Ideas - 12 is Sublime | The Greatest Numbers of All Time

Episode Date: June 23, 2026

Complete. Whole. Divine order. That's just the start of what makes the humble dozen extraordinary. It's one of only two numbers ever discovered in mathematics to be “sublime.” Twelve makes a number of appearances in pop culture, in religion, in non-fiction, everything from the 12 days of Christmas to the 12 people it takes to form a criminal jury. Still need convincing of 12’s perfection and indispensability? Check your watch.More episodes in our series, The Greatest Numbers of All Time:Listen to The Curse of 13Guests in this episode:Glen Van Brummelen is a professor of mathematical sciences at Trinity Western University.Ainsley Hawthorn is a cultural historian and nonfiction writer. She has a PhD in Near Eastern Civilizations from Yale University.

Hi, Steve Patterson here, host of the debaters, and while I love a funny fight, there's one thing that's not up for debate. The Stratford Festival is world-class theater right here in Canada. Whether you're a fan of Shakespeare, musicals, or classics like Death of a Salesman or Waiting for Godot, there's no better time to experience Canadian talent and no better place to see it than the Stratford Festival. So get your tickets now at Stratfordfestable.ca and experience world-class performance the whole family can enjoy. You know, we even taped the debaters there once, so I guess we're world-class now. This is a CBC podcast.

There can't be a friendlier or groovier introduction to counting than this. And frankly, only the Pointer Sisters could have carried it off so sublimely. But if this Sesame Street standard was about teaching counting, 12. Why to 12? Think of how most of us tell the time, how our calendar tracks the months, or the fact that we buy eggs or roses in dozens. Is a deeper question here?

How it is that some things are always counted in 12s, even when the rest of our lives have revolved for centuries around 10 as our basis for counting. When the number 12 did get used, it's sticky because it's such a friendly number. Friendly, and apparently 12 is also known in mathematical circles as sublime for reasons beyond its starring role in the inner workings of the universe and its popularity across the world's major religions. The 12 apostles in Christian tradition may have influenced this perception that 12 was the symbol of perfection, completeness, the ideal number of people.

There are actual organizations dedicated to the humble dozen, with adherents who'd even prefer the dozenal or duodecimal over the decimal system that we take for granted today. But you don't have to be a dozenalist to appreciate the many virtues of 12. My name is Glenn Van Bromelan. I'm a professor of mathematical science. sciences at Trinity Western University, and I'm especially interested in the history of mathematics. You're also the author of several books about the history of mathematics. Indeed, my specialty is the history of trigonometry. I was once told by people at a math camp that I am both the best and the worst historian of trigonometry in the world because I'm the only one.

Now, that's not quite true. Other people do study the history of trigonometry, but I study it across different cultures. And it's such a wonderful subject because it came about due to the ancient cultures looking up at the heavens and trying to understand what was going on up there to be able to model the motions of the planets. And that makes it the subject that's right at the beginning of where science starts to become an entity. So I'm curious if you could take me to the moment when you realized that the history of mathematics would become your life's work. Well, I was near the end of my undergraduate degree at a Canadian university, and it was a very intense program. In the last two years, I took something like 15 or 17 different math courses. And when I got to the end of that time, I found that they had been answering a lot of questions that I had never asked. So there was this whole wealth of knowledge that was completely untethered for me. I didn't know why we should. should be interested in one question rather than another. So I decided to basically go on a

belated teenage rebellion and switch into the history of math to try to find the answers to those questions and make the math meaningful to the rest of the world and the rest of culture. And, well, here I am 30 years later. In the 30 years since he started the quest to find more meaning in math, Glenn learned a thing or two about the history of counting. What do we know of the history of the history of of how we came up with the decimal counting system. What are some theories? Well, really, the simplest theory, which is almost certainly correct, is just hold up your two hands, and there you've got ten fingers. So for counting, it's as simple as that.

Base ten goes all the way back as far as we can tell from very ancient cultures. There were some ancient alternatives to that. You know, the famous Roman Neumannu, that we still use occasionally. That's a system. You might think it's base 10, but it really isn't. It's a system where you start by counting up to 5, and then you use 2 5s to get to 10, that goes from V to X.

Then you use 5xes, gets you up to the L for 50. So this is actually a system where you have an alternating base of 5 and 2. That's a lot more complex than base. 10. It's a little more complex, yes, which is why when you're reading the date that a movie was made at the end, it takes you a little while to figure it out. And the Mayans actually used a base of 20, which one can imagine if one wasn't wearing shoes, you could imagine where that came from. Right, hands and feet. There were also even earlier systems. Yes, that's right. The Egyptian number system may well be older than the system.

from ancient Babylon. This goes back earlier than 3,000 BC. There was a counting system in Mesopotamia, especially near Uruk, which started as a base 10 system. You go 1, 2, 3, 4, 5, 6, 7, 8, 9, up to 10. Then you count from 10, just like with the Romans,

you count not up to 100, but you count up to 60. So you need six symbols of 10, and then they would use a new symbol, which would be for 60. And so it would go back and forth, just like the Romans went back and forth between 5 and 2. The Babylonians went back and forth in this system between 10 and 6. And this system was the first of a number of counting systems that existed at the time that was converted into keneiform around the year 2,500 BC. And once it was converted, it was expanded into not just counting things, but also measuring quantities like weights and measures.

And finally, around the year 2000 BC, the tens and sixes came together, because using a mixed base is a really difficult thing to do when you're calculating. So if you combine the tens and sixes, it then turns into what's now called a sexagesimal system, which is a base 60. That sexagesimal system worked so well. It's still present in how we count seconds in a minute and minutes in an hour. But in arithmetic, measurement and money, base 10 is nearly universal. And yet, self-described dozen lists argue that base 12 would have been superior, because unlike 10, it's a highly divisible number, likely the same reason that dozen has been used and appreciated in everyday transactions for millennia.

We have 12 inches in a foot. We have 12 ounces in a pound, and those go back to ancient Rome, And I know somebody out there is jumping up and down and saying, wait a minute, there aren't 12 ounces in a pound. There are 16. But in Roman times, there were 12. And we still use this today for measuring precious metals. It's called Troy measurement.

And there are 12 Troy ounces in a Troy pound. And that word ounce comes from the Latin word unkia, which means a part of something. So an ounce is a part of a pound. And here's a bit of trivia. The word unkia is also the origin of our word inch. So for 12 inches in a foot, they come from the same Latin word meaning a part of something, and that meant a 12th of it.

You describe the number 12 as a, quote, friendly number. What does that mean? Well, the number 12 is willing to work with you in all sorts of different ways. Imagine you have 12 chocolate eggs, and you need to divide them among your kids. Well, if you have two kids, they each get six. If you have three kids, they each get four. If you have four kids, they each get three, and if you have six kids, they each get two. If you have five kids, you'll have to borrow a kid from the neighbor for a minute,

but it still is able to work and break things up in such a convenient way. If you have 11 eggs, you're in big trouble. You're 13 for that matter. Or 13. What about the word sublime? I was getting familiar with the number 12, and I found it described as sublime. What does that mean when a number is sublime? Oh, that's going to take a little while to explain.

It's a technical term. I have to first explain what a perfect number is. A perfect number is one, a number whose divisors will actually add up to that number. So, for instance, the number six divides evenly with three, two, and one, and three, two, and one add up to six. One plus two plus three equals six. So that makes it a perfect number. That makes it a perfect number. The number 28 is the next perfect number. I'll leave it as an exercise for your listeners to prove that. a sublime number is a number that has a perfect number of divisors.

And the sum of those divisors is also a perfect number. So if you take the number 12, its divisors are 1, 2, 3, 4, 6, and 12. So the number 12 has 6 divisors, and 6 is a perfect number. At the same time, if you add up those devices, 1, 2, 3, 4, 6, and 12, they add up to 28, which is also a perfect number. And if you can be a perfect number twice in one number, I guess that makes you sublime. This isn't a common condition for a number, is it? No, no, there are very few numbers that are sublime.

I mean, for me, every number is sublime, but in different ways. What a great answer. There are in fact only two numbers, two considered officially to be sublime. One of them has 76 digits. It was only discovered in 1995. It's 6086-5555-670-238. It'll take all day to say the full number. But you can find it on our website, cbc.ca.ca.

The only other sublime number is, of course, 12. A unique distinction, yes, but there's so much more that takes 12 into the realm of the sublime. Twelve makes a number of appearances in pop culture, in religion, in fiction, and nonfiction, everything from the 12 days of Christmas to the 12 people it takes to form a criminal jury here in Canada. But that fascination with 12 goes back a very, very long way. When you, Glenn, think of the past, what immediately comes to your mind when you hear the number 12? Well, the first thing that I think of is from Judaism, the 12 tribes of Israel. Jacob had 12 sons, and Israel was divided into these 12 tribes.

And from that, when the number 12 appeared, it was a sort of a symbol of wholeness or completion. Everyone was there. Everyone was included. And so this notion of inclusion and fullness got attached to the number 12. And of course, this continues in Christianity. We have 12 apostles. And even in the book of Revelation, you have 144,000 members of the redeemed community. And of course, that's 12 times 12 times a thousand.

Again, it's going back to this notion of it being complete. A complete or a whole number. Complete. whole, sublime, divine order. But I'm now left wondering, how did 12 come to inhabit such lofty spaces in so many contexts? My name's Ainsley Hawthorne. I'm a cultural historian and nonfiction writer based in St. John's Newfoundland and Labrador. I have a PhD in Near Eastern Civilizations from Yale University, and I've written for a variety of publications including National Geographic, The Washington Post, CBC, and Psychology Today.

To Glenn's list of holy 12s, Ainsley adds, In Greco-Roman tradition, you have the 12 gods of Olympus, the 12 labors of the hero Hercules. And among the Abrahamic religions, she adds one more. In 12 or Shia Islam, you have the 12 imms. Not to mention 12 comes up in Buddhism and in Hinduism. Do you have any theories as to why 12 keeps showing up in these religious traditions? I think there are a number of influences. believe the most important one is the way that 12 occurs in the natural world. Because the 12 lunar

months over the course of the solar year are so readily observable by people in different times and places throughout history, it isn't surprising that that would have picked up as an important aspect of how the cosmos is organized. And so you might incorporate it into a religion because many religions are about organizing and explaining the world. So if you, that the world already is partly organized in that way, it makes sense to extend it to religious beliefs, which is interesting because it shows how the material world can influence our abstract thought. We tend to think of religion as pretty symbolic. It is spiritual as opposed to physical, but I think this is a way we can see it was really influenced by the material

world. In the material world, we now know 12 is the number of particles that for the building blocks of all physical matter, all of it. They wouldn't have known that in the ancient world. But even in some of the earliest attempts to make sense of our universe, 12 appeared, like some kind of cosmic code, a code that led directly to how we keep time today. Our 24-hour clock actually goes all the way back to ancient Egypt. Egyptians divided their year into 12 months of 30 days each

for a total of 360 days. And the reason that they did that is based on something that was observable to people in many different times and places throughout history, which is the fact that there are 12 lunar cycles per solar year. So when people needed to measure a period of time shorter than a year, they generally look to the moon. There are consistent cycles of the moon waxing and waning, and naturally that takes about 29 to 30 days.

but peoples like the Egyptians wanted a more consistent version of the lunar cycle. So instead of just relying on what the actual moon was doing in the heavens, they systematized it and created a system of 12 months of 30 days each for a total of 360 days. Now, as we know, 360 days doesn't account for the whole solar year. The whole solar year is 365 and about a quarter days long. The ancient Egyptians knew that too, and so the way they reconciled the two was by inserting an extra month of five days at the end of every year so that they could match their 12-month calendar back up with the solar calendar. Each of these 30-day months was divided into three 10-day weeks, and these 10-day weeks were matched with stars that were rising on the horizon at the time each of the weeks was starting. We call these dechons today, based on the Greek word deca, meaning 10, because each of these stars was matched with a period of 10 days.

The Egyptians were using those stars to track time as early as about 2100 BCE. During summer nights, a total of about 12 deacons rose in the sky. So those could be used to track the passage of time overnight, and on the basis of these deacons, the night was divided into 12 hours. By analogy, the day was eventually divided into 12 hours two for a total of 24 hours in a day from one sunset to the next sunset. But something that's different from the way that we use time today is that the length of an Egyptian hour wasn't the same as hours. It changed throughout the year based on the changing of the season. So you have longer nights in winter and shorter nights in summer, regardless of the time of year, they always, was calculated 12 hours overnight, which meant that in winter the hours were longer, and in summer

the hours were shorter. Those nighttime hours and the number 12 took on a deeper meaning for Egyptian's eternal rest and the afterlife. The hours of night developed significance in Egyptian religion. The underworld is where the sun passes at night when it isn't visible to the living, and the Egyptians were of course very, very interested in what happens after death and specifically in giving people instructions on how they should handle their transition to the netherworld, what they can expect to see after they die, and how they should handle any people or creatures or obstacles that they encounter there. So we actually see funerary texts in ancient Egypt in tombs and in coffins

intended to help the newly dead navigate the underworld that talk about the hours of night and what they look like in the underworld. So there is a coffin text we call the hours of night, which is a funerary text that was included in some Egyptian burials. It shows a goddess for each of the hours of night, and each of the 12 goddesses is wearing a star on her head. So you can imagine an Egyptian woman with long hair in a dress standing upright with a star on her head representing that passage of time and the movement of stars through the heavens overnight. There's another text called the Amduat, which basically translates to what happens in the nether world that appears in Pharaoh's tombs in the New Kingdom period. And there,

each hour of night is associated with different gods, different perils that the Pharaoh needs to know about so that he can successfully make his way through the underworld past these 12 hours of night. Our eventual 12-based clocks developed with the help of innovations from other cultures, including the Mesopotamians. One of the innovations of the Mesopotamians was developing fixed units of time. So like the ancient Egyptians, the Mesopotamians divided night and day into flexible measures of time, that fluctuated with the changing seasons. So the units they used most of the time were we translate them as watches. There were three watches of the day and three watches of the night. So the watches of the night would be longer in winter. They would be shorter in summer.

But they also started dividing the whole day from one sunset to the next into 12 baru. Now we often translate the word baru as double hours since they had 12. for the whole day, the 12 equate to our 24 hours. So one baru is roughly two hours of our time. But what was different about Beru is that it was a fixed unit. So they were using Beru to mean specifically two hours of time. It didn't change seasonally. And the reason they chose 12 again was probably by analogy to the 12 months. It was a way of dividing time that pops up in the natural world. Ultimately, the inspiration that came from the natural world meant that 12 has repeatedly shown up in different contexts that nod to the idea that it symbolizes completeness. I think something that will be familiar to many people is 12 jurors in a court of law. Your right to a jury of your peers,

and we use the number 12 as the standard for the number of jurors to serve in our legal systems. system, that was actually adopted into our legal system from English common law. And the person who's normally credited with introducing a jury of 12 is the 8th century Welsh King Morgan the generous. And he supposedly based this system on the 12 apostles of Christianity, saying that Christ and his 12 apostles were appointed as judges of the world. Therefore, the king and 12 jurors should also be the correct system in a legal format to make decisions for the good of his subjects. Another example that people might be familiar with of the number 12 is that there are 12 stars on the EU flag. It's a circle of 12 gold stars on a blue background.

The EU flag that's used today was actually originally adopted in 1955 by the Council of Europe, which was kind of a precursor to the EU. the council had not 12 but 14 member states at the time. The reason they chose not to base the number of stars on the flag on the number of member states seems to have been because they acknowledged that the council could grow, that the number of member states might shift and change because indeed Europe has grown and continues to grow. So instead they adopted this circle of 12 stars.

And according to the description of the flag symbolism, at the time. The circle of stars represented the sign of union and the number of stars was 12 because it symbolized perfection and entirety. But you might ask, why did they consider 12 as a symbol of perfection and entirety? In 1987, one of the flag's designers, Arsend Heights, said in an interview that the European Union flag was the flag of Our Lady, referring to the Virgin Mary. And supposedly he was inspired by representations of Mary surrounded by or crowned with 12 stars. Blue also happens to be the color symbolically linked with Mary. Now, other people involved in the flag's creation, they reject this association, or they

say that, oh, Heights wasn't actually as responsible for the final design as he claims to have been. But it's very interesting that someone who was certainly very intimately involved with the process of the flag. In his mind, he was actually being inspired by Christian mythology. And even if it weren't specifically by the crown of 12 stars that Mary is sometimes depicted as wearing in Christian art, the 12 apostles in Christian tradition may have influenced this perception that 12 was the symbol of perfection, completeness, the ideal number of people. Cultural historian Ainsley Hawthorne, speaking to me as part of our

series the greatest numbers of all time. And as you'll hear, when it comes to music, there are few numbers as great as 12. This is Ideas. I'm Nala Ayad. Hi, Steve Patterson here, host of the debaters, and while I love a funny fight, there's one thing that's not up for debate. The Stratford Festival is world-class theater right here in Canada. Whether you're a fan of Shakespeare, musicals, or classics like Death of a Salesman or Waiting for Godot, there's no better time to experience Canadian talent and no better place to see it than the Stratford Festival. So get your tickets now at straptfordfestable.ca and experience world-class performance the whole family can enjoy. You know, we even tape the debaters there once, so I guess we're world-class now.

Surprise, it's me, Jan Carwana. I'll be filling in for Gavin Crawford this week on Because News. It's a news quiz show where we test the news knowledge of some of the funniest people across Canada. This week, I'm joined by comedians Martha Chavez, Tom Hearn, and Chris Siddiqui. I'll be asking asking about a new memoir from J.D. Vance. Trees from Ontario that smell like vomit. The reunion of the greatest prog rock band of all time and why protein is being injected into all our foods. Yuck.

Listen to me, guest host, by following Because News on Spotify, Apple Podcasts, or anywhere you download podcasts for free. You may not know the artist, but you may have recognized the pattern. 12-bar blues is a widely used musical structure in rock, jazz, and yes, the blues, that usually relies on three chords, played in progression over 12 measures. That is why it's long been the foundation for jam sessions,

enabling musical improvisation with little effort. But 12 is deeply embedded in music, far beyond jazz or the blues. 12 is, in fact, elemental to music, deeply in tune with sounds that appeal to human ears. I'm speaking with math historian Glenn Van Brumlin. I mean, we often hear how mathematics and music have a deep connection. But the number 12 has an especially deep connection with music, at least for Western music anyway.

Where does the number 12 fit in where music is concerned? If you take a group of people and all ask them to hum the same note, for instance, here's a note. And if you have an entire, audience singing that. Some people will sing this note. Others will sing this note. Right. An octave higher. It's an octave higher. That's the word for it. And if you play them together, they sound so harmonious together that we actually consider them to be the same note. Now, if you look at the lengths of the strings that this piano is hitting in order to play these two notes, you'll find

that one string, the high C, is exactly half the length of the lower string. That's if you look inside the piano and look at the strings that make the notes. Yes. Now, I am simplifying a little because it's not exactly the same kind of string in a piano. If they did, the piano would be 100 feet long behind you. But if you're using exactly the same string, then the high C-string is exactly half the length of the low string. And historically, this is what people believed to be why we appreciate music. The philosopher Godfrey Wilhelm Leibniz once wrote that music is a hidden practice of the soul, which does not know that it is doing mathematics.

Beautifully put. Yes. So we have this octave, but octaves are kind of boring. you need to have some notes in between. So we have chosen in Western music, and most cultures have chosen this, is to break that octave into 12 steps. So here we are.

We've got middle C. Imagine you're on a clock phase. And here we have the number at 12 o'clock noon. Then C sharp is 1 o'clock. D is 2 o'clock. D-sharp is 3 o'clock and so on. And as you count your way up, after 12 steps, you get to C. Now, the question is, why would you do it this way rather than another way?

Because if you play two notes beside each other, which are called a semitone, together, they sound awful. But it turns out, just by a numerical coincidence, that if you go from noon to six, seven o'clock on your clock of musical notes. That takes you from C to G. And they sound very nice together. And that's strictly a coincidence. The coincidence is that the string for G is almost exactly two-thirds the length of the string for C.

And that is a simple ratio. And again, Leibnett says, you know, we're appreciating the beauty of a simple ratio. when we listen to music. And this is actually the basis of a lot of Western music. Many Western compositions will use something called the circle of fifths. Now, going from C to G, that interval is called a perfect fifth. Okay.

You might wonder why it's called a fifth when I just said it was seven steps. Yes. It has to do with counting the white notes on a piano, keyboard or counting the black notes. So I'm just going to use the standard music terminology and call it a perfect fifth. So you can start at C. I'll go a lower one to have enough room. Then we go up seven steps to seven o'clock. You get G. Now do another seven steps. That takes you to two o'clock, and that will be D. Another seven steps from two o'clock. You get G. Now do another seven steps. o'clock takes you to nine o'clock, that's A, and so on. And if you do this long enough, you end up

getting an entirely new reordering of the 12 notes in something that's known as the circle of fifths. And if you move from one of these notes to the other, any one of these notes to the one beside it on the circle of fifths, it will sound very pleasing to you. So this is the basis of how chord progressions are often designed for music. If you want to move from one chord to another, a way to do this harmoniously is to move seven hours on your musical clock, and you'll get something that sounds harmonious. And this music trick goes all the way back, at least to Johann Sebastian Bach, his Brandenburg Concerto No. 2, all the way up to Salina Gomez. musicians all over the place will use this circle of fifths to create beautiful music,

and it only works with the number 12. And it isn't possible without those 12 steps on that what would be a chromatic scale? That's correct. I mean, if you tried to metricize music and turn it into base 10 with 10 notes in an octave, nothing would sound good. Right. So yet another kind of data point on this. idea that 12 is a complete but a sublime number.

Well, then, I mean, all of this music is sublime, so yeah, I'll buy that. Is there a piece of music that comes to mind when you think about the power of that circle of Hiff? One of my favorites is Frank Sinatra's Fly Me to the Moon. You're not going to make me sing, are you? Fill my heart with song. Let me sing for me. Is there ever more, you are all I long for all I worship and adore.

Is there something intrinsically about 12 that makes it ideal to be used in this way? I'm trying to, again, imagine what would have happened in the person's mind who decided that it made sense to have 12 steps on a chromatic scale. Again, that's lost to history, but I just told this story to my class yesterday, there is a legend, goes back to Pythagoras, who you might remember as being associated with the Pythagorean theorem in math. He's also, according to legend, considered to be sort of the originator a lot of this music. And the story goes that he went past a blacksmith shop. and as he walked past the blacksmith's shop, he heard the notes that hammers were making as they were hammering on the metal.

And some of these hammers, the notes they made as they hit the hammer, actually sounded harmonious together. And when he went off and weighed the hammers, he found that one hammer would weigh twice as much as another hammer or three halves as much as the other hammer, and they were making musical notes that correspond to those string lengths.

And from that, you know that roughly 712ths is the right kind of step to make, and then it's just natural to fill it in from there. But again, this is all, you know, all of this is hearsay and legend. Just if you just kind of unleash your imagination and think about whoever it was that came up with this, just how ingenious is it? It's something I could never have done. I mean, Pythagoras was using these hammers, and he came up with this ratio. The story then goes that he invented an instrument called a monocord,

which is basically one-sixth of a guitar, a single string with a movable fret, so you can change the note by holding down the fret, and you can measure the length of the string. but to be able to understand that what you want is 12 steps and not something else, that must have taken some form of genius, and we'll never know exactly how that happened. And not to really stretch the point, but without the number 12, piano just would not be piano. In fact, music would not be music.

While we're on the subject, beyond its hidden role in Western music, 12 does occasionally show up more explicitly in song. One of its greatest hits takes us back to religion and to a time when 12 played the role of peacemaker. On the first day of Christmas, my true love sent to me a partridge in a pear tree. Of course, it's really hard to think about 12 without thinking about the 12 days of Christmas.

And you've dug into this. and discover that there is more to the 12 days of Christmas than a partridge in a pear tree. Most of us today are only used to the 12 days of Christmas from the song because generally speaking, people who celebrate Christmas in Canada, they really only celebrated on one day December 25th. They may do things leading up to it and they may do things afterwards. but historically Christmas wasn't just one day. It was 12. It began on December 25th, but it actually

ran all the way until what was called 12th night on January 5th. And these days and all of the days in between them were holidays. In Europe, during the Middle Ages and Renaissance, all but the most essential workers would have taken the full 12 days off. Even monks didn't have to fast. They spent most of their year fasting, praying, doing penitents. but the 12 days of Christmas were considered a feast time for everyone. And they were celebrated with banqueting, with drinking. Lords would have hosted their serfs in their manor houses. All ranks of society welcomed guests.

They gave alms to the less fortunate, acting out the virtues of hospitality and charity. I understand, according to your writing on this, that the idea of having 12 days to celebrate Christmas actually came about almost as a diplomatic act within the Roman Empire? The 12 days of Christmas were invented as a way to reconcile the different liturgical calendars of the Eastern and Western parts of the Roman Empire. The Eastern Christian celebrated Christmas at the Feast of the Epiphany on January 6th. That was sometimes thought to mark the day of Jesus' baptism,

sometimes the day of his birth and sometimes the visit of the magi, the three kings who acknowledged Jesus as king of the Jews. Meanwhile, Christians in the Western Roman Empire were celebrating the Feast of the Nativity, the Feast of Jesus' birth on December 25th. When Christianity became the official religion of all of Rome at the end of the 4th century, churches on either side of the empire made both days and all the days in between them holy days so that they wouldn't have to do it. choose between the two and alienate one half of the empire. It was a historic feat of diplomacy, worthy of the special celebrations that ensued on those 12 sacred days. It was also a season of merrymaking and foolishness. When normal propriety was suspended in the social order was turned on its head, people went

house visiting sometime in costumes, so you have mummering in Great Britain and Ireland or Yule Bucking in the Nordic countries where people are going from house to house, singing, dancing, and exchanging entertainment for food and drink. The people in the houses that they were visiting would have been expected to kind of remunerate them with a nice quaff or a bite to eat for their troubles. And there was often a kind of class dynamic to these interactions where working class mummers were kind of demanding in a way hospitality from the local elites. And of Of course, people may be familiar with the fact that mummering has survived to this day in Newfoundland and Labrador in a way that is similar to the way it would have been celebrated in the past where people go door-to-door in costume.

Park, what's the noise out by the porch door? Granny tis mummers, there's 20 or more. Their old withered face brightens up with a grin. Any mummers, nice, mummers loud in. In Newfoundland, it was practiced the same. way over the 12 days of Christmas. You might have mummers going from house to house on any of those evenings, just visiting other people in their local community.

And the game here in this province was to try to guess who the mummers were. Have you ever gone mummering? No, but when I was a child, mummers came to my house. Apparently, I was terrified of them, which isn't really surprising. What they look like in Newfoundland and Labrador is people would just use whatever they had lying around their house to disguise their identities. So they would often wear something like Long John, stuff pillows into them to change their body shape. They might wear underwear on the outside of their clothing for fun. They would cover their faces with pillowcases or lampshades or

doilies, whatever you had that you had some way of kind of seeing through. And then what they would do is speak while inhaling instead of exhaling to disguise their voices. It would be kind of a fun game. because you knew everyone in your community, there was a lot of trust that was able to allow for cultural practice like mummering. It's become much more difficult in modern Newfoundland and Labrador because, say, in a city like St. John's, where there are a few hundred thousand people, people don't know their neighbors as well. So it's not as easy to do that anymore, but instead there's an organization in St. John's that has founded an annual mummer's parade. So people can still dress up in traditional costumes.

And instead of visiting houses, there's a big parade, which has taken place in the downtown area. And the past few years has been through one of our big parks. So it's still a nice way to do parts of the tradition. Everyone still dresses up, gets together, has a scuff and a scoff, which is a little dance, a little bite to eat, and just enjoy that tradition in a little bit of a different format. The traditional Christmas celebration in the Middle Ages ended with 12th night, the climax of the festivities, marking the feast of the epiphany. It was often a topsy-turvy party that inspired the name and likely the plot of Shakespeare's play, 12th night. If music be the food of love, play on, give me excess of it that surfeiting the appetite may sicken and so die.

On 12th night, this would kind of be your big blast before the 12 days of Christmas ended. People often ate what was called 12th cake, which was a spiced fruit cake with a bean baked into it. And whoever got the slice with the bean was crowned king of the bean and was the leader of the night's festivities. So it would be their role to keep the fun going to suggest crazy things for everybody to do. Sometimes a pea was baked in too to select a queen. of the peas, so you would have both a man and a woman or a boy and a girl who would be kind of leading everyone's celebrations. 12th night was the eve of January 6th, the feast of the Epiphany, which over time and in different places was said to mark different things,

one of the things people are probably most familiar with is the idea that it commemorates the visit of the three Magi, the three wise men, to the baby Jesus. And so Epiphany was also a and that was sort of considered the clue up to the Christmas period, although in some ways people sometimes extended their celebration a little longer as late sometimes as February 2nd. Twelve may have brought Christians together in Roman times, but in 18th century France, it divided people. When post-revolution, the government imposed the base 10 metric system, doing away with base 12 measurements. And for a short time, even the 12-hour clock became decimal, with each hour making 100 minutes. An episode in history when 12 became decidedly political.

French Revolution is a very complicated thing, but in part it was an uprising of the people against the upper class. And one of the things that was happening at this time was that there were all sorts of different systems of weights and measures and distances and so on going on, a giant historical hodgepodge of systems. And this gave opportunities for those who had the power to take advantage of this and gain financial resources through transactions where they were allowed to determine the rules. So after the French Revolution happened, one of the things that they decided to do, was to have a universal system of weights and measures and distances that would apply across all

parts of France all at once. This was what we now use, the metric system. But the number 10 wasn't the obvious choice. There was actually a debate between the number 10 and guess what? The number 12. So there are lots of proponents for both. I mean, the number 10 seems so obvious when you look at your fingers. But in fact, you can look at your hand and see a base 12 number system looking at your hand. There's an Asian system of counting. If you look at your palm of your hand, you've got four fingers with three bones each in them. You can use your thumb to count along each of the bones in your finger,

and there you go. your hand has produced a base 12 number system. So there's this debate going on between 10 and 12, and one of the mathematicians involved in this debate, Joseph Louis Lagrange, we think he was probably just trying to be provocative, he said we need to compromise between base 10 and base 12, and so he suggested base 11. Pretty much the unfriendliest number,

and he was making a point, because there actually is an advantage to choosing base 11, And that is, if you're using base 11, you will never have to reduce a fraction because 11 doesn't divide down into anything else. But base 11 is so awkward that you can even, even if you try to write the number one half, it's going to be an infinitely expanding base 11 fraction. And believe me, you don't want to deal with that. But ultimately, it was the base 10 system that prevailed. It was base 10, yes. The adoption of the metric system was just one of many milestones

on a centuries-long process that eventually made base 10 most of the world's numerical system. Others include the spread of decimal-based currencies. First, in Russia, in 1704, when the Russian ruble was standardized to equal 100 COPEX, followed by the U.S. in 1792, and Canada, which in 1858, discarded by the Russian rubble, discarded the British 12 pence shilling in favor of 100 cents to a dollar. Now, that doesn't mean that base 12 has gone away. There are two societies called dozenal societies, one in America that started back in 1944,

another in Great Britain started in 1959, who are still promoting a dozenal system of arithmetic today. And what's driving that? It's the same thing. 12 is a friendly number. Computations become a lot smoother than they are in base 10. But it comes down, I think, in the end, to how are you going to convince an entire world system that learned base 10 since we were in preschool? How are we going to convince everybody to throw all of that out for the seemingly marginal advantages of having a slightly more efficient number system?

So while I appreciate what they're trying to do, I don't think this is a goal that's ever going to happen. It may not be practically possible, but if you could wave a magic wand and choose, is there a system that you think would be better? Oh, absolutely. There's no question. Base 12 would be a better system. It has all the advantages of the base 60 system that the Babylonians use without the disadvantage of having to memorize hundreds of products along the way. I'm surprised to hear you say that, to be honest. Yes, that's right. I mean, I'm not going to reinvent my entire system of knowledge to convert to base 12 now.

But if after I was born, if as a baby I knew what I did now and I could make a choice, I'd go straight to base 12. One last thing. You are obviously passionate about numbers, and I'm just wondering why we should care about the stories of numbers like 12. Well, this is something that comes up a lot in the course that I teach right now, mathematics for elementary teachers, and a shout out to my classes. Those students, the ones who become your kids' teachers in elementary school, tend to be afraid of mathematics because the system in which they learned mathematics didn't work for them. It tended to be sort of an algorithmic pattern of calculations that didn't have a connection. to something in their world so much.

And so what's important, I think, to be able to speak to those people and others who, for whom mathematics has not been a friendly subject, is to see how deeply numbers and relationships in mathematics are embedded in everything around us. We should be learning mathematics by seeing these relationships out there in the world, and then we can connect our mathematics to something that we can see with our intuitions. I think we need more of this. So the number 12 is one of those examples. You know, when you factor the number 12 when you were in grade 6 or something, you said, oh, it has a lot of factors, and then you moved on. but if you knew that that had such a rich historical influence and makes a difference in your life without you even noticing it, then it's going to be something meaningful that's going to stick with you,

hopefully, for the rest of your life. I'm so grateful to you. Thank you so much for sharing with us. No problem. It's been a great pleasure. That was Glenn Van Brumlin, professor of mathematics sciences at Trinity Western University. Thank you to Glenn. and to cultural historian Ainsley Hawthorne for making this episode possible.

This episode was part of our series, the greatest numbers of all time, which also features 4, 13, 27, and 33,000. You can find the full series and a vast array of our podcasts on our website, CBC.ca.ca.com slash ideas, or wherever you listen to podcasts. Please review or follow ideas on your favorite podcast out. Thank you to Tom Howell for technical assistance. Lisa Ayuso is our web producer.

Technical production, Emily Kiervasio, our senior producer, Nicola Luxchich. Greg Kelly is the executive producer of ideas, and I'm Nala Ayyad. For more CBC podcasts, go to cbc.ca.ca.