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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 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-6eh8Ml-ruO0.html
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
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!
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
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!
@@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.”
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.
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
@@warpdrive9229yes but Greece knew about golden ratios and golden triangles without the need of the Fibonacci series. Chinese also invented it independently.
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.
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.
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.
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. :)
I'm a "RU-vid-educated" boor, but I'd like to see a collaboration between Jade and Elise Freshwater-Blizzard. Elise is a British caver on RU-vid, so they'd have to overcome some distance.
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.
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."
@@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.
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.
My group mates in Uni thought that 0 is a 1-digit number, whereas I argued that it's 0-digit. The program we wrote was to count the digits, so you naturally divide by ten until you get 0. But with 0 you've got it from the start! So they had to specifically include an answer for 0. I also had to because well, auto checking system.
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 RU-vid, and I'm planning of sharing this one with my class. Thanks a million for that, Up and Atom!
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
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 RU-vid, than actually practice real math problems in order to really understand and learn the field. RU-vid 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.
@@abhaysingh2334 Yes this is why ideas spread around the world and get adopted by other cultures, so we can talk about how great our "ancestors" were and insult each others mothers on the internet. Humans really are a pathetic bunch.
In our current positional notation, every integer has an infinite number of leading zeros that we don’t write. So most zeros still aren’t represented by any symbol, not even a blank.
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! 😊
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.
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?
We should INVENT a digit that is -1. Then we would not need to put a negative sign in front of numbers. Humans probably would not use it, but maybe it would have value in computers. Consider a base three system with three digits: x, 0 and 1 -- where x has the value of -1 if you did not guess. In this version of a base 3 system one counts forward from zero like this: 0, 1, 1x, 10, 11, 1xx, 1x0, 1x1 etc. And counts backwards from zero like this: 0, x, x1, x0, xx, x11, x10, x1x etc. 1x1 is 7 base 10 and x1x is -7 base 10.
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
@@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.
I watch a lot of educational content on RU-vid. 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✅
"Computers store data as 1's and 0's." But those are really just representations of two distinct values - we could use T and F if we wanted to. I certainly think the "maturity" that incorporating zero has brought to our mathematical abilities has helped us, and it's very possible that without it we wouldn't yet have developed computers. But the non-existence of zero doesn't "preclude their existence."
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.
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.
This channel brings one of the best props games on RU-vid, while expertly using homemade/prepped physical items for illustrations educating points pedagogically, also for thelr babythrowing shock value.
Zero has always existed. Modern zero is confusing because we use it in numbers like 10 and 100. But zero, it has existed since the first time someone drew a line. Geometry, building, measuring. You start from a singularity, a point, zero. The first dimension.
For many people, zero is banned even today as a number. When I was at primary school, I was told a division algorithm in which when the remainder is zero I should write "//" instead of "0". In typewriters, computer keyboards, and old telephone dials, 0 is near 9, far from 1, like if when counting you would get to 0 just after 9, not before 1.
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.
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.
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.
Here's one for you: Say I have 1 watch, and I give you that watch. How many watches do I have now? Zero (0) watches? Or do I now have minus one (-1) watch? Maybe just word symantics, but it give you something to think about. It feels like zero was necessary just to make math work on paper.
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!
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.
😳… 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..
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
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.
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.
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...
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.
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.
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.
There are various stereographic projections that make dividing by zero just fine. Those projections have a "point at infinity" explicitly added, so in the resulting number system "infinity" is actually a legitimate value, which it is not in our usually way of doing things. Since it exists as a value, saying 1/0 = infinity is fine, just fine.
By chance did you read Zero: The Biography of a Dangerous Idea by Charles Seife? Such an interesting history and is an easy read. This is where I learned of the struggles of adapting zero into acceptance
It's easy to mathematically prove the existence of ZERO... i'll show my workings. What are the chances i'd ever be lucky enough to get a date with Jade.... ZERO times ZERO to the power of ZERO, squared.
'IF' my latest TOE idea is really true, (and I fully acknowledge the 'if' at this time, my gravity test has to be done which will help prove or disprove the TOE idea), that the pulsating, swirling 'gem' photon is the energy unit of this universe that makes up everything in existence in this universe, and what is called 'gravity' is a part of what is currently recognized as the 'em' photon, the 'gravity' modality acting 90 degrees from the 'em' modalities, which act 90 degrees to each other, then the oscillation of these 3 interacting modalities of the energy unit would be as follows: Gravity: Maximum in one direction, Neutral, Maximum in the other direction; Electrical: Maximum in one direction, Neutral, Maximum in the other direction; Magnetic: Maximum in one direction, Neutral, Maximum in the other direction. Then: 1 singular energy unit, with 3 different modalities, with 6 maximum most reactive positions, with 9 total basic reactive positions (neutrals included). Hence 1, 3, 6, 9 being very prominent numbers in this universe and why mathematics even works in this universe. (And possibly '0', zero, as possibly neutrals are against other neutrals, even if only briefly, for no flow of energy, hence the number system that we currently have. This would also be the maximum potential energy point or as some might call it, the 'zero point energy point'.). And also how possibly mathematical constants exist in this universe as well. * Note also: Nobody as of yet has been able to show me how numbers and mathematical constants can exist and do what they do in this universe from the Standard Model of Particle Physics (SMPP). While the SMPP has it's place, I believe we need to move beyond the SMPP to get closer to real reality.
@@charlesbrightman4237 This is very interesting, particularly the 90 degree concept, which I wrote about in around 2015-16. I hope you pursue your ideas. (On a lighter note, please don't confuse it's and its ... for the crowd you are addressing, those are examples of what diminishes credibility. No, spelling/grammar are not prerequisites to genius, but carefulness is.)
@@xyz.ijk. Thank you. See also 2 more posts to you after this post. a. TOE idea; b. Gravity test for TOE idea. As far as grammar goes, I am trying to save at least 1 single species from this Earth to exist beyond this Earth, solar system and most probably collapsing spiral shaped galaxy. I'll let people like yourself correct any minor grammar mistakes I might make. (Job security for you and others, you are welcome). And as far as language itself goes, see also c. Language, after this post.
@@xyz.ijk. (copy and paste from my files) Revised TOE: 3/25/2017a. My Current TOE: THE SETUP: 1. Modern science currently recognizes four forces of nature: The strong nuclear force, the weak nuclear force, gravity, and electromagnetism. 2. In school we are taught that with magnetism, opposite polarities attract and like polarities repel. But inside the arc of a large horseshoe magnet it's the other way around, like polarities attract and opposite polarities repel. (I have proved this to myself with magnets and anybody with a large horseshoe magnet and two smaller bar magnets can easily prove this to yourself too. It occurs at the outer end of the inner arc of the horseshoe magnet.). 3. Charged particles have an associated magnetic field with them. 4. Protons and electrons are charged particles and have their associated magnetic fields with them. 5. Photons also have both an electric and a magnetic component to them. FOUR FORCES OF NATURE DOWN INTO TWO: 6. When an electron is in close proximity to the nucleus, it would basically generate a 360 degree spherical magnetic field. 7. Like charged protons would stick together inside of this magnetic field, while simultaneously repelling opposite charged electrons inside this magnetic field, while simultaneously attracting the opposite charged electrons across the inner portion of the electron's moving magnetic field. 8. There are probably no such thing as "gluons" in actual reality. 9. The strong nuclear force and the weak nuclear force are probably derivatives of the electro-magnetic field interactions between electrons and protons. 10. The nucleus is probably an electro-magnetic field boundary. 11. Quarks also supposedly have a charge to them and then would also most likely have electro-magnetic fields associated with them, possibly a different arrangement for each of the six different type of quarks. 12. The interactions between the quarks EM forces are how and why protons and neutrons formulate as well as how and why protons and neutrons stay inside of the nucleus and do not just pass through as neutrinos do. THE GEM FORCE INTERACTIONS AND QUANTA: 13. Personally, I currently believe that the directional force in photons is "gravity". It's the force that makes the sine wave of EM energy go from a wide (maximum extension) to a point (minimum extension) of a moving photon and acts 90 degrees to the EM forces which act 90 degrees to each other. When the EM gets to maximum extension, "gravity" flips and EM goes to minimum, then "gravity" flips and goes back to maximum, etc, etc. A stationary photon would pulse from it's maximum extension to a point possibly even too small to detect, then back to maximum, etc, etc. 14. I also believe that a pulsating, swirling singularity (which is basically a pulsating, swirling 'gem' photon) is the energy unit in this universe. 15. When these pulsating, swirling energy units interact with other energy units, they tangle together and can interlock at times. Various shapes (strings, spheres, whatever) might be formed, which then create sub-atomic material, atoms, molecules, and everything in existence in this universe. 16. When the energy units unite and interlock together they would tend to stabilize and vibrate. 17. I believe there is probably a Photonic Theory Of The Atomic Structure. 18. Everything is basically "light" (photons) in a universe entirely filled with "light" (photons). THE MAGNETIC FORCE SPECIFICALLY: 19. When the electron with it's associated magnetic field goes around the proton with it's associated magnetic field, internal and external energy oscillations are set up. 20. When more than one atom is involved, and these energy frequencies align, they add together, specifically the magnetic field frequency. 21. I currently believe that this is where a line of flux originates from, aligned magnetic field frequencies. NOTES: 22. The Earth can be looked at as being a massive singular interacting photon with it's magnetic field, electrical surface field, and gravity, all three photonic forces all being 90 degrees from each other. 23. The flat spiral galaxy can be looked at as being a massive singular interacting photon with it's magnetic fields on each side of the plane of matter, the electrical field along the plane of matter, and gravity being directed towards the galactic center's black hole where the gravitational forces would meet, all three photonic forces all being 90 degrees from each other. 24. As below in the singularity, as above in the galaxy and probably universe as well. 25. I believe there are only two forces of nature, Gravity and EM, (GEM). Due to the stability of the GEM with the energy unit, this is also why the forces of nature haven't evolved by now. Of which with the current theory of understanding, how come the forces of nature haven't evolved by now since the original conditions acting upon the singularity aren't acting upon them like they originally were, billions of years have supposedly elapsed, in a universe that continues to expand and cool, with energy that could not be created nor destroyed would be getting less and less dense? My theory would seem to make more sense if in fact it is really true. I really wonder if it is in fact really true. 26. And the universe would be expanding due to these pulsating and interacting energy units and would also allow galaxies to collide, of which, how could galaxies ever collide if they are all speeding away from each other like is currently taught? DISCLAIMER: 27. As I as well as all of humanity truly do not know what we do not know, the above certainly could be wrong. It would have to be proved or disproved to know for more certainty.
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 😎👍
Brilliant presentation. For our forbearers numbers were ideogram derived from and based on night-sky images or forms. In this worldview, there can never be nothing. The real problem started when the symbol for zero was derived at, the wheel, circle or diamond shape ( Arabic representation for Zero), these symbols represented completion, a container of everything, and whence everything came from. It is also in this context that we should understand Pythagoras’ assertion that numbers are everything. The shape of the beans, were seen to resemble the kidneys, and the kidneys were seen to represent two important star clusters linked to the Zero.
@@rachmondhoward2125 You are right. For example. To enumerate more complex polytope may be used (A)(D)simplician :positional natural A-ary D-digit number system. Where A,D - some natural number sequence arbitrary but equal length. Then 2D Maya/Egypt pyramid is are (3,2)(1,2)simplician.n (5 vertices+8 edges+3 hyperplanes+ I+ O=18=2*3^2, let's enumerate it: 100 is a vertex above square. 022 (=NOT 100) is opposite edge 020 002 is are 2 vertices between which lies edge 022=002+020. 120 (=100+020) is edge between vertices 100 and 020. 102 (=100+002) is edge between vertices 100 and 002. 122 (100+020+002) is infinity(content) located between 3 vertices 100 020 002 and 3 edges 120 102 022. 001 (=100+100) is vertex connected to vertex 100. 021 (=001+020) is edge between vertices 001 and 020. 010 (=001+001) is vertex connected to vertex 001. 011 (=001+010) is edge between vertices 001 and 010. 012 (=002+010) is edge between vertices 002 and 010. 101 (=001+100) is edge between vertices 001 and 100. 110 (=100+010) is edge between vertices 100 and 010. 111 (=100+010+001) is triangle between vertices 100 010 001. 121 (=100+020+001) is triangle between vertices 100 020 001. 112 (=100+010+002) is triangle between vertices 100 010 002. 000 is zero. 2D Maya/Egypt bipyramid is a (2,7)(2,1)simplicyan (6 vertices+14 edges+6 hyperplanes+ I+ O=28=2*2*7,infinity is like tethraedron and zero is like opposite triangle). Prism is a (2,5)(2,1)simplicyan (6 vertices 9 edges 3 hyperplanes +I+O=20=2*2*5, infinity is like triangle, zero is like opposite triangle). 3D PrizmTethraedron is a (1,7,1)(1,1,1)simplicyan (7 vertices+12 edges+7 hyperplanes+ I+ O=28=2*7*2, infinity is like volume and zero is like opposite volume (externity, background,shapeless forcefull field which can press shapes) ).
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
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
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.
My fav is Fractions You can create a Fraction that goes Beyond Infinity and NEVER REACH "0", which was a problem I had in school cause if you can't reach "0" then the negative numbers simply turn into directions NSEW or Up/Down.... etc
As the father of a 4yr old you lost me as soon as your threw the baby doll because all I could think about was how angry my daughter would be if I threw one of her baby dolls like that.
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 RU-vid. 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.
@@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.
That’s a beautiful video. But one big piece is missing IMO. The travel of the 0 from India through the Muslim world was not just a travel. In the Muslim world the 0 was not just transported but expanded upon. Famous Mathematicians like Alkhawarizmi (Algorithm) used the Indian number system to invent Al-Gebra. I feel that the video should’ve mentioned this aspect to show the interconnectedness of the world.
From India, the zero made its way to China and back to the Middle East, where it was taken up by the mathematician Mohammed ibn-Musa al-Khowarizmi around 773. It was al-Khowarizmi who first synthesized Indian arithmetic and showed how the zero could function in algebraic equations, and by the ninth century the zero had entered the Arabic numeral system in a form resembling the oval shape we use today.
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 with 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-cube. For n=1 d=2: if 1-chain (2 vertices + 1 edge) shift 1 times we receive 2-cube with 3^2=9 faces, i.e. square. For odd and not power -ary number systems: odd^n-ary d-digit number system is a d-cube_odd. For n=1 d=2: If (odd-1)/2-chain shift (odd-1)/2 times we receive 2-cube_odd with odd^2 faces. (2*3=6)^n-ary d-digit number system is a d-mebius. For n=1 d=2: If 3-ring (1D triangle) shift 3 times and "press" 1 chain into 1 vertex we recieve 2-mebius with 6^2=36 faces = 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 . For even and not power -ary number systems: (2*odd)^n-ary d-digit number system is a d-mebius_odd. For n=1 d=2: If (odd-1)/2-ring shift (odd-1)/2 times and "press" 1 chain into 1 vertex we recieve 2-mebius_odd with (2*odd)^2 faces . Conclusion. All positional natural a-ary d-digit number systems with a^d numbers are represented by 3 types of d-polytopes (simplex, cube, mebius) with a^d faces . For me as a programer, it's curious to know that difference in faces between consequent such polytopes is hexagonal numbers. To enumerate more complex polytope may be used positional natural A-ary D-digit number system , (A)(D)simplician. Where A,D - some natural number sequence arbitrary but equal length. Then 2D Maya/Egypt pyramid is are positional natural (3,2)-ary (1,2)-digit number system or (3,2)(1,2)simplician. "No distinction between numbers and shape. Numbers could not exist without shape." Pythagoras (reincarnation of Euphorbos).
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.
I love you. Your outro music is in the ancient mode, Aeolian, or natural minor. To use the raised seventh scale degree would’ve been anachronistic. Do you want to come to a Christmas party with me this Saturday?
The role of Zero in all number system is Digits.If there are no digits, there will be no Zero. 5+5 is 10 so you don't need zero to write 10. You can simply write 5+5 or invent a symbol for it. The Roman numerals confuses us not that zero confuse them.
I agree. I'm a "RU-vid-educated" boor, but I'd like to see a collaboration between Jade and Elise Freshwater-Blizzard. Elise is a British caver on RU-vid, so they'd have to overcome some distance.
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
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.
Some people think that the digit zero should be drawn as a circle and not with a varying width of the stroke - because it is not a "real digit". That is apparent in some fonts. Looks rather odd in my opinion.
The tag is to solve the problem of someone attaching a number between numbers. Even in modern numbers today, people still are able to attach values to documents which would call for tags to indicate when a number starts and ends or the maximum and minimum digits a number must be.
13:13 I have a question, as far as I know "0" is just a convention to represent "off" state of a transistor so can't we just use 2 or any other number for that matter to represent "off" and computer would work just fine? Am I wrong? ? Please tell me
In the abstract, you can. In reality, you can’t because of how numbers are represented. What would make a bit more sense is stealing the concept of null { }, the empty set in math, which is entirely different from 0. We use 0 to represent off but it’s actually not 0, it’s the absence of a signal. 0 has meaning, null has none.
@@anujarora0 Interesting question. In theory, perhaps. In reality, not as it does right now. Remember, computers do much more than store data, they manipulate it as well. For example, if you XOR 1+1 you get 0 with a carry bit. You also need to keep in mind that the magnitude of a current value changes so a 0 may really be a 0. Also, without a zero, how do you measure negative magnitudes? So I’d say no.
For a digital machine (e.g., a computer), to accurately store data and to perform transformations on the data (e.g., multiply two whole-numbers), the data must be represented with a symbolic system that includes positional notation and all positions must be defined. As you know, a written representation of a whole number that uses so-called Arabic numerals is an example of positional notation. As you also know, In English and many other languages, if a "0" (zero) occupies a position in the positional notation, it means "the value of this position does not affect the value of the whole number represented by this symbol. You might not know that in the Arabic language, nine of the ten characters that represent the numerals one, two, three, four, five, six, seven, eight, nine, and zero have a very different appearance than the English symbols. The two symbols for the numeral nine, however, are similar: 9 vs. ٩. Arabic has a character that looks similar to 0. The Arabic character ٥ is the numerical character for five. Finally, in Arabic, zero is represented by the numerical character ٠. One conclusion: Yes, the character that represents zero is arbitrary. When English-speaking humans represent whole numbers with so-called Arabic numerals in positional notation and the rightmost position has the smallest value, we say that we can drop the leading zeros from the symbol without changing the value. For example, the symbol 000617 has the same value as 617. But computers cannot do this. A computer stores data in discrete sections that all have the exact same size. Importantly, the data is stored in a literal physical location. Contemporary computers always store data in symbols with eight positions. (The computer can combine two or more symbols to achieve 16, 24, 32, or more positions.) Hence, each physical location of the symbol has eight physical positions for the positional notation. In this case, the concept of "leading zeros" doesn't exist. All eight positions must be defined. This reason alone requires that computers use zero at least in the sense of "no value here" for positional notation. There are other reasons, but maybe this will help a little. (I'm too tired to continue writing.)
Hello! After watching this, and then your video about if math is invented or discovered, I pondered for awhile. Without getting into the answer, a fun question I came up with that's related - "If physics happens, and a physicist isn't around to plot it, does it still make math?"
For the old question, if math is discovered or invented, I quite like the provocative answer: both. Since the term "invented" can be set to mean "discovered by the mind". An intuition relating to your question: in our world, our universe, all behind-the-scenes computation, enforcement of laws, causality and progression of time... appear "effortless", as if there was no "hesitation" and no "work" involved in making it function as it functions. But of course, that's only how it appears from the inside. Who knows, maybe Chronos sweats buckets ;)
@@DarkSkay Yeah my much longer reply was going to be something about how it feels like we're not addressing the real question which gets brought up at the end of that video about a re-framing of the question to be something like "Is our universe mathematical". Which I quite like over the initial phrasing because it better gets at a question worth answering. I agree with what you're saying though with that initial phrasing coming down to just a definition problem on the difference between "invent" and "discover". So I tried to think about the universe existing, just being there. That led me to spending like an hour reading about existence here on Standford - plato.stanford.edu/entries/existence/ If that's interesting, you might like this old vsauce video - ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-fXW-QjBsruE.html Anyway, started spending too much time on this didn't really finish the thought, but the highlight was that funny question. Largely the unfinished conclusion I came to was, If you consider existence as something that can be perceived (debatable), you could say that things have mathematical properties that can be perceived, and in that way, math fits to me like geology or astrology. Something to be discovered. However, I feel like I'm stumbling over probably decades of philosophy that doesn't address things like "essence". A good part in that Standford piece is what use is it to say things "exist", quoting "What is the difference between a red apple and a red existing apple? To be red (or even to be an apple) it must already exist, as only existing things instantiate properties. (This principle-that existence is conceptually prior to predication-is rejected by Meinongians.) Saying it is red and an apple and furthermore exists is to say one thing too many". So again, I feel I don't have enough context to explain correctly, but I hope that I could, verbosely, get my point across.
There's also a rather open approach, where (as a first layer) you declare everything entity that at least satisfies logical identity. So, in principle everything that can enter our language, senses, hands, minds, imagination. Examples: the number 17, a red apple, redness, mister Bean, an online tax form, random notes on a guitar, dragons, the wind blowing through this valley in 3000 years from now, word, Turing machine, contradiction, Poseidon, joy, untruth, inertia, a teapot orbiting Jupiter, a cloud that looks like an elephant, maybe, Cynthia's poem, our mood yesterday. Even before attempts to qualify: there is an infinite supply of such entities that are receptive to being nested, connected and arranged in infinitely many ways - with relatively few rules limiting the possibilities (at least for our world and especially for our language & imagination). Some of those entities express "meta", transcendent, recursive or self-referencing, behaviour or ambition, e.g.: entity, being, real, observer, understanding and touching (begreifen), suffering, hoping, dreaming, "that what cannot be talked about", God(s), all, nothing etc. Contemplated on an abstract, open and general level, diverse answers can be thought as "willing" (perhaps pre-existing; like a stone waits for the sculptor, to reveal what is already contained) to embrace diverse questions, which in turn can always be refined or will freshly appear, using elements of previous answers.
Every tume I get frustrated while studying Group theory, I think of how many centuries it took before even zero (the additive identity under group addition) was even invented and understood. Even the basic foundations of our modern mathematical disciplines took sometimes millenia to discover. It makes me wonder what "simple" things our ancestors will know that mathematics currently lacks?
I would suspect not a whole lot difference to be honest. Why? Because physics. We really only have one more foundational leap to go (integrating gravity with quantum mechanics). We don't really have much of an idea how we'll get there, and there almost certainly will be some new mathematics involved, but I suspect it won't be anything as groundbreaking as the invention of calculus, topology or group theory has been in getting us through Newtonian mechanics and into modern physics. There's always the possibility of something completely unexpected of course, but the places where such a thing could hide are getting rarer and rarer by the year. We can already see practically to the edge of the (observable) universe - as much as we'll ever be able to see. There's a little more room for surprises on the quantum side of the scale but not _that_ much room given how much we already know about the two things we need to combine - and short of something coming completely out of left field we're not likely going to have the engineering capability to probe even that level for many generations to come. That's not to say there isn't plenty of things to be discovered in both math and physics, there absolutely are. I just don't see those discoveries being as game-changing as some of the prior stuff has been. We're not at the _end_ but we're close enough to see the finish line in the far-off distance.
@@altrag Science is never ending! For example relativity has spawned many many more questions than answers. Mass/energy equivalence was mentioned in passing by Newton ... but presumably he didn't have a plethora of doctoral students to investigate it like nowadays. Note if course that Einstein didn't either ... but he published and thus his ideas and knowledge was disseminated along with other scientists ideas and examined in great detail by others ... including the aforementioned doctoral students. Remember that "there are more scientists alive now than have ever existed before" ... and there is an enormous resource in the academic and other "industries" and Government (military-industrial) to finance and support them. I suspect that the explanation of the quantum/gravity link will open up a huge number of questions. Perhaps it will be more like Newton's Laws than relativity. We have got many things from relativity used in everyday life (eg gps systems) ... what will we get from the solution(s) to "quantum gravity"?? Aside from this what about dark energy and "dark matter"? ... and why matter? ... it is only described as matter because the effect it has is similar to having excess matter but it could be another manifestation of energy remembering that matter itself is a (generally!?) stable manifestation of energy. The more we humans discover and explain ... the more we have to discover and explain.
@@simonblackham4987 Not really. There is an "end" to science. Once we have observed all we can observe even in theory, that's pretty much the end of it. We're certainly a long way away from that point, especially on the quantum side of the size scale. But that in itself is a bit of a problem - the next "obvious" step is so unbelievably far away that its unlikely we'll be able to take it for at least a few lifetimes. Namely, probing the Planck scale. I've seen it estimated that an LHC-style ring accelerator capable of reaching Planck energies would need to be approximately the size of Earth's orbit around the Sun. That is to say, we'd need to be a Dyson Sphere-capable species or damned close to it before that becomes practical from a purely engineering point of view. Of course, its perfectly possible in theory where we don't have to worry about trivial things like "costing trillions of dollars and requiring us to rip apart Mercury to get enough material to build it". But its not going to be happening in our lifetimes or that of our great grandchildren. Or maybe someone will invent some kind of device to reach similar energy scales while being a bit more realistic in terms of physical size and budgetary constraints. There's absolutely no known basis for how such a device might even theoretically work, but that falls squarely in the category of "its only impossible until somebody does it", so can't be ruled out. And.. that's about all we've got. We can build bigger and bigger colliders hoping that maybe some kind of supersymmetric particle will fall out, or maybe dark matter somehow merges with one of the other forces at an energy scale "only slightly beyond" what we currently can manage. But its all just "let's spend a trillion dollars and hope to hell". Unlike the LHC where we had at least one thing we were really really sure we'd find (the Higgs), the next accelerator would be purely a gamble. There is nothing "missing" from our knowledge until we hit the Planck scale. Of course, there could be something we don't even have a way to know is missing.. but there's many orders of magnitude between the LHC and the Planck scale. Such a hidden thing may be at 50TeV, but it could also be at 50PeV or 50EeV - and neither of those values are anywhere close to the Planck scale either. The next step that we know is a transition point (but believe we understand fairly well) would be the GUT scale where the strong and electroweak forces merge. But even that is way, way beyond any current or foreseeable-future accelerators (its about 13 orders of magnitude away - closer to that magic Planck scale than the LHC's capabilities). We simply have no leads for "reasonable" new physics in the next few hundred years is the problem. GR and QM are likely to stand for at least a similar amount of time as Newton's theories (which lasted around 400 years before Einstein came along). Sure there will be small tweaks here and there, maybe some reformulations, but I don't see any fundamental changes for a long, long time. That's not to say there's no work to be done. Astrophysics in particular is finding new stuff on a regular basis. But one thing to note is that the stuff they're finding tend to formulate new _solutions_ to GR. There hasn't been anything that points to a significant change in the underlying GR framework since the cosmological constant was recognized as an appropriate description for expansion. On the particle side of things, there's still lots of work to be done analyzing the stuff we do know - fields like condensed matter physics, attempting to build bigger and bigger atoms in hopes of finding the theorized "island of stability", searches for higher temperature superconductors, the list goes on and on. But again, they're all things that work within the framework of the standard model - nothing that would fundamentally alter the model. Its of course possible I'm wrong - I'm no better at predicting the future than anyone else. I certainly hope I'm wrong really, as that would be rather exciting. But unfortunately there's just nothing in our current theories that even vaguely hints at truly new physics being accessible in the foreseeable future. There is no modern equivalent to Newton recognizing that the ability to polish glass meant his corpuscular theory of light wasn't exactly correct (and even with that hint, it took a few hundred years for us to figure it out!) Not until we reach the Planck scale.
@@altrag ... what makes you think there is an end to science? Its like the early pioneers thought that once computers had solved the important questions of the day we would no longer need them! Your (our) present knowledge doesn't allow us to imagine what we don't know. What if we discover there are other universes with other physics? ... and if there are an infinite number then we will have to examine each one and then determine what is behind each possibility in the creation of each possible universe? Doesn't the possible existence of Dark matter and Dark energy hint that there is more undiscovered physics for us to find? I suspect we will still be looking for the answers to everything until the end of 'civilisation' in the solar system. But perhaps it really is 42 !!
This makes it sound like the geometric sum is finite because the geometric sequence converges to zero. But that isn't true. While infinite sums can only have a finite value when the sequence of numbers added converges to zero, that alone is not enough. The famous harmonic series is a sum of smaller and smaller numbers, eventually approaching zero, but the sum itself is infinite.
Indians didn't learn about zero from the Babylonians. If anything it is more likely that the babylonians learned it from India, it is well known that there were trade relations between the ancient Indian civilization of Indus valley and the masopotamians. The symbol for zero may have been given around 3rd centuary in the Bakshali menuscript, but the idea of zero as well as infinity are present in the most ancient of texts like Rig Veda, Upanishads and several others.
So I'm confused. The Ancient Greeks did have a state of nothingness that existed before the universe. They called it Chaos. Also, they didn't have a concept of God really, as they were polytheistic pagans. I suppose Gaia could be analogous to God but it's kind of a stretch. Did you engage with these ideas and decided to simplify or did whatever source(s) you used not engage with this? Otherwise an excellent and informative video!
Yeah those two points stuck out for me as well. The concept of the first gods coming out of nothingness or chaos, or sometimes when nothing/chaos was said to have been separated was a rather common belief in that part of the world and has seemingly cropped up a few times independently in other parts of the globe. Also they way they said that Pythagoras was worried that zero meant a denial of god rather than the gods sounds incredibly out of place.
@@UnlimitedLives1960 I don't think the ancient concept of chaos can be described as just 'nothingness'. i found this about ancient Greek χάος : 1-chaos, the primordial state of existence 2-space, air 3-abyss, chasm 4-infinite darkness Hesiod's talks about Chaos in his Theogony: "In truth at first Chaos came to be, but next wide-bosomed Earth, the ever-sure foundation of all1the deathless ones who hold the peaks of snowy Olympus, and dim Tartarus in the depth of the wide-pathed Earth, [120] and Eros （Love）, fairest among the deathless gods, who unnerves the limbs and overcomes the mind and wise counsels of all gods and all men within them. From Chaos came forth Erebus and black Night; but of Night were born Aether2and Day, [125] whom she conceived and bore from union in love with Erebus. And Earth first bore starry Heaven, equal to herself, to cover her on every side, and to be an ever-sure abiding-place for the blessed gods. And she brought forth long hills, graceful haunts [130] of the goddess Nymphs who dwell amongst the glens of the hills. She bore also the fruitless deep with his raging swell, Pontus, without sweet union of love. But afterwards she lay with Heaven and bore deep-swirling Oceanus, Coeus and Crius and Hyperion and Iapetus, [135] Theia and Rhea, Themis and Mnemosyne and gold-crowned Phoebe and lovely Tethys. After them was born Cronos the wily, youngest and most terrible of her children, and he hated his lusty sire." And this is Ovid's take on Chaos: "Before the seas and lands had been created,before the sky that covers everything,Nature displayed a single aspect only throughout the cosmos; 26 Chaos was its name,a shapeless, unwrought mass of inert bulk and nothing more, with the discordant seeds of disconnected elements all heaped together in anarchic disarray."
@@AlbertaGeek She very clearly says god, not gods, and it comes across as God (in the Abrahamic sense, e.g. 'deny the existence of God'), which most assuredly was not a thing in Greece at that time. So it's the use of the singular god that is out of place and is the issue, not whether they had a concept of gods in general (or a god, if you will).
The Hindu-Arabic numbers were introduced by Gerbert of Aurillac in the late 10th century, and he later became the pope (Sylvester II). However, it took some time to gain significance, and probably was really popularized by the Italian merchants of city-states like Pisa, Genoa, and Venice. For most ordinary people the Roman numerals were sufficient. Fibonacci is a brilliant mathematician and he already knew of the number zero before his travels. So the Church didn't ban the number zero, but churhc people was aware that the lack of common knowledge of zero could lead to fraud.
