Babylonian math and modern addition

Babylonians, who were very early astronomers, inherited a rather interesting counting system from the Sumerians, one that worked in Base 60, if you can believe it. It was basically derived from counting each of the segments of the fingers on one hand, not including the thumb (3 x 4) and then using all five fingers on the other hand to count each set of 12. Five times 12, of course, equals 60.

60 is a very useful number because it has so many factors: 1 through 6, then 10, 12, 15, 20, 30, and 60. It also has common factors with 8 (2 and 4) and 9 (3), and can easily create integer fractions with multiples of 5 and 10. For example, 45/60 reduces very easily. First, divide both by 5 to get 9/12, then divide both by 3 to get 3/4. It works just as easily in reverse — 60/45, 12/9, 4/3 which equals 1 1/3.

If you’re ahead of me, then you’ve already realized a very important place where we use 60 a lot.

Now, I would argue that the system is actually Base 12 counted in groups of 5, but the outcome is rather interesting, because to this day it forms the basis for some pretty basic things: Euclidean geometry and telling time.

A minute has 60 seconds and an hour has 60 minutes, of course. A circle has 360 degrees, which is 60 times 6. It’s a fortunate coincidence that an Earth year worked out to be so close to that in number of days — 365.25. And in case you’ve ever wondered why we add one day every four years, like we will this year, that’s the reason why. Our 365 day calendar loses a full day in that time, and we put it back by tacking it onto the end of February.

I still think that it was more Base 12 times 5, because there are some significant dozens that pop up, again thanks to the Babylonians. There are a dozen constellations in the zodiac, each one taking up 30 degrees of sky, giving us 12 months.

Of course, you can’t write “12” in Base 12 — those digits actually denote what would be 14 in Base 10. So how do you get around there only being 10 digits if you want to write in bigger bases?

If you’ve done any kind of coding or even HTML, you’re probably familiar with the hexadecimal system, which is Base 16. There, the convention was established that once a digit hit nine, the rest would be filled out with letters until you incremented the next digit up. So, once we get to 9 in Base 16, the following digits are A (10), B (11), C (12), D (13), E (14), and F (15). F is followed by 10 (16), and the whole process repeats following the rules I’ve described previously.

Now you might wonder, how did they do single digits in Base 60, and the answer is that the Babylonians didn’t. In fact, they sort of cheated, and if you look at their numbering system, it’s actually done in Base 10. They just stop at 59 before rolling over. They also didn’t have a zero or a concept of it, which made the power of any particular digit a bit ambiguous.

And yet… Babylonians developed a lot of the complex mathematics we know to this day, including algebra, a pretty accurate calculation of the square root of 2, how to figure out compound interest, an apparent early version of the Pythagorean theorem, an approximation of π accurate to about four digits, measuring angular distances, and Fourier analysis.

Yeah, not too bad for an ancient civilization that didn’t have internet or smart phones and who wrote all their stuff in clay using sticks, huh? But that is the beauty of the ingenuity of the human mind. We figured out this stuff thousands of years ago and have built upon it ever since. The tricks the Babylonians learned from the Sumerians led in a straight line right to the device you’re reading this on, the method it’s being piped to your eye-holes, the system of satellites or tunnels of fiber optics that more likely than not takes the data from source to destination, and even the way all that data is encoded.

Yay, humans! We do manage to advance, sometimes. The real challenge is continuing to move forward instead of backward, but here’s a clue. Every great advance we have made has been backed up by science. Within our own living memory — that of ourselves, or the still living generations who remember what their parents and grandparents remembered — we went from not being able to fly at all to landing humans on the Moon to launching probes out of our solar system, all of it in under one century.

We have eradicated or mitigated diseases that used to kill ridiculous numbers of people, are reducing fatality rates for other diseases, and are increasing life expectancy, at least when the voice of reason holds sway. For a while, we even made great advances in cleaning up the environment and quite possibly turning the tide back in favor of reversing the damage.

But… the real risk is that we do start moving backward, and that always happens when the powers that be ignore science and replace it with ignorance and superstition, or ignore the advances of one group because they’re part of “them,” not “us.”

To quote Hamilton, “Oceans rise, empires fall.” And when an empire falls, it isn’t always possible for it to spread its knowledge. What Babylon discovered was lost and found many times, to the point that aspects of it weren’t found again until the time of the ancient Greeks or the Muslims, or the Renaissance.

In order, and only in terms of math, those cultures gave us geometry; algebra and the concept of zero; and optics and physics — an incomplete list in every case. European culture didn’t give us much in the way of science between the fall of the Roman Empire and the Renaissance, while the Muslim world was flourishing in all of the parts of Northern Africa and Southern Europe that it had conquered, along with preserving and advancing all of that science and math from fallen old-world civilizations.

Yeah, for some funny reason back then, their religion supported science. Meanwhile, in other places a certain religion didn’t, and the era was called the Dark Ages. That eventually flipped and the tide turned in Europe beginning in the 16th century. In case you’ve ever wondered, that’s exactly why every college course in “modern” history begins at 1500 C.E.

Sadly, the prologue to this is the Italian war criminal Cristobal Colón convincing the Spanish religious fanatics Fernando y Isabel to finance his genocidal expedition originally intended to sail west to India but unfortunately finding some islands next to a continent in the way, on which he raped, pillaged, and slaughtered people for his own amusement. Or, in other words, the Dark Ages didn’t end until Colón and those Spanish rulers were dead and buried, meaning January 23, 1516, when they fed the last of them, Fernando, to the worms.

Oh, except that humans continued to be shitty as they sailed west even as science back home advanced. Dammit. And that’s been the back and forth since forever. What we really need are more people committed to the “Forth!” while determined to stop the “Back!”

Or, at the very least, push the science forward, push the bullshit back.

Look, up in the sky!

Throughout history, humans have been fascinated with the sky, and a lot of our myths were attempts to explain what goes on up there. In many cultures, the five planets visible to the naked eye (Mercury, Venus, Mars, Jupiter, and Saturn) were named after deities or attributes of the planets with surprising consistency.

Mercury was often named for its swiftness in orbiting the Sun; Venus was always associated with beauty because of its brightness; Mars’s red color led to it being named either for a violent deity or that color; Jupiter was always associated with the chief deity even though nobody in those times had any idea it was the largest planet; and Saturn, at least in the west, was named after Jupiter’s father.

This led to Uranus, which wasn’t discovered until the 18th century, being named after Saturn’s father, i.e. Jupiter’s grandfather. Neptune, discovered in the 19th century, and Pluto, discovered in the 20th century before being rightfully demoted from planetary status, were only named for Jupiter’s less cool brothers.

Since the planets were given attributes associated with deities, their relationship to each other must have meant something, and so the bogus art of astrology was invented, although it was obviously not complete prior to Uranus, Neptune, and Pluto being added, but then was clearly incorrect during the entire period of time that Pluto was a planet. (Hint: That was a joke. It was incorrect the entire time.)

Since humans are also hard-wired to see patterns, the stars above led to the definition of constellations, the night-time version of the “What is that cloud shaped like?” game.

It wasn’t really until the renaissance and the rise of science, including things like optics (one of Newton’s discoveries), which gave us telescopes, that we really started to take a look at the skies study them. But it is still astounding how so many laypeople know so little about what’s up there that we have had completely natural phenomena freaking us out since forever. Here are five examples of things in the sky that made people lose their stuff.

1. Total eclipse of the heart… er… Sun

Until science openly explained them, eclipses of any kind were scary. For one thing, nobody knew when they were coming until Royal Astronomer became a thing, but only the elite were privy to the information, so the Sun would go out or the Moon would turn blood red, or either one of them would appear to lose a piece at random and without warning. Generally, the belief was that the Moon or Sun (particularly the latter) was being consumed by some malevolent yet invisible beast that needed to be scared away.

But long after modern science explained that an eclipse was nothing more than the Moon passing in front of the Sun or the Earth passing in front of the Moon, shit went down in 1878, at least in low-information areas.

The thing about this eclipse was that it had been predicted close to a century before, had been well-publicized, and was going to put the path of totality across the entire U.S. for the first time since its founding. There’s even a book about it, American Eclipse. But there’s also a tragic part of the story. While the news had spread across most of the growing nation, it didn’t make it to Texas, and farm workers there, confronted with the sudden loss of the Sun, took it to mean all kinds of things. A lot of them thought that it was a portent of the return of Jesus, and in at least one case, a father killed his children and then himself in order to avoid the apocalypse.

2. Captain Comet!

Ah, comets. They are an incredibly rare sight in the sky and well worth traveling to see if that’s what you need to do. I remember a long trek into the darkness when I was pretty young to go see Comet Hyakutake, and yes it was worth it. It was a glorious blue-green fuzzball planted in space with a huge tail. Of course, I knew what it was. In the past, not so much.

In the ancient world, yet again, they were seen as bad omens because something in the heavens had gone wrong. The heavens, you see, were supposed to be perfect, but there was suddenly this weird… blot on them. Was it a star that grew fuzzy? Was it coming to eat the Earth? What could be done?

That may all sound silly, but as recently as 1910, people still flipped their shit over the return of one of the more predictable and periodic of “fuzzy stars.” That would be Comet Halley. And, by the way, it’s not pronounced “Hay-lee.” It’s “Hall-lee.”

And why did it happen? Simple. A French astronomer who should have known better, wrote that the tail of the comet was full of gases, including hydrogen and cyanide, and if the Earth passed through the tail, we would either be gassed to death or blown up. Unfortunately, another French astronomer at the time actually played “Got your back” with him, and that was all it took.

It was pseudoscience bullshit at its finest, propagated by the unquestioning and uninformed (when it comes to science) media, and it created a panic even though it was completely wrong.

The worst part about Halley’s 1910 appearance? It bore out Mark Twain’s statement, paraphrased probably: “I came into the world with it, I will go out with it.” And he did. Goddamit.

3. Meteoric rise is an oxymoron

And it definitely is, because a meteor only becomes one because it’s falling. And while we’re here, let’s look at three often confused words: Meteor, meteoroid, and meteorite.

The order is this: Before it gets here and is still out in space, it’s a meteoroid. Once it hits our atmosphere and starts to glow and burn up, it has become a meteor. Only the bits that actually survive to slam into the planet get to be called meteorites. Oid, or, ite. I suppose you could think of it as being in the vOID, coming fOR you, and then crash, goodnITE.

So the things that mostly cause panic are meteors, and quite recently, a meteor blowing up over Russia convinced people that they were under attack. It was a fireball that crashed into the atmosphere on February 15, 2013, and it actually did cause damage and injuries on the ground.

The numbers on the Chelyabinsk meteor are truly staggering, especially to think that they involved no high explosives, just friction and pure physics (Hello again, Sir Isaac!) The thing was about 66 feet in diameter, which is the length of a cricket pitch, or about four feet longer than a bowling lane. It compares to a lot of things, and you can find some fun examples here.

But there was nothing fun about this asteroid. It came screaming through our atmosphere at about 41,000 miles an hour at a steep angle. The heat from the friction of our atmosphere quickly turned it into a fireball of the superbolide variety, which is one that is brighter than the sun. It exploded about 18 miles up. That explosion created a fireball of hot gas and dust a little over four miles in diameter. The kinetic energy of the event was about 30 times the force of the atom bomb dropped on Hiroshima.

Over 7,200 buildings were damaged and 1,500 people were injured enough to need medical attention, mostly due to flying glass and other effects of the shockwave. Unlike other items on this list, these events actually can be dangerous, although this was the first time in recorded history that people were known to have been injured by a meteor. The Tunguska event, in 1908, was a little bit bigger and also in Russia, but happened in a remote and sparsely populated area, with no reported human injuries. Local reindeer were not so lucky.

4. Conjunction junction, what’s your function?

A conjunction is defined as any two or more objects in space which appear to be close together or overlapping when viewed from the Earth. Every solar eclipse is a conjunction of the Sun and Moon as seen from the Earth. Oddly enough, a lunar eclipse is not a conjunction from our point of view, because it’s our planet that’s casting the shadow on the Moon.

Conjunctions shouldn’t be all that surprising for a few reasons.

First is that most of the planets pretty much orbit in the same plane, defined by the plane in which the Earth orbits because that makes the most sense from an observational standpoint.

The inclination of Earth’s orbit is zero degrees by definition and the plane we orbit in is called the ecliptic. You can probably figure out where that name came from. Out of the planets, the one with the greatest inclination is Mercury, at 7º. Counting objects in the solar system in general, the dwarf planet Pluto has an inclination of 17.2º — which is just another argument against it being a true planet. None of the planets not yet mentioned have an inclination of more than 4º, which really isn’t a whole lot.

The second reason conjunctions should not be all that surprising is because each planet has to move at a particular velocity relative to its distance from the Sun to maintain its orbit. The farther out you are, the faster you have to go. Although this is a function of gravity, the airplane analogy will show you why this makes sense.

As an airplane gains speed, the velocity of air over the wings increases, generating more lift, bringing the airplane higher. In space, there’s no air to deal with, but remember that any object in orbit is essentially falling around the body it orbits, but doing it fast enough to keep missing.

If it slows down too much, it will start to fall, but if it speeds up its orbit will get bigger. This is directly analogous to ballistics, which describes the arc of a flying projectile. The faster it launches the farther it goes and the bigger the arc it makes. An arc in orbit becomes an ellipse.

Since every planet is moving at the speed required to keep it at the distance it is, things are likely to sync up occasionally. Sometimes, it will only be one or two planets, but on certain instances, it will be most or all of them. This video is a perfect example. Each one of the balls is on a string of a different length, so its natural period is different. Sometimes, the pattern becomes quite chaotic, but every so often it syncs up perfectly. Note that all of them did start in sync, so it is mathematically inevitable that they will sync up again at the point that all of the different period multiply to the same number. Our solar system is no different since the planets all started as rings of gas and dust swirling around the Sun. There was a sync point somewhen.

So conjunctions are a completely normal phenomenon, but that doesn’t mean that people haven’t gone completely stupid with them. The first way is via astrology, which isn’t even worth debunking because it’s such a load. The Sun is 99.8% of the mass of the solar system, so it constantly has more influence in every possible way over everything else hands down. What influence did the planets have upon your personality at birth? Less than zero. The only relevant factor, really, is that people’s personalities are formed by their relative age when they started school, so that is influenced by the season they were born in, but that’s about it.

As for the modern version of people going completely stupid over conjunctions, it happened in the early 1980s, after the 1974 publication of the book The Jupiter Effect by John Gribbin and Stephen Plagemann. In short, they predicted that a conjunction of the planets on March 10, 1982 would cause a series of earthquakes that would wipe out Los Angeles.

Since you’re reading this in at least the year 2020 and I’m quite safely in Los Angeles, you know how their prediction turned out. This didn’t stop them from backtracking a month later and releasing a follow-up book called The Jupiter Effect Reconsidered (aka We Want More Money from the Gullible) in which they claimed, “Oh… we miscalculated. The date was actually in 1980, and the conjunction (that hadn’t happened yet) caused Mount St. Helens to erupt.”

Still, just like with the whole end of the world 2012 predictions, at least some people bought into it.

5. The original star wars

The last item on our list is possibly a one-off, occurring on April 14, 1561 in Nuremberg, Germany. Whether it actually even happened is debatable since only a single account of it survives in the form of a broadsheet — basically the blog post of its day. If it had been as widespread as the story makes it seem, after all, there should have been reports from all across Europe unless, of course, the point of view from Nuremberg created the exceptional event in the first place.

It was described as an aerial battle that began between 4 and 5 a.m. when “a dreadful apparition occurred on the sun.” I’ll quote the rest of the paragraph in translation in full from the article linked above: “At first there appeared in the middle of the sun two blood-red semicircular arcs, just like the moon in its last quarter. And in the sun, above and below and on both sides, the color was blood, there stood a round ball of partly dull, partly black ferrous color. Likewise there stood on both sides and as a torus about the sun such blood-red ones and other balls in large numbers, about three in a line and four in a square, also some alone.”

The unknown author goes on to describe the objects — spheres, rods, and crosses — as battling with each other for about an hour, swirling back and forth. Eventually, the objects seemed to become fatigued and fell to the Earth, where they “wasted away… with immense smoke.

Now, what could have caused this phenomenon? The obvious answers are that it was a slow news day or that it was religious propaganda or some other wind-up. But if it were an actual phenomenon and really only remarked on in one village, then it’s quite possible that it was a meteor shower with an apparent radiant, or source, that happened to line up with the Sun.

It was a Monday, with a new Moon. The Sun rose in the east at 5:05 a.m., so the invisible Moon was somewhere around that part of the sky, too. But this also immediately calls the story into question, since the phenomenon seen coming from the Sun happened before sunrise according to the account. But if we consider that to just be human error, what we have is the Pearl Harbor effect. The attackers come in with the rising Sun behind them, making them hard to see or understand.

On top of that, if they’re coming in from that direction, they’re coming in at a very shallow angle. See the notes on the Russian meteor above. This can lead to some super-heated objects, which would glow red as reported, and anything not red hot against the Sun would appear black. If it happened to be a swarm of objects, like a bunch of small rocks and dust or a bigger piece that broke up, all flying in at once, the chaotic motion could certainly make it seem like a battle.

There is a meteor shower that happens around that time of year called the Lyrids, which is very short-lived, although I haven’t yet been able to find out whether its radiant was near the Sun in 1561. But a particularly heavy shower coming in at just the right angle could have an unusual effect in a limited area.

Or… the author just pulled it out of his ass for his own reasons. We can never know.


Photo credit: Staff Sgt. Christopher Ruano, F.E. Warren Air Force Base.

Why astrology is bunk

I know way too many otherwise intelligent adults who believe in astrology, and it really grinds my gears, especially right now, because I’m seeing a lot of “Mercury is going retrograde — SQUEEEE” posts, and they are annoying and wrong.

The effect that Mercury in retrograde will have on us: Zero.

Fact

Mercury doesn’t “go retrograde.” We catch up with and then pass it, so it only looks like it’s moving backwards. It’s an illusion, and entirely a function of how planets orbit the sun, and how things look from here. If Mars had (semi)intelligent life, they would note periods when the Earth was in retrograde, but it’d be for the exact same reason.

Science

What force, exactly, would affect us? Gravity is out, because the gravitational effect of anything else in our solar system or universe is dwarfed by the Earth’s. When it comes to astrology at birth, your OB/GYN has a stronger gravitational effect on you than the Sun.

On top of that, the Sun has 99.9% of the mass of our solar system, which is how gravity works, so the Sun has the greatest gravitational influence on all of the planets. We only get a slight exception because of the size of our Moon and how close it is, but that’s not a part of astrology, is it? (Not really. They do Moon signs, but it’s not in the day-to-day.)

Some other force? We haven’t found one yet.

History

If astrology were correct, then there are one of two possibilities. A) It would have predicted the existence of Uranus and Neptune, and possibly Pluto, long before they were discovered, since astrology goes back to ancient times, but those discoveries happened in the modern era, or B) It would not have allowed for the addition of those three planets (and then the removal of Pluto) once discovered, since all of the rules would have been set down. And it certainly would have accounted for the 13th sign, Ophiuchus, which, again, wasn’t found until very recently, by science.

So…stop believing in astrology, because it’s bunk. Mercury has no effect on us whatsoever, other than when astronomers look out with telescopes and watch it transit the Sun, and use its movements to learn more about real things, like gravity.

Experiment

James Randi, fraud debunker extraordinaire, does a classroom exercise that demolishes the accuracy of those newspaper horoscopes, and here it is — apologies for the low quality video.

Yep. Those daily horoscopes you read are general enough to be true for anyone, and confirmation bias means that you’ll latch onto the parts that fit you and ignore the parts that don’t although, again, they’re designed to fit anyone — and no one is going to remember the generic advice or predictions sprinkled in or, if they do, will again pull confirmation bias only when they think they came true.

“You are an intuitive person who likes to figure things out on your own, but doesn’t mind asking for help when necessary. This is a good week to start something new, but be careful on Wednesday. You also have a coworker who is plotting to sabotage you, but another who will come to your aid. Someone with an S in their name will become suddenly important, and they may be an air sign. When you’re not working on career, focus on home life, although right now your Jupiter is indicating that you need to do more organizing than cleaning. There’s some conflict with Mars, which says that you may have to deal with an issue you’ve been having with a neighbor. Saturn in your third house indicates stability, so a good time to keep on binge watching  your favorite show, but Uranus retrograde indicates that you’ll have to take extra effort to protect yourself from spoilers.”

So… how much of that fit you? Or do you think will? Honestly, it is 100% pure, unadulterated bullshit that I just made up, without referencing any kind of astrological chart at all, and it could apply to any sign because it mentions none.

Conclusion

If you’re an adult, you really shouldn’t buy into this whole astrology thing. The only way any of the planets would have any effect at all on us is if one of them suddenly slammed into the Earth. That probably only happened once, or not, but it’s what created the Moon. So probably ultimately not a bad thing… except for anything living here at the time.