TecC 24 - Reckoning Reality’s True Rules
From finding patterns to fashioning systems: the ultimate tool to grasp everything
In the previous episode we discussed the emergence of philosophy and early science - in other words, the systematic inquiry into things around us. Today let’s look at what’s perhaps the empowering means of pursuing such inquiry. This likely more than many other topics we have covered straddles both ‘artefactual’ and ‘institutional’ in the current technocentric paradigm.
It’s just after dinner and our ancient friends are taking it easy - since this is ancient times, post-dinner entertainment was more like Stargaze and Chill!
Steve and Bryan are lying on the grass, staring at the sky and chatting about the good old times, Steve recounting stories about what fun it was, back in the Stone Age, to have to heave huge boulders of rock long distances and how many milestones he himself had accomplished in his rock solid ventures, before Bryan interrupts that that was no longer a problem since the time he invented the wheel!
But after a while the conversation turns to serious matters of the here and now. They’re worried that the nearby river hasn’t flooded yet which means they can’t be sure about how to go about with the crops. In the previous year, they were able to capitalize on the river flooding to grow a bumper crop enabling them to live the good life! So Bryan and Steve are in an animated conversation about what to do.
That’s when Irene speaks up. She points out that that bright star over there has to move to be right above that tree over there which is when the flooding is going to take place. Steve brusquely dismisses Irene: come on Irene, don’t bother us now, we’re having an important man-to-man talk about crops and such vital stuff. But Irene insists, to which Bryan is like, Irene, how can the position of those twinkly things in the sky determine the river’s behavior or anything at all, don’t be silly!
Irene is resolute:1 see Iris our cat over there, I very clearly remember its pose and its gaze when that star like I said got to its highest position visible over that tree last time. Mind you, the star is indeed moving in that direction and in three or four days it should be closer to that position, and you shall see!
And so it comes to pass! Three nights later, they do observe the said star in its resplendent position above that same tree and perhaps more memorably Iris in exactly the pose and gaze Irene predicted! Iris does even suddenly turn to stare at Bryan and Steve at that moment and it’s as if they see in her iris the cat saying: lads, don’t be amateurs, I know the future, I always do!
And right enough, the next day the flooding does happen!2
When Stars Start Speaking
So the first breakthrough we’re chronicling here is the birth of astronomy! But there’s a few more of direct relevance as well. But let’s start with how some of this got going.
An important thing we must appreciate is that the night sky in such times as the ancient past revealed a lot more than it does in our industrialized present where we are beset by the problem of what’s called light pollution.
Beyond this, and what’s perhaps easier to imagine is that ancient peoples spent a lot more time at night outdoors and looking at the sky. (They didn’t need that rare unexpected night-time power cut / blackout to step out of their cozy comfort zone outdoors to meet their neighbors for the first time ever and check out the night sky!)
So you might say it is inevitable that they started to find patterns in the night sky, amongst the planets and the stars, not to mention our own moon. Their positions and movements alongside questions of how, why and what that implied. The intellectual leap I’m demonstrating above is how they went beyond just staring at the stars to connecting the movement of celestial bodies to things of relevance to them. Back on earth!
And this of course happened across geographies and across cultures - the night sky is available to gazers from anywhere on our planet, you just have to look up! But what’s perhaps most interesting and relevant to our story of exploring human innovation and progress is the early developments in Ancient Mesopotamia, a region we’ve looked at again and again in the context of some of the great Bronze-Age civilizations.
In good part because their legacy is still with us: to this day, to this minute, to this second! (You’ll soon see what I mean there.)
Starry Sky’s Secret Scores
The story above about the floods-prediction is not made up. This was really an important concern for such civilizations that arose around rivers as in Mesopotamia and perhaps more well-known, not-so-far-away Egypt, whose very existence as a civilization depended upon the seasonal flooding of the Nile to help irrigate the land and thus crops to flourish.
And that intellectual leap was crucial in this, in the development of agricultural cycles, in a system of managing the whole process. Thus this is intimately tied up to the emergence of civilization alongside other factors such as writing and standardization and urbanization we’ve discussed previously.
The Mesopotamians, not unlike the Ancient Greeks we observed in the last episode, systematized the study of the stars and their bearings to affairs on earth, in particular natural phenomena such as the flooding of rivers, but much more as we’ll see. Empowered with the technology of writing, the need to find good ways of documenting this study is what led to the emergence of mathematics in ancient Mesopotamia. Thus, and perhaps in a slight contrast with the ancient Greeks, there were more pressing and practical matters that spurred this development than what we may have seen last time as a bit more luxurious theoretical inquiry in Greece.
Such mathematical innovation in Mesopotamia, starting around 3000 BCE, which is roughly the beginning of the Bronze Age civilizations as we’ve touched upon, happened with the night sky as their laboratory, agricultural cycles as their testing ground, and temple administration as their development workshop. This soon became serious business and the purview and privilege of the priest-astronomer class that rose to a powerful position in society.3
The greatest legacy of these innovations in Mesopotamia is the development of the base-60 numeral system. Why 60? In number theory 60 is said to be a ‘superior highly composite number’. I won’t get into the technical details of this, but the gist of it is that 60 has factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 making it easy to calculate with fractions, with the implication that if something is made of 60 units, you can divide it into 2 thirties, 3 twenties, 4 fifteens, 5 twelves and 6 tens, far more versatile than the decimal base.
In other words, 60 is pretty damn useful! So useful that to this day this Babylonian system lives with us: 60 seconds make a minute, 60 minutes make an hour (so now you know what I meant there!)
Furthermore the circle has 360 degrees. In fact the word ‘hundred’ at some point in the past was also used to mean 120 (6 score) now referred to, for obvious reasons of avoiding confusion, as the ‘long hundred’, or twelfty! So now you have something to show off with at the next party!4
Time to Reckon
Ok, so some of you might be thinking, is this about astronomy or mathematics? And are you really talking about astronomy or astrology?
The answer is all of them in a sense. Let me first tackle the question of astronomy versus astrology.
Obviously, they both start off with the stars. More precisely, the movement of celestial bodies. The key element of this movement is order, even predictability. The ancients realized this. And this mattered. Because in a world that was fraught with sudden change, whether it was a failed crop, an invasion, a storm and a great many other vagaries man had very little control over5, in such a world, the constancy the celestial bodies showed mattered, it gave them solace, a sense of stability.
It gave them something to base the vicissitudes of their life on. In matters such as tides and floods, we may see a physically explicable connection. But they found it useful to extend it to other matters as well, such as whether the king would die this year, would he win in battle when the enemy invaded. The movement of the stars might not have physically caused actions here on earth, but they seemed to correspond, what we may call ‘correspondence epistemology’ - the patterns in the celestial realm provided a basis, a template to understand or pin down earthly phenomena.
In the earliest days in Mesopotamia, the people saw the earth as a flat reflection of the skies, so such correspondence was even more vivid. But even later, within the geocentric and later heliocentric realms of their understanding of our place in the cosmos, the celestial template seemed useful – cuneiform tablets record thousands of ‘omens’ documented along with what sort of remedies each one necessitated when manifest (usually by way of lots of money and ritual attention to the priests, so that was handy!) It was from these 60-based Babylonian developments that arose the zodiac which we are still familiar with to this day - some of us invariably think of a person’s zodiac at the mention of their birthday!
Flights of Chance
I won’t get into the epistemology of all this here in this series, but let me throw out a seeming paradox or contradiction to this. Ancient societies have relied on another element as a source for their decision making: randomness. Yes, this might sound strange to us. At least, with something so predictable as the movement of the stars and planets, one can make the case for order, but from random stuff?
A prime example is the Roman practice of augury, where these professionals called ‘augurs’ interpreted the movement of birds, yes, birds, before an important decision. This weird bird-watching was called ‘avispex’ (avis = “bird”, spec- “watch, spy”), which later became ‘auspex’ whence our word ‘auspicious’ when something augured well so you could proceed with the, erm, inauguration!
If you think that is weird, consider this. Modern-day computing relies on a similar principle. If you ever need to generate a new digital signature using modern cryptographic methods, you might be asked to move the mouse randomly on the mousepad for a few seconds. The computer is actually using this randomness to generate a digital key that is secure enough to be tamper-resistant! From birdwatching to mouseshaking…
Ancient minds didn’t perceive order and randomness as opposites, but as complementary. Even when couched in the language of the supernatural and the divine, (which is btw the source for the word ‘divination’), the ancients accepted the limitations of human reasoning that was available to them and found a way out in their decision making from such seemingly inexplicable external forces. But are they inexplicable? I will answer that question in my parallel series Polymathon with the right epistemological foundation to get closer to the explanation.
Recounting to Count on
Let me now move on to the other question: mathematics. Or, why I’m talking about astronomy and mathematics together.
When we use the word ‘math’ / ‘maths’ we first think of counting. Yes, it is that, but we know that it’s a lot more. With the need to systematize astronomy in ancient Mesopotamia arose a need to find a tool to express reality in a clear, precise manner. The observations of the planetary movements and so on. Because, as we saw, only after being able to express and document reality can we efficaciously make inferences from it. And that tool, in essence, is mathematics.
Yes, mathematics, at its core, is a tool, a language, a system that enables us to represent reality. In clear and precise terms. Numbers are but some of the symbols we have at hand to achieve this. Everything else builds on top of this tool.
When it comes to math, a lot of us have burned our fingers in school, so much so that it’s quite fashionable as accomplished adults to say “Oh, I’m not good at math”. (I’ve discussed some of the relevant challenges in my article about structure that might be worth reading in this context.)
But let me leave you with this. Life throws at us a fair set of problems. These problems are based on some things we understand and some we don’t. But we want to have the means to navigate the problem space and get to resolution.
Mathematics, at its most fundamental level, is a tool that not only allows us to represent reality, but with its sheer predictive power, offers us the best available means to find solutions. And this is why, echoing the words of Gauss, I’m calling it the Queen of the Sciences!
Join me in my other publication stream for more on this.
Article written by Ash Stuart
Images and voice narration generated by AI
Further Reading & Reference
Al-Rashid, Moudhy. (2025). Between Two Rivers: Ancient Mesopotamia and the Birth of History. W. W. Norton & Company. ISBN 978-1324036425.
Mason, Burton, Stacey. (2010). Thinking Mathematically. Pearson Education Ltd. ISBN 978-0273728917.
Boyer, Merzbach. (1989). A History of Mathematics. John Wiley & Sons. ISBN 047154397-7. (Foreword by Isaac Asimov.)
Devlin, Keith. (2012). Introduction to Mathematical Thinking. ISBN 978-0615653631.
Life by the Numbers. (1988). PBS Series.
She won’t give in to male chauvinism!
Since then Iris shall be long remembered and associated with stars, constellations, satellites and the like!
Such as the Chaldeans that emerged later as a distinct professional class housed in special quarters at Babylon’s temple of Marduk and maintaining astronomical expertise at Uruk and elsewhere.
“Are you 100% sure?”. “Even better, I’m twelfty percent sure!”!
If you think our life today is miserable, you just have to compare how much worse things were back in the ‘good old days’ and how far we’ve come since the Industrial Revolution in overcoming a great many adversarial forces of nature
I really enjoyed this piece, Ash. It is interesting, how people have built, and built on, knowledge over time. We thought the world was flat, until we figured out it was round. Mathematics itself, has been a continuing evolution.
And your story telling style, especially held my interest. Great job.
I have a series, called the Unfinished Question, where my latest piece is a take on Truth, and I think you might enjoy it.
https://kevinguiney.substack.com/p/the-unfinished-question-on-truth
Thank you! It's sort of astonishing what I was able to do with those modalities, actually. It really helped me see what incredible geniuses our ancestors were, working with such simple materials. They achieved so much!