Monthly Archives: September 2025

Whispers of the Odds

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He steps on a penny. 
That morning, lurking just below the horizon, the sun is ready to shine its first beams of light. A cool breeze, saturated with the humidity of the morning mist, whispers in his ears. Barely intelligible. He couldn’t quite decipher what it’s trying to say, or whether it’s trying to speak at all.
Intrigued, he looks down to notice the penny, starting to shine as the first morning beams flare its surface. He picks it up. Once in his palm, closer to his eyes, the carvings on the penny seemed unfamiliar. The more he looked at it, the stranger it appeared to his eyes.
The goddess of odds stood before him with her happy side majestically facing him. She smiled and whispered: the prayers you made the night before have been answered. Later that week, the rare penny was auctioned for a small fortune.

He steps on a penny. Intrigued, he looks down to notice the penny. It’s just a penny. He moves on.

Countless pennies get stepped on countless times day after day. And the rare pennies, sitting there defying the passage of time, get stepped on countless times before someone picks them up. When they finally do, the aura of mystery is never away. The presence of the goddess of odds feels as real as the penny being picked up. Her whispers carried by the morning breeze are heard loud and clear. She goes by many names. Some call it destiny, others call it divine, and many use words that start with para or meta or something along those lines… And then there are those, like myself, who just call it math. 

There is indeed a formula. A simple one that doesn’t need a major in science to grasp:

P=\dfrac{n}{N}  

or in a slightly different form:

n=P\times N

The first form is known as the definition of “probability”1. The second form is useful when making a tour at an auction gallery and being confronted with but a few of the most amazing stories, the type of which collectors are fond of. 

n is easy to measure. Those are the stories we tell. The ones we listen to with eyes wide open and jaws struggling to fight with gravity. P is hard to compute: it requires a complicated model of reality that even the most evolved AI on the planet doesn’t have enough neurons to describe2. But intuitively, we know when it’s small, when it’s impalpably tiny, and often we’d be right. The one that seems to be hard to grasp, that defies common sense and feeds into mystery and wonderment, is N.

N is what we don’t measure. The stories we don’t tell, those that remain unnoticed even by the protagonists themselves. Stories too insignificant to live and certainly too dull to listen to. We tend to forget they exist or at least fail to imagine their sheer numbers. Our ancestors, concerned with the number of prey they were able to catch and the number of predators they managed to escape, did not evolve brains to deal with huge numbers. After all, who needed to count the stars in the sky or the hairs on their head?

The truth of the matter is, that the rare penny was sitting there for centuries getting stepped on while waiting to be picked up. Sooner or later, somebody would have. The whispers turned out to be but the sound of the breeze caressing the leaves. And the goddess of odds, to whom we attribute more than what she actually does, was merely counting the steps and taking notes in her book of time, mainly for her own curiosity. Never she cared to intervene. Maybe by fear of biasing her own data. See, she’s as wholesome as a goddess can be.

And we, oblivious to the many untold stories, fill in the blanks of our nescience with stories fabricated by our minds. Another great skill of our imaginative brain: filling in the blanks. For some reason, those of our ancestors who took the time to investigate when they had incomplete data, got eaten by what turned out to be a predator. 

Mysteries, miracles, curiosities, wonders, omens, prophecies, paradoxes, coincidences, and the list goes on. Count the number of minutes that exist in the many lives there are, contemplate the many ways the next minutes could unfold based on the events of the minutes that came before, and the unlikely becomes foreseen3.

We seek mysteries in peculiar events that actually happen every day. Our brains crave wonderment and awe; and yet, recognizing that the unusual and the mundane are made from the same fabric of chance, shall make the story no less magical, only more real. Suffice to remember the greatest achievement of the goddess of odds: out of the endless possibilities of gene arrangements that never saw the light, it is us who are here, alive in this moment, wondering about the world — not simply as a coincidence to dismiss, but also as the most awe inspiring accident of all.

  1. The connoisseur here might object slightly and demand more rigor in the usage of the terms. I’m aware of that. I’m also aware that for what concerns the usefulness in this context, this is an accurate enough definition. ↩︎
  2. Those who studied probabilities at high school may remember how nontrivial it was to compute probabilities for problems involving a handful of colorful balls. Now imagine extrapolating this to a problem involving billions of people doing random things at random places all day long all over the planet, with the added complexity that what any one person does at any given time, may or may not impact what the others can or cannot do from that time onward. ↩︎
  3. The connoisseur requesting mathematical rigor might again protest that multiplying the very tiny with the very large (0 × ∞) yields an undetermined result. Here we’re talking about phenomena that occur frequently enough to get noticed, but not enough for our brains to get used to. So for the technical pendant, we’re interested here in the cases where (0 × ∞) yields a finite result. ↩︎

The Biological and not so Biological Aspects of Darwinian Evolution

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I don’t remember the exact day when I actually understood what the term “Evolution” means in the Darwinian sense. But I remember that it was a day.

Unlike the other pieces that constitute the largely incomplete knowledge baggage that I carry, understanding Evolution was not a graduate process. It was literally a click; a sudden revelation before which everything about this theory was ridiculous, dark and even sinister.

And then one day: Eureka! If there is a handful of men that could be described as the greatest scientist minds of all times, Charles Darwin is definitely one of them.

As a child growing in a non-secular society where superstition still rules over people’s intellect, Charles Darwin was introduced to me in an atmosphere of rather bad publicity: there was the deluded man who believed that once a monkey gave birth to a human baby from whom we all descend. Put in these terms, his ideas felt of the type that could only be preached by a crazy and wicked ignoramus.

Until I was old enough to read about them myself.

Then I understood the three simple elements that when put together, can elegantly solve the greatest mystery of all times; Life:

  1. Growth with Reproduction and Inheritance: the process by which a certain form of life creates copies of itself to ensure its own growth and continuity to at least one more generation.
  2. Variability: the imperfections in reproduction through which inaccurate copies of a given form of life are introduced into the next generation (mutations), thus creating diversity.
  3. Struggle for Life and Natural selection: the process through which those forms of life that are better equipped to succeed at reproduction are the ones that get preserved through generations at the expense of those that are the least.

How brilliant!

A very simple principle yet powerful enough to explain that from star dust consciousness can arise!1

The many elaborate and diverse ways of adaptation that can be witnessed in Fauna and Flora, were for so long mistaken for being carefully and purposely designed by a supreme being. And for a good reason; almost every feature of every living creature is useful in some way to its bearer. As amazing and mysterious as it may be to think of a higher order that pulls the knobs and puts the clockwork into action, it is by far more inspiring to ponder the fact that the higher order is but a set of simple laws of Nature.

And not only Life is explained, but also Death. No form of life could have ever been made so perfect from the first attempt: that would indeed be very unlikely and highly improbable. Death has to occur because it is Nature’s way of trying again, in order to come up with the best designs through a continuing cycle of trials and errors. The most brilliant engineers on the planet can certainly appreciate the power of this technique!

To allude that the sheer complexity of life is a proof of an unnatural aspect in the process of creation is to seriously underestimate Nature.

And not only biological life is concerned. Think of life as an abstract concept, a dynamic system that can exist in different levels of complexity; as long as its “design” is constantly subjected to some form of a “goodness” test, natural selection is bound to guide its evolution. Once I was able to grasp this, I could start to imagine the wide range of disciplines to which the Darwinian principles may apply.

Our human language, our sense of beauty, our political, economic and social systems, our culture in general and even our religions, if examined closely, all exhibit aspects that can most rationally be explained by Darwinian-like evolution.

To cite but one example, social studies have shown that local groups of people tend to come up with their own unwritten set of rules in order to organize common interests among each other, often ignoring the state laws2. This can be explained when we realize that under certain conditions the interest of the whole group is favored by a ‘tit-for-tat’ strategy of cooperation among its members. The question remains how this has become intuitive to humans? Some of it may be encoded in our DNA and constitute our natural inclination to altruism, but most of it can be understood through a tradition of trials and errors or the so called “lessons from those who came before us”. People learn, through their interactions with each other, what works and what doesn’t, and those ideas that work are passed along and become part of the traditions.

It is awe inspiring to contemplate how such a principle is so simply formulated and yet so powerful in its consequences and so general in its capacity to explain a wide range of phenomena spanning across many disciplines.

As Charles Darwin said in the closing statements of his famous book that started it all:

“It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. […] Thus from the war of nature, from famine and death, the most exalted object we are capable of conceiving, namely, the production of higher animals, directly follows. There is grandeur in this view of life, […], from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved”.
Charles Darwin — On the Origin of Species, 1859

  1. Research suggests that in early Earth, Life would have spawned from autocatalytic networks of increasingly complex chemical reactions. In a nutshell, these are chemical reactions that produce their own catalysts and therefore are able to self-regenerate. We can think of these networks as the ancestor of Life, and the process that led to DNA-based life from rudimentary self-sustained chemistry to resemble the process of evolution by natural selection. ↩︎
  2. See for example: Robert C. Ellickson — Order Without Law: How Neighbors Settle Disputes, 1991 ↩︎