Pythagoras the Digitizer

Imagine yourself in Crotone, around 530 BCE. There is no Internet, no Wi-Fi, no social networks, and no computers. The only way to spread an idea is to discuss it in an agora. And yet, in that corner of Magna Graecia, one man is laying the groundwork for a worldview that has become quite natural to us today.

Pythagoras was not just a philosopher and mathematician; he was the founder of a mystical sect called the Pythagorean School. If it had been a tech startup, we could say their stack was represented by integers, and their motto was "All is number."

Probably, if we live immersed in bits today, it is because he was the first to have the audacity to think that reality was not a chaotic mass of matter, but a system that could be encoded with integers and ratios between integers.

The First Rendering of Reality

For the Pythagoreans, the number was not an abstraction used to count sheep, but the very essence of things. A musical chord? A numerical ratio (2:1 for the octave, 3:2 for the fifth). The movement of the planets? A symphony of frequencies you can express with numbers.

We do more or less the same thing today. When we write an algorithm to process an image, we are saying that a breathtaking sunset is actually a matrix of tuples (R, G, B). When we listen to a track on Spotify, we are converting a sequence of 0s and 1s into sound waves. Pythagoras would have been overjoyed by a .wav file: it is the empirical proof of his theory. We have digitized the world, convincing ourselves that, with enough computing power, we could map the entire universe into a gigantic database.

The Analog "Glitch"

However, we know there is a "but." Digitalization is, by definition, an approximation. Take audio, for example: no matter how high the sampling rate is, we are always sampling discrete slices of time. It is like trying to reconstruct a perfect circle using only tiny LEGO bricks.

Hardcore audiophiles will tell you that vinyl has a warmth that digital audio cannot reach. This isn't just nostalgia; it’s the nature of the continuous. Analog contains nuances, harmonics, and frequencies that escape the sampling grid. This is the limit of the Nyquist-Shannon sampling theorem: we can reconstruct the analog signal, but the "ghost" of analog reality, that sense of infinity that exists between one point and the next, remains outside the file.

Pythagoras' Secret

Pythagoras collided with this same bug, and it was a systemic trauma. Legend tells of Hippasus of Metapontum, a member of the sect who dared to calculate the length of a square's diagonal using its side as the unit of measurement.

According to Pythagorean logic, the result had to be a ratio between integers. Instead, Hippasus discovered that it was the square root of 2, an irrational number! A number that never ends, which cannot be represented as a fraction of integers.

The discovery of incommensurability between the side of a square and its diagonal shattered the idea that the universe was a perfectly clean code made of integers. According to legend, Hippasus was drowned by his companions for revealing this "bug" in creation. Not everything was a (rational) number. Reality hid an abyss of continuity that Greek "digitalization" could not capture.

So, what is the point of digitizing the world? Well, it is convenient for processing information. Although we know that the digitized version of an analog phenomenon does not contain the same exact information, we can approximate its precision as needed. While we will never have a perfectly faithful representation of the world, at least in theory, we can get close enough to form a satisfying idea of it.

Pythagoras's Revenge

For centuries, we thought that reality was a "continuum" and that we, poor humans, were forced to "discretize" it to understand it, always losing something in the process. This is indeed what happens in the process of digitizing the analog. But here, the plot thickens.

Modern quantum physics is flipping the script again. If we descend into the "source code" of matter, at the Planck scale, it seems that space and time are not continuous at all. There is a minimum length below which the concepts of "distance" and "position" lose their meaning. Energy itself moves in "quanta," that is, in discrete packets.

Incredible, isn't it? After years of saying that digital is only an approximation of the analog, we discover that the universe itself might be... digital. Perhaps we aren't the ones approximating reality with bits; perhaps reality is made of bits, and it is our macroscopic perception that is "analog." Perhaps, in the end, Pythagoras was right.

A Longing for Infinity

We are still there, on the beach of Crotone, trying to understand if the world is a vinyl record that holds the infinite or a masterfully compressed file. The truth is that we have no idea, and the further we delve into the understanding of reality, the more we find something that eludes us: we try to capture the ineffable in discrete variables, knowing that there will always be a square root of 2 ready to remind us that the universe is more complex than we can comprehend. But perhaps, in the end, it is precisely in that small gap between reality and each of its representations that everything worth living resides: “…e il naufragar m'è dolce in questo mare.” (“...and shipwreck is sweet to me in this sea.”)