Saint 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. Oversimplifing 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 acquiring a bad reputation little by little 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”
I thought about making a post about the whole Bayesian community overreaction over CERN using p-values to announce that a Higgs like particle was discovered, but since I cannot possibly explain it better than Ms. Mayo‘s great blog in this post an others (specially if you like pink color), what I am going to do is to explain it different…
Warning for Bayesians: watching this video without sense of humor may cause difficulty breathing, swelling of your face, lips, tongue, or throat; chest pain; sweating and irregular heartbeats… Yes, just like Viagra, but just like Viagra it is worth it.
This video actually contains more reality that the sarcasm clothing might lead you to believe, so I’ll let you enjoy the game of figuring out what is real and what is not. 😉
I am tempted to make more posts about this so highly interesting and fun Bayesian vs Frequentist philosophical issue, but for now suffice to say that I basically agree with Mr. Bradley Efron‘s opinion in his science magazine article about the subject where he says:
My own practice is to use Bayesian analysis in the presence of genuine prior information; to use empirical Bayes methods in the parallel cases situation; and otherwise to be cautious when invoking uninformative priors. In the last case, Bayesians calculations cannot be uncritically accepted and should be checked by others methods, which usually means frequentistically.
Anyhow, for those interested, the Fuhrer scenes come from the fantastic movie Der Untergang. This is one of those great movies you can’t miss if you like history! Continue reading →
One would think that humanity would not have a need for good random number generators until computers and simulations were invented since, for most practical purposes, tossing a coin or throwing a die should suffice us all. So you can imagine my surprise when I saw in this four to five thousand years old Chinese divination book called I Ching a RNG algorithm that reminds modern Linear Congruential Generators! But why the need for such a complex procedure to render random numbers?
The I Ching divination process requires to randomly select two trigrams via a rather convoluted process using either stems of Artemisia or Yarrow. And although I acquired this ancestral book a long, long, time ago, truth is that when reading it as an oracle I always used the simplified version for lazy busy people consisting in simply tossing three coins and checking the combination of heads and tails.
I always thought that the traditional form was just a magical way to do the same thing that we can do by tossing three coins, but today, for no particular reason that having too much free time in my hands, I gave a deeper mathematical look to this traditional form and it turns out that it renders a complete different random result that tossing three coins!
Well, a mathematical curiosity you might think, but does it matter? It might! Millions of people seek advice using the simplified coin version to render the I Ching Yin Yang oracles. In this post I will show how the three coins method yields an equal proportion on Old Yin and Old Yang oracles signs whereas the traditional method yields three times more Old Yang signs than Old Yin!
This means that The I Ching, in its traditional form to draw oracles, promotes Yang behaviour over Yin, that is, it promotes among its users action, imagination, creativity, strength whereas, nowadays, with the simplified three coin version, the active and passive answers are even out.
I am not a sinologist nor a psychologist so I cannot really tell what version would have a better influence among practitioners lives, but I know though that the traditional form promotes Yang among those seeking advice which, at first glance, seems like a positive thing to do and, since this book is used by millions of people, maybe experts in the field should advice to practitioners not to use three coins anymore when using the I Ching. For those interested in having a traditionally sound oracle in terms of probability, I will show a few simple ways to achieve just that at the end of this post.
This book has impressed mathematicians like Leibniz, psychologists like Jung, poets like Jorge Luis Borges and all kind of intellectuals all over the world for centuries. And regardless you believe or not whether it has magical properties, what is certain is that it has deep psychological sapiential ones. This is not only the oldest book in human history, but a beautiful one. So, before we plunge into the mathematical details of the traditional algorithm to draw oracles, let’s share this poem from Borges about the I Ching to break the ice.
For a Version of I Ching
Para una versión del I King
The future is as immutable As rigid yesterday. There is nothing That is no more than a single, silent letter In the eternal and inscrutable Writing whose book is time. He who walks away From home has already come back. Our life Is a future and well-traveled track. Nothing dismisses us. Nothing leaves us. Do not give up. The prison is dark, Its fabric is made of incessant iron, But in some corner of your cell You might discover a mistake, a cleft. The path is fatal as an arrow But God is in the rifts, waiting.
El porvenir es tan irrevocable Como el rígido ayer. No hay una cosa Que no sea una letra silenciosa De la eterna escritura indescrifrable Cuyo libro es el tiempo. Quien se aleja De su casa ya ha vuelto. Nuestra vida Es la senda futura y recorrida. Nada nos dice adiós. Nada nos deja. No te rindas. La ergástula es oscura, La firme trama es de incesante hierro, Pero en algún recodo de tu encierro Puede haber un descuido, una hendidura, El camino es fatal como la flecha Pero en las grietas está Dios, que acecha.
Up to this day I defined my theological position as Agnostic, which is not saying much given the different interpretations and philosophical flavors we have to position ourselves when it comes to God. This is why sometimes I instead simply reply to The Question with something like “Both alternatives are equally crazy, so I don’t know.“ But, can we use statistics to better describe our position in these kind of philosophical matters, or even dictate how should we live our lives? Yes, we can.
WARNING: Beware agnostics!!! I will show mathematical arguments that might turn you into a full blown Believer or a hardcore Atheist… So if you keep reading don’t say I did not warn you.
If we envision probability as a measure linked to a random process then questions like “What is the probability that God exists?” imply a sort of Supra-God that creates universes with Gods with a frequency p. But then some might argue that this Supra-God is actually God so, at the end, these kind of philosophical questions make no statistical sense for such frequentist interpretation of probability.
Then we have those that interpret probability as a degree of belief on matters subject to uncertainty, this interpretation is the one hold by Bayesian Statistics.
So if I wear a Bayesian hat and I am asked The Question then, instead replying “I don’t know” to describe my ignorance I should reply with “50%” or “p=1/2“. This is so because when Bayesians (The Objective Kind) have no information on a problem they use a plethora of principles in a Groucho style fashion to figure out a prior distribution to kick off Bayes’ Theorem machinery.
But there are an infinite number of prior distributions with an expected value of 1/2 so, which among this infinite number describe better my agnosticism? Is there such thing as a unique agnostic prior to rule them all? Well, it seems this Holy Grail does not exist since we can read in highly commendable Bayesian books like Bernardo & Smith thing like:
In general we feel that it is sensible to choose a non-informative prior which expresses ignorance relative to information which can be supplied by a particular experiment. If the experiment is changed, then the expression of relative ignorance can be expected to change correspondingly. (Box and Tiao, 1973 p.46).
Wait, what? We change the experiment and our prior ignorance changes too? In fact not all Bayesians agree with their existence; (Howson 2002; O’Hagan 2006; Press 2003) they regard any Bayesian Objective “non-informative” priors simply as well formed beliefs… So I’ll pick on the Subjective kind interpretation and in this post I am going to well form my belief in God.
Plus, in the process of cooking my Agnostic prior I’ll discuss why Bayesians should measure their beliefs from 0 to π instead from 0 to 1; This later measure is too frequentist for them and π makes more mathematical sense since trigonometrical functions are going to naturally pop up everywhere in our prior belief endeavor. Continue reading →
Human minds are the mother of all interesting things since anything that we might consider interesting is so because our minds make us believe so. Seems then reasonable that all kind of philosophical issues and scientific problems cannot be properly addressed unless we correctly understand how our minds work, but what we know about how they work?
Cognitive Science offers many theories on how any mind might work, but when it comes to our minds there seem to be evidences put forward by psychologists that, whatever the way they work, human minds do not abide to the laws of probabilities.
Several attempts have been made to explain these results, and one of the latest comes from the hand of Quantum Mechanics… No kidding.
So when I saw this valiant attempt from theoretical physicists to explain how the human mind works by using their all mighty and powerful Quantum Hammer, I thought it was a good moment to explain an alternative solution that I myself worked out long, long ago, after being exposed to this problem by philosopher Paul Thagard in his excellent book MIND.
Also, Sister Hot is my assistant and I need her to prove my point which is that our minds might abide to probability laws more than we think after all. If you want to know how she is going to assist me you need to keep reading; probability can be sexy 😉 Continue reading →
Missouri Congressman Todd Akin’s infamous comment about women being able to avoid pregnancy in a “legitimate” rape and the subsequent media frenzy made me wonder if there was any truth in it, if you think about it, the stress and depression a rape generates could be so extreme that women’s body might after all “shut the whole thing down”. So I’ve estimated the chances for this to happen and it turns out that this politician was… oh, surprise.
After the Akin’s foot in mouth we could read all over the Internet media quoting gynecologists saying that chances of pregnancy are the same regardless whether a woman is raped or not. So people’s snarly comments and the “this is obvious, you gotta be stupid to believe otherwise” attitude we observe when anything gains political momentum spread like wildfire. It is at this point when questioning the crowd makes us feel uncomfortable but, since I know how much trust and credit I can give to media, I overcame my lack of comfort by running the numbers myself, and well, turns out that Mr. Akin might be as right as wrong since Continue reading →