Objectivity Videos: th-cam.com/users/objectivityvideos Patrons can enjoy some extra pictures and scans from this video here: www.patreon.com/posts/115548802 Rob's book Much Ado About Numbers... Amazon: amzn.to/3zFinog
It kinda makes sense, though, given how far away England is from where this number system originated. It had to metriculate its way thru the rest of Europe (from Greece and Turkey all the way west to France) before reaching England. Each city, town and village along the way needed some amount of time to get accustomed to the new system before it went viral to the next population center. Given, also, that this was during a time long before the arrival of the internal-combustion engine and, first, telegraph/telephone cables and, later, fiber-optic cables, the average speed of information-sharing was somewhere between a human's walking pace and a horse's full gallop -- as had been the case for millennia many prior
@@shruggzdastr8-facedclown Arabic numerals did not spread town to town the way spoken vernacular spreads. They spread from one scholarly community to another by distribution of written manuscripts and occasionally books. The reason the spread was so slow was the limited knowledge of Latin in England and, more importantly, the inability to print much in volume. Uptake of Arabic numerals in England was rapid following the invention of the printing press. It's worth pointing out that it wasn't just England that rarely used Arabic numerals before the 15th century. That was true in all of Europe outside of Al-Andalus, even in Greece. Italian merchants did adopt Arabic numerals earlier due to the influence of Fibonacci, but the general literate public did not. It never had any significant spread outside of Italy until after the invention of the printing press, when it started to spread in incunabula. The thing is, even a century after these started to become mainstream in England, they had not displaced Roman numerals, as you see here. Both continued to be used by most literate people, and to some extent, they still are (though Arabic numerals had displaced Roman numerals for most purposes by the end of the 18th century).
I have a feeling it is not so much a mistake but a deliberate convention. If it were a mistake is would be a one time thing but in his chart X=X and then it appears in the text. Also it keeps the number to be a single digit taking up less space, which is part of the efficiency to use Arabic numerals in the first place. I say this since I made a program once for cards and 10 is the only card that needed two spaces (annoying for what I was trying to accomplish) so turned it into an X. There are benefits to its usage.
It also shows that he's still using x for 10 so he doesn't throw anyone off. He's made so many changes to his accounting it's important to let people know what hasn't changed.
@@LarsHHoog Ah so the animation at 10:55 is misleading, but the audio may be correct. The missing carry is in the tens digit of 12345 x 2 = 24690 not 24680
@BobStein the animation is also wrong, the issue is not the addition of the numbers, but the first multiplication itself. Like @pcsledge mentioned the 8 should be a 9.
A point about the multiplication exercise... Since Roman numerals don't work like that, he was likely doing it to better learn how to, given the new methods the new number system allowed.
You made a mistake in explaining the mistake. The missed carried 1 wasn't on the first line, multiplying 3 by 12345, but in the 2nd line multiplying 2 by 12345. He forgot to carry the 1 when he multiplied 5 by 2 to get 10. The 8 when multiplying 4 by 2 should have that 1 added to it to become a 9.
Fun (?) fact: the "long tail" of the 1 looks perfectly normal to me, and probably to most French people too. And if you wonder how we differentiate our 1s from our 7s, the question's never occurred to me (not the same angle?), but 7 has an extra dash anyway.
Yes, came here to say the same thing. All my mainland European friends and acquaintances will write a 1 with a tail, often more so than the example at 7:40. And I am in the habit of putting a dash through a 7, even though that's not how I was taught in the England of the 1950s.
I thought the figure he pointed at was actually a one with a 'cap' rather than a tail. Ones can still be written today with a cap, but if so they usually also have a horizontal base added to help differentiate them from twos. I also put a dash across my sevens.
3:33 I think what's interesting is the use of the more convenient modern script for years, which if written out in roman numerals can prove to be quite long, while sticking to roman script for everyday accounting numbers which are more important to get right in the short term.
One of the fun things I found browsing around the Digital Vatican Library on-line was that things that looked _exactly_ like Excel Spreadsheets went back even further than the use of Hindu-Arabic numbers in Europe. The only difference was that the had separate columns for I, X, C, M etc, to make the math easier.
10:58 He made a mistake in the multiplication, not in the final addition. 3+0 = 3, 0+8+5 does equal 3 (carry 1) and 1+7+6+4 = 8 (carry 1), so that would be correct. The problem is the 8 in 24680. That should be a 9, because 2x5 = 0 *_(carry 1),_* 2x4 *_+1_* = 9 (not 8). So he forgot to carry the 1 there. The number 10 was definitely his weak spot :D
I love these videos about the history of mathematics (and science). I hope you'll make more! The Objectivity channel has been great for the same reason.
7:40 I was taught to always write a 1 with the top serif. Never had a problem until one day I was filling out a form at an office and the receptionist got snippy with me that I had "written the date wrong". I hadn't, she'd just assumed my 1 was a 7 (despite my writing an actual 7 nearby, again the way I'd been taught, with a crossbar). When I told her that was a 1, she said in an annoyed and condescending voice that my 1's look like 7's, then made a point of thickly scribbling a fat vertical line over it. Anyway, all this to say, that one looks perfectly fine to me and it does *not* look like a 7.
Draw a foot serif on a one if you draw the top serif, that is what I do. And I write months in letters, cos 12 10 2024 means December or October, to an American or a Brit. But everyone can figure out Dec 10 2024!
I grew up in Australia, but now live in Europe, so I had to start adding the serif on the 1. I've always written a line/bar through the 7 though for clarity since my handwriting is awful, but I can totally appreciate your story as I've made the same mistake when I've forgotten to switch back to my old habits for forms in Australia or the UK!
few people know this but Shakespeare was the first non-royal person to own a stake (12.5%) of a theater in the UK, putting together the "content creation" with the "content distribution" for the first time. The Globe was like the iTunes of the time
I can't say for sure about Shakespeare's times, but comparing the three pounds made by the Shakespeare play to some examples of the value of money a hundred or so years later (from Liza Picard's book "Restoration London"). In the 1660s, one penny would buy you a loaf of bread, or a pound of cheap cheese, or a few herrings. A pound of bacon was nine pence. A roast beef dinner for four in an inn was five shillings. A pair of boots cost 30 shillings. Samuel Pepys paid £24 for a silk suit at some point. A servant or maid earned about £4 per year (960 pence), a shopkeeper or tradesman about £10 per year, a layer £22 per year.
@@widmo206 Yeah, the three pounds was the recorded total for the "posh seats". In a 1660s theatre, the expensive seats were four shillings (48 pence) in a box or one shilling (12 pence) in the gallery.
Those numbers are really interesting! A typical loaf of bread is about £1.75 today, and you would be hard pressed to find any cheese for less than £3/pound. But if we say that a penny in the 1660s is about £2 today, then the lawyer's annual salary would correspond to only £10,000 today. Or conversely, if we normalize the conversion on a lawyer's salary of £50,000 (which is the current average), that would mean that a loaf of bread in 1660 was worth almost £10.
They're the sort of thing that teachers put in to make it easier to see what's happening, and get used by people who don't do much hand calculation, but which get quietly dropped by anyone actually working with numbers as so much wasted ink.
Number systems are great - it's fascinating how different cultures have developed different systems to count and then to make their way of writing those numbers simpler.
The bar in the "1" in handwriting is the normal here in Germany and I think many other European countries too. We make an extra line across at the 7 like a wonky plus with a ribbon 😅 I kinda like that more then the "I" as a one, cause it has somehow more structure as a symbol imo 😅
Mmm... in France I've seen the '1' bar go all the way down to the baseline -- /| -- so it's sometimes longer (by Pythagoras) than the upstroke. I write a normal 1 with a short bar or no bar, but I always cross my 7 as well. And sometimes my zeroes, but that's more a programmer thing!
That is absolutely fascinating. He's heard of a new technique and is playing with it to see how much easier it is to use than the old way of doing things.
What an incredible artifact. One of those concepts I never would’ve thought about, but when pointed out is astounding. And it being theatre-related is icing on the cake.
They are in Dulwich College, which was founded by Edward Alleyn, who acted leading roles in Shakespeare and Marlowe, and which is where PG Wodehouse and Raymond Chandler went to school.
11:32 - at least three performances of The Jew of Malta by Christopher Marlowe are listed there in Feb-Mar 1591, quite soon after it was written. Fascinating, thank you.
I had to chuckle at the "scripty one" with the "long tail" that took a long time to disappear. Guess what, it many handwritten scripts it hasn't disappeared 🙂 In German-speaking countries, people still write "one" with a flag, and "seven" with a longer flag and, to be really sure, a bar crossing the stem.
I (also German) learned to write 'one' as a diagonal line going up and right from about the middle of the space to the top and then a vertical line down (to be honest not that different from how it looks here: 1, just the diagonal is longer) and 'seven' as a horizontal line at the top going right, followed by a diagonal line going left all the way to the bottom and then cross out the diagonal somewhere in the middle (also like '7', just with a crossed out diagonal to keep it distinguishable from 1 when you write it sloppily)
I love that he was practicing the multiplication with the new numerals. A huge multiplication like that would have been a nightmare to calculate in Roman numerals, so I suspect it must have been quite novel and amazing to people of that time to see how useful this new number system was!
the „1“ with the long tail is actually still a thing outside the UK/US, in german speaking countries it‘s quite common. To avoid confusion, 7s are written with a horizontal line.
2:40 why does the screen shake with random zooming in/out? Is the camera guy shaking it on purpose and actually pushing the zoom in and out? Or is it done after recording for some design decision?
6:02 In Greek, a final sigma takes a different form. Four Hebrew letters have different final forms. I don't know any more about why this is, but it is not an isolated practice.
When I was at school (many, many years ago) I was taught when adding up to put a dot over the appropriate column if I needed to carry one. In the case of the £211/9/0 I think the dots are carries.
It's interesting that Roman Numerals went on to become the sort of upper class or more formal method for a very long time. Like you might see Chapter XV in a book or MDCCCXLII on a building.
This had me curious. I never thought before about how arithmetic would have been done in Roman numerals. Perhaps a following video on how to multiply xiv b iil
8:40 The dots on top of the 1's are not because he's romanised them, it's surely because as he's done the addition these dots represent the carry over. I do the same thing since it's faster and smaller than writing a 1.
The example of unit systems coexisting is a good example of things transitioning as needed and fluidly. Another good example is that we are still using Roman numerals today
It was interesting the Henslowe aways used the new numerals to write the year of the performance, since one of the places were Roman numerals are often still used is to write the year for the copyright at the end of the credits of a film.
For a moment I also thought that those dots were carries but it made no sense to not write the one on top of the leftmost 2, unless the writer had forgot it. However, I checked the video and at 3:38 the dots appear over the 1. They also appear thereafter. Therefore, those dots are not carries, they are part of the 1. Go figure.
For a second there, I thought I had forgotten 2nd grade arithmetic. The mistake in the 12345 x 123 problem isn't a forgotten carried 1 from 3x3, but the forgotten carried 1 from 2x5 in the row below, which should have read 24690.
Oh reminds me of reading a letter to the King of Portugal regarding the "discovery" of Brazil, happened and written in 1500, I was surprised to see it used Roman numerals still and was curious to see when the change happened... I haven't watched it fully so maybe it will be mentioned too but iirc Russia used Cyrillic numerals up until the 1700s?
I think the reason marking the ends of numbers was important was that words and units were made of the same symbols. If the gap is a little small and the next word starts with a letter used in Roman numerals, it would be easy to misinterpret.
The j as 1 at the end in lowercase Roman numerals lasted well into the 19th century I believe, and is more like a flourish than anything else. Remember that I and J were not seen as separate letters until relatively recently. Same with U and V
Well, if you were the one that wrote that, you probably know from the context, for exaple, in that notebook, years were written in arabic and money in roman
@@unvergebeneid That's true too :D, though in that guys case he had a system he was keeping to, so, assuming he didn't quit the job and stop doing it, he wouldn't have forgotten that easily
Actually, this way of handwriting the ones and the nines is still common in the Netherlands. A q goes strait down (like your nine), a nine has a bend to the left (like in your manuscript) and a g has a curl backwards (so it forms 2 circles). Besides, a Dutch 8 will start in the center and both end do not have meet.
These indo-arabic numerals have standardised to today's. In the Royal Society library there is a 1473 almanac which demonstrates the introduction of numerals for calculating Easter alongside Roman numerals, but in that book the '4' is different - it looks more like an 8 with the bottom cut off. 7 is an upside-down V (like modern Arabic) and 5 is different, too.
@@ThomasRichardson-lj1ig 4, 5, and 7 in medieval texts often looked different. You can find the old bowtie 4 on early dated coins, paintings, some manuscripts. I don't remember seeing any printed books or incunabula with it but there probably are some. The Prague astronomical clock has the medieval numeral forms on it as well.
@@JohnMichaelson Sorry, I meant I was specifically interested in the book as an introduction of Hindu-Arabic numerals. I find the transition between the two types of numerals interesting, and I'd love to see many primary sources.
@@ThomasRichardson-lj1igMy reply got deleted when I added the link. But search for Objectivity John Green, and the book I'm talking about is at 2: 37 of that video.
I must admit I'd never realised this transition even happened. We are so used to our current numerals. I vaguely sort of assumed that Roman numerals left when the Romans did! And of course potentially the final remaining use of Roman numerals today is when you carve the date your house was built?
At grammar school in the mid '60s we explored different systems of numerals and bases, and Roman numbers were part of that. Trying to do Roman arithmetic - especially multiplication (forget ever doing division) - was such a pain that I am delighted I have forgotten how we were taught to do it. 6:10 I still have the Midland Bank guide to writing a cheque - given to me when I signed up in '71 when beginning university. It was multi-paged and of the aspect ratio of a cheque. The recommendation was to use a dash rather than a decimal point, to write the pounds in words and the pence (we had _just_ gone decimal) in numerals. If there were no pence the word _only_ was to be used instead. A scribed line to the end was suggested. 10:38 Tut tut! Not casting out nines to check. Is the suggestion that we got joined up writing bceause raising the qulll caused blots? I can do joined up writing but it is a write-only system.
I'm pretty sure the transition happend much earlier, at least on the continent. Since the 15th century Arabic numerals were commonly used for dates and were definately used in accounting and banking.
Even now in UK primary schools we still use a bastardised version of Roman numerals to teach how a positional number system works and wonder why children find arithmetic so hard - we need to get rid of Dienes blocks (sometimes called base10 blocks.)
A fascinating video would tell the story of how Arabic numerals spread throughout Europe. Considering that Fibconacci introduced positional notation to Europe in 1202 in his book Liber Abacci, what took it so long to come to England? I know this is a broad topic but an important one in the history of math and science. When Newton was Master of the Royal Mint, was he still recording financial data in Roman numerals?
No. At least I don't think so. English coins used Arabic numerals almost from moment numbers of any kind were ever put on them, and that was more than a century and a half before Newton came along.
When people learn of Fibonacci's Liber Abaci, they often get the wrong impression that Hindu-Arabic numerals spread rapidly from then on. But that is in fact not the case. It was not until the printing press that Hindu-Arabic numerals started spreading rapidly and came into widespread use across Europe. In the 13th century, Hindu-Arabic numerals became used in Abacus schools in North Italy. But beyond that, the general public (and other European countries) largely did not use it until it spread following the printing press.
There was a relatively long period where there was not much progress in mathematics in England, between Thomas Bradwardine (c. 1300 - 1349) and Robert Recorde (c. 1510 - 1558). Robert Recorde largely established the English mathematical school. He wrote several popular math textbooks, and he helped popularize the Hindu-Arabic numerals, as well as the already-existing plus (+) and minus (-) symbols, and he invented the equals sign (=).
Have you ever tried to score bowling with Roman numerals? The second ball per frame is a huge pain on those tiny sheets so I would recommend being very good or very bad.
1:20 or so, I do think that could be accounts of something! In front of 1000 for ex. there is "of" and after the dash we have 14. So let's say that those could be tallies of how many performances had a certain amount of people (rounded down) seated in the theatre. So 14 nights had 1000, 1 had 900 (cause it's not too likely for something to be hyped enough to get 900, but somehow not hyped enough to get 1000) and only 1 night had a measly 30 people. I'm not saying that is what this was, just trying to show how he could have gotten this data. It could be for (effectively) graphing out and getting a sense of how many people were seated. He wanted extra precision on the low end, or more likely didn't wish to bother graphing out every set of 20 all the way to 1000. (Or could be the amount of money gotten per night, or anything else. I just used an example to get the point across. I didn't translate the text above it.)
At 3:40, does the top line read ‘29 of february 1591’? You can also see it clearly at 3:16 between ‘28 of february’ and ‘1 of march’. But 1591 wasn't a leap year.
That addition at 8:26 why there aren't dots over "11" in 2nd row tho? Wouldn't they rather mean to remember to add 1 in the column with dot? I do something like that (but just write 1 above instead)
Astonishing that within just a couple of generations of adoption of Hindu numerals (late 1500s) we have Newton(1660s) developing calculus! Also I wonder how Napier got to log when roman numerals were the more commonly used system.
As a follow-up to this - is there a reason why TV programmes in the UK used to (or perhaps still) showed copyright dates with Roman numerals? e.g. the end credits to the last episode of Blackadder Goes Forth are simply "(C) BBC TV MCMLXXXIX", rather than 1989. Why is this transition still going on, five hundred years later?
To be honest it was a lot more interesting in the 1400s when the forms of the numbers were different. '4' looked like a bowtie, something like an awareness ribbon. '5' looked like '7', and '7' was an upside down 'V'. The earliest dated European coins used Roman numerals all through the 1400s, but in 1424 one city minted the first using Arabic numerals. Finally by 1500 just about everywhere had abandoned Roman numerals on them.
Oh actually, when you said cards, maybe that was the reason for X, if you ever dealt with playing cards 10 is the odd 1 out, if you are drawing them, 10 always messes with the edges of the card, for notation you want a single number/letter for every card, which is why we use T for Ten today, and stuff like that, which is why I guess it could have prevailed
Re. the dots above the number 211 in the money addition. I think those dots marks that there is a carry (carryover). He did not dot any of the other 1s. ps. It also looks like he used a dot (and missed it) in the multiplication that went wrong :)
I'm wondering if in the arithmetic with the two dots above the 1's that those are carry marks, since there was a carry from the shillings to the pounds and then another carry.
I don't think he was being random in his mixing of numbers. He used denary where it was a lot shorter, and the more familiar Roman numerals where it didn't make much difference (or even shorter as with the X for 10 on the clock face).
Maybe they had trouble wrapping their heads around the concept of 0 at first, so they kept using X for 10 alongside Arabic numbers, and the habit stuck around even after they adopted 0 for other numbers? The diary isn't really mixing up the two systems apart from that specific case, and 1/I which does look similar in both
7:40 - 7:44 Doesn't scripted 1 on the Continent still looks like that? It's why they put a dash through the vertical riser. 10:19 In the 1970s, we (in the US) were taught that we could skip the placeholder 0s.
I’ve often wondered why it took so long for Indo-Arabian numbers to get general Europe use. After all, Spain had been under Moorish control since the 8th century. Was the resistance to change driven by dogma?
7:37 confusing to any Germans, since that is literally how they still write these both 1 and 9. (also note how they look kind of like this when you type them)
I always wondered if and how people did floating point math with Roman numerals, thing like long division and such. Or were they constrained to integers? Can you do a film on this?
At 6:05, he mentions something called “checks”, and it sounds like they were a form of money or receipt. I wonder if Keith would have examples at the Royal Society archives? Could be an interesting topic for Objectivity. :)
You can still use cheques. You basically give a cheque to a person or a company with the amount you want to pay and hope you have the money in your account when your bank receives it.
Really interesting! Could the slip of using x instead of 10 when all the other numerals were arabic be because the numeral of zero was also a new concept?
This is fascinating. I'm a numbers guy and a calligraphy enthusiast. I'm totally out of my depth trying to read these numbers on the page. Makes me wonder what people would think of my scratchpad 400 years down the road if they happened upon it.
This could have been before the letter j was really considered a separate letter from i, so it wouldn't have been confusing to use a j in place for an i
Being able to easily multiply numbers easily must have seemed amazing back then when moving to the new number system. This guy seems to have embraced the new numbers but at times he was still thinking in the old system. x=x is understandable as he might want to use a single digit for X instead of needing 2 digits for 10. Especially if he really didn't want to lift the pen.
7:37 Well, that form never really did go away in some places, did it? That seems pretty typical in France. Certainly it looks more like a French 1 than a French 7.
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Please can you tell him to wear GLOVES when he touches the pages!!!!!!!! This is our history!!!!!!!!!!!!!!!!!!!
This conversion to the modern system came much later than I thought, very interesting!
It kinda makes sense, though, given how far away England is from where this number system originated. It had to metriculate its way thru the rest of Europe (from Greece and Turkey all the way west to France) before reaching England. Each city, town and village along the way needed some amount of time to get accustomed to the new system before it went viral to the next population center. Given, also, that this was during a time long before the arrival of the internal-combustion engine and, first, telegraph/telephone cables and, later, fiber-optic cables, the average speed of information-sharing was somewhere between a human's walking pace and a horse's full gallop -- as had been the case for millennia many prior
@@shruggzdastr8-facedclown Arabic numerals did not spread town to town the way spoken vernacular spreads. They spread from one scholarly community to another by distribution of written manuscripts and occasionally books. The reason the spread was so slow was the limited knowledge of Latin in England and, more importantly, the inability to print much in volume. Uptake of Arabic numerals in England was rapid following the invention of the printing press.
It's worth pointing out that it wasn't just England that rarely used Arabic numerals before the 15th century. That was true in all of Europe outside of Al-Andalus, even in Greece. Italian merchants did adopt Arabic numerals earlier due to the influence of Fibonacci, but the general literate public did not. It never had any significant spread outside of Italy until after the invention of the printing press, when it started to spread in incunabula.
The thing is, even a century after these started to become mainstream in England, they had not displaced Roman numerals, as you see here. Both continued to be used by most literate people, and to some extent, they still are (though Arabic numerals had displaced Roman numerals for most purposes by the end of the 18th century).
that X = X mistake is such a relatable mistake, looks perfectly fine until you read it back a day later...
I have a feeling it is not so much a mistake but a deliberate convention. If it were a mistake is would be a one time thing but in his chart X=X and then it appears in the text. Also it keeps the number to be a single digit taking up less space, which is part of the efficiency to use Arabic numerals in the first place. I say this since I made a program once for cards and 10 is the only card that needed two spaces (annoying for what I was trying to accomplish) so turned it into an X. There are benefits to its usage.
It also shows that he's still using x for 10 so he doesn't throw anyone off. He's made so many changes to his accounting it's important to let people know what hasn't changed.
Hey, it worked for Apple's iPhone numbering!
It’s the Laurie Anderson Theorem
1 Doge still equals 1 Doge
iykyk
At 10:48 the actual mistake is that the "8" in 24680 should be a "9", so 24690.
He may have doubled then from right to left and forgot about a carry from 2×5
@@LarsHHoog Ah so the animation at 10:55 is misleading, but the audio may be correct. The missing carry is in the tens digit of 12345 x 2 = 24690 not 24680
@BobStein the animation is also wrong, the issue is not the addition of the numbers, but the first multiplication itself. Like @pcsledge mentioned the 8 should be a 9.
@@BenjaminNagelBN ...because in multiplying 12345 by 2 there's a carry from the 1's place to the 10's place. That's why the 8 should be a 9.
the audio is also incorrect as it's going through the rightmost digits of 12345×3 instead of considering 12345×2
A point about the multiplication exercise... Since Roman numerals don't work like that, he was likely doing it to better learn how to, given the new methods the new number system allowed.
I can imagine his delight to see multiplication done so easily. Multiplying Roman numerals must have been a nightmare.
Surely the dots in the addition at about 9:10 are the carried ones from the previous column.
Seeing tidbits of normal everyday life from long ago is the most fascinating part of history for me. Great video!
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the j at the end instead of the last i: foreshadowing electrical engineers.
Compare also the Dutch “ij”, as one of its origins is the long-i.
Linguistically at this time J was just considered a special kind of I. So it makes more sense than it seems.
@@DruHarden In Italian J is still called 'I lunga' - long I - to this day (and used very rarely/archaically where 'I' has a semi-consonantal value).
to me it is similar to arabic writing, where the last letter of a word often has a curvy tail added
@@deinauge7894also Greek sigma!
You made a mistake in explaining the mistake. The missed carried 1 wasn't on the first line, multiplying 3 by 12345, but in the 2nd line multiplying 2 by 12345. He forgot to carry the 1 when he multiplied 5 by 2 to get 10. The 8 when multiplying 4 by 2 should have that 1 added to it to become a 9.
Exactly. I was getting so confused about the man's explanation.
thank you ❤
I think we need a name for this. How about Parker Multiplication?
I never really realized there was an transition from roman numerals, but as soon as I saw the title of this video I was interested! Great stuff
Fun (?) fact: the "long tail" of the 1 looks perfectly normal to me, and probably to most French people too. And if you wonder how we differentiate our 1s from our 7s, the question's never occurred to me (not the same angle?), but 7 has an extra dash anyway.
I write a seven with a dash through it, but I would never write a one anything like a seven. That just looks ugly and confusing.
Look at the computer digit 1. Even here in this line.
It doesn't look like a l and not like a 7.
same for Germany
Yes, came here to say the same thing. All my mainland European friends and acquaintances will write a 1 with a tail, often more so than the example at 7:40. And I am in the habit of putting a dash through a 7, even though that's not how I was taught in the England of the 1950s.
I thought the figure he pointed at was actually a one with a 'cap' rather than a tail. Ones can still be written today with a cap, but if so they usually also have a horizontal base added to help differentiate them from twos. I also put a dash across my sevens.
3:33 I think what's interesting is the use of the more convenient modern script for years, which if written out in roman numerals can prove to be quite long, while sticking to roman script for everyday accounting numbers which are more important to get right in the short term.
I love Brady's videos. He asks the kind of questions that the viewer would ask.
One of the fun things I found browsing around the Digital Vatican Library on-line was that things that looked _exactly_ like Excel Spreadsheets went back even further than the use of Hindu-Arabic numbers in Europe. The only difference was that the had separate columns for I, X, C, M etc, to make the math easier.
yup! ledgers are so cool and I kinda want one
10:58 He made a mistake in the multiplication, not in the final addition. 3+0 = 3, 0+8+5 does equal 3 (carry 1) and 1+7+6+4 = 8 (carry 1), so that would be correct. The problem is the 8 in 24680. That should be a 9, because 2x5 = 0 *_(carry 1),_* 2x4 *_+1_* = 9 (not 8). So he forgot to carry the 1 there. The number 10 was definitely his weak spot :D
Suspicious boss: "So we took EXACTLY 400 pounds?"
Box office: "Uhh... and sixpence! Four hundred pounds and sixpence."
in 2 days!
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I love these videos about the history of mathematics (and science). I hope you'll make more! The Objectivity channel has been great for the same reason.
Feels like a mix of objectivity and numberphile. Love it
This is a wonderful video,for anyone that worked on it, thank you! It was lovely!
7:40 I was taught to always write a 1 with the top serif. Never had a problem until one day I was filling out a form at an office and the receptionist got snippy with me that I had "written the date wrong". I hadn't, she'd just assumed my 1 was a 7 (despite my writing an actual 7 nearby, again the way I'd been taught, with a crossbar). When I told her that was a 1, she said in an annoyed and condescending voice that my 1's look like 7's, then made a point of thickly scribbling a fat vertical line over it.
Anyway, all this to say, that one looks perfectly fine to me and it does *not* look like a 7.
Draw a foot serif on a one if you draw the top serif, that is what I do. And I write months in letters, cos 12 10 2024 means December or October, to an American or a Brit. But everyone can figure out Dec 10 2024!
I grew up in Australia, but now live in Europe, so I had to start adding the serif on the 1. I've always written a line/bar through the 7 though for clarity since my handwriting is awful, but I can totally appreciate your story as I've made the same mistake when I've forgotten to switch back to my old habits for forms in Australia or the UK!
few people know this but Shakespeare was the first non-royal person to own a stake (12.5%) of a theater in the UK, putting together the "content creation" with the "content distribution" for the first time. The Globe was like the iTunes of the time
The 'tail' on the 1 is still very prominent here in Italy.
And in Germany.
And in Portugal.
And in Poland.
And in Belgium.
I can't say for sure about Shakespeare's times, but comparing the three pounds made by the Shakespeare play to some examples of the value of money a hundred or so years later (from Liza Picard's book "Restoration London").
In the 1660s, one penny would buy you a loaf of bread, or a pound of cheap cheese, or a few herrings. A pound of bacon was nine pence. A roast beef dinner for four in an inn was five shillings. A pair of boots cost 30 shillings. Samuel Pepys paid £24 for a silk suit at some point. A servant or maid earned about £4 per year (960 pence), a shopkeeper or tradesman about £10 per year, a layer £22 per year.
That was for the "posh" seats
He mentions just after that regular people paid a penny
@@widmo206 Yeah, the three pounds was the recorded total for the "posh seats". In a 1660s theatre, the expensive seats were four shillings (48 pence) in a box or one shilling (12 pence) in the gallery.
Those numbers are really interesting! A typical loaf of bread is about £1.75 today, and you would be hard pressed to find any cheese for less than £3/pound. But if we say that a penny in the 1660s is about £2 today, then the lawyer's annual salary would correspond to only £10,000 today. Or conversely, if we normalize the conversion on a lawyer's salary of £50,000 (which is the current average), that would mean that a loaf of bread in 1660 was worth almost £10.
@@egodreas it makes sense to me that lawyers are more in demand in today's society than they were back in the 1500s.
at around 10:30 ... Placeholder zeros? We certainly don't use them over here in austria. So that came as a surprise to me.
I wasn't taught them in the US either
Same in Sweden.
In the US, I learned to use them as a kid, but we probably stopped using them by the time we were in 6th grade.
Same, Israel
They're the sort of thing that teachers put in to make it easier to see what's happening, and get used by people who don't do much hand calculation, but which get quietly dropped by anyone actually working with numbers as so much wasted ink.
Number systems are great - it's fascinating how different cultures have developed different systems to count and then to make their way of writing those numbers simpler.
The bar in the "1" in handwriting is the normal here in Germany and I think many other European countries too. We make an extra line across at the 7 like a wonky plus with a ribbon 😅 I kinda like that more then the "I" as a one, cause it has somehow more structure as a symbol imo 😅
Mmm... in France I've seen the '1' bar go all the way down to the baseline -- /| -- so it's sometimes longer (by Pythagoras) than the upstroke.
I write a normal 1 with a short bar or no bar, but I always cross my 7 as well. And sometimes my zeroes, but that's more a programmer thing!
That is absolutely fascinating. He's heard of a new technique and is playing with it to see how much easier it is to use than the old way of doing things.
What a fun story! Have never thought about transition before
What an incredible artifact. One of those concepts I never would’ve thought about, but when pointed out is astounding. And it being theatre-related is icing on the cake.
They are in Dulwich College, which was founded by Edward Alleyn, who acted leading roles in Shakespeare and Marlowe, and which is where PG Wodehouse and Raymond Chandler went to school.
11:32 - at least three performances of The Jew of Malta by Christopher Marlowe are listed there in Feb-Mar 1591, quite soon after it was written. Fascinating, thank you.
I had to chuckle at the "scripty one" with the "long tail" that took a long time to disappear. Guess what, it many handwritten scripts it hasn't disappeared 🙂 In German-speaking countries, people still write "one" with a flag, and "seven" with a longer flag and, to be really sure, a bar crossing the stem.
I (also German) learned to write 'one' as a diagonal line going up and right from about the middle of the space to the top and then a vertical line down (to be honest not that different from how it looks here: 1, just the diagonal is longer) and 'seven' as a horizontal line at the top going right, followed by a diagonal line going left all the way to the bottom and then cross out the diagonal somewhere in the middle (also like '7', just with a crossed out diagonal to keep it distinguishable from 1 when you write it sloppily)
I love that he was practicing the multiplication with the new numerals. A huge multiplication like that would have been a nightmare to calculate in Roman numerals, so I suspect it must have been quite novel and amazing to people of that time to see how useful this new number system was!
the „1“ with the long tail is actually still a thing outside the UK/US, in german speaking countries it‘s quite common. To avoid confusion, 7s are written with a horizontal line.
2:40 why does the screen shake with random zooming in/out? Is the camera guy shaking it on purpose and actually pushing the zoom in and out? Or is it done after recording for some design decision?
I like these historical math videos. Keep them coming.
6:02 In Greek, a final sigma takes a different form. Four Hebrew letters have different final forms. I don't know any more about why this is, but it is not an isolated practice.
When I was at school (many, many years ago) I was taught when adding up to put a dot over the appropriate column if I needed to carry one. In the case of the £211/9/0 I think the dots are carries.
I was taught to use dots for the carry as well.
It's interesting that Roman Numerals went on to become the sort of upper class or more formal method for a very long time. Like you might see Chapter XV in a book or MDCCCXLII on a building.
This had me curious. I never thought before about how arithmetic would have been done in Roman numerals. Perhaps a following video on how to multiply xiv b iil
8:40 The dots on top of the 1's are not because he's romanised them, it's surely because as he's done the addition these dots represent the carry over. I do the same thing since it's faster and smaller than writing a 1.
Milton was the rockstar during Shakespeare’s time. It wasn’t until afterwards that they made him this for whoever they are iconic figure.
Don't you mean Marlowe? Milton was a bona fide puritan, so not exactly a rock star, by definition.
The example of unit systems coexisting is a good example of things transitioning as needed and fluidly. Another good example is that we are still using Roman numerals today
It was interesting the Henslowe aways used the new numerals to write the year of the performance, since one of the places were Roman numerals are often still used is to write the year for the copyright at the end of the credits of a film.
At 08:39, those not dots on top of the 1, but the carries that are marked by a dot, the 2 + 1 + carry was obvious. No other 1 have dot on top...
For a moment I also thought that those dots were carries but it made no sense to not write the one on top of the leftmost 2, unless the writer had forgot it. However, I checked the video and at 3:38 the dots appear over the 1. They also appear thereafter. Therefore, those dots are not carries, they are part of the 1. Go figure.
@@Juan-qv5nc Have you considered they are carries in one context and not carries in another.
For a second there, I thought I had forgotten 2nd grade arithmetic. The mistake in the 12345 x 123 problem isn't a forgotten carried 1 from 3x3, but the forgotten carried 1 from 2x5 in the row below, which should have read 24690.
But with X, V and I. They can be sent as arm signals much faster right?
Oh reminds me of reading a letter to the King of Portugal regarding the "discovery" of Brazil, happened and written in 1500, I was surprised to see it used Roman numerals still and was curious to see when the change happened... I haven't watched it fully so maybe it will be mentioned too but iirc Russia used Cyrillic numerals up until the 1700s?
I think the reason marking the ends of numbers was important was that words and units were made of the same symbols. If the gap is a little small and the next word starts with a letter used in Roman numerals, it would be easy to misinterpret.
Yup, "one two" -> "i ii" could be misread as a three, but "j ij" wouldn't be.
@AthAthanasius I was also thinking of iL. Is that 49, or 1 Pound Sterling? Putting a tail on the end of the number distinguishes them.
2:15 "That's a strange L"
* looks at notes in notebook *
that "L" is virtually identical to my handwriting
The j as 1 at the end in lowercase Roman numerals lasted well into the 19th century I believe, and is more like a flourish than anything else. Remember that I and J were not seen as separate letters until relatively recently. Same with U and V
Dotting your 1s seems risky when mixing Arabic and Roman numerals. How do you know if ii is 11 or II?
Well, if you were the one that wrote that, you probably know from the context, for exaple, in that notebook, years were written in arabic and money in roman
@@guiorgy Yeah, like I definitely always remember what the weird two-word reminders I write for myself were supposed to mean two weeks later ;)
@@unvergebeneid That's true too :D, though in that guys case he had a system he was keeping to, so, assuming he didn't quit the job and stop doing it, he wouldn't have forgotten that easily
I don't think he's doing that intentionally, might just be him being more familiar with i for 1
Actually, this way of handwriting the ones and the nines is still common in the Netherlands. A q goes strait down (like your nine), a nine has a bend to the left (like in your manuscript) and a g has a curl backwards (so it forms 2 circles).
Besides, a Dutch 8 will start in the center and both end do not have meet.
These indo-arabic numerals have standardised to today's. In the Royal Society library there is a 1473 almanac which demonstrates the introduction of numerals for calculating Easter alongside Roman numerals, but in that book the '4' is different - it looks more like an 8 with the bottom cut off. 7 is an upside-down V (like modern Arabic) and 5 is different, too.
Do you know what the book is called or what I should google to find it? I'm very interested, and I'd love to see the source if possible
@@ThomasRichardson-lj1ig 4, 5, and 7 in medieval texts often looked different. You can find the old bowtie 4 on early dated coins, paintings, some manuscripts. I don't remember seeing any printed books or incunabula with it but there probably are some. The Prague astronomical clock has the medieval numeral forms on it as well.
@@JohnMichaelson Sorry, I meant I was specifically interested in the book as an introduction of Hindu-Arabic numerals. I find the transition between the two types of numerals interesting, and I'd love to see many primary sources.
@@ThomasRichardson-lj1igMy reply got deleted when I added the link. But search for Objectivity John Green, and the book I'm talking about is at 2: 37 of that video.
@@PopeLando Thanks a lot! I'll check it out.
Simply put, Roman Numerals are great for adding and subtracting, but not so much for multiplication and division
And useless for floats.
Roman numerals are okay for adding and subtracting, but you still have to deal with making change when you try subtracting LII from DXV
@@haraldmilz8533 never seen someone refer to reals as "floats" before (only ever seen it used when specifically referring to IEEE-754 floating point)
I must admit I'd never realised this transition even happened. We are so used to our current numerals. I vaguely sort of assumed that Roman numerals left when the Romans did!
And of course potentially the final remaining use of Roman numerals today is when you carve the date your house was built?
At grammar school in the mid '60s we explored different systems of numerals and bases, and Roman numbers were part of that. Trying to do Roman arithmetic - especially multiplication (forget ever doing division) - was such a pain that I am delighted I have forgotten how we were taught to do it.
6:10 I still have the Midland Bank guide to writing a cheque - given to me when I signed up in '71 when beginning university. It was multi-paged and of the aspect ratio of a cheque. The recommendation was to use a dash rather than a decimal point, to write the pounds in words and the pence (we had _just_ gone decimal) in numerals. If there were no pence the word _only_ was to be used instead. A scribed line to the end was suggested.
10:38 Tut tut! Not casting out nines to check.
Is the suggestion that we got joined up writing bceause raising the qulll caused blots? I can do joined up writing but it is a write-only system.
My high school calculus teacher joked that when the Romans wanted to do some math they kidnapped an Arab to do it for them
Fantastic.
I'm pretty sure the transition happend much earlier, at least on the continent. Since the 15th century Arabic numerals were commonly used for dates and were definately used in accounting and banking.
Even now in UK primary schools we still use a bastardised version of Roman numerals to teach how a positional number system works and wonder why children find arithmetic so hard - we need to get rid of Dienes blocks (sometimes called base10 blocks.)
A fascinating video would tell the story of how Arabic numerals spread throughout Europe. Considering that Fibconacci introduced positional notation to Europe in 1202 in his book Liber Abacci, what took it so long to come to England? I know this is a broad topic but an important one in the history of math and science. When Newton was Master of the Royal Mint, was he still recording financial data in Roman numerals?
No. At least I don't think so. English coins used Arabic numerals almost from moment numbers of any kind were ever put on them, and that was more than a century and a half before Newton came along.
When people learn of Fibonacci's Liber Abaci, they often get the wrong impression that Hindu-Arabic numerals spread rapidly from then on. But that is in fact not the case. It was not until the printing press that Hindu-Arabic numerals started spreading rapidly and came into widespread use across Europe. In the 13th century, Hindu-Arabic numerals became used in Abacus schools in North Italy. But beyond that, the general public (and other European countries) largely did not use it until it spread following the printing press.
There was a relatively long period where there was not much progress in mathematics in England, between Thomas Bradwardine (c. 1300 - 1349) and Robert Recorde (c. 1510 - 1558). Robert Recorde largely established the English mathematical school. He wrote several popular math textbooks, and he helped popularize the Hindu-Arabic numerals, as well as the already-existing plus (+) and minus (-) symbols, and he invented the equals sign (=).
Have you ever tried to score bowling with Roman numerals? The second ball per frame is a huge pain on those tiny sheets so I would recommend being very good or very bad.
How do you choose the time for uploading the video?
1:20 or so, I do think that could be accounts of something! In front of 1000 for ex. there is "of" and after the dash we have 14. So let's say that those could be tallies of how many performances had a certain amount of people (rounded down) seated in the theatre. So 14 nights had 1000, 1 had 900 (cause it's not too likely for something to be hyped enough to get 900, but somehow not hyped enough to get 1000) and only 1 night had a measly 30 people.
I'm not saying that is what this was, just trying to show how he could have gotten this data. It could be for (effectively) graphing out and getting a sense of how many people were seated. He wanted extra precision on the low end, or more likely didn't wish to bother graphing out every set of 20 all the way to 1000.
(Or could be the amount of money gotten per night, or anything else. I just used an example to get the point across. I didn't translate the text above it.)
At 3:40, does the top line read ‘29 of february 1591’? You can also see it clearly at 3:16 between ‘28 of february’ and ‘1 of march’. But 1591 wasn't a leap year.
At 8.40 you say "he likes romanising his ones" - could they be "carry the one" marks that you see sometimes?
That addition at 8:26 why there aren't dots over "11" in 2nd row tho?
Wouldn't they rather mean to remember to add 1 in the column with dot? I do something like that (but just write 1 above instead)
Astonishing that within just a couple of generations of adoption of Hindu numerals (late 1500s) we have Newton(1660s) developing calculus! Also I wonder how Napier got to log when roman numerals were the more commonly used system.
As a follow-up to this - is there a reason why TV programmes in the UK used to (or perhaps still) showed copyright dates with Roman numerals? e.g. the end credits to the last episode of Blackadder Goes Forth are simply "(C) BBC TV MCMLXXXIX", rather than 1989. Why is this transition still going on, five hundred years later?
To be honest it was a lot more interesting in the 1400s when the forms of the numbers were different. '4' looked like a bowtie, something like an awareness ribbon. '5' looked like '7', and '7' was an upside down 'V'. The earliest dated European coins used Roman numerals all through the 1400s, but in 1424 one city minted the first using Arabic numerals. Finally by 1500 just about everywhere had abandoned Roman numerals on them.
This was very interesting!
Oh actually, when you said cards, maybe that was the reason for X, if you ever dealt with playing cards 10 is the odd 1 out, if you are drawing them, 10 always messes with the edges of the card, for notation you want a single number/letter for every card, which is why we use T for Ten today, and stuff like that, which is why I guess it could have prevailed
Did you see the big X near the multiplication?
It looks like a casting-out- nines
If so, why did he not point out the error?
Re. the dots above the number 211 in the money addition.
I think those dots marks that there is a carry (carryover).
He did not dot any of the other 1s.
ps. It also looks like he used a dot (and missed it) in the multiplication that went wrong :)
I'm wondering if in the arithmetic with the two dots above the 1's that those are carry marks, since there was a carry from the shillings to the pounds and then another carry.
3:05 the only human thing in maths is suffering!
I don't think he was being random in his mixing of numbers. He used denary where it was a lot shorter, and the more familiar Roman numerals where it didn't make much difference (or even shorter as with the X for 10 on the clock face).
Really interesting!
Maybe they had trouble wrapping their heads around the concept of 0 at first, so they kept using X for 10 alongside Arabic numbers, and the habit stuck around even after they adopted 0 for other numbers? The diary isn't really mixing up the two systems apart from that specific case, and 1/I which does look similar in both
7:40 - 7:44 Doesn't scripted 1 on the Continent still looks like that? It's why they put a dash through the vertical riser.
10:19 In the 1970s, we (in the US) were taught that we could skip the placeholder 0s.
11:49 That is the question.
I’ve often wondered why it took so long for Indo-Arabian numbers to get general Europe use. After all, Spain had been under Moorish control since the 8th century. Was the resistance to change driven by dogma?
7:37 confusing to any Germans, since that is literally how they still write these both 1 and 9. (also note how they look kind of like this when you type them)
"What's that in old money?"
I always wondered if and how people did floating point math with Roman numerals, thing like long division and such. Or were they constrained to integers? Can you do a film on this?
At 6:05, he mentions something called “checks”, and it sounds like they were a form of money or receipt. I wonder if Keith would have examples at the Royal Society archives? Could be an interesting topic for Objectivity. :)
You can still use cheques. You basically give a cheque to a person or a company with the amount you want to pay and hope you have the money in your account when your bank receives it.
Really interesting! Could the slip of using x instead of 10 when all the other numerals were arabic be because the numeral of zero was also a new concept?
No, you can see him use 0 when adding revenue from 2 days
Is the ONE written with the leg because people mistaken it with cursive i? Is that why I type 1 and not |?
is this a reupload or a remix ?!?
No
Much Ado About Umbers?
The dots above the I's at 9:22 seem like theyre denoting the carry over. It looks pretty much the same as when I do long addition!
That was really fun
This is fascinating. I'm a numbers guy and a calligraphy enthusiast. I'm totally out of my depth trying to read these numbers on the page.
Makes me wonder what people would think of my scratchpad 400 years down the road if they happened upon it.
So, the semicolon is a holdover j?
This could have been before the letter j was really considered a separate letter from i, so it wouldn't have been confusing to use a j in place for an i
Being able to easily multiply numbers easily must have seemed amazing back then when moving to the new number system. This guy seems to have embraced the new numbers but at times he was still thinking in the old system. x=x is understandable as he might want to use a single digit for X instead of needing 2 digits for 10. Especially if he really didn't want to lift the pen.
7:37 Well, that form never really did go away in some places, did it? That seems pretty typical in France. Certainly it looks more like a French 1 than a French 7.
8:35. I wonder if the dots above the 211 are the carrier flags.
8:37 Aren’t the dots over the 1s to indicate the carries? There aren’t dots over the other ones in the sum.