A Device for Randomness

Ancient Athenians elected people by lottery. Are eight-dimensional quasi-creatures doing the same to us?

A kleroterion was a randomization device used by Athenian cities during the period of democracy. Think of it as a huge lottery system, used to select citizens for different committees — the city council, state offices, and court juries.

Athenians were aware of the risk of corruption; they knew that a judge could be bribed but not a crowd.

That’s why they used to form enormous juries. About five-hundred people showed up each time, randomly selected before the trial. To make this selection happen, every citizen was given their own pinakion at the beginning of each year: a personal ID made of wood or bronze.

The kleroterion was simple to operate. Holes in the stone, cut into several vertical slots, held the tokens or pinakia of each potential judge. A wooden tube was held in place next to the lines of tokens, and on top of that tube was a funnel holding black and white balls. These balls would fall through the tube all the way to the bottom, where they’d be stopped by a crank- driven device.

When the crank was turned, one ball would drop out. If it was black, the first row of pinakia was removed, and their owners were dismissed. If the ball was white, the first row of tickets remained in place, and their owners were judges for the day. Another ball was released, another row of candidates dismissed or accepted, and so on.

At last, the final ball was dropped and the trial began.

The kleroterion was the first application of randomness in politics. Athenian democracy was based on the concept of isonomia, or equality of political rights: each person, they said,  should get an equal chance.

This system of choosing our overlords or legislators based on sortition or random selection just belongs to the past. Today our overlords are just elected, intolerable and corrupted people. The fact that we elect them has failed to make them better persons. And if we had paid any attention to our Greek forebears, we would have known that it was Aristotle that said “elections produce oligarchies, but random selection produce democracies”…

In Athens, the complex  allotment machine known as the kleroterion was their way of making sure the positions on ruling committees were allocated fairly — which is to say, randomly.

So, yes. Even for a while they had democracy back then.

But what is randomness?

In ancient history, the concepts of randomness and chance were intertwined with that of fate. Pre-Christian people along the Mediterranean threw dice to determine fate, and this later evolved into games of chance. There is also evidence of games of chance played by ancient Egyptians, Hindus and Chinese, dating back to 2100 BC. The Chinese of 3000 years ago were perhaps the earliest people to formalize odds and chance.

According to Wikipedia randomness is the “lack of pattern or predictability” in events. A random sequence has no order; in fact, randomness is the quality of having no apparent order.

Individual random events are by definition unpredictable: you can’t predict which side the dice will fall on next. But in many cases, the frequency of different outcomes is predictable. If you have enough trials — which is to say, roll the dice enough times — you can predict how often one outcome will occur compared to another. Unless the dice are rigged, you’ll get a five ⚄ about ⅓ as often as an even number ⚁⚃⚅.

In this view, randomness is a measure of uncertainty of an outcome. But does randomness really exist in our world?

According to the textbooks of biology, large molecules —such as proteins — were initially formed randomly on the primordial earth.

Today, this theory is showing some limitations. Scientists modelled amino-acids blindly floating around, and calculated how likely they were to form a 150-unit-long protein chain, purely though chance by running a simulation.

It came out to 1 in 10¹⁶⁴. That’s one out of, well, a one followed by a hundred and sixty-four zeroes. On average, you’d need to construct that many amino-acid chains to find a useful one.

In order to run this simulation, it has been hypothesised that the entire supply of carbon, nitrogen, oxygen and hydrogen was available to form all the complete sets of amino acids used to build proteins. Moreover, it has been hypothesized that the amino acids in this primordial earth were protected from UV rays and chemical contamination (highly unlikely back then) and that each protein will self assemble in one second. Furthermore, for this simulation, they took for granted that they knew in advance that a “correct” sequence of the protein had to be found during the simulation and that somehow implies determinism or super-determinism, the exact opposite of randomness.

Considering now that the age of the earth is estimated to be 4½ billion years, give or take half a billion, in this time frame only 10⁵⁸ (probably failed) attempts could have taken place. Were we really that lucky?

To make us understand how long it takes to wait for 10¹⁶⁴ failed attempts in this simulation, scientists have built a hypothetical bridge that spans the diameter of the observable universe: a distance of 90,000,000,000 years. Then they placed an amoeba on one end of the bridge — a single-celled organism carrying one atom on its back, travelling at the breakneck speed of one foot per year.

So, according to this simulation, while we are waiting for one protein to form by chance in the prebiotic soup, the amoeba moving at a just one foot per year and carrying one atom per trip, will transport the entire universe atom-by-atom more than 56 millions times.

That’s how long it will take to build one functional protein randomly.

Of course, proteins are only a part of this story. The probability that the rightly-sequenced molecules just randomly formed the first cell is next to impossible.

In fact, we have no idea how the basic set of molecules (carbohydrates, nucleic acids, lipids, and proteins) were made, and how they could have coupled into the proper sequences, and then transformed into the ordered assemblies until they ended up constructing a complex biological system and eventually forming the first ever cell on this planet.

So, if randomness is excluded, does determinism plays a role? Was the first protein, or the first cell, or the first organism predetermined and pre-designed to happen? And if the idea of determinism in our physical world has been ruled out by the famous double-slit experiment (experiment cornerstone of modern physics, that initiated the era of the free will), then what is really going on?

Nature is filled with examples of complex behaviours that arise spontaneously from relatively simple elements. Researchers have even coined the term “emergence” to describe these puzzling manifestations of self-organization, which can seem, at first blush, inexplicable.

Emergence is a process where apparent randomness can give rise to complex and deeply attractive, orderly structures, and events that can’t be predicted or explained on the basis of previous terms.

Where does the extra injection of complex order suddenly come from? Scientists are just beginning to understand why and how these phenomena emerge without a central organizing entity. In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own. These properties or behaviours emerge only when the parts interact in a wider whole.

In 1999 the economist Jeffrey Goldstein defined emergence as: “the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems”.

Consider an ant colony. The queen ant does not give direct orders and does not tell the ants what to do. Nobody is technically “in charge”. And yet, somehow, the ants manage to behave in astonishingly complex ways.

Without centralised instructions, they quickly determine the shortest distance to a nearby food source and  shift roles among the colony members in response to changing needs. Despite the lack of centralised decision-making, ant colonies exhibit complex behaviour and have even demonstrated the ability to solve geometric problems.

A broader example of ‘emergent properties’ in biology can be seen  in the biological organization of life. Individual atoms can be combined to form molecules such as polypeptide chains, which in turn fold and refold to form proteins. Then these proteins interact together and with other molecules to achieve higher biological functions and eventually create an organism.

At the highest level, all communities in the world have their human participants interact to form societies, and the complex interactions of these meta-social systems form the stock market.

Interestingly, when groups of human beings are left free they tend to produce spontaneous order, rather than the meaningless chaos often feared. This has been observed in society at least since Chuang Tzu in ancient China. Whenever there is a multitude of individuals interacting, order emerges from disorder!

Spooky as emergence can seem, a formal understanding of it might be within reach. So, do we have a scientific explanation for emergence?

Emergence theory is a new physics model currently being developed by a Los Angeles based team of scientists. At the root of Emergence theory’s is a concept that all of reality is made of information. What is information? Information is meaning in the form of symbolism.

A language or code provides this information conveying symbolism; in fact, these scientists believe a geometric language exists in the form of geometric symbolism, literally everywhere.

Here, there’s a subtle line between free will, or doing whatever one wants, and determinism: having everything pre-decided for you or fated to happen.

All languages and codes are groups of symbols that convey meaning, and the various possible arrangements of these symbols are governed by rules. The language user makes choices on how to arrange the symbols (free will) to produce meaning, but always according to the rules (determinism). In this concept, the existence of information must, therefore, imply a “chooser” or some form of consciousness, in order for the information to be actualised.

A central feature of our reality behaving geometrically is that all fundamental particles and forces in nature can transform into one another.

If you want to get technical, the transformation happens through a process called gauge symmetry transformation, in a manner that corresponds precisely to the vertices of the 8D polytope of a crystal called the E8 lattice — except that we don’t appear to live in an 8D universe, so scientists believe the true answer lies in the language and mathematics of quasicrystals.

If that went over your head, just remember that, because of their calculations, scientists think quasicrystals are key to the question.

A quasicrystal is aperiodic: not having a regular repeating pattern, but not quite random either. In any given dimension, this pattern is created by projecting a crystal (a periodic pattern) from a higher dimension to a lower one It works the same way as a 3D cube projecting square shadows onto the 2D ground. Or hexagonal shadows, depending on how you hold it.

So, is life a shadow of an object existing in a higher dimension? Apparently yes, according to the emergence theory. And according to this theory, ordinary life is a 3D quasicrystal that has one type of proto-tile —  a 3D tetrahedron — when the projection is made by “something” living in the eighth dimension.

Yes, we have some “friends” living in the 8D world: we can’t see or talk to them, but scientists tells us that we are their 3D shadow.

It gets even weirder. When our eight-dimensional friends in their 8D reality project themselves on planet earth in our 3D reality, they do so by sending us information or 3D pixels of reality (trillions of tetrahedrons) that combine with one another according to specific, geometric rules, to populate all of space.

So yes, we are shadows made of tetrahedrons, like TV images are made of pixels. And emergence is just rules and a code.

In this 3D tetrahedron model, consciousness is viewed as both emergent and fundamental. Whatever that means. I didn’t get it either, but they’re probably  saying that each tetrahedron has a mini-consciousness — and when all the tetrahedrons are combined to form our 3D reality, their mini-consciousness collide forming a mega-consciousness.

A god? We don’t know.

To put it differently, the spontaneous order that emerges from the apparently disordered “things” is just the result of an observer and a geometric code. Each 3D tetrahedron is just a letter, but they come together to form the words and paragraphs of  consciousness.

Going back now to the origins of life and the formation of the first molecule.

According to the emergence theory, it’s the specific laws of physics inside this geometric code (reality) that cause electrons and quarks to self-organise (emergence) into 81 stable atoms, and from there self-organise to molecules and from there into a human consciousness: an ocean of 37 self organized trillion living cells (a network). Always following the same rules that dictate the structure of our geometric reality.

But what randomness and emergence have to do with Ancient Athens?

More than two thousand years ago the kleroterion was used to produce randomness in Athens, while randomly selecting state officials to run the city. By doing so, Athenians were making sure that corruption was excluded from the state.

Two thousand years later, we have just begun to understand the existence of apparent randomness in our 3D geometric reality, and in particular why apparent chaos produces spontaneous order in this geometric reality.

Does that mean that randomness produced by the kleroterion was just a “key” to unlock the geometric code of our reality, and “produce” in an unbiased way crowd wisdom to run the city of Athens?

Apparently… yes.

Nowadays, as corruption corrodes the fabric of our society, undermining people’s trust in political and economic systems, and in institutions and leaders, every decentralized but most importantly “unbiased” emergent system that uplifts crowd wisdom is more likely our way out of corruption.

If that sounds random, it’s because it probably is.