What is Zero? Getting Something from Nothing – with Hannah Fry

What is Zero? Getting Something from Nothing – with Hannah Fry

Is it possible to get something from nothing? This is the story of a very important number,
but a number that wasn’t always a number. In fact it was much less than a number until
relatively recently. This is the story of Zero and it’s a story that takes a tortuous and
meandering route through 1,500 years of human history. Today we enjoy zero in all its glory where
it takes on two roles: The first is as a placeholder within our positional
number system. Zero notes an absence of a value and it allows us to create huge numbers without the need to create new digits So we know 30 is larger than 3 and 300 is larger than 30 and 3. The second use of zero is as a number in its
own right, the middleman between positive and negative
one and enjoying nearly all the same benefits
as other numbers. We can subtract, add and multiply by zero… but dividing by zero just doesn’t work. For example, you can’t divide 1 chicken by
no chickens. You might suggest that the answer is infinity,
but it’s not, because infinity isn’t really a number, it’s a concept. Mathematics developed from a very practical
desire to count things, such as the passage of days or the quantities of chickens you owned. To manage this, ancient civilisations developed
rudimentary number systems, for example the Babylonians used two symbols
in different arrangements to create unique numbers 1-60. The Ancient Greeks and the Mayans also developed
their own number systems and all of these civilisations are thought
to have created their own rough concepts of zero as a placeholder. But it wasn’t until the Indians begun developing
their own number system that zero would be defined explicitly. Their early number system would also evolve
into the one we use today, initially with 9 number symbols and then a
small dot used to mark the absence of a number. In the 7th Century mathematician Brahmagupta
developed terms for zero in addition, subtraction and division, although
he struggled a bit with the latter, as would academics for hundreds of years to
come. As the mathematics of India matured it found
its way Eastwards to China and Westwards, influencing the Islamic and Arabic cultures
where it was instrumental in trade. But Zero found resistance in Europe as the Hindu-Arabic system was opposed by
the Roman Empire’s established numeral system. However, by the 13th Century academics such
as Italian mathematician Fibonacci were championing the new number system in
their work, helping zero gain a solid foothold across
Europe. Over the next 400 years as mathematics evolved
from practical applications to ever more abstracted functions, zero would
form the cornerstone of calculus. Calculus allowed anyone to break dynamic systems
down into smaller and smaller units approaching
zero, but cunningly avoided the trap of having to
divide by zero. Zero had now became a celebrated tool in the
mathematical arsenal and as the binary numerical system formed
the foundation for modern computer programming, zero once again stepped into the limelight
to prove its worth. And so it seems after all this time, it was
finally possible to get something from nothing.

100 thoughts on “What is Zero? Getting Something from Nothing – with Hannah Fry”

  1. Oh, so you cannot divide 1 chicken with no chicken, but dividing 1 chicken with minus 5 chickens is perfectly OK. Makes perfect sense. The whole concept of minus numbers (and infinite while I'm at it) is absolute nonsense.

  2. Do you want to read on this topic further more?… Read Charles Seife author of an interesting book on this subject.

  3. Is it just me, or are the chapters in binary?

    Also, the positinal number system always met resistance when it came up against established systems. We forget about earlier instances because they happened before the most-recent example and thus the most resent one is the one people focus on.

  4. All numbers are just concepts when they are not bound to the rules of physical existence by units of measurement. If you choose to bind it to reality, then there is no addition or subtraction of zero units, and zero units also can not be divided into smaller units, nor can you have any multiples of zero units. You can use logic systems to understand what would happen if the rules of reality were different. Mathematics when attached to units of measurement is one such logic system. There is apparently another one philosophers use, but I have never grasped it's use of symbols.

  5. Zero and Infinity are of the same kind. Either both are numbers or both are concepts … or both are something else.
    If calculus has no trouble in treating them both the same.
    And yes, you can divide by zero: http://en.wikipedia.org/wiki/Surreal_numbers
    Also, this video is nothing but a bunch of unfounded statements. It explains nothing, but just caters to blind memorization monkeys. (Those who still parrot that “you can’t divide by zero” because they never think for themselves. Ever.)

  6. Can you explain why anything to the power of zero is one? I believe it's related to the concept that zero actually means nothing rather than a number.

  7. A huge thankyou to the person who translated this video into Spanish! We like to think that mathematics is something of a universal language, but English is certainly not. If you can speak another language and want to help share this video with a wider audience, you can contribute subtitles here: http://www.youtube.com/timedtext_video?ref=share&v=9Y7gAzTMdMA

  8. fine video, but I love it win "science" plunges into illogic… multiplying AND dividing by 0 is identical to doing those things by 1. dividing by 1 is like multiplying by 1, you remain with original number you started with… you aren't added or subtracting anything from the original number. since 0 has no value, when multiplying and dividing by it, you are in fact not multiplying or dividing at all and you arrive at the original number. that sounds logical to me. good vid!

  9. Numberphile deja-vu. Zero is a more special case in general terms. My dog for example knows that no other dogs means no competition (absence of males), however, another dog means competition and more dogs than him means a tight competition. From survival point of view it looks like simple abstraction in terms of quantity appreciation is built-in to us. It only took for a brain like ours to really put it out there 🙂 which is fantastic.


  11. This was great, guys! Hope you don't mind that I shared it on my facebook page about mathematics & film: https://www.facebook.com/mathematicsandfilm/

  12. no están claros de 0 que establece y sea un numero; y infinito que es algo que describe al limite de los números

    si algo surge es por que lo extrajeron de las vivencias lo que se presenta día a día sumar amontonar, restar apartar cosas del montón, multiplicar para grandes sumas abastecer, y dividir para distribuir entre los de mas.

    todo tiene respuestas, no saber algo no quiere decir que no hay solución hay que profundizar ir a los cimientos.

    si cero entre cero no tuviera respuestas 0/0=?

    pues entonces por que existen problemas y tienen funciones que no se saben
    y es así entonces si tiene respuesta.


    este problema 0/0=?

    las conclusiones

    2*1=2 2/2=1
    1*0=0         0/1=0
    1*1=1         1/1=1

    por lo cual  

    y el numero dividido por el mismo numero da 1 mientras no sea 0/0
    y 0 dividido por un numero da 0
    y 1 dividido 1 da 1

    la respuesta correcta es 0/0=0

    0*0=0 0/0=0

  13. there is a Remarque that worth adding , using anti derivative you can write all possible universe equations starting from 0

  14. The theory that the universe can come from nothing has one major flaw in it. Here is a link:


  15. The answer is infinity. You could say that 1 + 1 is not actually 2 because numbers are just concepts if you wanted, but that's not a very good argument.

  16. Zero doesn't enjoy ALL the things that other numbers do. Pick a positive or negative number. Whatever you pick, you can't pick zero. 😉

  17. You can't really say anything interesting AND useful about 1/0 if you don't talk about limits and hint to the quite different case of 0/0. "Infinite is not a number, 'nuff said" is both a true and useless statement. Sound better than content.

  18. In some sense, saying "Infinity is not a number is a concept" is like saying " 1 is not a number is a concept" ( are you saying 1 is not a concept?). Infinity is still a concept don't get me wrong. The opposite of infinity is infinitesimal and that's what you get when you divide by 0. Infinitesimal is not a number, it's a concept.

  19. Zero is the god of numbers, it's also the center of every singularity. The zero is truly worth to be worshipped. ^^
    Thanks for sharing.

  20. Ancient Indians did not just invent the Number system, If you are someone who loves Math, Look up – "Vedic Mathematics". They came up with ways to calculate Square roots of 10 Digit numbers in just 3 seconds, Transforming you into a Human calculator. Ancient Indians used these "Simple Tricks" to calculate Insanely large numbers, Like the ones mentioned in Buddhism.

    Buddha was once asked – What is the largest number in existence in the Universe ? He replied 10 to the power of 540. That's 10 followed by 540 Zeroes. Whether the Buddha was simple making it up, It doesn't matter and is a whole different topic. What matters is there was a Culture of recognizing and using such crazy large numbers in Ancient India !!!

  21. matter and antimatter meet to cancel and create nothing.
    0 = nothing

    If you multiply anything by nothing you get nothing

    But you can create something if you divide nothing 0*0 = nothing 0/0 = not nothing, it becomes an expression

  22. If you divide anything by no-thing then there is no division. I don't get why it is so hard for many mathematicians to acknowledge that the issues and requirement for special considerations with zero are of their own creation. Algebra being the main culprit causing confusion. It seems simple and intuitive. 1+0=1. 1-0=1. 1*0=0. Yet divide by zero and suddenly the definition of 0 changes?

    0 is none, no-thing, absence within the context of whatever things you are discussing (As in: Using a numeral describe how many chicken emojis exist in this sentence). So if we divide 1 chicken by no chickens (bad example) or 1 centimetre by 0 centimetres we are making no change as the function is negated and there is 0 division. We could try to carry out the function as a subtraction and find ourselves in infinite iterations because as someone else commented 0 goes into any number infinite times…but this is simply not true because 0*x=0. Zero provides context, an interdependent opposite to denotations of value or magnitude. If you have a box of zero and you divide it with a zero width division, x times, there is no division. 0 is the argument at which the value of a function is negated and disappears. It is not positive or negative or even or odd, it is a denotation representing the concept "no-thing" and hence is clearly defined. Not undefined or infinite. Zero as a numeral is confusing because in contradiction to its core meaning it also has a value in mathematics in terms of indicating magnitude in multiples of ten. With the right axioms maths can "prove" anything but that doesn't make it true. See Gödel's work. It is a miracle that maths is as useful as it is to science when it is an incomplete, often misunderstood and contradictory theory.

  23. The video concludes something can come from nothing. Can someone explain to me how this explains the beginning of everything/existence.

  24. But is it a number? It only functions as a multiple of the base, or nothing at all. The Babylonians came up with zero twice. It is the boundary between positive and negative numbers, but has no force as a number. Twice zero equals thrice zero, and some part of nothing equals no part of something. || 0/2=0/3.
    Also a line has length, without having volume. 1/0, so why prattle on about nonsense? 0/1=0, so does 1/0, because 0 signifies the lack of quantity.

  25. If you have one chicken and you divide it among nothing, you have everything that is there of it – the things you are aware of and can count, as also the things you are not aware of and so can not count. Everything is a concept, not a number.

  26. NOTE FOR AMERICAN VIEWERS: 2:33 By "Roman Empire", she means Byzantium, the eastern empire that survived for centuries after the fall of Rome. Although Byzantium had once belonged to Rome, it was Greek-speaking and had a somewhat different culture, and was influenced at first by Persia and later the Islamic empires.

  27. But is there anything outside the number system that can confirm that the distance between 1 and -1 is 2? (To me, it seems infinite.)
    Numbers are representatives of relative quantity. They all represent some quantity more or less than the quantities represented by other numbers. But just as 'infinity' is not a number, but, rather the absolute, non-relative concept of infinite quantity; so too, is 'zero' not a number, but, rather, the absolute, non-relative concept of infinite non-quantity. The absolute absence of quantity, in other words, and thus not a proper number.
    We use Zero for place holders to represent empty orders of magnitude. It's very useful and convenient, because our minds are finite capacity, so that we can not work with infinite digits. But that is a quality of our minds' abilities, not of external reality itself. An omniscient mind would have no need of a zero place holder, but, rather, would do math with infinite single digits.

    To me, both of our uses of zero are convenient, but ultimately misleading. And I think this has potentially extremely far reaching consequences for both math and physics.
    For example, in our number system, we understand that infinity is not a number, so that infinity – 1 is still infinity, basically, because you simply can't subtract a number from a non-number.
    But when it comes to zero we don't recognize that. So we allow that 0+1 = 1, and so on. But does that correspond to reality? I would say that in reality, if there is true, absolute nothing, there's nothing to add or subtract. It is an immutable absolute conceptual state. So that 0+/- anything still = zero, just as infinity +/- anything still equals infinity. Because you can't add or subtract anything from absolutes, because absolutes are immutable and timeless. They're not measurements of quantity.
    And measurements of quantity, btw, are divisions of everything. It's probably best, imo. to think of zero and infinity as the opening and closing brackets of the set [All] . Ultimately, they are the same, the duel expressions of the boundary of [All].
    Note that this doesn't work within our number system. But consider that she said in the video that Calculus works so well because it avoids having to divide by zero. It's not that our system for numerical notation and the math we do with it works so well because of using zero as a digit. Rather, we manage to make it work very well specifically by avoiding the paradoxes caused by using an immutable absolute concept as the lowest number in the number system(a system of relative quantities.)

  28. Clickbait title, video does not actually answer the question it poses, it simply gives a history lesson and then ends upon reaching the present day. Find your answers elsewhere.

  29. I gotta have a good day at work and the speaker boxes of ghost adventures season and the speaker boxes of ghost adventures season and the speaker boxes of ghost adventures season and the speaker boxes for am too tired and she teleport the cat food is dead in the water

  30. dividing any number by zero means that that number will never come in the multiplication table of 0, so the table will go on till infinity to get to that number. The answer is infinity for sure, concept or not.

  31. Whenever people ask why isn’t 1/0 infinity the answer always seems to be ‘infinity isn’t a number it’s a concept’. Well, isn’t maths as a whole a concept in itself? It just seems that people are bent on not getting infinity as an answer?

  32. Thanks for sharing this great clip The Royal Institution. We used it in our story "Golden Age Of India", here: https://taletown.org/real-life-stories/696-golden-age-of-india

  33. then please why you are not able to count 0 As natural number rules saying ,could anyone teach me if the zero is not using in counting then why it is zero? or what is before 1?why we cannot call nothing as a zero? or what could we call to Space? everything that exist in world might be has a space before it or after it then what will call them?

  34. funny because i saw all of Hannah's arguments with peter atkins, and she denies the use of the trickster word nothingness, as well as the creation of math from nothingness like a meta-physician. Was annoying to me and my genius friends. Sorry i got the wrong Hannah…lol….

  35. This video tells us how the number came to be. It does not tells us what it is… the title should be “history of number zero” not “what is zero”… you still did not mention the answer to that question. What is zero?

  36. If you divide 6/2 you get three. Give six apples to two people and they eat the apples each. Let's say you want to give those six apples to someone who doesn't exist. How many apples will he eat, before all the apples are eaten? The answer is infinity, because the person who never exists will not be able to eat all of them, not in a million times. 6/0=infinity. He will keep eating forever.

  37. I was always astonished and fascinated about the miracles taking place all over the world but having no logical or scientific explanations behind, and that made me believe in the existence of God when I was a child. Since then, I feel myself slightly curious about spirituality and use to relate everything with that.
    When I was in my highschool, my first mathematics chapter was "Number System" and while studying it I've got a concept of "God". Recently, I was having a conversation with one of my anonymous friend on the internet and came to know that he is an atheist but I personally believe that no one is actually atheist, everyone believes but in various different forms and images., so I thought to share that concept with him which I'm going to share here..

    So., earlier, all that was known to me was that God or the Divine is something which is perfect, and while studying about numbers I found a number having properties similar to God. That number is Zero!! Let's understand this with a simple example, suppose I'm giving you 100 rupees then all you have from me is just rs. 100/- but you can buy some of the shares with that and make it to rs. 500/- or rs. 50/- or any other figure. But how 100 can become 500 or 50 as I've given you just 100..!? The answer is that 100 is not perfect, it is just a number like many others. But if I say that I'm giving you 0 rupees, then what you do have..!? The answer should be "nothing" but I've given you "something"!! So, 0 is something which doesn't have its existence physically but it does as it is the origin of the number system and no number could ever be possible without it no matters whether one believes in its existence or not.. I also think that this concept is somehow related to the Big Bang theory too, as it states that "Something was exploded when there was Nothing".. Well, by this way 0 can be related to God, but it should not be misunderstood that God is 0.. I would say God is something different actually., saying much more precisely, it would be fair to take god as the concept of "infinity ('∞')" as every number is contained by it. But it is much more complicated to understand as we all already know that it is something which is undefined and the word itself means that it can't be defined!., for this reason, proceeding further, I'm taking the help of a sanskrit verse of one of the upnishad (उपनिषद्) from yajurved (यजुर्वेद) to understand it much clearly:
    " ॐ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते |
    पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते || "
    ( "Om poornamadah poornamidam poornaat poornamudachyate.
    Poornasya poornamaadaaya poornamevaavashishsyate.." )
    Now, this verse tells that something would be taken as perfect if
    "when the whole is taken away from it, then also it remains as a whole.."
    relating this idea to numbers, we find that "zero minus zero equals zero ('0-0=0')" as well as "infinity minus infinity also equals infinity ('∞-∞=∞')".

    But this whole theory would be of no use if we leave it here only., in order to know God, now we know that one must reach to infinity but I guess we all think that it is impossible to reach there, as by proceeding one by one on the number-line we'll never ever going to be there. But there is actually a way to reach there, as we know that
    "any number when divided by 0 gives infinity ('x÷0=∞')"..
    Now, the point here is that we all are alike the numbers which are imperfect, but we all have a soul which can be related to 0 due to which every number has came into existence and the Divine can be taken as infinity and both are perfect. Now what we have to do is just to divide ourselves into 0 to reach the infinity.. Sounds pretty confusing I know but just try to think about it.

    : Adarsh (India)

  38. Nice video but incorrect. The Mayans/Olmec civilizations had a place holder value a shell. As it has been proven the Mayans performed astronomical calculations. These civilizations had this system down thousands of year BC. The evidence is in their pyramids, codices, etc. Recently, many scholars have agreed only the Mayans had the zero as a place holder and they had the concept down.

    What is general taught today is from an European/Asian point of view.

  39. Hey um. Fibonacci lived before the proposed idea of heliocentrism, There should not be a globe there. Fibonacci was a flat Earther

  40. Every number can have a corresponding relationship in the material world except for zero. It is impossible to have zero of anything. Even in binary computing systems it only implies a length of time between 1s.

  41. …-3,-2,-1,0 (brains dematerialised through electromagnetic brain flux into mind – , Black hole into Big Bang, frontier between quantum and relativist universe, etc)  1-2-3… 0 = (x invariant, y infinite variable) 0,1 on Aleph nul.

  42. Can we take a little moment to appreciate the fact that they numbered their chapters beginning with zero (which is common in computer science, but not in every day life) and numbered the chapters in binary, just so they could better show off zero?

  43. 🤯🤯🤯

    co incidence, the dislikes is currently at 101 !?!?!?

    i call “zero”, MAMA.
    The sacred Womb .

  44. 0 is reset, 00 is refresh and 000 is re-arrange. 2020 is basically 'two fucken zeros'. Year 01 of history. 'Knowledge is History'.

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