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, 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.

Welcome to Momentous Monday

In continuing efforts to improve your blog-reading experience here, as well as to make it easier for me to keep cranking out content, I’ve decided to theme the week, similarly to what I did starting right after Thanksgiving in my Countdown to Christmas, which is what led to me deciding to post every day in the first place.

Since the theme thing for the aforementioned thing helped me so much, I’ve decided to bring it back now, as it applies to the subjects I like to write about. I’ve already established the Sunday Nibble, which is a short piece on a random subject, and recently also started your Saturday Reading as I excerpt parts of a novel written as a bunch of short stories.

That takes care of the weekends. The weekdays will cover history, language, science, and theatre — in that order — with Friday being a potluck of whatever has struck my fancy that week.

This being Monday, the subject is History, and I’d liked to dub it Momentous Mondays. Looking for inspiration, I searched for things that happened on this particular Monday, February 10, and turned up one that is sort of relevant to now, but not for reasons that anyone might read into it. But that will be explained shortly.

* * *

When I looked up events that happened on February 10, I came up with two interesting choices. The first is that it was on this day in 1961 that the artist Roy Lichtenstein opened a show which included his painting “Look Mickey,” featuring his first use of so-called Ben-Day Dots, a general thievery (inspiration?) from/by golden age comic books, and something which would go on to somehow be the quintessential 80s pop-art stereotype. You may not know his name, but if you see one of his paintings in this style, you’d probably go, “Oh, yeah. That guy.”

But… I decided against that one because I find that kind of pop art gone commercial to be banal. While Lichtenstein tried to be edgy with the dialogue he put into the speech bubbles on a lot of his work, in retrospect a lot of it seemed to be punching down at women in general and feminists in particular. And don’t tell me that the woman in this painting, lamenting her lack of motherhood, doesn’t look a hell of a lot like Judy Garland who did, in fact, remember to have children.

For the kind of pop art gone successful that I do like, follow Banksy, who has managed to remain anonymous (and might even be a collective instead of a person) and pulled off the most brilliant art world troll ever with his insta-shredded painting that was, itself, probably a faked work of art.

So I went with the other event that happened on February 10 that caught my eye, and it was this one: On this day in 1967, the 25th Amendment to the U.S. Constitution was ratified. It had been passed by Congress for approval by the states on July 6, 1965, and it was approved one year, seven months, and four days later.

As amendments go, that’s pretty damn fast — the ERA started the process in 1972, and may or may not have been finally ratified in January 2020, when Virginia voted to do so. So what was the impetus for passing the 25th Amendment? Well, first, what is the 25th?’

First off, it codifies the idea that the Vice President actually becomes President if the current President leaves office for any reason. Believe it or not, before that, there wasn’t really a definite rule one way or the other. It just sort of became tradition when John Tyler took over after William Henry Harrison kicked the bucket after 30 days in office.

He didn’t make a lot of friends doing this and, ultimately, when it looked like his own party was going to reject him for nomination for re-election in 1844, he formed his own independent party and ran as a single-issue candidate: Annexing Texas, which had only recently become independent from Mexico. You know — the usual America invading shit. When Andrew “Yeah, I’m a Racist” Jackson threw his support behind Tyler but the writing was on the wall that Tyler wasn’t going to win, it gave him the excuse to drop out of the race, and so he joined the less-than-one-term club.

The second bit of the 25th Amendment deals with what happens when the Vice Presidency becomes vacant and, believe it or not, there wasn’t anything set up to deal with this, either. Nobody automatically succeeded, and there was no clear mechanism for the President to pick someone to fill the spot. Consequently, throughout our history, there have been some big-ass gaps in the position, with the winner being Tyler again, who never had a Vice President.

Most of these four-year pushers happened in the 19th century, with the two notable exceptions being Theodore Roosevelt (1901-1905), who never picked a successor after McKinley was assassinated, and Harry S Truman 1945-1949), who never picked a VP during his first partial term after FDR died.

The most recent time there was a gap of more than a few days was in 1974, when Gerald Ford took over when Richard Nixon resigned and it took about four months before his VP choice was confirmed.

The third part of the Amendment involves the president sending a letter to the President pro tempore of the Senate and the Speaker of the House basically saying, “Hey, y’all. Can’t do the President thing right now. Homie gonna ride the Oval until I tell you otherwise.”

This one has actually been used a couple of times but, oddly enough, generally only when a president is about to get a colonoscopy.  It’s also clear, in Section 3, that the VP is only acting President.

The fourth part of the Amendment has never been invoked and is somewhat the nuclear option. In this one, the Vice President and majority of the Cabinet Officers send letters to the aforementioned congressional officers basically saying, “Hey, y’all, homie can’t handle doing the President thing, Blair House represents and requests promotion to the Oval.”

Or, in other words, the Vice President becomes acting President and the President is shut out, until they send their own letter saying, “Nu-uh.” There’s no time limit for this response other than, presumably, what would have been the end of the President’s term, but then the Vice President and Cabinet have four days to respond to the response, in effect transmitting their “no backsies” statement. Congress then has 48 hours to assemble and decide, by two-thirds majority of both houses, who wins.

Section Four has never been invoked, and, honestly, it really feels like a hand grenade that nobody from either party would ever fall on short of a full-on Madness of King George situation. It’s also a bit odd that the Constitution would give a prominent role to someone — the Vice President — with a vested interest in the process.

Good idea, poor execution. And at the point that Section Four were ever invoked, it seems like the congressional standard of removal should be simple majority, not two thirds. Not to mention that it sets the bar higher for the House than it is for impeachment.

So much for the what. It’s the way that is informative and scary. You see, basically, the assassination of JFK in 1963 reminded lawmakers of one thing: There was a hole in the Constitution bigger than the one Oswald put in Kennedy’s head. The Founders really hadn’t provided all that well for what happened when the President or Vice President or — OMFG! — both of them suddenly wound up out of office or unable to serve for whatever reason.

Resignation? Assassination? War? Revolution?

Now, granted, given the separation of powers enshrined in the Constitution, it’s possible that the Founders figured it would be possible to go for a maximum of slightly under four years without a President or Vice President, and that Congress and the Courts could handle it on their own, or that the Vice President would only assume the powers of the President but that Congress and the Courts would decide on a replacement method if it became necessary.

They did make an attempt in 1792 — probably not coincidentally around the time George Washington was saying that he was not going to run for a second term. Popular sentiment convinced him otherwise, but the Presidential Secession Act of 1792 is a hot mess. Not only does it create the clusterfuck that is the useless Electoral College, it only stipulates what happens when both the Presidency and Vice Presidency are vacant, something that has never yet occurred in the history of the country.

Of course, Tyler was their first test of what happens when only one office goes vacant, and Congress set precedent by pretty much saying, “Oh. Okay,” once Tyler took the oath of office and moved into the White House.

The other two attempts were in 1886, goaded by the assassination of James Garfield and the death of Vice President Thomas Hendricks both leaving vacancies, and in 1947, after FDR died while World War II was still going on.

While the assassination of JFK was the obvious public impetus for the first parts of the 25th Amendment, the fourth section may seem a bit of a mystery, but it’s also dealing with an historical precedent, and one that not a lot of people know about. In 1919, just after the end of World War I, President Woodrow Wilson suffered a debilitating stroke. Wilson’s wife went into full-on Nancy Reagan mode, limiting access to a bedridden president and, really, becoming the de facto president for the remaining two years of his term. She certainly limited the Vice President’s access to the man and, as history later revealed, only she and his doctor knew, and she forged his signature on documents left and right.

The 25th Amendment would certainly give a modern Vice President confronted with the same suspicious activity a good chance of rallying the cabinet and rooting out a hidden illness or manipulative spouse — although if that spouse had the balls to forge things the way that Edith Wilson did, it would probably become moot as well.

So the lesson regarding the 25th and the whole Constitution really is this: the Founders were only human, and they left so much wiggle room in there that it’s ridiculous. And that’s a big problem. Your mission, should you choose to accept it, is to start urging your lawmakers to take sides and close those holes, as well as to adjust things to accommodate life as it is now, not as it was in the late 18th century.

Which brings up another thought: Why is it only politicians who get to invoke the 25th? Shouldn’t that also be the domain of doctors, psychologists, and the like? That certainly would have caught out Wilson’s lie quickly.

Like a prayer

This began as an attempt at a Sunday Nibble, but then I took such a deep-dive that it turned into a full article. Riffing on language does that to me.

Pop quiz. Can you identify this fairly well-known piece and the language it’s in?

Fæder ūre, ðū ðē eart on heofonum,

Sī ðīn nama gehālgod.

Tō becume ðīn rice.

Gewurde ðīn willa

On eorþan swā swā on heofonum.

Urne gedæghwamlīcan hlāf syle ūs tōdæg.

And forgyf ūs ūre gyltas,

Swā swā wē forgyfaþ ūrum gyltendum.

And ne gelæd ðū ūs on costnunge,

ac alȳs ūs of yfele.

It may look like something very foreign, and it both is and isn’t. It’s also a good clue as to why one of the biggest barriers to time travel might not be the technology, but rather the language. Jump in your time machine, set it for 1,025 years in the past, and that’s the language you’d have to figure out… in what would eventually become England. c. 995 C.E.

Yep. That quote above is in Old English and it’s the Lord’s Prayer. Whether you’re religious or not, or if the religion you grew up with was not Christianity, if you grew up in the west, you’ve been exposed to it, so you probably kind of know the words.

Notice, too, that a few words stand out as being completely unchanged:  and, on, and of. Everything else, nope. This was the original native language of the British Isles — at least the parts with the Angles, Saxons, and Jutes, because the Gaelic tribes were doing their own thing — and it didn’t even begin to resemble what we speak know until the French came along.

A couple of centuries after the Norman Conquest in 1066, the text had changed to the following, which should seem a lot more familiar. This is the version as of 1389:

Our fadir that art in heuenes,

halwid be thi name;

Thi kingdom cumme to;

be thi wille don

as in heuen and in earthe;

giv to vs this day our breed ouer other substaunce;

and forgeue to vs oure dettis,

as we forgeue to oure dettours;

and leede us nat in to temptacioun,

but delyuere vs fro yuel.


Other than the v/u swapping going on and the strange spelling, it’s mostly readable to a modern audience. Also notice that there are now a lot more words that are unchanged to this day, and not just short ones. But jump ahead to 1526 and see how much more modern it sounds:

O oure father which arte in heven,

halowed be thy name;

let thy kingdom come;

thy wyll be fulfilled

as well in erth as hit ys in heven;

geve vs this daye oure dayly breade;

and forgeve vs oure treaspases,

even as we forgeve them which treaspas vs;

leede vs not into temptacion,

but delyvre vs ffrom yvell.

For thyne is the kingdom and the power,[4]

and the glorye for ever.


Finally, there’s the King James version which was quite understandable, and which was written near the end of Shakespeare’s life, after he had almost single-handedly created Early Modern English.

Our father which art in heaven,

hallowed be thy name

Thy kingdome come.

Thy will be done,

in earth, as it is in heaven.

Giue us this day our daily bread.

And forgive vs our debts,

as we forgive our debters.

And lead us not into temptation,

but deliver vs from evill:

For thine is the kingdome, and the power,

and the glory, for ever,


By this point, we’re only a hop, skip, and a jump away from the modern version:

Our Father, who art in heaven,

Hallowed be thy Name.

Thy kingdom come.

Thy will be done,

On earth as it is in heaven.

Give us this day our daily bread.

And forgive us our trespasses,

As we forgive those who trespass against us.

And lead us not into temptation,

But deliver us from evil.

For thine is the kingdom, and the power,

and the glory, for ever and ever.


And now circling back to the original topic of language and time travel, this is something I don’t think I’ve ever seen tackled in any depth, but more than anything, language could be the biggest barrier to any time travelers, even if they’re going back in time in their own country, or at least in their own culture — and traveling back five hundred or a thousand years wouldn’t be the only difficulty. Ironically, jumping back to any point prior to a decade ago and after the American Civil War would also be fraught with language problems.

Why? Because language evolves at the speed of communication. In the 10th century, English remained its own isolated thing and didn’t begin to change until French soldiers under William the Conqueror came in and took over. They brought in both a lot of new vocabulary and a class division in language. The nobility spoke French. The peasants spoke English. Where the two met — i.e. where the peasants served the nobility — vocabulary bled into each other. That is why we have two distinct classes of food words, one set old English and the other French.

Basically, the living animal got the English and the cooked version got the French, so we have cow and beef; chicken and poultry; lamb and mutton; and pig and pork, to name a few.

Once the age of exploration kicked in at the end of the 15th century, English also began to take on a lot of words from other languages. At first, these came from Spanish, Dutch, and more French — the big colonial powers of the time — but eventually also began to come in from the places colonized. This era was the lead-up to the acceleration of change and the development of modern English after Shakespeare’s time, which ended when he died at the beginning of the 17th century.

Now there’s one thing to keep in mind, and that’s the phenomena of regional dialects and slang, which were common in English in both Britain and the U.S. up until the early 20th century. Again, it came down to communication, and people living in isolated pockets didn’t really communicate that much with people in others. Only the upper classes got to do that kind of traveling, but they were also not prone to speaking in slang.

This led to things like completely different accents even across as small a space as England, which is about the size of California. And in other countries, it was even more extreme. In what eventually became Germany, people from the west could not understand people from the east and vice versa, since dialects there turned into a continuum. Likewise, in Spain, things broke down into Castilian (i.e. “real” Spanish), Catalan, Galician, and Occitan.

Back to English in the 20th century, though, and once movies with dialogue and radio became a thing, boom. That speed of communication accelerated, and the rate of evolution and homogenization of the language took off. For a while between the 1930s and 1950s, there was even such a thing as the “Mid-Atlantic” accent, which was a hybrid of British and English designed to resemble neither but be understandable by both. Cary Grant, Katharine Hepburn, and James Mason used it a lot.

During this era, dialect and slang became national, accents started to smooth out, and the new defining feature of vocabulary went from being location to cohort.

Or, in other words, the quickest way to give away your approximate age rapidly became the way you spoke. At least up until a point, and that point was when communication became immediate and instant with the rise of the internet. Over the last decade, the evolution of language has become a constant, with new words being created and old words being dumped every single moment. And every neologism instantly propagates and is adopted or dropped.

In modern terms, then, the separators have gone beyond location and cohort, or have at least landed on a different definition. No, instead of where you are and how old you are, it has more to do with where you are online and what you’re aware of. This still doesn’t help with time travel, though, because even with the internet, you can’t prepare enough.

Go on. Jump into your time machine and go back, say, fifty years, to 1970, and land in Manhattan. Try to have a conversation with a local and see how long you can go without saying something that makes them say, “What?” Or, conversely, how long it is before they say something that makes no sense to you at all.

Try various intervals back to a century ago, or more. Feeling out of your depth? That is the rapid evolution of our language in action. It’s also why complaining about changes in it is futile, and yes I’ll flag myself for this one, because I do love to bitch about abuse of grammar. Although I will contend that abusing grammar and creative or novel uses of words are two very different things. Give me a clever neologism, hooray you! Fuck up the use of an apostrophe? Fifty lashes!

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