The Big X and Multiplication - 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...

Also discussing the origin of the multiplication symbol.

NUMBERPHILE

Video by Brady Haran

[ididagood]

“You’re like a 10 without the 1” harsh burn from Shakespeare once again

[forthrightgambitia]

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.

[pyros]

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"

[Tekay]

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

[Oler-yxxj]

I love how he used (1:43) X to stand for "ten" in "X. of Millions". Such a fun quirk of the language of the time

[tonelemoan]

Robert Recorde, the noted inventor of writing stuff down.

[ketv]

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'

[dugferd]

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.

[mikew]

Such a banger of an episode… classic numberphile!

[thekaxmax]

'He's a cipher' is a saying that means 'he's an unknown' is the sense of 'we know zero about him'. Can also be used to call someone meaningless.

[smylesg]

11:52 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.

[mytube]

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).

[ZetaFuzzMachine]

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

[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)

[ObadaSaqqa]

Cipher sounds exactly as صفر which is zero in Arabic

[darkpulcinella]

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

[johannesvanderhorst]

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

[mihir]

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?"

[StoryMode]

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.

[KyleMaxwell]

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