The Big X - Numberphile

Cipher, Shakespeare and some Ye Olde Multiplication with Rob Eastaway. More links & stuff in full description below ↓↓↓
Rob Eastaway's book Much Ado About Numbers...
Amazon (US): amzn.to/3zFinog
Amazon (UK): amzn.to/3VIIp1u
And on bookshop.org: uk.bookshop.org/p/books/much-...
More Rob books: amzn.to/3XR6N3Q
Rob Eastaway's website: robeastaway.com
Objectivity Videos: / objectivityvideos
With thanks to Dulwich College Archive: www.dulwich.org.uk/about/hist...
Check out The Ground of Arts by Robert Recorde on Google Books: books.google.co.uk/books?id=i...
Also discussing the origin of the multiplication symbol.
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[@forthrightgambitia1032]

I don't know if the author has seen this but this topic is actually mentioned in what is probably the nerdiest book every published, the 1928 two volume "History of Mathematical Notation" by Florian Cajori. It is available free on the Internet Archive. On pp. 254 and 264 he mentions Recorde and his method and on a later page he reproduces the cross you see in the book with the same multiplication, and notes that the same method had appeared in earlier works on the continent, for example in the French translation of Tartaglia. He traces the "cross" symbol originally back to Leonardo of Pisa aka Fibonacci in the Liber Abaci of 1202 who used it in a different method known as the "process of two false positions". He talks about this specifically in the context of the origins of the multiplication symbols and notes that this usage of the cross was one of several ways in which a cross like this was used in various arithmetic algorithms. He then procedes to enumerate and detail each usage. He comes to the conclusion that as symbols that bore a resemblence to the St Andrews cross were used in a wide variety of different methods - and that there were also competing notations that lost out - that we have no evidence to specifically trace Oughtred's innovation in 1633 to any previous use, except, perhaps tenatively, the use of the letter x by Napier in a 1618 book. As it currently stands the Wikipedia page actually uses this as a reference when stating that attempts to tie the notation to previous usages are unfounded in evidence. That said, perhaps, as you say Recorde's book was sufficiently well known that it has priority over other claims, especially in England. This is certainly plausible, especially as famously another book by Recorde, The Whetstone of Witte was most certainly the origin of the equals sign, which naturally suggests the degree to which it captured the public imagination. It is impossible to prove definitively though. The word cipher is directly from Arabic as other people here have mentioned, where it is zero. The term "cipher" to refer to someone as a nobody was still relatively common until the 19th century/early 20th century. See for example chapter XVII of Jane Austen's Mansfield Park. It came to associated with codes because a lot of early codes in the 16th and 17th century used substitutions between the Latin alphabet and Arabic numbers, obviously something encoded this was would be a collection of unintelligble of digits - ciphers - that needed to be reconverted into Latin letters, deciphered. In a strange way this does seem rather familiar to modern users of encryption algorithms like AES where the output may well be in hexadecimal digits! Also the verb 'to cipher', that is to reckon, to do arithmetic still existed in Victorian times, it is used in this sense in chapter VII of Great Expectations for example. Indeed at this time the term ciphers was still used to refer to what we would now call digits.

[@bernhardglitzner4985]

Thank you for this 😃

[@hugofontes5708]

Thank you for compiling this here As a bonus you made me realize something about the Matrix character Cipher

[@anyuru]

9:35 finally someone challenged Rob Eastaways conjecture!

[@davidneuway3412]

For a more lowbrow reference, the use of "ciphering" as slang for doing arithmetic can be found in the 1960s sitcom The Beverly Hillbillies. Specifically, in season 1, episode 2 Jethro does some ciphering for Mr. Drysdale -- "one and one is two, two and two is four, four and four is eight" before he runs out of fingers on which to count.

[@stephenbeck7222]

Surely he’s read Cajori. Cajori says that Oughtred himself probably is the author of the appendix in Napier’s book where the ‘x’ symbol is used. So Napier (if that is correct) gets no credit for the use of x.

[@Tekay37]

Can't wait for all the youtube shorts showing this method and asking the question "why didn't we learn this in school??".

[@justforplaylists]

Sadly, whenever schools teach a new method of division or whatever parents complain.

[@diamondsmasher]

@@justforplaylists I’m assuming OP is being facetious and making fun of KZbinrs as no one in their right mind would teach this nowadays

[@ElderEagle42]

It's a lot more work than just learning the full tables

[@Tekay37]

@@ElderEagle42 Yes, but making a video about is also content.

[@bobh6728]

But to multiple the 8x7, you have to multiply 2x3. So how do you do 2x3?

[@Oler-yx7xj]

I love how he used (<a href="#" class="seekto" data-time="103">1:43</a>) X to stand for "ten" in "X. of Millions". Such a fun quirk of the language of the time

[@jasonwalter-tz4qz]

And C. of millions and M. of millions, or a billion

[@RFC3514]

@@jasonwalter-tz4qz - Thousands of millions was not "a billion" in English until Americans started using it. A billion was a million millions (still is, in most languages). In UK documents before 1974, 10^9 is "one thousand millions", and "one billion" means 10^12.

[@JacksonBockus]

Makes sense that he wouldn’t say “10s of Millions”.

[@frankmalenfant2828]

​@@RFC3514 In french, a billion is a "milliard", a trillion is a "billion", a quadrillion is a "milliard" and so on, usine the "ard" suffix doubling each prefixes use for 3 more orders of magnitude. Living in a bilingual country where people speak both french and english, I anticipate this will cause lots of confusion as these trillion figures pop up more and more in our lives.

[@tonelemoan]

Robert Recorde, the noted inventor of writing stuff down.

[@shohamsen8986]

Like lord discoverye, the first man to have come up with the concept of discovering

[@deltalima6703]

You only get to see his writings if he is your uncle. Unless bobs your uncle, there is no recorde.

[@chriscreations8853]

You beat me to it. Just what I was about to say 😂

[@RFC3514]

Apparently he invented some kind of flute, too.

[@ObadaSaqqa]

Cipher sounds exactly as صفر which is zero in Arabic

[@ciaranhenderson9464]

Yeah that's where it comes from. The English, and assumingly many other European nations, got the word from French, which in turn got it through Arabic in colonial times. Many Arabic words make their way into European languages through the French. Really fascinating word etymologies if you dig into it a little

[@catakuri6678]

i'm Arabic, but i didn't realize that until i read this comment

[@calholli]

All of these numbers are Arabic

[@ciaranhenderson9464]

@calholli The symbols, yes, but not the names, they're all germanic (until you get to millions and higher, in which case they're latin)

[@maximkhan-magomedov431]

And Russian word "цифра" (cifra) for digit also has the same etymology.

[@TheMoroe1]

In german a "digit" is also knows as a "Ziffer"

[@vytah]

The big X reminds of this method that uses fingers: show (a-5) fingers on one hand and (b-5) fingers on the other. Then, the tens digit is the sum of straight fingers, and the units digit is the product of numbers of bent fingers on each hand. In other words, a×b = 10×((a-5)+(b-5)) + (10-a)×(10-b)

[@topherthe11th23]

@vytah - Is there a version of that method that is widespread in Korea? Do you remember the name for it?

[@numberphile]

Rob Eastaway's book Much Ado About Numbers... Amazon (US): amzn.to/3zFinog - Amazon (UK): amzn.to/3VIIp1u Objectivity Videos: kzbin.info

[@johnjeffreys6440]

Can I submit an idea for a video?

[@Becky_Cooling]

3 hours ago? You seem to have stolen Tom Scott's time machine.

[@guepardiez]

You probably want to pin this comment.

[@oportbis]

People in the XVIth century: How to multiply two one-digit numbers? Robert Recorde: So start by multiplying two one-digit numbers

[@fahrenheit2101]

In fairness, memorizing wasnt a fun idea, and it still simplifies the problem, provided the 1 digit numbers are larger than 5...

[@topherthe11th23]

@@fahrenheit2101 See my comment above. This method (a) assumes that the problem for the user occurs only when the product is larger than 10 (because if ALL products of single-digit numbers are beyond the user then the step where you do another multiplication is never easier than the original problem); and (b) it requires a proof that after only a finite number of iterations you will always end up with a multiplication for which you do not have to reiterate this method but which you can do in your head. A proof that you'll get to a multiplication where both numbers are less than 4 would entail such a proof, but that's not the only exit of the re-iterating, if you ever get to a point where one of the two numbers is "1", you can quit, and you can also quit at four times 1 or 2, or three times 1, 2, or 3.

[@darkpulcinella9690]

So basically Recorde is a 16th century Matt Parker (writing fun books about maths destined to general public)

[@42isEverywhere]

I'm starting a petition to rename the multiplication symbol to "the Parker X"

[@RFC3514]

@@42isEverywhere - The parker X is actually the _addition_ sign.

[@mikew6644]

Such a banger of an episode… classic numberphile!

[@mytube001]

It's worth noting that the Arabic word that here was used to indicate a zero, and now is just "cipher", became the main word for "digit" in the Scandinavian languages (Swe: siffra, Nor: siffer, Dan: ciffer).

[@Filipnalepa]

In Slavic (at least in Polish) too, the word for digit is "cyfra" (starting with ts, not k sound)

[@christopherellis2663]

Sifr الشفرة. Shifera

[@ShinySwalot]

Add to this "Cijfer" for Dutch! ("ij" is sort of similar to a "y" sound)

[@aceman0000099]

Multilingual W

[@vladyslavsmirnov1875]

Same in Ukrainian! We say "цифра" (cyfra) for digit and "шифр" (shyfr) for cypher Never occurred to me before that these two are related 🤯

[@smylesg]

<a href="#" class="seekto" data-time="712">11:52</a> That's ironic he called 1 a "crooked figure" because in baseball if a team has scored only one run in a number of innings, they hope to "put a crooked number up there"; that is, to score more than one run in an inning.

[@dugferd2266]

I always wondered about a term like 'zip' in North America to mean zero or nothing. It was probably one of those mishearing or adaptations from other languages' version of 'ciph' for 0.

[@ZetaFuzzMachine]

You're the best, Brady! Please, never stop doing this

[@pyros6139]

By the way, the word "zero" actually comes from the same Arabic source as "cipher". According to Wiktionary: Arabic "sifr" --> Medieval Latin "zephirum" --> Italian "zero" --> French "zero" --> English "zero" Arabic "sifr" --> Medieval Latin "cifra" --> Old French "cyfre" --> English "cipher"

[@johannesvanderhorst9778]

Interestingly, the proof here about why this cross method works, doesn't even use the fact that we are working in base 10. For example, when we do base 100, one can use it for multiplying 78 and 86. 78 * 86 = 100*(78 - (100 - 86)) + (100 - 78)*(100 - 86) = 100*(78-14) + 22*14 = 6400+308 = 6708

[@nicomal]

It's a pretty nifty trick when you multiply two numbers greater than or equal to 90. For instance: 92 x 95 (try and do it mentally) = 8740

[@mytube001]

Also, a mid-height dot is more commonly used as a multiplication symbol today in some countries, like my own. Using an "x" is mostly for the first years in school, when basic arithmetic is taught. A dot is better once you start using "x" as a variable in algebra. Now, it's not supposed to be used together with a decimal dot, as they look identical except for the vertical position on the line, but I prefer the look of a decimal dot instead of comma, so I use both. Just have to write them clearly.

[@notnek12]

<a href="#" class="seekto" data-time="100">1:40</a> why is there a 9 in the middle of the "Six" row?

[@Kyle-nm1kh]

I think it was written by hand

[@notnek12]

@@Kyle-nm1kh You mean it's probably a typo?

[@Kyle-nm1kh]

@notnek12 yes. I'm wondering if it's stamped even

[@RFC3514]

That's actually a Parker 6.

[@Jimorian]

The lines may have been hand drawn, but if this was from a printing press, getting a 6 upside down in the type pieces would have been hard to catch in the tray.

[@mihir2012]

I love the title and the flow of this video! Neither the title and the start of the video give away anything, but leads into "where did the multiplication symbol come from?"

[@bhatkrishnakishor]

Vedic maths cross (X) method for multiplication 2 digits (10a + b) x (10c + d) = 100ac + 10 x (ad + bc) + bd 3 digit multiplication (100a + 10b + c) x (100x + 10y + z) = 10000ax + 1000 (ay+bx) +100 (az+by+cx) + 10 (bz+cy) + cz

[@bigsarge2085]

Ten without the one, what an insult!

[@alpardal]

In portuguese we have the expression "zero à esquerda" ("a zero on the left"), which is an insult meaning you are useless

[@richardfarrer5616]

I like the Shakespeare links. The only one I disagree with is the wooden "O". I think that a clear reference to the circular Globe Theatre.

[@numberphile]

The roundness of either o or 0 is certainly riffing on the roundness of the theatre... Both are of course rather round symbols (and the Globe was not a perfect circle)... It is certainly debatable... But if it is pronounced "nought" or similarly, it may then create the logical rhyme with "Agincourt' in the next line...? And there is a reference to cipher within a few lines of it too...? It was certainly written at a time when Shakespeare seemed to be have been rather taken with the concept of zero... Who knows for sure?

[@forthrightgambitia1032]

​@@numberphile I actually think Shakespeare probably meant both things at once. Part of his genius was to layer very complex meanings on top of each other in metaphors that are sometimes strained to their limit (which was kind of in fashion back then) but sometimes quite inspired. The idea that the Globe Theatre was an theatrical O that was also in some ways a kind of nothing fits a lot with his reflections of human existence and life being a reflection of the stage and vice versa.

[@topherthe11th23]

@@forthrightgambitia1032 Edit: I typed this comment below before I had seen that at 12:20 Eastaway DOES discuss this speech by Chorus in "Henry V" in greater detail, making many of my points. However, I'm not deleting this because Eastaway omits the pun on "account" to mean both "a story" and "a piece of accounting (work by an accountant), a calculation, a sum". Also he doesn't nail it down that the "O" is both the Globe's shape and is also to mean "the space within a theater is as but nothing compared to all of France", Shakespeare's idea that it is FITTING that the Globe should be an "O". It didn't seem to me that a character of Shakespeare's would "break the fourth wall" by speaking of the theater the actor is in and the play being performed, so I tracked this down. It turns out I actually have a dim memory of Derek Jacobi reciting the words in Branagh's movie-version of "Henry V". This below is "Chorus", before the drama begins, from the Folger website's text. Derek Jacobi concluded the speech by throwing the huge brass fork-switches that enable the electricity for the all the theater's (or the film-studio's?) stage-lighting. QUOTE: O, for a muse of fire that would ascend The brightest heaven of invention! A kingdom for a stage, princes to act, And monarchs to behold the swelling scene! Then should the warlike Harry, like himself, Assume the port of Mars, and at his heels, Leashed in like hounds, should famine, sword, and fire Crouch for employment. But pardon, gentles all, The flat unraisèd spirits that hath dared On this unworthy scaffold to bring forth So great an object. Can this cockpit hold The vasty fields of France? Or may we cram Within this wooden O the very casques That did affright the air at Agincourt? O pardon, since a crookèd figure may Attest in little place a million, And let us, ciphers to this great account, On your imaginary forces work. UNQUOTE Now that I know that this is NOT a character breaking the fourth wall but an intro, I'm totally satisfied that "wood O" is the theater in which this is performed, while setting the theater up to be a zero a few lines later, because a theater, to use a common phrase, "is as nothing" compared to the vastness of France. (The assertion that the Globe wasn't a perfect circle is irrelevant because the normal person wasn't/isn't conscious of that fact, and no letter "O" or digit zero "0" is a perfect circle either.) To continue, "A crook[e]d figure may Attest in little place a million" is a reference to the digit "1" which (if Chorus intends the Hindu-Arabic numerals which came to England later than to Florence) would be a "crooked" way to write the Roman Numeral "I". This crooked figure attests a million because it's in the seventh place: "1,000,000". But this way of having a "1" represent a million depends on the very "ciphers" (zeroes) that Chorus mentions in the next line, while also punning the other use "ciphers" and "zeroes" to mean "nobodies, non-entities, (such as actors, who are of low status)" by saying that's who "us" are. "Figure" means both "digit" and "a person". "Crook[e]d" is beyond my ability to unwrap, because it would require reading every Jacobethan drama to get all the possible flavors of "crook[e]d". Is it a disparaging way to refer to "crooked" members of the acting profession (in the alternate reading in which "figure" is a person rather than the digit "1" in which the crookedness is obvious)? Or is it an arcane reference to a stage technique (the Broadway show of "The Producers" had an awesome one) by which one actor (a "cipher") more-credibly portrays millions (figuratively) of people by using devices incorporating bent staffs or rots called "crooks"? Then Chorus says they are "ciphers TO this great account", not "ciphers IN this great account", in which "account" means two things: "a story, related under some circumstances of greater formality than relaxed speech". In a sworn deposition a story is an account or an accounting, but the formality can be less than a sworn deposition for a story to qualify as an "account". The second thing that "account" means, at the same time, is the running of a calculation or the adding of a sum, a piece of work by an accountant. To add ciphers "TO an account" (not IN it) is to multiply it by ten, or one hundred, or one thousand, etc., depending on how many ciphers are added. Chorus is saying that just as the most insignificant of all possible digits (zeroes) turn small numbers into large ones, so the mere actors who are ciphers will turn themselves into large numbers of combatants on a battlefield. Or if THEY don't do it themselves, your "imaginary forces" (in the last line quoted above) will do it. The "to" that isn't "in" might also be a comparison, as would be "He's but an ant 'to' his rival's elephantine strength and majesty", in which in Shakespeare's time it'd be normal to omit the word "compared" before "to". That "to" couldn't be changed to an "in" without creating a different sentence. There may also be a sense in which "an account" that is orated may be written down using symbols, which could then be called "ciphers TO the account", not "in" it. This is more of a conjecture, as it's debatable whether "cipher" was already used in its modern "cryptography" sense in Shakespeare's time, and if so it would require the additional wrinkle that a secret code isn't necessary to use the word "cipher" because there mere translation of SPOKEN words into WRITTEN words would ALREADY constitute, even WITHOUT encryption, some kind of "ciphering". Just as an aside, "Assume the port of Mars". As a child I thought that was some typesetter's error for "pArt of Mars". (Could ALL of Shakespeare's works have been typeset without ONE SINGLE ERROR that proofreading Shakespeare did not catch?) "Assume the pArt of Mars." But it turns out it really IS "port". I've seen it said that "port" means "demeanor, mannerisms, personality". Why not just say "a variation of the word 'deportment'" which is the easiest and most credible way to assert the same? How "port" might have these other meanings is a head-scratcher until the obvious synonym of same derivation "deportment" is mentioned, after which NOBODY would doubt it.

[@topherthe11th23]

TopherThe11th: Just to avoid debate, common sense would dictate that in Shakespeare's time CRYPTOGRAPHY was DEFINITELY used. I think Julius Caesar was seen (by a contemporary who wrote it down) to be toying with mono-alphabetic substitution ciphers, although I can't seriously believe he really used them for confidential communications as they'd be too easy to crack. All I meant was that while Elizabeth I and James I/VI MUST have used cryptography, the English-speakers of that time didn't CALL it "enciphering" or refer to the techniques as "ciphers". I will even wager that around the time there began to appear scientific instruments in brass and silver, and fine wood, of great beauty, there were similarly-beautiful machines for cryptography, and that wouldn't be TOO long after Shakespeare, and maybe even during his lifetime.

[@forthrightgambitia1032]

@@topherthe11th23 they mainly used cyphers that substituted non-Latin alphabet symbols for thosr of the Latin alphabet. One form of this was to replace letters by numbers - not in the order obviously - and thus the term cipher came associated with codes. There was no concept of statistical analysis of letter frequency at the time.

[@KyleMaxwell]

The history of mathematics is, for me, one of the most fascinating fields of study. Thank you for sharing this!

[@neilwoller]

Another fantastic video, Brady. You are a fantastic interviewer.

[@graduator14]

The book "Ground of Arts" is a second edition! The first title was actually "Sound of Farts" but it didn't catch on!

[@ke9tv]

Recorde introduced not only the multiplication symbol × with that big X, but also the equal sign =, which Recorde justified as 'no two thinges can be more equalle'

[@StoryMode180]

How have you not plugged Objectivity before this Brady?! I just watched your intro video over there, and that channel looks absolutely AMAZING! I've been a Numberphile subscriber for years, and had absolutely cipher idea that you had that channel just, hiding in the wood work. Instantly subscribed, it looks like I have an enormous backlog to watch now.

[@macronencer]

When I saw the thumbnail, I assumed this would be about the trick for multiplying two 2-digit numbers :)

[@martinwhitworth3989]

I enjoyed Rob’s talk on this at Cheltenham Science festival 2024. The reference to cypher is interesting, since I’ve long known the Henry V quote and thought I understood it but never really did. This makes sense and I’ll look up the other references.

[@DavidRoberts]

The equals sign guy! (Now I've watched the video, I see the invention of = is not discussed. .. 😢)

[@DavidRoberts]

"Cross-over"... groan

[@squidward5110]

The equal sign is honestly the least neccesary math symbol, in every language you could use the "to be" verb in its place and everyone would get it. I'd even go so far as to claim based on just a hunch that the = is a shorthand of the e in est

[@piepiedog1]

@@squidward5110 How do you mean? Are you saying the symbol itself should be replaced with a word, i.e. "a + b = c" replaced with "a + b is c" for English? In that case, it would defeat the purpose, given that the symbols are intended to replace words. Not to mention, there are other versions of equals that are not as easily replaced, like ≡, ≢, ⊨, ⊢, ≥, ≈, ≃, ≟, and ≔, among many others, and they are all based on = given some logical relationship to its meaning.

[@squidward5110]

@@piepiedog1 symbols are not intended to replace individual words

[@piepiedog1]

@@squidward5110 I didn't say that, I said they are intended to replace words. And in the past, a lot of math was stated only in terms of words which ended up making simple facts fairly cumbersome to write down. Plus, symbols are standardized for the most part, and thus you can read math regardless of what language you speak.

[@schemen974]

This is so fascinating!

[@waddupbro]

Please have Domotro from Combo Class appear sometime 🙏

[@wyattstevens8574]

"Heeey, welcome to Combo Classss... *dives for a falling clock* I'm your teacher, Domotro..."

[@Kwauhn.]

I would love to see him just talking about math in a semi-casual setting without the chaotic character and set pieces. Not saying I don't like those, though, just that it'd be nice to see him under the Numberphile format.

[@YonDivi]

That'd be so fun

[@tomkandy]

Nottingham uni might take exception to him setting their offices on fire lol

[@ND62511]

I second this, he would make a great addition to the Numberphile cast!

[@MichaelLoda]

Well that's the most fascinating I've watched this week

[@LAOMUSICARTS]

Amazing!

[@MagisterHenrik]

Wonderful

[@devttyUSB0]

This was fun! Thanks!

[@SG2048-meta]

Great video! (Not like I’ve watched it all the way through yet)

[@fphenix]

Who noticed the 9 in the 6s line?

[@CheatOnlyDeath]

Could that be very strange kind of historical typo? ...the printing press glyph for a 6 being laid out upside down and not caught until publication when it was too costly to reprint?

[@topherthe11th23]

@fphenix - To answer your question, @notnek12 is one person who, like you, noticed it. (I did not, until you and notnek called my attention to it). If you search the Comments you will find at least two and possibly more other people who noticed it. This is a horror to some people, because they are convinced that such a blunder is way too obvious to be a typesetter's mistake that got past a proofreading, and they'll go down a rathole for years trying to figure out the intended steganographic meaning of that "misprint", and whether it pertains to a hidden treasure-trove or not. If you're one of them, you need know only that the false king's nacreous hippos chew Bulgaria to ingest the teal galena's nutrients in order to find the Holy Grail.

[@Kyle-nm1kh]

Stamp was upside down

[@RFC3514]

It's a Parker 6. It's the right way up if you're Australian.

[@smylesg]

<a href="#" class="seekto" data-time="252">4:12</a> It makes sense it was only designed for digits 6 through 9 because otherwise the second column would be (difference from ten). You'd just be starting over again.

[@worldnotworld]

A small complication arises as soon as the multiplication of the left digits has a two-digit value: you have to "carry" the ten's digit calculated on the right and add it to the digit calculated on the left. For example, 6*7 gives us [6 over 7] on the left of the X, and [4 over 3] on the right multiplying 4 and 3 gives us 12. The one's digit stands; the ten's digit, here a 1, needs to be "carried" over the the diagonal difference of three, and added to it: 3+1. Then you get 42. So the notion of "carrying" digits appears here, as it inevitably will. It's a clever and possibly pedagogically useful trick -- but it doesn't get around the step of "carrying" digits that strikes fear into those who would make arithmetic painless... Is it better just to memorize "6*7=42," or to learn this technique to calculate it?

[@jansenart0]

The Bard had BARS!

[@steveb1243]

"the multiplication sign" is such a mouthful when referring to the symbol. I might edit Wikipedia and note that Numberphile viewers have long referred to it as a "haran". It might catch on.

[@Dreamprism]

🤯 Very enlightening on the times sign notation. And I'm reading in the comments about the equals sign notation too.

[@jesusthroughmary]

It's called The Ground of Arts because arithmetic is the first of the four mathematical arts (the Quadrivium, which along with the Trivium make up the seven classical liberal arts).

[@deltalima6703]

Why not list the others?

[@peterk822]

@@deltalima6703 Wikipedia

[@jesusthroughmary]

@deltalima6703 why list them, but ok The Trivium is grammar, logic and rhetoric, and the Quadrivium is arithmetic, geometry, music and astronomy.

[@NabeelFarooqui]

This was fascinating

[@Wolfram47]

“even if you’re a 10, you’re nothing without sum 1” - Shakespeare.

[@FishSticker]

Yay new numberphile upload I love you!

[@unvergebeneid]

Oh so is this why the multiplication symbol is × in English-speaking countries whereas a centre dot is used in some other countries?

[@robertolson7304]

The cipher is when you overlay the base numbers. Like 1/0 and 1/1. You can do amazing things with that. The 1/1 sets the rule it is always a whole number. 1/2 and 1/0 set the rule that its binary. The remainders are always half of 2. There's more, but it gets complex quickly.

[@sarahgargani5836]

The book was published in 1542. Henry the 8th split with the catholic church in about 1530 (he started trying to leave Catherine of Aragon in 1527 and it took a couple of years for him to see the church as an enemy in this endeavor.). If England was significantly behind in Mathematics in 1542, the schism can only have been a small part.

[@ErikRyde]

More math history videos please

[@chiquiramser9421]

Muchas bendiciones para usted y sus familias mucha hracias❤❤❤❤

[@whig01]

If Zero were a number, you would be able to divide by it. It has some but not all the properties of numbers. We treat it as a number, as with negative and complex values, but these are structures.

[@whig01]

If someone insists there are many kinds of numbers, then that is a terminology which needs refining to natural and unnatural.

[@Becky_Cooling]

I thought that the big X was what I got on my Geography homework...

[@ZedaZ80]

Actually, the big X is what I put on my cartography homework, and now I'm being followed by pirates :(

[@MattSeremet]

I'm loving hearing about these people who are famous for other things having a passion for math.

[@waterdragonlucas8263]

love u numberphile 🥺❤

[@riadsouissi]

chiffre, cypher, zero, etc all originate from the same arabic word, صفر , or sifr, which means empty.

[@criskity]

I wonder if "cipher" is where the word "zip" for zero came from.

[@Bacopa68]

Maybe, but then where'd "zilch" come from? For readers not from the US, "zilch" is a slang word for nothing. There is even the phrase "zip, zilch, nada" to mean "nothing". Of course, "nada" is from Spanish.

[@CheeseAlarm]

More videos on the history of maths please! (But not, of course, less of everything else)

[@robertolson7304]

mean median mode range is what is generally considered your zero. So it's not what is or isn't with Zero. 1 over 0 is a function. 0 over 1 is your (M,M,M,R). You can also have 0 over 2 .. that is when you have 2 functions at once.

[@alan2here]

(95 * 97) --> ((100 - 95, 100 - 97) = (5, 3), (5 * 3 = 15), (95 - 3) = 92) --> (92, 15) --> 9215

[@alan2here]

def multiply2(A : int, B : int, C : int): X = C - B return (A - X) * C + (C - A) * X # if C is a power of 2 then "(…) * C" # could instead be a bit-shift operation N, M = 58, 65 similar = 64 print("" + N + " times " + M + " = " + multiply2(N, M, similar))

[@azrobbins01]

Brady, do you have a link to the clip with you and the King?

[@jaromir_kovar]

Of course I've checked the wiki page right away and although Oughtred is credited, the proposed origin of the symbol is not there (yet) 😊

[@arpitkumargahlot]

This is one of the Sutras in Vedic Mathematics by Sri Bharti Krishna Tirtha Ji. While this work is more recent, this method can be traced back in ancient Indian arithmetic.

[@the_eternal_student]

I have not read the book about Shakespeare and numbers, but one thing you would want to include and speaking of King Lear is when the fool asks " Can nothing be made of nothing." And Lear says, no fool. nothing can be made of nothing. Most websites of favorite quotes from King Lear only include the quote from the exchange between Cordelia and Lear says something like, what will you speak?, and Cordelia says, nothing and be silent. And lear says, come now. nothing will come of nothing, speak again.

[@boerhae]

is there a reasonable way to do this for larger numbers? 603 x 367 left side: 603 over 367 right side: -593 over -357 multiply right side. i don't know how to do that in my head and getting a calculator seems to defeat the purpose. could i just do the process again? it just went in a loop when i tried. -593 x -357 left side: -593 x -357 right side: 603 x 367

[@DecayedPony]

Really would've been neat to learn this in elementary

[@JohnDlugosz]

<a href="#" class="seekto" data-time="67">1:07</a> This book is introducing Indio-Aribic numerals, but note that it already uses page numbers! The table explaining numerals and positional notation is on page 23. What were Britons using before? I suppose Roman numerals from the Roman influence, but what did they use before that?

[@elraviv]

<a href="#" class="seekto" data-time="123">2:03</a> in Arabic sifr (صفر) is zero

[@Peterseli3]

I'm Dutch and we use ''cijfer'' and it means digit or number.

[@robertfallows1054]

Pretty crazy. Gutenberg invents the printing press 1440 and 100 years later a handbook for arithmetic. Knowledge being spread - maybe not quickly but nevertheless. Question is - who could read it?

[@noterictalbott6102]

I like this guy

[@cristianseres1353]

The multiplication symbol in Finland is an interpunct or a middle dot ( · ) and this probably applies to Germany as well. We use a non-breaking space as a thousand separator and a comma as a decimal separator so there is no risk of confusion. Apparently all this is according to the SI system. 1 000,45 · 123,45 ≈ 123 456

[@phizc]

We use the same in Norway.

[@msolec2000]

Recorde also invented the equals sign, saying what could be more equal than two parallel lines of the same length.

[@birdoulini]

At the table of numbers, in the row of six (6) there is a nine (9) on the X. Of millions column. Is this a typo error or is something else???

[@ZaherHamiyah]

it came from france bcoz the origin was from Adalosiya where arabs pronounced it (seefer = صفر) and written by the french cipher not something myterious or code.

[@dennis2376]

Cool.

[@wiseSYW]

the big X method can be used in any base...but what's the point of multiplying something in hexadecimal? :P

[@calholli]

How am I just now hearing of your other channel?? WTF. I feel left out

[@numberphile]

Well get to work - kzbin.info - and tell your friends...

[@jb76489]

I’d be really interested to learn the history of orders of magnitude like million billion etc. Specifically when the average person on the street became familiar with the concept

[@bhatkrishnakishor]

That 8x7 method is also applicable to any number. This method is from Vedic Maths.

[@muhammetboran8782]

Now I know why 0 (zero) is called "sıfır" in Turkish. (Because the Turkish pronunciation of the word "sifir" is very similar to the English word "cipher".)

[@puyaa3000]

I believe, the word Cipher, is actually the Arabic word for zero "Sifr", and since the number entered by translation of Arabic literatures to Latin and then to English I think this is a more plausible origin. Please let the professor know about this.

[@lemuel32]

So Mercutio makes fun of Tybalt's novice swordsmanship in which he's simply drawing X's in the air! I think we've all wielded swords like that as little children

[@ForOrAgainstUs]

Interesting that Cipher means 0. In the Matrix, Cipher was a bad guy, the zero, the Judas, the betrayer of Neo, the hero, who was the One (1). 01. Also the name of the AI-Robot city in the Animatrix short, The Second Renaissance, Zero One (01).

[@jimbobago]

Google Books has a version of "Ground of Arts" but this section is on page 102 in that version instead of 71 as in this video.

[@roundaboutone]

I knew it worked with whole nr. squares, with n² having the same remainder as (10-n)², but not that this accounts for rectangles too; great.

[@fredg8328]

The common explanation is that the english "cypher", comes from the french "chiffre", which in turn comes from the arabic "sifr" which was thought to mean zero. Because we started to use indo-arabic numbers in Europe after translating arabic books.

[@emilellenius]

The big X method is actually great for doing the ~12 to ~20 times tables in your head since most people know up to 10-12 by heart! I tried it on 19×19 for example

[@Kyle-nm1kh]

There are faster techniques. 19x19 for example is just 19x20-19=19x2x10-19=380-19=380-20+1=361

[@Kyle-nm1kh]

You can also go 9x9+10x10+9x10+10x9. Which is 81+100+90+90=361

[@emilellenius]

@@Kyle-nm1kh I think -9×-9+10×(19-(-9))=81+280=361 is quite fast too. And while there are faster techniques for each specific case, this method would be quite fast up to the 20 times table while still being general.

[@Kyle-nm1kh]

@emilellenius I don't think it's faster and I don't think it's simpler and I think it's harder to do in your head too. I don't see a practical use for it outside of teaching.

[@TheWhitequark]

This is “cipher” which is transliteration of the Arabic word “صفر”, which means zero in Arabic, Urdu, and many other languages

[@hoppywern9057]

OMG ITS ROB

[@psmirage8584]

This is fascinating math history. Thank you. PS - I tried 7 x 3. That's why this trick isn't used for numbers less than 6.

[@phizc]

Still works, but you end up having to do 3×7 anyway in the second column. 😂 1×2 would be worse than useless.

[@rudranil-c]

I am not an expert, but looks like techniques inspired by ancient Vedic math in India. Vedic math students may confirm if that's the case.

[@bhatkrishnakishor]

Yes

[@fugithegreat]

Wait so is this process with the X where the symbol for multiplication comes from? 😮

[@manuelka15]

In Spanish we have the expressing "ser un 0 a la izquierda", to be a zero at the left (completely useless) 😂

[@jpkievit763]

In Dutch numbers are called 'cijfers'

[@U014B]

So people latching onto squares of numbers with big X's through them goes back even further than we thought...

[@meguellatiyounes8659]

always wondered how old math books made ?

[@awandererfromys1680]

<a href="#" class="seekto" data-time="752">12:32</a> It's not in the movie because it's a stage line, it's exposition for the audience. You can't fit a lot of people on stage so the audience is regularly told here's a multitude of people just off-stage to the left, use your imagination. In a movie you can just show that multitude. A lot of text gets skipped when adapting a stage play to a movie because it's considered 'scene,' not 'dialogue.'