Objectivity Videos: ruclips.net/user/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 many millennia 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).
Weren't those numbers introduced through Muslim Spain and Northern Italy? I remember reading that Toledan scholars were familiar with the number system through translations of Arab works and Fibonacci encountered the numbers during a travel to Algeria and introduced them to Northern Italy at his return. Then when the printing press became available the system expanded from those places where it was being used locally.
@@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.
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.
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.
I (an American) write my 1s with the "tail" (never would have thought to call it that) when it's on its own, but as just a vertical line when it's a part of a longer number.
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.
@@wes643 The shift to using Arabic numerals kind of went hand-in-hand with the shift to doing math on paper rather than with casting-counters. So people using Roman numerals would do multiplication with counters, which is comparable to using an abacus. I sort of suspect that's why the receipts were still in Roman numerals. A lot of otherwise illiterate merchants could still do their accounts with counters, so maybe monetary values still tended to be in Roman numerals.
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!
Reminds me of how Mt. Everest is exactly 29000 ft, but if tour guides say that then hikers would assume they're rounding off. So they instead say Mt. Everest is 29003 ft
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.
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.
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
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'm quite surprised that the switch from Roman to Arabic numerals happened as late as the 1500s. I don't know when exactly I'd have thought it occurred, but certainly I'd have guessed centuries earlier.
8:55 I think maybe the dotted I's for 211 are actually being used as carry indicators. The 11 shillings don't have them, but where there are carries, he does have them.
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.
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!
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.
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?
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.
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.
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!
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.
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.
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.
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)
This video is fascinating, absolutely stunning how much maths the everyday man - you, and I - are doing even for fun and you would never know until maybe a thousand years later
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.
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?
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.
I love all this! At 8:36 I think the little dots on top of the ones in 211 are the carries! They might also be a pun on Roman numerals, but the other ones in this example don't have dots.
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.
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.
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?
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.
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
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
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.
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.
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.
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
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.
This was playing and I was doing something else not looking at the screen but when I heard this bit i knew immediately it was from Shakespeare In Love 😃 I love that movie!
If the number was XI (11), one could add an X to the end to make XIX which is 19. Though many examples of adding a character to the end would result in an invalid format, some examples would in fact result in a valid (larger) number. You can add any character after a lone I You can add the last character until there are 3 at the end (except L and D) You can add V or X to anything ending in XI You can add C or X to anything ending in CI You can add M, C, or X to anything ending in MI ...and those are the obvious ones.
I thought it was Johnson who was considered the best playwright of Shakespeare's time. At any rate, it wasn't until about a century after Shakespeare's death that his work was re-examined and re-evaluated. Naturally, immediately after his death his work was deemed old fashioned, as would happen today... er, would have happened in The 20th Century. I remember reading once that The Yale Library had a copy of Shakespeare's plays "for light reading". Not to say he wasn't popular in his time, but in the same way that a hit filmmaker is appreciated today as opposed to great artist. I think that's an interesting comment on society and culture.
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
They were still transitioning to Indo-Arabic numerals in the late 1500s and by the 1670s Newton was working on calculus. I never realised that gap was so short.
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.
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 (=).
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.
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.
"Henslowe was an ignorant man, even for the time in which he lived, and for the station he occupied: he wrote a bad hand, adopted any orthography that suited his notions of the sound of words, especially of proper names (necessarily of most frequent occurrence), and he kept his book, as respects dates in particular, in the most disorderly, negligent, and confused, manner. Sometimes, indeed, he observes a sort of system in his entries; but often, when he wished to make a note, he seems to have opened his book at random, and to have written what he wanted in any space he found vacant." Harsh! (from J. Payne Collier's Introduction to "The Diary of Philip Henslowe from 1591 to 1609", published 1845)
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.
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.)
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.
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
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.
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)
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.
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.)
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.
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
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
I've always drawn my x's in one pen stroke! Not quite as fancy as what is seen here, imagine more like a backwards alpha. I feel so validated now to see it wasn't uncommon historically. Take that, multiple teachers throughout my life!
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.
Robert Recorde's 1543 book "The Grounde of Artes" was the turning point, one of his several popular English arithmetic books using Hindu-Arabic numerals. Recorde virtually founded the English mathematical school. Napier, born in 1550, grew up learning from Recorde's books, and Napier's book explaining logarithms was published in 1614 (and also uses Hindu-Arabic numerals).
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?
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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 many millennia 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).
Weren't those numbers introduced through Muslim Spain and Northern Italy? I remember reading that Toledan scholars were familiar with the number system through translations of Arab works and Fibonacci encountered the numbers during a travel to Algeria and introduced them to Northern Italy at his return. Then when the printing press became available the system expanded from those places where it was being used locally.
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
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
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.
I was going to mention this. It's quite common to find in many places around the world.
I (an American) write my 1s with the "tail" (never would have thought to call it that) when it's on its own, but as just a vertical line when it's a part of a longer number.
I love Brady's videos. He asks the kind of questions that the viewer would ask.
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
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.
@@wes643 The shift to using Arabic numerals kind of went hand-in-hand with the shift to doing math on paper rather than with casting-counters. So people using Roman numerals would do multiplication with counters, which is comparable to using an abacus.
I sort of suspect that's why the receipts were still in Roman numerals. A lot of otherwise illiterate merchants could still do their accounts with counters, so maybe monetary values still tended to be in Roman numerals.
Seeing tidbits of normal everyday life from long ago is the most fascinating part of history for me. Great video!
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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 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!
Suspicious boss: "So we took EXACTLY 400 pounds?"
Box office: "Uhh... and sixpence! Four hundred pounds and sixpence."
in 2 days!
Reminds me of how Mt. Everest is exactly 29000 ft, but if tour guides say that then hikers would assume they're rounding off. So they instead say Mt. Everest is 29003 ft
Said Nobby.
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?
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.
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
Feels like a mix of objectivity and numberphile. Love it
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.
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
Patrons can enjoy some extra pictures and scans from this video here: www.patreon.com/posts/115548802
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'm quite surprised that the switch from Roman to Arabic numerals happened as late as the 1500s. I don't know when exactly I'd have thought it occurred, but certainly I'd have guessed centuries earlier.
8:55 I think maybe the dotted I's for 211 are actually being used as carry indicators. The 11 shillings don't have them, but where there are carries, he does have them.
This is a wonderful video,for anyone that worked on it, thank you! It was lovely!
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.
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!
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.
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 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.
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.
Surely the dots in the addition at about 9:10 are the carried ones from the previous column.
I agree completely, but please don't call me Shirley.
The 'tail' on the 1 is still very prominent here in Italy.
And in Germany.
And in Portugal.
And in Poland.
And in Belgium.
And everywhere else but US/UK, I'd bet.
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!
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.
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.
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.
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)
This video is fascinating, absolutely stunning how much maths the everyday man - you, and I - are doing even for fun and you would never know until maybe a thousand years later
2:15 "That's a strange L"
* looks at notes in notebook *
that "L" is virtually identical to my handwriting
I wouPd Pove to Pook at your Poopy caPPigraphy.
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.
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?
What a fun story! Have never thought about transition before
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.
I like these historical math videos. Keep them coming.
I love all this! At 8:36 I think the little dots on top of the ones in 211 are the carries! They might also be a pun on Roman numerals, but the other ones in this example don't have dots.
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.
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.
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?
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.
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
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
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.
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.
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.
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
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.
The writer might have been enjoying a little "pun", making the carries look like Roman dots.
This was playing and I was doing something else not looking at the screen but when I heard this bit i knew immediately it was from Shakespeare In Love 😃 I love that movie!
But with X, V and I. They can be sent as arm signals much faster right?
One of the best ever!
If the number was XI (11), one could add an X to the end to make XIX which is 19. Though many examples of adding a character to the end would result in an invalid format, some examples would in fact result in a valid (larger) number.
You can add any character after a lone I
You can add the last character until there are 3 at the end (except L and D)
You can add V or X to anything ending in XI
You can add C or X to anything ending in CI
You can add M, C, or X to anything ending in MI
...and those are the obvious ones.
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.
And also a different generation.
I thought it was Johnson who was considered the best playwright of Shakespeare's time. At any rate, it wasn't until about a century after Shakespeare's death that his work was re-examined and re-evaluated. Naturally, immediately after his death his work was deemed old fashioned, as would happen today... er, would have happened in The 20th Century. I remember reading once that The Yale Library had a copy of Shakespeare's plays "for light reading". Not to say he wasn't popular in his time, but in the same way that a hit filmmaker is appreciated today as opposed to great artist. I think that's an interesting comment on society and culture.
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
They were still transitioning to Indo-Arabic numerals in the late 1500s and by the 1670s Newton was working on calculus. I never realised that gap was so short.
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)
Fantastic.
Those iij are still present in gregorian chant books, specially to indicate repetitions in the Kyrie
How do you choose the time for uploading the video?
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 (=).
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.
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
11:33 Apparently there was a play performed on February 29, 1591. Did they have different leap years back then?
This was very interesting!
Really interesting!
"Henslowe was an ignorant man, even for the time in which he lived, and for the station he occupied: he wrote a bad hand, adopted any orthography that suited his notions of the sound of words, especially of proper names (necessarily of most frequent occurrence), and he kept his book, as respects dates in particular, in the most disorderly, negligent, and confused, manner. Sometimes, indeed, he observes a sort of system in his entries; but often, when he wished to make a note, he seems to have opened his book at random, and to have written what he wanted in any space he found vacant."
Harsh!
(from J. Payne Collier's Introduction to "The Diary of Philip Henslowe from 1591 to 1609", published 1845)
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.
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.)
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.
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
At 8.40 you say "he likes romanising his ones" - could they be "carry the one" marks that you see sometimes?
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.
If you look at the multiplication problem, to the right is the cross for a single digit multiplication that the X sign comes from.
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)
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.
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?
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.)
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.
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
3:05 the only human thing in maths is suffering!
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
I've always drawn my x's in one pen stroke! Not quite as fancy as what is seen here, imagine more like a backwards alpha. I feel so validated now to see it wasn't uncommon historically. Take that, multiple teachers throughout my life!
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.
Robert Recorde's 1543 book "The Grounde of Artes" was the turning point, one of his several popular English arithmetic books using Hindu-Arabic numerals. Recorde virtually founded the English mathematical school. Napier, born in 1550, grew up learning from Recorde's books, and Napier's book explaining logarithms was published in 1614 (and also uses Hindu-Arabic numerals).
Wow! caught a numberphile video within the first 5 minutes
You mean the first V minutes?
9 minutes for me
😃yeah i guess
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
That was really fun
@9:15 so the dots on the ones suspiciously coincide with the carried over ones...
But there isn't one on top of the 2.
Was thinking the same! Haha
iibv~2b? at 11:48 is a nice touch, i see what you did there!
Roman numerals can be fascinating. I heard there was a movie about Malcolm the tenth.
The 1 with a tale is still written in Poland. U cross the 7 over to distinguish these two.