The I Ching, random numbers, and why you are doing it wrong

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?

artemisia
         Artemisia Stems

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.

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Astrology: The woo-woo that works

French psychologist Michel Gauquelin gained notoriety in the 50’s after publishing data showing that sportsmen were born in a non random fashion when considering the movement of planet Mars, the nicknamed Mars Effect has been the core of passionate discussions over its statistical validity since then but, beyond whether this effect truly holds or not, there are many reasons why genuine statistically significant data can be found in the astrology world, so we’d do better not to ignore planets and stars entirely.

mars_effect
Number of sportsmen born given the position of planet Mars according to Gauquelin’s data

We humans develop efficient strategies in our daily life that are useful for most situations, for example, if we see dark clouds and a few moments later it rains we associate dark clouds with rain and, voilà, next time we see dark clouds we take measures. The problem begins when we break a leg right after seeing a black cat, our association machine, a.k.a brain, does its magic and next time we see a black cat we take measures too. But you know what? The brain is right!

What is not so right is human difficulties to removed associations once they are set in our brains, a.k.a stubbornness. We humans develop all sort of strategies too keep our associations alive and demand extraordinary amounts of evidences to break them yet, even when those evidences are presented, we keep fighting them by doubting the methodology or the honesty of the persons bringing them up. There might be evolutionary advantages explaining why we create associations so easily but cannot break them with the same ease, but whatever the reasons are the problem only worsens when in some cases our stubbornness makes the associations come true! And that is what astrology is all about. These are a few examples of how astrology makes spurious associations come true: Continue reading