Physics Rediscovered #1: Knowledge from the void

I don't believe in miracles.

However, if I really had to name one, it would be the fact that our monkey brains are capable of understanding anything about the world we live in.

We have lifted ourselves by our bootstraps from the mire of ignorance into a vast landscape of knowledge and understanding.

Unless the dolphins are hiding a base on the moon, our species has become the only one to leave this planet and contemplate the possibility, that this Universe may not be the only one.

The road to the stars and beyond was a long and rocky one, and still is. But how it all began? I like to think it all started when a smart monkey started noticing something weird happening to the lights in the sky.

Not ancient aliens

If you look at the night sky in a truly dark environment, away from any light pollution, you can see a part of our Milky Way galaxy and its neighborhood in all its majesty. Unless, you live in a place, like I do, where the cloud coverage is nearly full and permanent throughout the year. Can't see shit then, can you?

Anyway, it's an overwhelming sight and you can almost feel the pressure of the sky bearing down on you. To make things worse, the whole thing is moving resulting in a vertigo. It's one of those breathtaking and dizzying experiences but with clothes on. Obviously, you can witness it with clothes off to make it special - up to you.

We are actually very lucky to experience this both as individuals and humanity. In a different time the night sky could've been empty, lightless and depressing but this is a story for the future.

With light pollution in the olden days not being an issue, people just couldn't look away and as they looked, they began to notice something spooky.

They noticed that the dark void of outer space speaks to us.

How's that for a lovecraftian realization?

And it speaks in phrases stuck on repeat. These are messages that tell us that the Moon has about the same shape when your wife screams at you for no reason. They tell us that the Sun rises differently each day, but once in a while it does so at the same spot, which make it a perfect place to build a temple dedicated to human sacrifice, obviously.

People had all kinds of fun back then but the ones to take it to the next level were the Babylonians.

They listened in and they started counting the repetitions. Counting over decades, over centuries, they figured out the periodic movement of planets, stars, the cycle of lunar eclipses, among others. And they did it all in the sexagesimal system (or base 60) just to show off. If you ever wondered why a circle has 360 degrees or an hour 60 minutes...

Let's do some base 60 calculations? Say less.

In our base 10 notation we have: 69 = 6 x 101 + 9 x 10?

If you mean 69 as a base 60 number then: 6 x 601 + 9 x 60? = 369 (in decimal)

How to get 69 in base 60? 69 = 1 x 601 + 9 x 60? or 19

How would they write this in their ancient notation?

Yes, I did a sex joke in cuneiform. Top that!

We did take one thing for granted here and that is the place-value notation. What is that, Captain Explanation Man? It's the convention that gives a digit additional value based on its position in the number sequence. 111 in a base 10 system grants the first 1 a value of 100, the second a value 10 and the last is just itself, no exceptions.

However, this was not standard practice in the ancient world and you know it. Roman numerals, anyone? XXI is 21 but XIX is not 21. This one forces you to look ahead in the sequence.

So while we use the place-value like it's always been there, guess who first came up with that.

The Babylonians were an inventive bunch and we have solid evidence for all this. One of most prominent is the MUL.APIN. However, if you're not really into ancient clay tablets, just know that it's like their astronomical wikipedia of the time.

All that counting and measuring required proper math tools and skills to pull off. What the MUL.APIN and similar artifacts (like YBC 7289, BM 85196 or AO6484) tell us is that the Babylonians had some mathematical chops and used them to make things more organized.

For example, they were fully aware of the Pythagorean principle and visualized it in the problem of the ladder leaning against the wall (typical problem during sieges). Paraphrasing, if the ladder has a length of 30 and the wall a length of 26, how far away from the wall do you need to place the bottom of the ladder? Any mathematical savants here?

Apparently, they also had to deal with square roots, like the √2. They even approximate it as: 42/60 + 30/3600 = 17/24 ≈ 0.7083. Why √2? You have a square with the area of 1 something and you fill it with your stuff. However, you have more stuff coming in so you need to make your square larger, say double it. What should be the side of the new square?

As you can see, the mathematical snowball is starting to form...

Everyone wants to be cool

The astronomical swag of the Babylonians didn't go unnoticed in the hood and soon everyone wanted to get in on the action.

Like the the ancient Indians or Chinese. It so turned out that the major civilizations were all present on the northern hemisphere, so they observed roughly the same sky. Each developed similar observations and calculations as necessitated by nightly observations and daily life.

As the Babylonians, the Indians were aware of Pythagorean properties of triangles and listed specific examples in the Sulva Sutras. We can even find a statement of the theorem itself:

“the diagonal of a rectangle produces both [areas] which its length and breadth produce separately.”

What's really trippy is that the Indians considered the concept of infinite numbers. This must've been the result of a 4 AM session with Dr. Greenthumb.

The Chinese being a bit late to the civilization game, compared to other heavyweights like the cultures of Mesopotamia, still had a fair share of math problems to solve. See if you can tackle this one, from the Nine Chapters on the Mathematical Art:

There are two piles, one containing 9 gold coins and the other 11 silver coins. The two piles of coins weigh the same. One coin is taken from each pile and put into the other. It is now found that the pile of mainly gold coins weighs 13 units less than the pile of mainly silver coins. Find the weight of a silver coin and of a gold coin.

For some end-of-the-world vibes, the Mayans get an honorable mention. Anyone remember 2012? December 21, 2012 is when the longest of the Mayan calendars ended its count and because of that people lost their shit, prophesizing the armageddon. And I still think the world was less insane back then.

But modern superstitions aside, the Mayans deserve a slow clap for the precision of their observations.

Some clarification is needed as there is a lot of bullshit out there. If you see statements like: "The Mayans calculated the length of the year to be 365.2722 days.", then know also that, while they were accomplished mathematicians, we have no evidence that they used fractions. Especially not decimal fractions as they operated in a base 20 system. The decimal representation is the result of modern calculations based on historical findings.

Rather than in fractions, they thought in cycles. Instead of dealing with a part of something you can wait long enough until many such parts combine into a new whole and account for it. Exactly like we do with the leap year, every 4 years.

So where did that precise year estimation come from?

Over long periods of time the Mayans were able to determine the number of days between notable events, like a solstice or a planet crossing the horizon in the same spot. It's not entirely clear, which tools they used to arrive at accurate measurements. However, we some hints.

One is El Caracol in Chichen Itza, which seems to be a form of observatory, with narrow windows exposed to important direction in the sky. Observing events through such windows allowed for a more precision than just eyeballing it.

Another one is the fact that their civilization was located in the Yucatan Peninsula, which lies just below the Tropic of Cancer. This means that once in a while the sunlight will hit the ground directly from above, allowing you to see the bottom of a deep well fully illuminated, for example.

Once we have the passage of time recorded with Mayan calendars, we need to relate that information with our, more contemporary ones. With evidence coming independently from historical records, astronomical analysis and archeological findings, we are confident that the Mayan 13.0.0.0.0, 4 Ajaw, 8 Kumk?u is equivalent to August 11, 3114?BCE in Gregorian terms.

Now, if we take the numbers of days as counted by the Mayans and divide that by the number of years in the Gregorian sense, we arrive at the final value.

For example, take this analysis. The Mayan inscriptions on certain monuments indicate the passage of 8035 days between two events. For reasons described above we estimate this to be the equivalent of 22 years. What you get is:

8035 / 22 = 365.2722 days per year.

I'm sure the Mayans were up to other shenanigans as well. Unfortunately, a lot of their knowledge is lost to us as the Spanish decided to throw a giant barbecue party in the 16th century using Mayan manuscripts as fuel.

Now, we can't talk about ancient astronomy without mentioning the Egyptians. Talk about being obsessed with stars. Jeez... Not unlike the Mayans, they seemed incapable of placing a stone anywhere, unless it aligned with one stellar object or another.

Then again, if I throw two stones, each in a random direction, the line between them will probably point to an "important" object in the sky. So which way does the correlation go, I wonder...

Regardless, their obsession was justified. How else could the priests predict when the Nile is going to flood, or the Sun going to go black and scare ordinary people. Talk about knowledge being power...

The same was probably true for all civilizations after the agricultural revolution. Knowing when things are supposed to happen was probably necessary for survival. Is today the day we sow or is it tomorrow? Or maybe in a week or two? If you wanted to have something to eat, you had better been good at astronomy or it's back to picking berries.

Much like the Babylonians, the Egyptians were also into kinky mathematical stuff, like fractions and algebra. Wanna solve an ancient Egyptian quadratic equation problem?

"the area of a square of 100 is equal to that of two smaller squares. The side of one is ? + ? the side of the other."

Here is the answer.

Looking across the civilizations, we can see that they all used the sky to measure the passage of time either due to fascination, necessity or both. Observing the sky told them what's the time of day, month or a year. What they and many that came after probably didn't realize is that it also told the the time of the Universe, but that story comes later.

In the mean time, while the Mayans were sacrificing people to make the eclipse go away and Egyptians were busy making calendars full of hot babes with animal heads, another civilization was cooking something in the basement and it wasn't meth (as far as we know). This is the story of the next episode of Physics Rediscovered.

See you there.