Where do Mathematical Symbols Come From?

Where do we get our mathematical symbols from? Why is the set of integers called ℤ ? When was the equals sign first used? How about zero? Good notation tends to catch on quickly, whereas bad notation can obscure beautiful theory.
The lecture explores how the introduction of new notation has paved the way for new leaps in understanding, and considers some mathematical quirks of language, such as what the number 4 in English has in common with the number 11 in Russian.
A lecture by Sarah Hart
The transcript and downloadable versions of the lecture are available from the Gresham College website:
www.gresham.ac....
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[@AdamLovesMusic]

I love her energy and passion!! You can tell that she is very excited about what she’s talking about and it is lovely to see ❤️

[@theolguins2843]

What a lovely well delivered lecture! Her excitement for the subject is infectious, I wish all lecturers had this level of love for their craft!

[@SuLorito]

PRECISELY my sentiment.

[@Roedygr]

It is amazing how numbers started out complicated and evolved simpler,

[@jeaniebird999]

I don't think so, because, as humans, we like efficiency and it's part of our growth, as a culture, to learn from our past and improve what we already have. Necessity IS the mother of all invention and every time we make something easier, we have more time to focus on other stuff.

[@kokayiufanifu8309]

Simple is more efficient! Love is Caring, Sharing & Cooperation . . .

[@paulembleton1733]

Seems the other way round. Simple numbers is just knowing how many, as other animals seem to do. That became very cumbersome not because the system was complicated bur because things are complicated.

[@JJONNYREPP]

Where do Mathematical Symbols Come From? 2006pm 27.4.22 The nine figures of the Indians are with these nine figures, and with this sign o, which in Arabic is called zephirus....

[@epgui]

And yet we're doing the same thing today with programming languages, trying to make them look like English, but culture and tradition is so deeply embedded that it's hard to convince anyone that simpler syntax or more expressive symbols might be better.

[@renewable20002000]

Thank you .Very interesting and informative presentation. As an Indian, I am happy to have 28% in the 'whole world equation'. I am from Kerala, India. In Kerala we speak a Dravidian Language known as Malayalam. In Malayalam all roads leads to 2.

[@explorerc607]

I am always convinced that mathematical history and development is equally important to mathematical formulas as well as theorems, because knowing the origin will be definitely deepen the understanding of beauty of maths.

[@lisamuir4261]

This lecture makes it all so attractive. I've always been drawn to the 9s and apparently the writings of the numbers. I love this one.

[@shindousan]

48:08 Triangles, quadrangles, cinkangles (latin) vs trigons, tetragons, pentagons (greek). He was just being consistent with translations.

[@leosmi1]

LoL

[@user-xk2ot7eg7f]

Tri is Sanskrit , so is Kona.

[@user-xk2ot7eg7f]

And Pancha (Penta) too. Its not all European (as Latin and Greek). i.e : All modern numbers are Tamil letters.

[@mahatmaniggandhi2898]

🤡​@@user-xk2ot7eg7f

[@swamihuman9395]

Fantastic. Thoroughly enjoyable :) As a lover of math AND language, I was enthralled the whole way. Plus, I'm a teacher, so will surely pass some of this along...

[@jimroe850]

I just love this lady - could listen to her all day

[@leocomerford]

Turn on the English-language captions to witness a pretty memorable speech-to-text fail at 4:57 .

[@noelpucarua2843]

Well spotted. That was fun.

[@leocomerford]

@@forbidden-cyrillic-handle I always get the wrong one, thanks.

[@skuizhopatt5318]

And that seems not automatic transcription here...

[@motmahp]

So just a little town then.

[@horacenyc492]

awesome

[@mutualbeard]

A wise person once said that the limits of our language is the limit of our existence (paraphrase). It is fascinating to learn some of how language morphed into mathematics and from the concrete to the abstract. The pursuit of mathematics has given us powerful tools.

[@PaulTopping1]

The definitive book on this subject is "A History of Mathematical Notations", published in 1929 and written by Florian Cajori, a professor at UCLA. It is amazingly detailed.

[@Paraselene_Tao]

1:06:57 she did make a comment about Cajori. Thank you.

[@PaulTopping1]

@Polite Comments On Current Affairs Actually, not that much has really changed in math notation. Or maybe it changes so slowly that one can't notice it. I suppose there might be some notations used to teach mathematics but those are mostly new kinds of diagrams, rather than true math notation. Stephen Wolfram (Mathematica) tried to establish double-struck 'd' and 'D' as differential operators but, AFAIK, it didn't stick. With the advent of Unicode, mathematicians can use all kinds of odd symbols more easily but I'm not sure I would count that as a change in math notation itself. Systems like LaTeX probably have had a standardizing effect on math notation. An update could talk about math notation on computers, something I know a fair bit about, but that would stretch the topic too far, IMHO. It's probably one of those cases where there is either nothing to say or too much to say. It would be hard to know where to draw the line.

[@Paraselene_Tao]

@Polite Comments On Current Affairs Haha, that was a little bit my opinion at first, but the majority of mathematical notation hasn't changed in 92 years. Many books about niche subjects remain powerful for many decades after their publication. I'll take a look at the book next chance I get.

[@chrisg3030]

The Greek alphabetic representation of numbers reminds me of what an amazingly useful invention alphabetical order is. It enables you to find a name like Kuczynski, Ishak in 10 seconds in the London phone book, something which would otherwise take as many hours or even days (though of course this advantage has now been outmoded by the computer random access memory). When I was a kid I was as proud of reciting the alphabet as of counting to a hundred.

[@vekyll]

outmoded - not at all. Computers use binary search as much as people, perhaps even more. Random access memory is what makes binary search possible, after all. There it's a matter of milliseconds vs minutes, but still a pretty big deal.

[@chrisg3030]

@@vekyll I'm interested to read that alphabetical order still has its uses even in computers, which admittedly I don't know much about. What I was vaguely thinking is that you can have a long list of names, say a million, which have been entered into a computer memory in completely random order, unlike in an old-fashioned printed phone book, and the computer will scan them all in a second or two and pick out the one it's been told to. But maybe there's more to RAM than that.

[@skepticmoderate5790]

@@chrisg3030 That is called linear search. It is fine when your phone book only contains up to thousands of names. But some lists of sorted items that computers deal with may be up to the millions. In this case the difference is stark. Using linear search on a million names could take more than 1 million memory accesses. Using binary search on a sorted version of this list takes log2 1000000 == 20!. That's 5 orders of magnitude faster! This adds up when you are doing such computations many thousands of times per second as many servers are. If we didn't use binary search, computers would grind to a halt. The study of such relationships is called "time complexity analysis." Similar analyses can be conducted for space (memory) usage. This is known as space complexity analysis. The interplay between data structures and algorithms leads to trade-offs in time usage and memory usage, known as time-space tradeoffs. These form the very foundations of computer science.

[@GordieGii]

@@chrisg3030 They can be entered in random order and it will take several seconds (or minutes) to scan them all for a match, but when the computer is sitting idle it can sort them so the next time someone searches for Kuczynski it only has to scan all the names that start with K, and the next time it only has to scan the names that start with Ku, etc, each time finding the target faster than the last.

[@davidhanson8880]

This was wonderful! Thank you so much for making this public!

[@GordieGii]

The dollar sign: We use the S with a vertical line through it, but it used to be an S with two vertical lines. (you may have seen it) originally it was an S with a tall skinny U through it. U.S. Before that the S overlapped the right half of a normal width U. The word 'dollar' came from the Germanic word 'thaller' (pronounced taller) which referred to a silver coin that was used all over Europe.

[@Merione]

15:00 In Italian to this day we still say "fare i conti" (= make calculations) to someone if there's an argument to settle down or a situation to resolve.

[@olivier2553]

Living in Thailand, math is the only topic I can help my kids with, because of the internationality of the language.

[@HuckleberryHim]

I would hope you can at least speak Thai, though I know the reading and writing is very difficult

[@olivier2553]

@@HuckleberryHim Oh I speak Thai, and can read the signs on the road (and the menu at the restaurant) but if I can copy a word, I definitely am not remembering the spelling of the words by myself.

[@DynestiGTI]

There's a reason the division symbol is not on the golden record. NASA didn't want aliens to lose their minds with BODMAS

[@royjohansen3730]

To paraphrase Julius Caesar: "Divide by zero and conquer."

[@klammer75]

Awesome! Love this connection between notation and language which of course reduce to abstraction which IMHO is the key to our minds and perhaps intelligence and cognition itself! So cool🤪🤩🤯

[@climbeverest]

It is a privilege to see and hear a true mathematical genius speak, just imagine if we had lectures of descartes or newton available in 1040

[@chennareddyb6261]

Wonderful lecture. Thank you professor 👏👏

[@barrycrump6189]

A thoroughly enjoyable and informative lecture. Thank you.

[@leosmi1]

It's mindblowing how the symbols affects the complexity of mathematics

[@ichigo_nyanko]

As a mathematician (and I admit, I've only watched until 2:20 thus far) I have some criticism with the first slide. The examples of the operations isn't done well in my opinion. The division sign isn't defined in any meaningful way at all. Without the concept of our notation of a fraction these examples are quite useless(think about how different fractions and decimals are - imagine what other ways aliens could have come up with to represent the rationals), as well as the mixture of mixed and complete fractions muddling it up further. A simple way we could have avoided that is by stating a simple identity (an identity which in fact is essential to fractions in mathematics) and built up from there. Reciprocals. Now imagine we wrote this instead 1x1=1 1x2=2 2x3=6 ----------- This first section gives a basic understanding of multiplication. As none of the other basic binary operations has O(1, 1) = 1 except division 1/2 x 2 = 1 1/3 x 3 = 1 1/4 x 4 = 1 ... ----------- This now shows the alien that 1/x is our representation of a reciprocal. Reciprocals are very important in mathematics and the aliens will no doubt understand what they are. Along with 1x1=1 and 1x2=2 showing the aliens that 1 is our identity for multiplication, it is very natural for them to understand exactly what division is (the inverse of multiplication) due to the nature of the reciprocals. We can now move on to the complex examples shown to reinforce our notation in particular and its quirks. In my opinion it would be beneficial to repeat this entire process for addition and subtraction (show how 0 is the additive identity and then show negatives are the reciprocals of positives and subtraction is the inverse of addition). By doing the same process twice here the aliens, if they only understand one of the concepts well, can apply it to the other.

[@twosongs7396]

Where are all these BEAUTIFUL people whom are not only so intelligent but also most passionate about their chosen scientific field? I need them to roam in my immediate circles.

[@shahzadmughal7666]

So zero '0' was most useful and underrated sign. Edit: and as a move to watch I realize that minus or negative ' ➖' was most hated sign.

[@DavidLindes]

21:21/21:29/21:39/21:43 - this gives me hope. It will take time, but eventually, we’ll all use tau instead of pi. 😁 Also, just a super cool talk overall! (at least so far! I shall now continue. 🙃)

[@DavidLindes]

P.S. re 51:09/51:35 - and here, those who’ve seen arguments for the use of tau, among certain others, may have a sense of intuitive understanding of why these do relate to each other. I believe 3blue1brown talks about it (somewhere in his library) without necessarily adopting tau, and of course the tauday manifesto talks about it as well.

[@DavidLindes]

52:46 - Hmm. And I thought pi went back to Euler as well... though is the person cited here the one who popularized the particular value, from one of the several that Euler would use (at least three: circumference/radius ≈ 6.28, semicircumference/radius ≈ 3.14, demisemicircumference*/radius ≈ 1.57) depending upon the needs of a particular problem? * given that word with all the z’s, I figured I’d call a quarter circumference this way. ;)

[@Plut0-YT]

Great lecture! Some entertainment when the summer break has started! // Student of the Royal Institute of Technology in Sweden

[@OBGynKenobi]

The record has a record of record. What a record!

[@Oscar1618033]

"what's a mile?" Neither most of the world knows.

[@pedrosso0]

A swedish mile is equivalent to 10 km

[@benjaminwasfound2]

1.6km.

[@Oscar1618033]

@@benjaminwasfound2 yeah, I know how to use Google, it was a joke on the fact that other than the USA almost no one else in the world actually uses it...

[@Markle2k]

@@Oscar1618033 Never been to the UK? Her point with the mile example stands as firmly with the kilometer. An alien is not going to find much use in the original definition of 1000 (kilo) times 1/10,000,000th the distance from the equator to the North pole along the meridian running through the Paris Observatory.

[@Roedygr]

I really enjoyed this lecture. It was full of surprises.

[@Li.Siyuan]

Just for you edification, Arabic always writes numbers left to right, NOT right to left, so unless they changed things in the last 400 years or so, your presumption is incorrect. Secondly, the Arabic for 'zero' is, (transliterated), 'sifr' from whence comes cypher/cipher, zero, etc.

[@DanielVCOliveira]

Maybe Fibonacci commited the exact same mistake as her lol

[@shubhammeena5177]

How did Shunya (Sanskrit for Zero) turn into Sifr in Arabic? Any idea? What word did Khawarizmi use in his book?

[@peterholzer4481]

Arabic is written from right to left, so if an Arab writes the first nine natural numbers down in order (i.e. first "1", then "2", then "3" etc. until "9") the "1" would be at the right edge and the "9" at the left edge. A European would write them in the same order but starting at the left, so "1" would be at the left side and "9" at the right side. Therefore it is curious that Fibonacci wrote the numbers in this order and it is plausible that he copied the line from an Arabic manuscript, preserving the optical order (and thus reversing the logical order). Also I always find the claim that "numbers are written from left to right in Arabic" a bit dubious. If somebody writes in Arabic (or Persian or Hebrew or other language written right to left) "this video has 37518 views", do they really write "this video has" from right to left, then jump a bit to the left, write 3 7 5 1 8 from left to right, then jump left again and write "views" from right to left? That doesn't sound plausible.I think it is much more likely that they would write "this video has 8 1 5 7 3 views" continuously from right to left. Note that result on paper looks the same (3 is on the left, 8 on the right) you can only tell the difference if you watch somebody actually writing.

[@carultch]

@@peterholzer4481 QUOTE: Also I always find the claim that "numbers are written from left to right in Arabic" a bit dubious. If somebody writes in Arabic (or Persian or Hebrew or other language written right to left) "this video has 37518 views", do they really write "this video has" from right to left, then jump a bit to the left, write 3 7 5 1 8 from left to right, then jump left again and write "views" from right to left? Response. To answer this, I'll write an example in a mirror imaged Latin script. .ƨwɘiv 37518 ƨɒʜ oɘbiv ƨiʜT The text is written from right to left. The number has its one's place on the far right, and its ten-thousands place on its far left. The number is still written optically, the same way it would be written in English, just with the text reversed around it. Even if using the traditional Arabic script for the numerals, it would be written this way. Hebrew numbers in text would also work the same. If there are unit terms that go with the number, they would appear on the left of the number. For instance, suppose I'm writing: "The cup is 25% full.". It would appear as: .llυʇ %25 ƨi qυɔ ɘʜT

[@peterholzer4481]

@@carultch Yes, I know what the result looks like. What I'm interested in is the order it is written. In ".ƨwɘiv 37518 ƨɒʜ oɘbiv ƨiʜT" obviously the first character written is the T at the right and the last one is the "." at the left. But what about the number in the middle? Do write down the "8" first immediately after the "ƨ", then "1", "5", "7", "3" steadily progressing in your normal writing direction? Or do you write the "3" first (leaving enough room for the other 4 digits) and then "7", "5", "1", "8"? If it makes a difference, I am more interested in how it is done with pen on paper than with a computer (because the technical constraints are very different). (Also, since your name looks even less Arabic than mine, do you speak Arabic or any other language written RTL? If so, when and how did you learn it?)

[@davidjones5319]

Thank you. Loved it

[@rogerparker3422]

A very enjoyable lecture - thank you!!

[@mz1rek]

Answer to the rhetorical algebra question 25:04 is 15. 1/3 is 5 1/5 =3 3*(5-3)= 6 and 15-5-3-6=1

[@54m0h7]

26:05 There are 15 bees. Great lecture!

[@Paraselene_Tao]

I got 15 bees too. I used modern algebra though. I don't know how I can solve something like that without algebra. 😁

[@ksbrook1430]

A gem of a lecture.

[@rodaross]

This is very interesting, but the question about colonialism is verging spooky. Mathematics is currently expressed in a universal language constructed throughout OUR history. That is the only cultural thing to consider. It is not the result of one culture is the result of many cultures. It is the result of human culture. A long time ago a Chinese man created a much better numerical system than the one in use in China at the time because he needed to do the computation to build the Chinese wall. That system was sadly forgotten. None is sure why was forgotten, but it seems that in a country that valued tradition over innovation that change was not possible. On the other hand, when Indian numbers came to Europe they were adopted in a century.

[@IZEASGT]

One interesting thing about exponentiation - in type theory, it corresponds to function types, like how tagged unions and tuples are sum and product types. But whereas exponents are commonly written like 2^5 (or with a superscript 5) for 32, the equivalent function type would also be written 5 -> 2. Which makes some sense, because A -> B is the type of a function with input A and output B; we think in chronological order from left to right. And the other notation has some mental logic to its order too - “take this, multiply it by itself this many times”. So in a world where the same notation was used for both function types and arithmetic, which order would the terms go in?

[@jamcdonald120]

Well that explains why we get descriptions of gravity being "inversely proportional to the square of distances"

[@Jatski_pelaa]

this is so wonderfully interesting

[@timothylunde]

Absolutely fascinating 👍

[@danilojrdelacruz5074]

58:23 Alamblak has yima yohtti tir yohtti hosfirpat for 28 which has 28 letters.

[@Piaseczno1]

Insightful lecture. Thank you. But what in the world is that popping or knocking noise in the background?

[@joepike1972]

It sounded like a bored student or someone chopping wood.

[@alwantamalus3709]

In maths X is symbole of unknown or undefined thing or quantity, X came from arabic Sh (ش) first letter of word "Shay' " which means "Thing unknown/undefined", Latin translators turned Sh to X as pronounced in Spain.

[@LuckyXPUltra]

Wow. I really like this. Maths is the queen of science. Imagine if there was a symbol that will represent repeating exoplements.

[@redapplefour6223]

we have a couple. it's generally called tetration, and there's quite a few ways of notating it. the most used ones are the number you want in the "exponent" being written before the number in super script, like ⁿa, which is nice, but of course after tetration we have pentation and hexation and such (although tetration is the highest one with any practical use), but there's the knuth up arrow notation which extends it which is a bit complicated to explain in a comment so you'd just look that up on your own, and there are other ways of going higher, but it gets very complicated indeed after there.

[@mrpedrobraga]

@@redapplefour6223 I go python style and use a ^^ b

[@MrAlRats]

The symbols that we use for logarithms, n-th roots and exponents are all terrible. We should be using symbols which clearly show the relationship between those three operations.

[@epgui]

It would be interesting to take this same lens, and turn it towards programming language syntaxes. I would strongly suspect all the languages that are trying to look like English (eg.: python) are going in the wrong direction, and that some stranger notation (eg.: lisp with its simplicity, or even APL with its expressivity) is actually more what the future will be like.

[@CLipka2373]

Interestingly enough, the word "sine" happens to sound similar to the German word "Sehne", which literally translates to "sinew", but is also used to denote the string of a bow - and, in geometry, any straight line between two points on a circle.

[@kenbob1071]

You could have used decimal points on the voyager record without them being mistaken as damage by including the number in decimal form after each fraction. It'd be too much of a coincidence that there was damage in each number.

[@FalkBay]

you made my day, thank you

[@jyleehk]

i just wonder in case Alien mis-interprete "=" as one of the digit, it will confuse them for a while :-)

[@metametodo]

I thought the same at the moment, I actually thought and think she wouldn't adress it, but then she did. However, now that you mentioned, I think it'd be a little bit safer to think of = as comprehensible, as it showed up everywhere and yet in a strategic location, being different from other symbols. Still, That record seems quite the challenge for aliens to understand overall.

[@MrAlRats]

Realistically there is no possibility of any aliens deciphering the golden record even if they find it, so don't worry about it. There's no reason to think that aliens would have any notion of visual symbols. If they even have sense organs capable of detecting electromagnetic radiation, it is likely to be a different part of the spectrum to what we see. Even if they can biologically sense visible light, for them it may not play the central role that it plays in us for forming our perception of reality. Imagine if they are creatures who communicate via chemical signals and their perception of the world is primarily shaped by sense organs that detect the rate of heat flow. Also the aliens may not be able to manipulate objects of the size and shapes that are found on the spacecraft. Suppose they have to invent machinery and invest huge resources to be able to just handle, dismantle and manipulate the objects. They may not bother with it. Another thing is that if it is found in a few billion years it may not be readable any more.

[@tudornaconecinii3609]

@@MrAlRats Our sight, while confined to a narrow slice of the electromagnetic spectrum, is not confined to an *arbitrary* slice of the electromagnetic spectrum. The reason why visible light is the interval that is visible to us is because that is the interval within which the emission spectrum of G-type stars peaks. And our sun is a G-type star. So it makes sense for us to evolve eyes that are best at detecting *that* radiation, since it's the radiation that we get the most of and thus would be the easiest to detect. So actually, it wouldn't be that surprising or coincidental if there are alien species out there who not only have evolved the sense of sight, but see a similar part of the spectrum as us.

[@nickieshadowfaxbrooklyn5192]

If you have kids, you might notice how 2/3 graders play with it, by cracking cyphers where randomly usual symbols are replaced with some pictures or pictograms. Works perfectly fine for 5-7 year olds. Why wouldn’t it be the case for highly intelligent beings? Don’t see any problem as long as logical bases are the same. Yet with animals tests show that logic works without language or even culture background. Cuz it is logic. Similar to math, it is universal. Coincidentally universe is a word of the same root. Pun was indeed intended.

[@lowenzahn3976]

​@@MrAlRats If they are a spacefaring species they surely have tools that can detect and measure physical quantities beyond their own limited perception just like we have.

[@DevilishScience]

Excellent talk.

[@ПетърПетров-ъ9л]

Personal offense so hard, so it has to been banned, not by legislative, but by mathematical laws. "Oh, you are not nothing, my king. Somehow, your Majesty, you are not even that." So how it is possible that the king is somehow less than nothing? No, he is not! Not even that. He is not a negative number, nor anything else. At best, he is just not. So nowadays if someone tells me that I am a zero, then at least, I would be something, I am nothing, but still am something.

[@allanrichardson9081]

As an American, I have never heard of Gresham College. Does it have any connection with the economist who posited Greshams Law, that cheaper money drives more valuable money out of circulation? I love your lecture, by the way.

[@paululje4555]

About the Dutch who do not understand the language say: its Latin to me. We rather say it is Abacadabra. Perhaps Arabic? :-) Nice lecture by the way!

[@91099Babar]

Hi , I have a Question . I have understood where they have come from . Actually, I am interested to find out the Symbols used in Maths, Calculus & Physics . What is the secrecy behind introducing Symbols & Notations while investigating an economic or engineering issues ? Cheers !

[@RenatoRamonda]

One interesting bit of numeric notation that had very little standardization (and that people tend to forget about): money amounts. Non only where the currency symbol goes (in front of the number, or not, with a space or not, but also (and this is highly local/cultural) how (if at all) are cents (or other fractional amounts) noted? Especially when the number is whole, with no cents? With non-decimal systems like the old British one of course there was a lot of odd notations, with and without fractions, but even today in countries that simply use decimal based systems... in Italy with the Lire (in the post-war period) the problem was non existent: due to inflation, the smallest coin denomination was 50 Lire, and decimals were only relevant when doing accounting. Now with the Euro cents are common, and GENERALLY But for example in Switzerland It's pretty common to write like... Sfr 10.- (to denote there are no cents). This looks super odd to most Italians, I'm sure. Or, it's very common to see sign with the cents written really small at the exponent position, like $ 10.⁹⁹ (I've seen it with dollars, and I think with Pounds).

[@josephswafford7578]

I'll watch tomorrow..

[@MrGerryodonothing]

The symbol Pi was first recorded in éire in Bronze age times (according to archaeologists). It is a member of the Ogham class. It is more of a key as 3.14 is only one of it's attributes. Of course it is much older than the Bronze age.

[@staninjapan07]

wonderful

[@ollimekatl]

The Egyptian and Sumerian counting systems are similar to Olmec, Mayan, pre-invasion "mesoamerican" counting system. I’m not surprised because theres evidence of humans migrating here as far back as 400k, 200k, 100k, 90k, 50, 40, 25, and 10k years. For the time of pre-olmec civilizations there was 0 and it’s symbol was the conch, but it was not used in math but in cosmology, representing energy and matter emanating from the quantum realm and spiraling out in fractal form, hence we have the half conch symbol worn by Olmec etc scientists, exposing the spiral which meant you had this understanding . The numbers 1-4 were dots …. and 5 is a dash -. Two dashes = were 10 and instead of 20 being 4 dashes, within a square work space, it was a dot placed at a higher level, with single number dots and dashes represnting 5 being at the bottom of the square work space. So a dot placed at the top of your square could be added to, subtracted from, and divided by dots and dashes. 1-5 were also used to represent the female body and so creativity. 6-10 as well used for counting and represented the male accompanying numbers to the female numbers. Obviously there were larger numbers but you can look that up and maybe find something reliable. 13 symbols were a week. There were 20 months that used those 13 symbols only. There were 5.25 days to complete the cycle. 52 years are 1 full asrtological alignment cycle. The solar, lunar, venus, martian and other planetary counts were considered and part of the count as well. Math was used to build thousands of structures from central mexico to central america, all of which were aligned with constelations or marked solar, lunar, and planetary zeniths. There is evidence that corn was being cultivated as early as 9k years ago - also that it’s a central theme in the culture and philosphy with 8k year old figures showing corn symbols on their heads, in Baja Ca - there are paintings of a calendar count 8k years ago in Guerrero Mexico, showing an aligator which represnets day one of a certain count and dog which represents the end of that count, showing its a section of a calendar and not a complete count which was already known - these symbols were used from that time up to the Olmec civilization that probably perfected and formalized it - they were shown recently to be a language and not just symbols - and it is largely ignored and underrepresented in world history. Thats 8k years of continuous development of a culture, language, philosophy, count/calander, and civilization. Don’t mind us, we’ve been here for a while.

[@joepike1972]

40:41 You are as likely to need to differentiate a variable 8 times as you are to need to raise cut a piece of toast in half eight times. Generally three is the max you will used to determine the curve of a function. And for students performing algebra the Leibniz notation looks and feels as cumbersome as using p. for plus and m. for minus in the other notational system. Students much prefer using y' or y'' vs dy/dx and d^2y/dx^2, infact they often get really confused but why the two is placed where it is. I say this as a tutor of calculus.

[@terahlunah]

It's been a while since I used d^2y/dx^2, and I forgot why the 2 is placed that way, it used to make sense to me but now it's back at confusing xD

[@ampleyfly]

But what about functions of multiple variables?

[@Toastwig]

thanks for this, really interesting!

[@johnstfleur3987]

UNDERSTANDING.

[@aku7598]

4k is only recently popular where previously 4 thousands were used.

[@christophersedlak1147]

thanks

[@book3100]

That was fun!

[@EyeLean5280]

Does anyone know if the math and art lectures will be available on KZbin?

[@Joseph-tm5vv]

Feynman diagrams are derived from when he was high on psychedelics!

[@joboteyechew3751]

Great lecture. It got me thinking and wondering: why do we have (in English) eleven and twelve and not oneteen and twoteen? And why thirteen and fifteen and not threeteen and fiveteen, yet we have fourteen, sixteen, seventeen, eighteen and nineteen?

[@stephanierichards150]

I don't know, but here are some of my initial thoughts. Eleven and twelve probably come from the idea of base 12. As for thirteen and fifteen, we also say thirds and fifths, as opposed to threeths and fiveths, so they probably have the same origin (which I don't know).

[@andrew7955]

They come from the original Germanic words for them. If you notice in the start of the words, there is ele- and twe-, both of which are clearly related to one and two (ele is like the word for one in all other Germanic languages). Therefore, eleven and twelve are similar to oneteen and twoteen. As for why it's thirteen and fifteen, that would come down to shifting pronunciation based on the surrounding sounds. It's much easier to say thirt rather than threet and fift rather than fivt. It's basically just how speakers say words in such a way that is easier to them based on what the other sounds are. Also, related to Stephanie's above comment, I suspect the reason we use fifth and third is for similar reason. Before language was mass produced by the printing press it was much more fluid (just take a look at all the words that meant church or egg in England before 1400 AD). Whatever was dominant and was easiest for those using the language to say was what became used. Of course, these reasons are all my somewhat educated speculation

[@peterholzer4481]

@@andrew7955 eleven is e-leven, not ele-ven. Similarly, twelve is twe-lve. They mean one left and two left (over ten) respectively. I think Stephanie is right about 13 and 15: "third teen", "fourth teen", "fifth teen", "sixth teen" with the "th" being assimilated makes a lot of sense. A pronounciation shift only affecting 13 and 15 less so.

[@carultch]

Might have to do with coming-of-age traditions. In Spanish, the number names are unique from 11 through 15, and don't start following the equivalent of our "teen" pattern until 16 (teen would be diesi followed by the number in the one's place).

[@AbuMaia01]

Very disappointed that only = was discussed near the end of the video, + got barely a mention, and nothing said at all about "x" (multiply) or the bar with two dots for divide, or - for subtract.

[@williamevans9426]

Robert Recorde - hurray from a fellow Welshman!

[@harrisibrahim2225]

so jiba -> Juba -> Cavity -> finally sine precedes Pythagorus ?

[@MrBeen992]

15:22 What was the purpose of erasing Arab from the Arabic-Indian Numerals ? Although the Hindu-Arabic numeral system was developed by Indian mathematicians around AD 500 quite different forms for the digits were used initially. They were modified into Arabic numerals later in North Africa. So Arabs were responsible for popularizing the decimal numeral system AS WE KNOW IT TODAY.

[@PhilBagels]

Right. And the symbols 1, 2, and 3 were from a fairly universal notation - they're based on simple tally marks. Similar to the Chinese numerals for 1, 2, and 3. One vertical tally mark is the number 1. Two horizontal tally marks, dragging your pencil to connect them, forms the numeral 2. Three horizontal tally marks, dragging your writing implement to connect them, makes the numeral 3.

[@Subudhdh]

no the digits themselves are from India.. only . (bindu/sunya) od India became an oval shape zero.. rest of the digits and not just digit but the properties of additions, subtractions come directly from Hindu books

[@Subudhdh]

so it is not just digits but the formal decimal system, properties of additions, additive identity etc that came from India..

[@PhilBagels]

@@Subudhdh What do you mean by "properties of additions, additive identity etc". Those things are properties of the numbers themselves, regardless of the system of notation.

[@Subudhdh]

@@PhilBagels what do you mean those are properties of number themselves, whole science/physics is property of nature itself, but somebody needed to discover them, Hindus/Indians defined the properties of zero, and also the way you do sum today, so zero is not some dumb concept like just nothing that they discovered but the place holder, its properties, how you add and carry over, so the decimal number system that you use today was invented by them and initial algebra as well, which then Al Khwarizmi wrote about in his book Hindu mathematics. Hindus taught world how to write, count, how to sum, subtract decimal numbers the way you do today.

[@yousteveaaaa]

I have read about a different origin for + and - ... Denis Guedj talks about it in his book "the parrot theorem". Maybe he made up the story or maybe Stiffel was the first to use the symbols officially

[@asimt2507]

Simply Superb !!!

[@oswaldoramosferrusola5235]

4 is my favourite number too.

[@platypao]

Lovely talk.

[@dyamiconley9448]

You are adorable the way your just so full of energy talking maths. Hel yeah

[@chrisg3030]

I just about managed that Bhaskara one about the bees with my trusty but rusty high school algebra, where x is the number in the swarm so formulate it as x/3 + x/5 + 3(x/3 - x/5) + 1 = x. How would it have been done without that symbolism? Maybe knowing that the answer must be a multiple of 5 and 3, so start with the smallest number satisfying that, namely 15, and try it?

[@parlabaneisback]

I attempted it, but ended up with an Eric-the-half-a-bee left over. Not sure what the symbol for an Eric is; perhaps an antenna, half a head and 3 legs - \DIII

[@joepike1972]

1/3+1/5 was also written on the voyager plate. I thought about it while I did the problem in my head. I didn't formalize it with any kind of algebra. I just considered adding the 1/3+1/5 first. That reminded me of the 8/15 on the voyager tablet. I recognized the remaining bees would be seven, provided there were 15 bees. I then kind of stumbled over the difference between five and three was two, which when multiplied by three did give you six, which happened to work out that adding a bee gave you the seven. I suppose you would have incremented by multiples of fifteen otherwise.

[@scragar]

You get the right answer pretty quickly by just assuming a large number of bees(1000). 1000/5 = 200 bees 1000/3 = 333 bees 3 times the difference = 399 bees If our 1000 bees was correct we should have 1000-932 = 68 bees left to account for, which we don't, we only have 1 so really 68 bees in our 1000 assumption are really 1 bee. 200/68 ≈ 3 333/68 ≈ 5 399/68 ≈ 6 68/68 = 1 So adding them up we get an answer of 15 bees. I expect this is probably how most people would solve the problem before being able to write it as algebra as it's a very intuitive solution(try with a huge number so rounding errors are negligible, get a conversion, work back to the original answer and verify).

[@timharig]

You could do it using geometry. You could for instance use a circle to represent your unknown, and apply the known quantities like slices of a pie chart. When you have removed everything else, you are left with the remaining area representing the value of the lone bee and its fraction of the full circle.

[@anonymic79]

If you're lecturing on number systems and the writing systems used you should know that 63 in Babylonian would be written 13 in base 60 so the "60" is in fact a one. Its not problematic, its literally how you use numbers everyday.

[@KaiHenningsen]

That is exactly what I took from the lecture, so I'm unsure what your point is here.

[@anonymic79]

@@KaiHenningsen She said the 1 in 63 was problematic, its not, its how you write 63. She's speaking about this kind of thing like she's just seen it for the first time.

[@0Coeus]

@@anonymic79 She did not say 63 was problematic, but the system. This was because their representation of 60 and 1 was indistinguishable outside of context.

[@anonymic79]

@@0Coeus it is not out of context, its 63. There aren't any other numbers it can be. You don't look at 13 and wonder what this 1 is for in decimal.

[@0Coeus]

@@anonymic79 again, the problem number is not 63, it is 60. We all agree with you that 63 is unambiguous, the lecturer included. She said the problem was with the number 60. 60 and 1 look the same since they did not have our equivalent of 0 as a signifier of nothing in the units place.

[@ronaldjorgensen6839]

IS THERE BEST BOOK ON mathematical symbols SAW ONE BEFORE HAD MY SYMBOLS MEMORIZED INCLUDING ORIGION USE FORGOT MOST NEED HELP?

[@skepticmoderate5790]

I wouldn't say that Leibniz notation is superior to Newton's. Newton's notation is most amenable to physical functions of one parameter (usually t) because we usually only care about the third derivative or lower, thus no more than 3 dots are needed. Lagrangian notation (not described in this lecture) is like Newton's notation, except the variable with respect to which we differentiate is explicitly written as a subscript (f_x would be the derivative of f wrt x). This allows us to generalize derivatives of one parameter to derivatives of many parameters, which are extremely useful for things like heat transfer. If we need to use derivatives of very high degree, or many parameters, then Leibniz' quite verbose notation finally becomes necessary. IMO we should avoid Leibniz notation like the plague unless it is required, because it is so verbose.

[@georgesos]

In Greek the cycle is between 4 and 7 (τεσσερα and επτα)

[@JaniceLHz]

In German, everything eventually goes to 4. My reasoning: The only way to get a cycle is if the word for a number has more letters than that number. There are only 3 such numbers in German: 1"eins", 2 "zwei", 3 "drei". 4 "vier" also has 4 letters, so every number larger than 4 will eventually go to 4. Examples: 20 "zwanzig" -> 7 "sieben" -> 6 "sechs" -> 5 "fünf" -> 4 "vier" ⮌ 67 "siebenundsechzig" -> 16 "sechzehn" -> 8 "acht" -> 4 "vier" ⮌ 110 "hundertzehn" -> 11 "elf" -> 3 "drei" -> 4 "vier" ⮌ 747,797 "siebenhundertsiebenundvierzigtausendsiebenhundertsiebenundneunzig"-> 65 "fünfundsechzig" -> 14 "vierzehn" -> 8 "acht" -> 4 "vier" ⮌ The longest numbers up to 999,999 are 65 letters long, so surely every number larger than that is named with fewer letters than the number is.

[@kd1s]

Then we get into number systems like binary, octal and hexadecimal. Those play very big in my life and career. Regards dimensions are we a 3D world or 4D if you include he dimension of time.

[@christophersedlak1147]

Thanks!

[@clydecessna737]

Thank you.

[@quinktap]

How would one translate brush strokes on a canvas, a musical composition? What are the math's one may use to explain creativity?

[@ansfridaeyowulfsdottir8095]

The Babylonian system is not "Base 60" any more than our system is "Base 100". Their system was _based_ on the number 60 as they used finger joints as well as fingers, but it was not "Base 60" and I don't know why people say it was. If it were "Base 60", we would have to count something like: 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, α, ß, Γ, δ... and so on up to 10. 60 in so called "Babylonian Base 60" is 60 in Base 10, so it's obviously not Base 60. If it were Base 60, then a Babylonian 10 would be 60 in Base 10. Compare with Base 2, Base 8, Base 16 and so on. 10 in Base 16 is 16 in base 10, and 10 in Base 10 is A in Base 16. QED. {:o:O:}

[@vincentm9174]

Fascinating 😊

[@endhimrightly3408]

1:03:09

[@millaheska3351]

Muhammad ibn Musa al-Khwarizmi was Persian, not Arabic, so were most of that time scientists. Yes, there's a huge difference.

[@tomasruzicka9835]

shouldn't there be a zero before you introduce 10? (on the voyager)

[@peterholzer4481]

They still didn't like zero.

[@davypi2]

About every four or five seconds in the background you can hear a thump or some sound like something is hitting the ground. Its really annoying. I realize you probably wont re-record this, but maybe you can be more mindful about studio noise in future recordings.

[@neosokretes]

You got cat ears 😹

[@peterholzer4481]

@@neosokretes Yeah, I didn't notice it either. Probably because in a lecture you expect some random noise. Listening again, I think that's her shoes - at least the noise very often coincides with her doing a step forwards or backwards.

[@RonJohn63]

58:16 *Of course* we know amashumi amabili nesikhombisa is the Zulu word for 27! Do you take us for idiots???? 1:03:16 This question pains me, but honestly it shouldn't be unexpected.

[@karthikeyansundararajan2391]

Now at least College in Britain accept that numbers system traveled from India

[@jamcdonald120]

2:12 boy I sure hope they work out what = means

[@VulcanOnWheels]

This is the homework assignment in Esperanto: unu - tri du tri kvar kvin - kvar ses - tri sep - tri ok - du naux - tri or kvar dek - tri I'll stop there.

[@epozofortunic]

yes, what is a mile?

[@carultch]

1.609 kilometers.

[@TraceeRae]

I guess you have to start somewhere, but what if we are more advanced then they are, and they don’t understand what we are try to communicate. And what if they don’t come in peace, what if they come to conquer?