partner you might find increases considerably. So again, it is up to us Ms. Fry how much risk we take, no up to your model.

But that is the plot considering you will have exactly 20 candidates to choose among which, as I have already mentioned, is one of Ms. Fry’s completely unrealistic assumptions. If we instead assume we will have on average 5 serious candidates in our lives then turns out that this more realistic simulation moves the “optimal” threshold to a higher 50%.

Well, I have been a bit tough on Ms. Fry, she is probably a really nice girl and everything and it doesn’t make happy to be vehemently critical about her and her talk. In fact I believe that TED is truly at fault here, but if we allow Science to become a 100% show business with disregard of the scientific truth we all just better become clowns and join televangelists in their ways… Oh! I miss Carl Sagan. Anyway, when it comes to love, let’s forget Ms. Fry and let’s remember Blaise Pascal.

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2 thoughts on “Data Science vs Bimbo Math

  1. Hi there Fran, once more into your online abode.

    Since i think we share an interest in haikus. Let me comment on the complex (sic) relation of love and math with a haiku

    I solve an equation
    what a joy!
    I got a date because of that
    The p-value, favorable!
    

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