Why the number 0 was banned for 1500 years
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- čas přidán 2. 05. 2024
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Most of the material from this video was from the book Zero: The Biography of a Dangerous Idea by Charles Seife.
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0:00 Intro
0:46 The Time Before Zero
2:00 Humans Invent Zero
5:40 Zero's Exile
9:44 Zero's Reincarnation
11:05 Zero's Reign
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Creator - Jade Tan-Holmes
Script - Zoe Cocchiaro
Cinematography - Simon Mackenzie
Animations - Tom Groenestyn
Music - epidemic sound - Věda a technologie
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a master piece as always! Big fan here! Do you have OnlyFans?
The “under the rock” scene in the beginning definitely had to draw some more attention of men viewers to the screen 😅
Joking aside - nice episode, didn’t realize the_drama around “zero” in the past 😅
Hi upandatom! LOVE your video. Zero is my hero!!! :) "We could never reach a star without his zero; my hero; zero, how wonderful you are."- Schoolhouse Rock
czcams.com/video/6eh8Ml-ruO0/video.html
It has been widely accepted and recorded that it was Aryabhatta who first used zero. He was born around 476ce
Zero was an Indian invention. And no we didn't learn it from anyone including babylonians.
Indians invented lots mathematical theories including Pythagoras theorem.
And the Concept of binary number system is also from India.
Indians learning the number 0 from babylonian it is like saying the communication between humans give humanity the internet
The number zero must have been invented immediately after the first maths exam
🤣 probably due to nobita
Lol
no you just get
int main{void}
Relatable Life Incident 😂!
Well done sir :D :D :D
I know zero is very important in mathematics but didn't know that Pythagoras and Fibonacci were both involved along with the Indians in such rich history and drama. Thanks as always Jade!
Good stuff 👍
🙏🇮🇳 hopefully u r having wonderful day
The major credit goes to a guy named Aryabhata
3 rubber bands x 0 = 0 rubber bands
I thought indians were all savages living in trees
Brilliant stuff. I really must commend you on the effort you've put into this video and for condensing the history of zero to 16 mins! Keep up the amazing work!
Very well done! Informative, well researched, well organized, and clearly presented. Bravo!
I can't believe they banned it for 15 years
Heh, nice.
Thanks maths professor!
I see what you did here :D :D :D gg
Surely you mean 15 years not 15 years?
The clergy approves this message saving ink
That bit with the baby at 1:34 caught me off-guard. It was very funny.
I had a Ray William Johnson flashback when the baby was thrown!
This was a very good look at the history of Zero! Love your videos, please keep going!
0:07: 🔢 The concept of zero didn't exist for 1,500 years and caused controversy when it was invented.
3:48: ! The Babylonians invented the symbol for zero as a placeholder to distinguish between numbers.
7:42: 🔢 The Greeks rejected zero in their mathematical system due to its association with non-existence and the denial of God.
10:08: 🧮 The concept of zero in mathematics originated in ancient India and played a crucial role in the development of modern algebra.
13:13: 🤔 The video explores the significance of zero in mathematics and how different cultures' beliefs influenced its invention or discovery.
Recap by Tammy AI
Thanks for mentioning the use of AI. I had a feeling it was made by one but did not want to discredit the author if it weren't the case.
I love the effort you put into your videos by making all those props. Hope you keep doing it!
Pingala (c. 3rd/2nd century BC[32]), a Sanskrit prosody scholar,[33] used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), a notation similar to Morse code.[34] Pingala used the Sanskrit word śūnya explicitly to refer to zero
He was the one who invented the discovered the Fibonacci sequence as well. Fibonacci himself has credited this to Indian mathematicians.
@@warpdrive9229yes but Greece knew about golden ratios and golden triangles without the need of the Fibonacci series.
Chinese also invented it independently.
there was no pingala its a mythology invented by Brahmin fraudsters
it's misbelief that Indians borrowed concept of zero from Babylonians.
the concept of zero and decimal system based upon it, already present in the ancient Indian scriptures like RigVed, Yajurved, Atharv Ved, Vedang Jyotish, Shulvasutra and many others. There is a name for every power of 10 till 12th power. Decimal system is incomplete without zero.
mathematician Laplace also stated that ' it is India that gave is the ingenious method of expressing all numbers by ten symbols (1 to 9 and 0).
There are more quotations about Indian mathematics that can be found in a book written by American Mathematician Florian Cajori " history of mathematics (1909) "as well.
Classics of Indian mathematics written by Henry Thomas Colebrook (1817) tells you more about it.
Babylonians invented zero. Indians borrowed it.
Thank you very much Jade. You are really fantastic teacher. I love your method of explaining that uses different animations and other stuff to deliver a concept.
Indian history on science is still under rated what we discovered in those fields are unbelievable for that era but no one want to show it
@Bernhard Schwarz i am talking about the researches and documentation which were done in India and no civilization was properly know India back then
Actually it would be interesting to hear you cover all the math of mesopotamia.
I once heard that the Egyptian pyramids were built with the aid of measuring instruments that were simple in design, like two sticks connected by a piece of rope or string. The circles and lines they would get from them would be like compasses, and the geometry of the interaction of those shapes would go towards the design of their architecture (would need to verify, this is something from way back in school). If there's info on it, it would be neat to know what type of geometry and math the Mesopotamians were using to do things like build their ziggurats.
That base 60 is pretty wild and kinda scary for those Babylonian school kids!
@@jonstfrancis I'm sure we've lost some IQ points along the way, can you imagine how you would feel explaining the metric system.
@@swicked86 I'm sure we have too
Great video as always Jade! You are so very good at explaining things and keeping it interesting. You have a knack of keeping it flowing ... like finishing explaining a point and then saying something like "there's just one problem". Like the cliffhanger between chapters. And your explanations are so clear. You're a natural teacher! 😊
That was really clear, and it was enjoyable to watch too! Thanks. :)
I admire the way you present mathematics. You make math interesting and fun
As usual it is a very interesting topic and so well presented in a very clear and entertaining way. Thanks for your excellent work.
Zero wasn't always around but it was certainly always a round.
Lmao that's clever
Smartass time!
Didn't you watch the video? the symbol the Babylonians used wasn't round! :P
@@nachoijp I did but I couldn't resist the play on words, even if it resulted in a fallacy.
You just magically showed up in my suggestions.
This is the kind of thing I'm preoccupied with as my mind wonders during my many hours of freeway driving.
Well, one of them.
I think I'm going to get a lot of enjoyment from your content
During one of my trips to Central America, I had learned that the Maya and the Aztecs were well aware of the number zero. Your research is great and I learned a lot. It will be good to complement this superb documentation with history from the peoples of the Americas. A big thank you.
I wish people would stop calling zero a number. Zero is not a number in any way. Zero means no number and no number is not a number.
You are right.
For example.
Preface. Positional natural a-ary d-digit number systems can represent some kind of polytopes. For example:
binary d-digit number system is a d-vertex simplex.(vertices is a numbers whith digital root=1, edges is a numbers with digital root=2 and so on)
2^n-ary d-digit number system is a n*d-vertex simplex with 2^(n*d) faces (for simplexes externity is considered to be face).
3^n-ary d-digit number system is a d-cuban3. If 1-chain (2 vertices + 1 edge) shift 1 times we receive 2-cuban3 with 3^2=9 faces, i.e. square.
5^n-ary d-digit number system is a d-cuban5. If 2-chain shift 2 times we receive 2-cuban5 with 5^2=25 faces, i.e. 4 square joined together.
(2*3=6)^n-ary d-digit number system is a d-mebius6. if 3-ring (1D triangle) shift (2-1)*3 times and "press" 1 chain into 1 vertex we recieve 2-mebius6 with 6^2=36 faces = (3-2)*3 square + 2*3 triangles + 2*3*3 edges + (3-1)*(3+1)+1 vertices , because in 1D-rings shapeless Zero (wich in simplex is a Externity) is "pressed" into 1 vertex and can't generate new shapes .
7^n-ary d-digit number system is a d-cuban7. If 3-chain shift 3 times we recieve 2-cuban7 with 7^2=49 faces, i.e. 9 square joined together.
(2*5=10)^n-ary d-digit number system is a d-mebius10. if 5-ring (1D pentagon) shift (2-1)*5 times and "press" 1 chain into 1 vertex we recieve 2-mebius10 with 10^2=100 faces = (5-2)*5 square + 2*5 triangles + 2*5*5 edges + (5-1)*(5+1)+1 vertices .
11^n-ary d-digit number system is a d-cuban11. If 5-chain shift 5 times we recieve 2-cuban11 with 11^2=121 faces, i.e. 25 square joined together.
(2*6=12)^n-ary d-digit number system is a d-mebius12.if 6-ring (1D hexagon) shift (2-1)*6 times and "press" 1 chain into 1 vertex we recieve 2-mebius12 with 12^2=144 faces = (6-2)*6 square + 2*6 triangles + 2*6*6 edges + (6-1)*(6+1)+1 vertices .
13^n-ary d-digit number system is a d-cuban13. If 6-chain shift 6 times we recieve 2-cuban13 with 13^2=169 faces, i.e. 36 square joined together.
(2*7=14)^n-ary d-digit number system is a d-mebius14.if 7-ring (1D 7-gon) shift (2-1)*7 times and "press" 1 chain into 1 vertex we recieve 2-mebius14 with 14^2=196 faces = (7-2)*7 square + 2*7 triangles + 2*7*7 edges + (7-1)*(7+1)+1 vertices .
(3*5=15)^n-ary d-digit number system is a d-mebius15.if 5-ring (1D pentagon) shift (3-1)*5 times and "press" 1 chain into 1 vertex we recieve 2-mebius15 with 15^2=225 faces = 100 faces of 2-mebius10 + 125 faces of 3-cuban5.
And so on.
So amount of faces of above type a - ary d-digit polytopes =a^d.
Conclusion. For me as a programer, it's curious to know that difference in faces between consequent such polytopes is hexagonal numbers.
So all natural numbers of all possible positional natural a-ary d-digit number systems exists with shape, realy:
"No distinction between numbers and shape. Numbers could not exist without shape."
@@PYTHAGORAS101zero is a number with no value
@@velvetcorridor You are half right; it has no value. It does not belong amongst the counting numbers. It is not a number because it does not share any of the properties that define what a number is.
@@PYTHAGORAS101 If you are restricting your definition of a number to the natural numbers, then 1/2, or pi are not numbers either. Of course zero is a number, it stands a concept and as long as it serves its purpose as an arithmetical value, then it will always be a number.
Your excitement and love for mathematics and science is intoxicating. I wish you had existed when I was a kid. Maybe I wouldn't have failed math in school so much. :)
This channel deserves so many more views. Great videos
Fantastic presentation both in manner and order of revelation not to mention skill and research. Well done to you and your team. Thank you for this 'tube and thank you for what you do!
great video as always, thanks Jade!
Hi Jade this was an excellent episode, wish all maths teachers had your talent
Hi Jason :)
As a teacher, your comment bothers me a bit.
I really loved this video and wish I was able to create a lesson even 10% as cool as her video.
But we can't compete with this. As we have to do tens of lesson in 1 day, with the preparation time sometimes around 10 minutes.
Dealing, next to preparing lessons, with emotional problems, parents, meetings, administration, accidents, e-mails, jammed printers, cleaning up the class, planning out a schedule, and more.
I'm a Dutch teacher, and around 25% of teachers in the Netherlands are dealing with a burn out. It's incredible how much pressure has increased on teachers in the past decades.
I am sure there are 1000s of super talented teachers out there, who wouldn't always compete with this.
Btw, how much would you remember if you would get a test about this subject in 3 weeks?
A video can explain a lot at once, but isn't always the most effective way of learning.
I do believe teachers could use these gems in CZcams, and I'm planning of sharing this one with my class.
Thanks a million for that, Up and Atom!
@@MeesterG hi obviously my comment was just meant as a compliment to Jade, not as an insult to teachers or lectures.
:)
Great video, and fun to see you out in the field doing a little archaeology! Well done Indiana Jade.
or (lara)-jade croft
I'm a "CZcams-educated" boor, but I'd like to see a collaboration between Jade and Elise Freshwater-Blizzard. Elise is a British caver on CZcams, so they'd have to overcome some distance.
Indiana Jade 😂😂 good one, but seriously, this was one of Jade's really interesting episodes
And if she shaves her head, she'd be GI Jade 🙃
Such a wonderful video, it's cleared many of doubts regarding invention of zero. Keep doing more and by the way it's a great research.
Wow, I love your channel. I haven't been in a lecture hall for almost 30 years. An excellent refresher for knowledge I had forgotten due to lack of use. I studied as far as 2cnd year university calculus, but I only need algebra in my career in the trades lol.
Egyptian and Chinese mathematician- indian mathematician ke laude par
01:11 The number "two" immediately comes to mind.
Love the production value & theming on this one!
Awesome work.. very informative. Thank u lots
Finding your channel feels like I've unlocked the conceptual vocabulary to better describe reality and my relationship with it (what some might call the meaning of life.)
Thank you so much!
Also you are the only CZcamsr who successfully convinced me to get nebula, can't wait to see your documentary.
I honestly don't understand how anyone can find math or science dull.... The more I learn the more it feels as if I am revealing the secrets of reality.
And it leads to more questions ... that feel as if they too are addicting mysteries.
It's a endless amazing cycle.
They find it dull because it was presented as dull when they where kiddos, i argue that math and science should be "prohibited" in schools, and the math and science books hidden in a "hidden library" that students "should not enter". All te books written like it was hidden lore of course.
I am joking, but that may work surprisingly well now that i am thinking about it.
It is very different to watch entertaining sci and math videos on CZcams, than actually practice real math problems in order to really understand and learn the field. CZcams videos like this give the illusion of learning but it mostly a colorful surface learning without any real depth. :/
@Jordbær I know ...I have my degree physics. You assume that I only mean here? I honestly just love surrounding myself with as much of it as possible. It's my life blood.
I might be crazy, but I literally wake up and fall asleep with questions from the field.
When it comes to science educators... I can rewatch some of my favorite concepts relentlessly.
I have been watching Sagan for....well mh entire life.
Imagine a drill, ask a child to cross the room in 10 steps. Go back and then ask to cross it with 16 steps.
Present geometry and ask to build an arch the old way, with sand and hollow blocks.
Play with see-saw with different lengths and weights. Make all this as competition, cooperation or "new inventions".
That's the way from kindergarten to grade 4, present them with actual fun problems. The way we do it now is to kill curiosity, math and science.
Throughout school, teach children theater, dance, sports and literature. Teach them citizenship, organization and politics.
At 8 grade start teaching Biology, Chemistry, Physics, Math, History, Geography. You will notice they have already learned the basics for every class.
This is not my idea, several parts of this strategy is in place in other countries.
@@kapoioBCS Of course. But they also serve to introduce people who would never have encountered these ideas to different ways of thinking. You can go from this to MIT online courseware, or to the IAS, or to a million other in-depth lectures and classes. If you've never been interested in something like 'Where Zero comes from', and this video pops up, you might just search out more on the subject. You can find nearly anything you'd like to learn on your own these days, and pop-sci CAN help as a starter. Certainly it's no replacement for deep study, but should you choose to pursue something, the internet is like having multiple Libraries of Alexandria in your pocket.
The tally bone reminded me of how the tally stick was used to create a verifiable accounting system. You make your marks then split the stick lengthwise to make two sticks you can fit together to verify that the number of notches has not been altered by one party or the other
Kind of like early version of blockchain verification of contract?
Great job on this subject!
Excellent video, Jade! I'd never really thought about it but the idea of number zero could be deeply bound to the very conception of universe and existence ancient cultures had: the idea of nothingness and the abstraction of things vs the concrete. Interesting 😎👍
Welcome to all the Indian commenters who will be here in 3, 2, 1…zero
I'm here
Commentators... Learn some English.
I am here
Hi
@@simesaid”A commenter is someone who makes isolated comments. These days, the word most often refers to people who post comments on blogs and news websites. A commentator is someone who provides commentary.”
Thanks for getting me interested in the history of mathematics and numbers. Never gave it much thought before.
Back in the C64 days, the simplest way of dividing in assembler was to repeatedly subtract the divisor until it was less than the numerator. The number of subtractions was the answer and the remaining numerator was the remainder. If the divisor was zero, you'd end up in a never-ending loop as the numerator never decreased.
Not sure if this was actually "infinity" since infinity is where parallel lines meet and recurring results converge but zero would actually never converge like that. I think.
Well done, I thought I knew this but you have enlightened me, thank you. It’s not often I can say that, thanks again.
Easily top 5 science and philosophy explainers on CZcams! Excellent work!
4:21 "This column was intentionally left blank"
I liked this video very much mainly for its open approach. But I have explained in my book that zero was probably discovered around 200 BCE. I do not think it had to be invented; because it was all along there, but it just did not occur to any till that day. The earliest reference to zero is found in the book called "Chanda Sastra" 4.32. It is created by Sage Pingalacharya around 200 BCE. The reference in that goes like this in Sanskrit. “Gaayathre shadsankhyaamardhe apaneethe dvayanke avasishtasthrayastheshu roopamapaneeya dvayankaadha: soonyam sthaapyam” Meaning: In gayatri chandas, one pada has six letters. When this number is made half, it becomes three. Remove one from three and make it half to get one. Remove one from it, thus gets the 'Soonya' (zero). Clear evidence for the existence of definite rules for calculations using zero appears many years later in the year in 1029 CE, in 'Siddhantha Sekhara' authored by Sripati, though it might have been in existence earlier. It says “Vikaaramaayaanthi dhanarunakhaani na soonya samyoga viyogathasthu soonyaaddhi suddham swamrunam kshayam swam vadhaadinaa kham khaharam vibhakthaa”. Meaning: Nothing happens (to the number) when a positive or negative number is added with zero. When +ve and -ve numbers are subtracted from zero, the +ve number becomes negative and -ve number becomes +ve. When multiplied with zero, the values of both +ve and -ve numbers become zero, when divided by zero, it becomes infinity ('khahara'). The place value of numbers seems to have been known around 650-700 CE. “Yathaa ekarekhaa sathasthaane satham dasasthane dasaiam chaikasthaane yathaa cha ekathvepi sthree mathaa cha uchyathe duhithaa svasaa cha ithi” (Sankaracharya, in 'Vyasa Bhashaya' to 'Yoga Sutra' - 650 CE). Meaning: In the unit place the digit has the same value, in 10th place, 10 times the value and in 100th place 100 times the value, given.
Also “Yathaachaikaapi rekha sthaananyathvena nivisamaanaika dasa satha sahasraadi sabda prathyaya bhedhamanubhavathi” ('Sankaracharya', 'Vedanta Sutra Bhashaya II.2.17 - CE 700) Meaning: One and the same numerical sign when occupying different places is conceived as measuring 1, 10, 100, 1000 etc.
May refer the book "The Hidden Messages in Indian Scriptures" (Chapter 13) ASIN: B07XL58DPH.
I really enjoyed this video, thank you very much 😀
I watch a lot of educational content on CZcams. I've recently discovered your channel...and you are one of the best creators ever... explaining such complex theories so well. Keep up the great work 🫂. I'm gonna binge watch all your videos soon✅
Thanks for this great timetravel. Now I and all the other viewers know much more about the hard time zero had to get accepted.
You putting up so much work on your videos! I'm always amazed :D :D
'Never let a learning opportunity pass you by' ... I wasn't looking for, or expecting this one, but I'm glad I tripped over it. Thank you
This one is incredibly well done!
Brilliant!
Such an engaging and lucid explanation of zero's place in mathematics.
Zero was never banned from Western thought. The Greeks opted for the use of 27 greek letters to represent numbers from 1 to 999 and they already used a small circle to indicate that a 3-digit column was empty. The Romans used the minus sign, normally used to represent negative numbers (debts essentially) without any figures to mean zero.
In India, Zero is called Shunya.
Indians were ofcourse familiar with it as it is mentioned even in Vedas, and it became one of the most important thing in Indian philosophies, from Vendanta to Mahayana Buddhism.
Brahman is said to be ultimate reality who is full in itself, but it is also shunya at the same time.
There is verse in Isha Upanishad "That is perfect, this is perfect, what is taken from perfect is perfect and what remains after taking it out is also perfect"
It was Aryabhatta who invented symbol for 0 and other numbers, which were taken by Arabic traders and are Known as Arabic numerals instead in the west.
(Aryabhatta was also the person who first said that earth rotates on its axis and he calculated accurate circumference of the earth, he have done some other cool stuffs also)
Brahmagupta introduced concept of negative numbers.
0 is necessarily not nothing but where both opposite qualities combine.
Like if there is elevation of ground, that will be positive and if there there is depression, it is negative, the place where the ground neutralises is the 0.
That is how concept of negative numbers took place.
Brahmagupta was also the first person who proved that 0 divided by 0 is infinity.
He also have done some other cool stuff.
good
Lol
0/0 isn't necessarily infinity though.
Non null number divided by zero is infinity, but zero divided by zero is undefined
@@gengis737 Nothing is infinity. "The limit is infinity"
It’s always easy and fun to learn from you, thanks for sharing your knowledge 🙏🏼
Loved this one. Great job. One thing, though, while you were seeking the ultimate dramatic example @ 13:08, 1's and 0's are representation of "On" and "Off" or "Yes" and "No" for electricity to travel down one pathway or another in a transistor. This is a physical property of the transistor. If Zero didn't exist this property would still exist and electricity would still travel, when signaled, down one pathway or another, it would just be represented in some other symbolic language than a 1 or Zero. If you drop a rock, even with out Zero, when it hit the ground it would reach Zero velocity. Alan Turing's Machine was completely mechanical in nature, though it ran on electricity, it had no circuit boards using 1's and 0's. My long way around to the point is a computer could still exist without Zero. Other than that LOVE your stuff, keep it up.
I love this! Clear, comprehensible explanations with historical background. I especially enjoy all your videos on the various paradoxes. One quibble though; since the ancient Greeks were polytheistic, so to contemplate zero was to question the existence of gods.
The Maya also used a positional system with a symbol for zero. Upon European contact, this was one of (many) the reasons Diego de Landa, a Catholic bishop, had almost all Maya books burned.
Lol nope. 0 was irrelevant there. Diego de Landa was soon removed from his place after his superior was informed of what he did, and not even allowed to return to America until his superior died.
shame for Christians !
@@author7027 that’s one of many
A true act of vandalism.
Rubbish 🗑 you invent this because you have Calvinist roots or are a professional atheist How would a sixteenth century Spanish soldier know how to read them in the first place? He would have been disgusted with the human sacrifice and accompanying cannibalism. Chilli 🌶 con Chihuahu anyone?
The way she threw the baby without any emotion got me 😂
Rather brilliant presentation of a concept!
Interesting video! I learnt something today! Thankyou!
This channel brings one of the best props games on CZcams, while expertly using homemade/prepped physical items for illustrations educating points pedagogically,
also for thelr babythrowing shock value.
Yeah, I laughed out loud when she casually threw the baby away.
Great video Jade.
It's funny how you explained calculus in a sentence when my calc teacher in uni couldn't do it at all. She was the worst teacher I had and you explained limits in a single breath. Good job =D
Yeah, being able to do math doesn't mean that you can explain it in English. Most math is taught as a religion...there are questions you don't ask.
@knoahbody69 yeah, she did yeah it like a religion. "Because that's what the book says" was her answer to "how did you get that answer? "
@@OdinMagnus In our country the teachers are supposed to teach math as a language, but most of the grade school teachers went into grade school because they didn't understand math as a language.
@@knoahbody69 WOOOW.
I was an English major. Isn't calculus just percentages? Go easy mathies, I'm 59 with a TBI.
Good info. Thank you.
Great work, but I wanted to push back on a few things:
1. We don't really know how prehistoric people "felt" about zero. You're probably on the right track when you say the issue really didn't come up. At least not for practical purposes.
2. The concept of the number line is modern. No one thought of multiplication as stretching rubber bands in ancient times, that I know of. The number line serves well to teach 0 and negative numbers today, and if that was ever how anyone thought about numbers, people would have been happy with 0 and negative numbers long ago.
3. Ancient mathematicians had geometry and had counting numbers. The Pythagoreans tried to merge the two by having lengths as multiples of other lengths, but the fact that the length of a side of a square and its diagonal cannot be both measured as whole numbers of the same length (what we would today call the irrationality of the square root of 2) forced the Greeks to separate geometry and counting numbers. The organization of Euclid's elements makes more sense once you realize this.
4. Thus, the notion of 0 has two different meanings: the geometric and the arithmetic. Geometrically, 0 is a line with no length, which even modern people would say is not a line at all (or some mathematicians would say is a degenerate case). Arithmetically, it's a matter of definition. What do you consider a counting number? Actually, the ancient Greeks didn't even consider 1 a number, since the term "number" implied you had a multiplicity of something. They called it a unit (or at least that's what my English translation of Euclid calls it).
5. For calculations: this is something most histories of 0 omit. Long before Fibonacci, people in Europe used the abacus. They were not doing calculations with pencil and paper, with rows of Roman numerals. The abacus represents numbers positionally, like we do today. The abacus was used throughout Eurasia and already existed over a millenium before Fibonacci. The predecessor to the abacus, available to the ancient Greeks and even earlier, was the counting board with pebbles, which is like an abacus without the rods to hold the beads. Same concept. The Chinese used counting rods instead of pebbles, and there is a numeral system based on it that is not the standard Chinese numeral system most people know today (see Suzhou numerals). Thus, having a 0 in a positional system is something that was used for quite some time. By the way, our word for "calculate" (and "calculus") comes from the Latin word "calculi", which means pebble.
6. The Mayans also had a positional numeral system in base 20, and had a symbol for 0 in this system. Though it might have predated the Maya. This predates the appearance of zero in our known Hindu sources.
7. The Greeks didn't think of Zeno's paradoxes in terms of 0, but rather infinity. They made a distinction between absolute infinity (which they knew led to paradoxes and suspected was incoherent as an idea) and potential infinity, meaning the result of an unending process of finite things. Archimedes's arguments about the area of the circle or volume of the sphere use notions of potential infinity. He basically came up with the notion of integration, but avoiding the problems with infinity.
8. In fact, the development of calculus depended on being willing to stretch notions of logic to some extent. What is dx? This is the sort of thing that would show to the Greeks that the whole thing was absurd, but Newton and Leibniz were willing to go with it because it seemed to explain the results of Fermat, Descartes, and others. But George Berkeley pointed out that it made no logical sense. Only the work of Bolzano, Weierstrass, Cauchy, and others helped make this rigorous, and that was in response to other paradoxes that had come up in the 19th century.
9. Negative numbers show up occasionally as possibilities in these numeration systems, but they are not used in algebra, especially in the days when algebra was only being applied to geometric things. See points #3 and #4 above. Indeed, Cardano's Ars Magna, he separates the cubic into a large number of cases like a cube equalling a multiple of x plus another number, versus a cube plus a multiple of x equalling a number, etc. because he couldn't just move all the terms to one side of the equation, whether they are positive or negative. This is the 1540s! I would argue that 0 (the number, not the numeral), and negative numbers, start making a difference in math only when you have algebra, because it helps merge all these different cases into one thing. Come to think of it, complex numbers play a similar role.
10. Do you have a source on the Church considering 0 to be of the devil? I don't know of one, and the Church is famous for writing all of its rules down and debating them. Nor am I aware of any Church teaching regarding 0 and the existence of God. Also, Aquinas was over a century after Fibonacci's work, but when he lays out the arguments for and against the existence of God, the number 0 does not merit even a mention. There is a Church doctrine about God creating the universe from "nothing" (ex nihilo) but since God and by some accounts the angels already existed, this is not a claim that "there was nothing" at the time, but rather that God was not shaping one thing into another, like when we "make" a chair out of wood and nails, but was just willing the universe into existence.
Anyway, great work on bringing this stuff to CZcams. Seems like you've reached quite an enthusiastic audience.
Offering corrections is a vital part of mathematics, science, and critical thinking in general, so credit to you for taking the time to lay out all these details.
That said, if you're going to go into this level of detail and want it to be accepted as more authoritative than the video, you really need to back them up with sources and citations. Otherwise, you're just offering unsupported counter-assertions against the assertions made in the video, leaving readers with no particular reason to think your assertions are more correct. Perhaps it is you and not Jade who is misquoting or misremembering historical details. Or perhaps you are right on some or all of them.
@@scotte4765 sometimes I wonder how much of our historical details (widely accepted ones) would be just assertions if we could see in the past.
@@kapilsethia9284 Quite a few, I'm sure. It's human nature to latch onto and repeat versions of stories which are more dramatic, heroic, or shocking than the reality actually was.
@@scotte4765 who has time in a comment? It's still valuable to lay out objections in searchable terms. Skepticism is good, but the video doesn't cite anything either.
@@KalonOrdona2 The commenter who typed out an entire page of ten numbered objections probably does. You're right that the video doesn't give any citations, and that's a valid criticism of it, but my point is that if you're going to go to some effort to criticize it and want your criticisms to be _more_ convincing, you need to do a _better_ job, not just an equally poor one.
It's interesting that somehow I have ever think about Zeno's paradox when my teacher taught us about HCF on early year of Elementary School. It was a wild ride until I realized it is not a paradox at all, just misguided process of thinking
I could listen to and watch your videos all day! I wish you could post more often :( Haha
It's been 4 weeks, and I can't seem to progress much further than a minute past 0:50.
Quantity is a shape (polytope)!!!
4:50. 2+2 stones have different(bigger) shape then 2 stones.'
4:55. 4-2 has different(smaller) shape than 4.
5:00 Zero is absence of shape!
1:49 Absence of something is a thing in itself.
6:00 no distinction between shape and numbers. Numbers could not exist without shape! Pythagor(reincarnation of Euphorbos).
Yes, roman abacuses numbers is a 1-positional(1-digit) number system with operator "*1000^n", which need not "0".
If to "open" content of shape, then it will be broken to peaces!
YES. So called negative numbers do not exists, and they a fake.
They exist only for 4 active observers: '+', '-', '*', '/' composing Zero.
Number line is a fake, line has no shape, has no closed content.
DIVIDE/MULTIPLE BY ZERO MEANS THAT YOU CAN BE DISCONNECTED FROM NUMBERS BUT WHEN DISCONNECTED YOU NEVER CAN CONNECT TO THEM AGAIN. THIS LAW IS CALLED "INFINITY IS CLOSED BUT ZERO IS OPEN". ZERO IS OPEN AND IT'S IMPOSSIBLE "FROM ZERO TO HERO".
Yes. Number theory is not perfect.
Conclusion:
Preface. Positional natural a-ary d-digit number systems can represent some kind of polytopes. For example:
binary d-digit number system is a d-vertex simplex.(vertices is a numbers whith digital root=1, edges is a numbers with digital root=2 and so on)
2^n-ary d-digit number system is a n*d-vertex simplex with 2^(n*d) faces (for simplexes externity is considered to be face).
3^n-ary d-digit number system is a d-cuban3. If 1-chain (2 vertices + 1 edge) shift 1 times we receive 2-cuban3 with 3^2=9 faces, i.e. square.
5^n-ary d-digit number system is a d-cuban5. If 2-chain shift 2 times we receive 2-cuban5 with 5^2=25 faces, i.e. 4 square joined together.
(2*3=6)^n-ary d-digit number system is a d-mebius6. if 3-ring (1D triangle) shift (2-1)*3 times and "press" 1 chain into 1 vertex we recieve 2-mebius6 with 6^2=36 faces = (3-2)*3 square + 2*3 triangles + 2*3*3 edges + (3-1)*(3+1)+1 vertices , because in 1D-rings shapeless Zero (wich in simplex is a Externity) is "pressed" into 1 vertex and can't generate new shapes .
7^n-ary d-digit number system is a d-cuban7. If 3-chain shift 3 times we recieve 2-cuban7 with 7^2=49 faces, i.e. 9 square joined together.
(2*5=10)^n-ary d-digit number system is a d-mebius10. if 5-ring (1D pentagon) shift (2-1)*5 times and "press" 1 chain into 1 vertex we recieve 2-mebius10 with 10^2=100 faces = (5-2)*5 square + 2*5 triangles + 2*5*5 edges + (5-1)*(5+1)+1 vertices .
11^n-ary d-digit number system is a d-cuban11. If 5-chain shift 5 times we recieve 2-cuban11 with 11^2=121 faces, i.e. 25 square joined together.
(2*6=12)^n-ary d-digit number system is a d-mebius12.if 6-ring (1D hexagon) shift (2-1)*6 times and "press" 1 chain into 1 vertex we recieve 2-mebius12 with 12^2=144 faces = (6-2)*6 square + 2*6 triangles + 2*6*6 edges + (6-1)*(6+1)+1 vertices .
13^n-ary d-digit number system is a d-cuban13. If 6-chain shift 6 times we recieve 2-cuban13 with 13^2=169 faces, i.e. 36 square joined together.
(2*7=14)^n-ary d-digit number system is a d-mebius14.if 7-ring (1D 7-gon) shift (2-1)*7 times and "press" 1 chain into 1 vertex we recieve 2-mebius14 with 14^2=196 faces = (7-2)*7 square + 2*7 triangles + 2*7*7 edges + (7-1)*(7+1)+1 vertices .
(3*5=15)^n-ary d-digit number system is a d-mebius15.if 5-ring (1D pentagon) shift (3-1)*5 times and "press" 1 chain into 1 vertex we recieve 2-mebius15 with 15^2=225 faces = 100 faces of 2-mebius10 + 125 faces of 3-cuban5.
And so on.
So amount of faces of above type a - ary d-digit polytopes =a^d.
Conclusion. For me as a programer, it's curious to know that difference in faces between consequent such polytopes is hexagonal numbers.
So all natural numbers of all possible positional natural a-ary d-digit number systems exists with shape, realy:
"No distinction between numbers and shape. Numbers can't exist without shape." Pythagoras (reincarnation of Euphorbos).
Always a pleasure to learn something. One can even look at the Romans and there numerical system, which I still can do. Thanks Jade.
You can argue from an analytic (as in real analysis, or the extension of rigorous calculus) perspective that zeno's paradox resolves to 2m without using 0. For any epsilon that is positive, enough terms can be added to get more than that distance from 2. Simply note that for 2-epsilon, you can continuously divide the distance between 1 and 2 by 2 until you pass the point.
The whole point of analysis is seeing what happens when stuff gets small (very generally). You can still do that if you have no 0.
Also, the fact that Binary uses 0 and 1 is more of just a notational thing. It's the concept of there being nothing (as in, a transistor is off), but it doesn't mean it has to be 0. You can just as easily use a and b or 1 and triangle.
that's why romans could write their numbers without an empty space holder
Exceptionally well done Jade.
A very interesting presentation on nothing. Well done. I now realize how important nothing is and how we could be able to get along without having nothing. In the end, on your computer, you had nothing in your savings, but you seemed somewhat pleased about it, that's the only part I didn't understand. Well, good work, keep it up and we'll see you next time.
I enjoyed the video, but I think you misunderstood a few things about Zeno's paradoxes.
First, I could be wrong about this, but, from what I've read on the topic, it seemed that Zeno really did believe Achilles could never reach the tortoise. He saw the only logical resolution to the paradox to be that all motion is impossible. Rather, our minds experience a series of completely motionless states, like individual frames in a video, and piece them together. Or perhaps there is no past and nothing can ever change; our memories lie to us. Most people, both then and now, would reject those ideas out of hand, but they are indeed logical consequences of his two assumptions: that a process with infinitely many steps is impossible to complete, and that space can be infinitely subdivided. Calculating the place where Achilles will catch up to the tortoise doesn't really resolve the paradox because it silently assumes, rather than proving, that one of Zeno's assumptions was wrong.
Second, while zero is certainly relevant to the calculation, it isn't necessary. The ancient Greeks had rational numbers. Even if they couldn't say, "The distance between Achilles and the tortoise approaches zero," they could easily say, "The distance between Achilles and the tortoise decreases without bound." In fact, they pretty much did have calculus, but with a different name and based on geometry rather than algebra. It was called the method of exhaustion, and Archimedes used it to calculate many things that seem impossible with just Euclidean geometry. The method uses a pair of proofs that two infinite sequences converge to the same value. The method of exhaustion can also calculate where Achilles will overtake the tortoise, without explicitly appealing to zero.
Zeno's paradoxes are still a great introduction to the concepts of calculus, but it's wrong to say Greek mathematics of the time couldn't handle the calculations. Rather, Greek philosophy (including natural philosophy, the precursor to modern science) wasn't always as mathematically consistent as it tried to be.
Geometry, for example, get rid of such paradox by assumption that "internity of simplex is closed by faces but externity is open".
And when you increment dimension of simplex infinitely times you "opens" internity of simplex or other figure, what is forbidden.
Take triangle.if increment dimension then: 1. Internity of triangle became ordinary face. 2. Chunk of externity became new internity of tethraedron.
If to do "1+2" by incrementing dimension infinitely then internity wil be constantly connected to externity and became "opened" untill you stop to do this
( then "infinitally" disappears).
Love the crawling lecture, very uplifting
One of the things I enjoy about math is how well everything works together. Like, in current year, I study all kinds of math, from calculus, to statistics, to set theory and proof writing. And I think a lot about how nice it is that everyone else already figured this stuff out.
Listening to you talk about the invention of zero and how people literally had to change mathematics seems crazy to me. I imagine it was similar for fractions, irrational numbers and complex numbers. For all of mathematical history, there was a rule that said, "Nah, you can't have a number between 1 and 2," and then one day, someone said, "But what about 1 and a half?" and boom, fractions. "Can't take the square root of a negative value," boom, i comes around.
It would be absolutely wild to be around for a significant change in math. What if I wake up one day and someone figures out how to divide by zero? It probably won't happen, but who knows?
We have significant changes in math all the time as children grow into adults. We teach young children about fractions. Only later do they realize a fraction is simply a division which hasn't been calculated. While describing a problem to a child I wrote a number with a decimal point, a line under it, and another number below the line. He accused me of mixing decimals and fractions. I had no idea what he was talking about. Seems he thought a line was used to write fractions and a division sign was used to write division. He hadn't quite reached the point where they would teach him they are both the same thing. Life is far more difficult when you don't grasp the concept needed to solve a particular problem.
Computational theory is in the similar position right now math was in 15th to 16th century.
4:14 The Babylonian placeholder was not used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked the same, because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them.
Interesting video very well told. You may wish to look into Chinese mathematics and maybe Egyptian mathematics to see if a concept similar to zero was in use there. Also, the Babylonia concept of a position holder is a pretty close concept to zero for an ancient. It was not the same, but it was getting there
Zero has value. In the early days of eBay, someone tried posting "nothing" for sale. It sold for $1.14.
Thanks. It took 80 years for me to come across this channel. thanks again.
I knew a mathematician that was so afraid of negative numbers that he would stop at nothing to avoid them! 😁
Funny!
Your children must really hate you.
Boom, as they say, boom...
If he's a good lad, try not mention minus zero
Some bad dad jokes are zero's
0:23 that facial expression 😂 exactly me looking at my balance too 👍
13:22 "So next time you're in this situation [$0.00 in the bank], just think 'Maybe zero isn't so bad after all'." -- Ah, the classic category/instance confusion, lol.
Thanks Jade! Blessings, Jim
As zero was independently created/discovered by the maya with no relation to the other systems, I think it is a necessary abstraction. Much like how the empty set confuses a lot in set mathematics, you have to have a place that can be either empty or identifying to perform mathematics past most basic addition. That being only that which a positive result can occur. If you run out, that is all you need to know most of the time.
From today's perspective, looking at the elegance of the integer line: ... -3, -2, -1, ?, 1, 2, 3...
The foundations, the potential for discovering negative numbers and 0 must be very old. Perhaps they were and had to be proposed several times, until the first societies were ready to adopt them. The integer line also introduces a symmetry between counting up and counting down, the latter no longer stopping at "nothing", at 0. However, integers are still a huge abstraction, distant from everyday experience.
I like you guys. Emotioji"s/emotions and mathmatics are congruent,
Zero was discovered by Aryabhatta an Indian mathematician. From India the mathematics spread out. Indian Vishwavidhlaya( Univerties) exits more than 200BC where they all studied about the mathematics, Astrology and others.
Right, Agreed
I thought it was Brahmagupta (from India too)
the mesopotamians and the mayans had both discovered zero about 500 years before india did. "The first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth."
@@MyBinaryLife Do you know about indian culture?
India has world's oldest civilization, When the rest of the regilion were not even born, Gurukul used to run in India. Hope you got the point.
An inferiority complex see here I
This is one of the best videos I've ever seen. Extremely interesting. That Pythagoras. What a a goof. ;)
Great Video 🙏🏻
There is a theory also that they started circling the whole number, so they would circle the 3600, circle Nothing, circle the 1. Imagine the circle with nothing between the 3600 and 1 is a 0.
wicked!
😳… wait.. wt actually f did I just read?!..🤔.. But Thanks❣️.. You really got Me thinking here.. cant let this go away today.. and thats a good thing👏🏼😌. Thank You for planting this seed😊👌🏼.. very interesting..
you mean babylonians? is there any evidence this theory is based on?
That's unlikely for the Babylonians. Their writing relied almost entirely on straight lines because they were easier to work on the clay tablets.
I wouldn't be surprised if other cultures with more flexible writing tools would have chosen a method like that - essentially columnating the digits like Jade did but with a bit more work involved (circles instead of straight lines).
Actually it is possible to imagine number line in this way. It is called residue classes of division by some number n, in this case 3600, i.e. we denote as 1 all of numbers which has residue 1 when they are divided to 3600, and so on till 3600. Then it is possible to write following expression 3600+3= 3. Then all of them located in circle, with starting with 0 which correspinds to 3600, and ending with 3600 which corresponds to 0. And 0 in this case won't make sense, cuz we can omit it and write 3600 instead
11:00 Weren't negative numbers taboo in Europe for many mathematicians - even in the 13th and 14th Centuries, and possibly well beyond. From memory it was a real issue when they were looking for a general solution to cubic equations. This is well covered in the Welch Labs series on Complex Numbers, Veritasium has covered it, and Mathologer too. But the whole story might be worth re-telling here :-)
The problem with solving cubics is not the use of negative numbers but the fact that, if you look closely, somewhere in the middle of the solution you take square roots of a negative number. If you pretend that it makes sense to do that, imagining that there's some sort of number that squares to become a negative number, it all cancels out in the end, and you get a real number out as a solution, but you do have that pair of imaginary numbers in the middle...
@@rmsgrey That is one problem with cubics and negative numbers, IIRC there are others.
No, they weren't taboo by the time they were looking at cubic equations. The idea of negatives (particularly account balances) had been around a while by then (though negatives did have their own fraught history earlier on due to that "what does a negative area mean" connection with geometry that earlier mathematicians still insisted on, inherited from the Greeks).
It was the square root of negative numbers (ie: imaginary numbers) that were the problem child during the time of solving cubics.
@@altrag From a Quanta article, for instance: "In the 16th century, algebraic equations were still expressed rhetorically - in words, not symbols - and all coefficients had to be nonnegative, since mathematicians did not recognize negative numbers as legitimate."
My understanding was that the depressed cubics "had" to be expressed with positive values only.
Within some solutions complex numbers appear (I think this was mentioned in the Veritasium video) but there were other objections to negative numbers _per se_
Regardless, negative numbers were a source of controversy for centuries eg web.stanford.edu/class/me161/documents/HistoryOfNegativeNumbers.pdf
@@guest_informant Considering you can flip the sign of any term simply by moving it to the other side of an equation, requiring all the co-efficients of a polynomial to be non-negative has no more of a limiting effect on mathematics than requiring them all to be on the left hand side.
I haven't looked into it lately, but it wouldn't surprise me if you couldn't still find people arguing, in all seriousness, that negative numbers are not proper numbers, but merely mathematical fictions.
Hi. Love these stories and your paradox series. You did one last year about why the night sky isn't bright even though there are hundreds of trillions of galaxies with hundreds of trillions of stars in them. This got me thinking. The most distant galaxies are moving away from us faster than nearer ones. Doesn't that mean they were travelling faster in the distant past? How do we know that they are still travelling as fast (for example gravitational pull from other galaxies could be slowing them down). We can't know their "current" speed unless they are actually closer than they were when the light left them. How do we know the universe is expanding when our data about the most distant galaxies is so out of date?
The absence of a symbol for zero amongst what archaeologists have found is only an indication that archaeologists have not yet done their job properly and have not found it. There is ancient evidence of a word for zero, but it was not written 'zero'. It is what is currently translated into English as 'no', none, nil, etc
This is a video for the man of culture, Jade you are outstanding in this video, congratz!
i really loved your explanations at 0:50
Great info ... 👏👏👏
When you posed the Zeno's paradox problem, I paused it to try & work it out. I immediately realised that they would get closer together at an infinitely shrinking rate. I decided it would be infinitely close to 2, so my answer was 1.9 recurring. This, I think, solves the problem mathematically but is actually physically impossible as you can't measure a recurring distance accurately - you can always add another digit to improve accuracy. This ties in with a debate I had last week in the comments of another video where I argued that 0.9 recurring is not a real number as it can't be accurately measured - if you tried, you'd be measuring smaller & smaller distances forever as you added 9's. This principle applies to all recurring numbers & I don't think any of them are real numbers. They can't be called imaginary numbers, as they're not on the imaginary number line (with numbers that contain i. [Sorry, can't make it do the i in italics.]) They're on the real number line but still aren't real numbers, in my opinion, they're akin to pi. They should be called something like theoretical, hypothetical or conceptual numbers.
Yes, I agree with you. And Pi could not be an exact number because you could not get an exact number of squares into a circle to form it's "area" by counting squares - remember squares form the unit of area. The old "squaring the circle" problem. A circle cannot have an exact area. And what you say about 1.9 recurring is spot-on - you've seen the glaring philosophical error in mathematics versus reality. Parmenides and Xeno knew this very well, Plato fudged round it setting us all on a terrible philosophical MISTAKE lasting until today and more.
See my comment earlier, if you're interested.
@@BR-hi6yt Had a look for your comment but couldn't find it.
Real numbers are defined as limits of sets. 1.999 recurring is exactly equal to 2. In fact that's how 2 is defined in real numbers. 2 is the max limit of the set {1,1.9,1.99,1.999 ...} . It can be limit of any other set so not that set specifically..As far as real numbers are concerned. 1.9999 recurring is just a different way to write 2.
Though you are correct in a sense that all recurring numbers of type 1.999999... are akin to pi. The normal numbers you think about are rational numbers.
"They should be called something like theoretical, hypothetical or conceptual numbers." They are already called something different they are called real numbers.
It's the rational numbers which are close to what we usually think of as numbers.
Great video, you skipped Al-Khawarizmi, which is the Persian Mathematician who used the zero concept from the Indians and build on top of it to solve second degree equations, he named this "Al-Gaber", which is changed to "Algebra", the word Algorithm is also derived from his name since he put forward how to solve equations using steps.
Will make a good stand alone video
This girl has an OUTSTANDING teaching talent! To be unable to understand her, one needs not only be dumb ; one must be dead! Learning with her is not only instructive, not only easy : it is enjoyable!
Yes, she is so articulate.
Great video Jade. You're so well suited for this. The world is better for you being in it. Keep being you. You're hilarious too. "You either have children... or you don't". LOL. Well played.
I love the insight---no, the REVELATION---that you shared at about the 13:30 mark ... that one's ingrained ideas or "prejudice", per the very definition of the word, often influence how you feel about EVERYTHING. Often, even to the extent that it prevents you to see what's there right in front of your eyes.
Beautifully explained, lots of love from India 🇮🇳