The Nothingness of Zero

Why did the Ancient Indians invent Zero ?

To indicate Nothing in a place value based numerical system, like the binary, decimal etc.

So in the number 101, 0 means there is NO value in the tenth’s place. If there was no zero then 101 should have been written as 11, which leaves no room to differentiate between actual 11 and 101. The introduction of a new symbol, o to indicate Nothingness solved this problem. In other words, Zero was invented by ancient Indians NOT as a main concept, instead it was a feature required by the place value system which they originally invented.

If a team scores zero goals in a soccer match, it means the team has scored NO goals.

If a student scores zero marks in an exam, it means the student has scored NOTHING

and so on

Now let us see how the idea of zero has become non-zero in some of the contexts.

The arrays used in computer programming languages have a zero based index!

For those who dont know what an array means in a software program, well it is just a sequential collection of things. The thing can be a number, a text, an object etc.
In an array this each thing can be accessed by just using a number (called index) which denotes the position of that thing in the array.

An example of an array would be
Weekdays = [Sunday,'Monday,'Tuesday,'Wednesday,'Thursday,'Friday,'Saturday]
Here Weekdays is an array containing a list of the names of the days of a week.

Now there is something non-zero about zero here. Zero is not Nothing here, its actually Something!
For instance, to access the first item Sunday in this array, we will have to say Weekdays[0] !!

This is what we mean when we say, zero-based index, i.e item positions have to be counted as 0,1,2,3 etc, NOT as 1,2,3,4 etc

Shouldn’t it have been Weekdays[1], since Sunday is the first term, not zeroth in the array?

All C-like languages (C,C++,Java,C# etc) implement this concept of zero based index.

Some Non C-like languages like Visual Basic on the other hand followed one based index, even though off late Visual Basic.Net has converted to zero based index! There is conversion even in computer programming languages

So in these C-like languages which rule almost the entire computer programming industry, when software developers say Zeroth index, they actually mean First Item!

This concept of non-zero usage of zero is not just limited to arrays or computers either. Have a look at some other cases.

The ground floor of a building in US is indicated in an elevator by 1′ (which makes sense), where as in India it is 0′! 0 going by its mathematical definition means there is no such floor, so it shouldn’t be there in an elevator at all unless and until that elevator takes us on a time travel

The current Gregorian calendar does not have 0 CE! Because 0 CE means there is no such year! The calendar directly jumps from 1 BCE to 1 CE which is quite natural when you consider the definition of Zero

Having said this, why do we start with zeroth index in almost all computer programming languages?

The reason is because it makes things easy in terms of computational purpose. Suppose there are N items in an array, then the zero based index means representing each item’s index as

0 < i < N

On the other hand, using 1 based index would mean

1 < i < N+1

As you can see, the ease of zero based index is,

  • In terms of representation you dont need any number greater than the number of elements N
  • You dont need additional overhead of adding 1 every time you compare with the upper bound, in other words in zero based index the upper bound is the number of elements itself, where as in 1 based index it is NOT.
  • The zero based index of an item also denotes the number of items prior to the current item

Now what about 1 < i < N ? Well, in the above two cases the difference between the bounds gives the number of items in the array, where as in this case it gives N-1 :) In other words, zero based index provides more scope for optimization while compiling.

Division By Zero

I have asked this to question to many people, and sadly nobody gave me a satisfactory answer! The question is of a very elementary mathematical concept. How can we say that

Division of any number by zero = infinity

We have been doing this mathematics ever since our primary school. But to accept something without inquiring into its accuracy, is unscientific. I dont do math without understanding it, instead I prefer not to do it if I dont understand it, for I am not a computer to do things without understanding what it means. Deep Blue might have defeated Kasparov in Chess, but it never understood what it was doing/calculating while playing with Kasparov

I have seen a lot of people who do differential calculus without even understanding the meaning of limit, continuity, differentiation etc. They simply apply formula and get answers without even understanding what they are doing, just like how machines(computers) work!

If we solve problems with such an approach, then we get lost into the symbols of mathematical equations and we end up wandering on the path instead of marching firmly towards the destination.

I am not saying dont do mathematics. All I am saying is dont do mathematics without understanding what you are doing. Summation of indices in tensors without understanding the purpose is a total waste of time and energy. Abstraction at the cost of understanding is of no use.

If we do mathematics without understanding what exactly we are doing, then we wont even know when we are wrong, and there are very little chances that we will discover it, unless and until we happen to check the correct answer.

Not that we wont do mistakes if we understand what we are doing. But the chances are less, or at least we will understand the mistake!

Coming back to division by zero, it simply means, division by Nothing. Now how can that become infinity?

We should remember that while multiplication is repeated addition, division is repeated subtraction. So 23 means repeatedly add 2, 3 times. Where as 6/3 means how many times can I repeatedly subtract 3 from 6 till I run out of everything in 6?

So when we say 30=0, we mean dont add 3, not even once, which means there will be nothing left which is Zero.

On the other hand, 6/0 means how many times can I remove Nothing from 6 till I run out of everything in 6? Well, as many times as we want, because no matter how many nothing’s we remove from 6, the 6 still remains!! So any number divided by zero is infinity, because you can remove infinite nothings out of something!

Now what about zero divided by something? For instance 0/6?

Well, here it means how many sixes can I remove from Zero? The answer is none! Because zero is Nothing, there is nothing you can remove from zero. So zero divided by a number is Zero.

Okie, finally what about zero divided by zero (0/0)?

What it means is, how many nothings can I remove from nothing till nothing is left?

Well, Undefined is a polite mathematical way of saying, the question is stupid

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  • Swayam Narain

    Interesting article, but often times, numbers are used in daily life in the relative sense, and not the absolute. So, the logic of using ’0′ for the ground floor instead of one is that it means zero levels above the ground, which means the ground itself, and ’1′ means 1 level above the ground and so on. This also applies to your array index example, where arr[0] is actually read by the compiler as adding a zero*[element size] to the array’s memory address, which will give the first element. This because by design, the memory location of arr is same as arr[0]. 

    The nothingness of Zero is used, by design, to define the constancy of objects, environments and other variables.  

    • Anonymous

      That’s fine when conventions are defined based on local convenience.

      In US, China, Singapore, Russia etc ground floor is 1, in Europe, India etc it is 0.

      In C/C++ etc first index is 0, in old VB is was 1 and so on.

  • Sheshank Joshi

    My prev post continuation…

    In my previous post i forgot to mention a solid statement in support of the working of the universe. There is a wording which most of us know. The thri Murthis are said to have been rulers of this world and a statement tells that they are referred to as 

    “Tri Murthyah, srushtihi Stithi laya karakah”. (From Devi Maha Bhagavatam-the first ancient script on how universe born) 
    This tells that tri murtis are the responsible of the travel of this universe for setting up the platform/space(srushti-lord shiva), position and influence (stithi-Lord Narayana) and laya (motion of the universe). That’s what is happening. The whole universe, according to Quantum theory, is that they are moving in the space under the influence of gravity. So, the three aspects are covered. This is the latest invention of 20th century taught by Indians as one basic of the basics. It is taught even before vedas, and almost before everything. We praise the three. And we say that our fate is decided by brahma, which means we are travelling in time, in a path and way decided by lord brahma, termed as fate.When our journey ends, the energy changes its form and reappears in other form-obeying modern ‘conservation of Energy’ theorom. This can be compared to wave-particle interaction/mass energy conversion. Hats off the Vedas again.

    One more word i forgot to mention in support of lord shiva referring to Zero (empty space). It is never mentioned, not in a single & original compositions-unlike some versions of ramayana which supports the existance of Laxman rekha-often lead to controversies, that Lord shiva is born out of something. (Not even Devi Bhagavatam).
    Which means Lord shiva is born out of nothing, out of empty space. He is mostly referred to as mrityunjaya and told to be born without parents. 

    Presently I am trying to link the time to all these tri murtis. Time is relative to motion. So, anyone try to solve this mystery. Its a challenge ! 

    According to theory of relativity- and is proven- that time travels with speed of light where there is no vacuum, no gravity. It travels slower and slower as we increase our speed i.e.., if we bend the space. Bending space is possible only by the presence of mass. Its a kind of controversy like ‘egg first or chicken’. We don’t know whether gravity/space distortion causes the mass to be accumulated or mass causes the space distortion creating/spreading gravity. But one thing for sure is that its kind of play-explained by many great scientists-that goes round and round. Once we enter, there is no exit way. We need to go round and round and round. No exception or no escape. Very great people can only get past through the circle. 

    Here is a my great(small) story/theory originated out of my thoughts (may be outdated) based on all my previous statements:

    For the Universe to work, we need something. Something which is unusual and which is not where it is supposed to be. That means it should not be confined to a particular place. And thus, there is a vibration (oscillating about mean position-from basic definition of vibration) is required for the universe to run. That vibration is what we refer to as our ‘OM’. Most scripts support that its the Adi pranava Nada which means the first vibration which caused the pattern. That vibration is generated out of energy (Shakti-whose whereabouts are unknown and not described in any script as far as i know). There are few people who argue that shakti is born out of OM, and i don’t want to argue with them, because i don’t know it precisely more than they do immediately after reading this statement.

    OM created disturbance in empty space, causing the space to respond to the pattern of vibration creating disturbances in and beside the place of origin. That created the Energy in and around the space to accumulate/duplicate (at) those space disturbances. (Modern string theory also supports this saying that at the beginning of universe there might be a single, high energy, high tension string, out of which the other strings duplicated and originated to form an array of such crores and crores of strings) That increased within seconds and expanded. Due to energy’s presence, more than space could accommodate at that point-without the spatial distortion occurring-caused the energy to turn into small particle masses. That caused all the energy to accommodate at a single place in and around the main energy creating small small masses. That continued on and on creating small and tiny bends to spatial fabric. Latest discovery, suggested by Einstein and one more scientist, that spatial fabric is elastic in nature. This is also experimentally confirmed. So, coming back to my story, the fabric, elastic in nature, pushed all those small masses into a single, deep well kind of thing which is major mass. That is when, according our vedas, the journey, the barhamam started. The travel started. When all the matter accumulated forming a mega Energy, mega mass, thus creating heavy space distortion (we can assume Lord Vishnu is formed). Out of the centre of this heavy distortion the bast occured. Brahma is said to have born from the navel of Lord Vishnu. Now as the distortion caused, which ultimately created Lord Vishnu-set the platform for a huge supernova explosion thus setting world into motion. This we call as Bigbang explosion. As from the big bang every object is moving, and each moved object is influenced and played on Space and gravity which are like Shiva and Vishnu. 

       The patterns of the motion decided by Lord Brahma, or simply we can consider as the Brahmam and its motion as assumed by our ancestors, created/classified (may not be by brahmi, but claimed by our ancestors to be done by Brahma) the lokas-depending on pattern and the movement. That is how relative motion takes place. Everthing, every object moves with respect to each other. The whole central thing moves with respect to the main central energy. The sub-classification of prajapatis etc.. etc.. are done according to the patterns and the relative motions. These motions definitely effect us (scientifically and spiritually) because of the reason they also form, lead to small small spatial distortions due to their motions
     (also masses they have under the influence and guidance of the ultimate Tri murtis). We need to remember that its not just the main distortion i.e.. big bang or the main expansion caused, led to the fact of formation of Earth and human beings. Similar is the case with Prajapatis. Those five prajapatis (According to Devi Bhagavatam) influence us, deal us and decide us. Brahma is not involved in everything. It is said in Devi Bhagavatam that Brahma created parajapatis who created this material earth and decide the fate of people. 

    I am sure that is strictly applicable to space as well. Its not just the Big Bang which caused the formation of earth, infact its influence is initial, until the creation of the galaxies (compared to prajapatis), from them these galaxies, their motion and everything effect the way earth is formed and Sun is formed. Still, they influence us with their movement. (This is the exact main concept behind learning astronomy. Learning leads to guess the way prajapatis wrote our fate i.e.., how Earth’s gonna get influenced by those stars) According to our puranas, these prajapatis rule us. Those prajapatis created sub-workers, sub-things etc. etc..about which i don’t know much (have not yet framed story on it. Still thinking :D LOL..). I need to read Devi Bhagavatam again and decide, reframe the entire story. Remember its just a theory, just like a big bang theory, which unfortunately unites my religious feelings and my scientifical ideas (very small and foolish ideas). I don’t have any proofs for all this stuff just like our ancient sanskrit texts, Ramanujan theoroms. Its just a theory. 

    Continuing with my fictional story, about formation of human species by God, let me say my perspective. God treats everyone as his children. So, i framed it carefully. So, according to hindu mythology prajapatis created one or two people who in turn created the whole population. So, they created one fellow and sent him to earth, which is formed/created by that time. (i didn’t find any story regarding the origin of Earth related to our vedas. Will be glad to hear them). We all know how earth was created according to modern science, and even according to Hindu mythology. It is said that they came out of Sun ( both spiritually and scientifically). It is said that Sun came, originated out of Vishnu’s eyes. (I don’t have explanation/confirmation on that). Earth is the daughter of Sun (Some one correct me if I am wrong). Whatever its is, but coming back to story. When Earth was ready prajapatis sent his messenger, or a part of him, or he himself came upon Earth to create the first life under the influence of lord shiva, brahma and vishnu (space and gravity). This can be interpreted to the stellar object (asteroid) which caused the life on Earth under the influence of Gravity, random motion and in the space (brahma vishnu maheshwar). That collision caused various life forms to form (i am not much interested in theory of evolution.I am sorry Darwin ! But, i refuse to accept it). Thus life took place. 

    We know the later story about all those avatars and Lord Vishnu coming to Earth, Lord shiva and his influence. i think Lord Vishnu is a man born on earth with special ability, distorting space around himself, defying gravity.That means any man who is heavy, heavy enough to influence the space around himself is Lord Vishnu. We feel the gravity when there is a space distortion, which is nothing but we like to meet, talk and feel attracted to his force.(Can also be compared to that Lord Vishnu was black in color. Usually heavy objects/black bodies emit radiation. That is what we call one’s tejassu). Such special person is born under the influence of the stars/extra terrestrials is so good to create such people (may be the messenger thing happened again). We need to remember that it was not shown frequently that Lord Vishnu was born. He was born once or twice in a yuga-which had lacks of years. So, it may be possible to happen. 

     So, wherever Lord Vishnu as the nine avatars is said to be roamed are the places where there was once heavy spatial distortion. In support of these statements, it is described in vedas and all the puranas that Rishis, people always worshipped, went to where Lord was born. They, even the people, get attracted because of heavy spatial distortion caused by the man. It may seem impracticable for people like us, since we have no proofs for such scientifical in thoughts into puranas. But, i don’t have proofs again. Neither i have proof, nor its mentioned in any book. These are just the mild possibilities. Coming back, suppose if a God can be described in a way i just told, there how can we say that its the Lord Vishnu who took nine incarnations in such way as described in puranas. I have a small example for that.

     Its human psychology that whenever someone does good to us, helps us we say that they are Gods. we praise them, compare them to God. Similar is the case here. Those humans who incarnated on Earth in such way, helping everyone, doing good more than anyone else in the world, doing great,er things, kill the bad (removing their problems) etc. We say they are Gods. When everyone in and around your praise you as God, you will be the God. That’s what, i guess, happened with them. We need to one more point as said by Guru Dev once that, no one not even Rama, Narasimha etc.. said they are Gods. People said. In the entire puranas, all the epics never did one say he is god (except sri krishna in Bhagavad gita, that also to take a couselling session for Arjuna). So, God is always great. People treat them gods. Coming back, no religion treats this way. they never treat their fellow being as God. The only person known to world-a major person- said to be God is Jesus Christ. He may be the son of god, which is almost equivalent to god. We all know what happened to him. We, Hindus believed in real Gods, gods in humans, while they saw god only as a superficial being who does magic. They treat the God as the person who is just not like them. Atleast not as ordinary as they are. They always expect the God to have some special abilities, special magic powers. Even if God comes infront of them, they will not be ready to accept him to be the God. Where as in our religion, we treat our parents, teachers, guests, kings equal to God. Proud to be a Hindu.

      And yet they say their religion is greater than us. What a pity! 

    Note : We need to note here that Lord Narayan and Bhu matha (mother Earth) are a couple. it can be contrasted with the gravity-space distortion which are a couple, just as i described previously.

     This is the angle in which I am thinking presently and People ! you also think about it. Frame your own thoughts and find the God, thereby the destiny of your life. I believe, like most of you do, that we are sent down to perform our duties on this Earth. People die even before they do their duties. So, decide your destiny, take it and follow righteousness always. Its that which comes even after your death. Live like a hindu die like a hindu. Follow hindu Dharma(Sanathana Dharma) according to Manu Shastra. Dharmo rakshati rakshitaha

    Righteous ness is as righteousness does. Remember, Mahabharata war occurred and almost 14 billion people died only because the whole mahabharata says what is Dharma, yet no one follows it strictly, instead take exceptions. As a result we saw that Lord Vishnu himself has led the war killing all the people and establishing Dharma.

  • Sheshank Joshi

    I recently discovered from my thoughts (may be outdated). Few of them i like to express are that 

    zero (shunya) represents lord shiva. May be the shiva linga is the same reason its oval in shape.(no controversies, Comments are accepted). Shiva is said to be Adi deva, which means everything starts from him and he is the first one. If anything is to start it starts from him. Infinity (anatam) represents lord Narayana.(taken from the praise by Narada-don’t know where exactly- that Narayana is referred to as the Adi madya antara rahitudu. This means that Narayana is the ultimate one and the infinity and he is the one who lives after Adi and Madhya.)The connection between these both (Brahmamu, which means the universe) is Brahma. The universe said to have been created out of Brahma according to our Hindu Mythology. Lord shiva says in Shiva purana (don’t know where exactly) that everything has to start with him and end (may be ending at Narayana). Now our sceintific advances are unable to chase down the mystery of both Zero and Infinity! We are still learning only a part of Brahma. It is said in Vishnu purana by Vamana that one has to learn about Birth (origin) and abide by Brahma to reach Narayana (infinity). Brahma (Brahmamu referring to this world by The great Annamacharya in his sanskrit sloka, from the world Brahmanda-referring to the whole world to an egg) is the one uniting both these out of which the present world is generated.It also has one more meaning that Brahma is the time. and one has to start with fusion (referring to an article about lord shiva, which says linga is a symbol of human mating) and ends with the sleep (Yoga nidra, which Narayana is always in) travelling through time (fate).We know a small sloka-which we read everyday-which says that Narayana and Shiva are one and the other. Shivaya Vishnu rupaya
    Shiva rupaya Vishnave
    Shivasya Hrudayam Vishnu
    Vishnoshcha Hurdayagum Shivaha
    Yadha Shiva mayo Vishnu
    Revam Vishnu Maya ShivahYadhantarana ApashyamiTathamo Swastirayushi(I don’t know the exact meaning of the last four lines. I just read it during my everyday ritual of morning Sandhya Vandanam)Mathematics of infinity, Zero, undefined etc.. can be applied here to get spiritual feelings and some secrets with better understanding-which i failed to do (Need the help of someone).Our recent discoveries doesn’t suggest what happened. We say Big bang happened some 14 billion years ago. But, from where did the matter come out at once? No one has an explanation. What was the condition before Big bang? I think you might have got an idea-which most scientists has to agree obviously- that universe was born out of nothing (Shunya-Lord shiva). We say universe is expanding. But how long will it expand? And what happens after a long long expansion, expansion to as tiny as sub atomic particles? They just vanish! They just disappear into infinity (after a long travel from nothingness to somethingness they mix up with everything ness-where the whole universe will be filled with sub-atomic particles due to big bang expansion- and ultimately turn out into nothing ness. This means universe starts again) Modern discoveries suggest that they reunite.(God knows whether is true or not).But our ancient vedas already did it. Infinity and Zero are both the things where the modern scientists failed to connect, while our ancient vedas already connected. (Feeling a little proud of my self looking at what all i wrote). You can also find few references of what i told in Bhagavad Gita. What is feel is that universe is completely filled of empty space (can be referred to lord shiva-nothing but zero) and in some places some places there are massed objects influenced by the heavier masses through space distortion (Refer to space-time article by Guru Dev ji), and finally but ultimately influenced by the most heavier mass/gravitational pull at the center of a black hole (Just a mild assumption)-which we term as Krishna Shakti or Black energy-more precisely black hole energy. This also adds upto the phrase said by Sri Krishna in Bhagavad Gita

    “I am in everyone. Where ever there is a thing, there i am present in it”

    Can be compared to the fact that, wherever there is mass, there is the space-time curvature and is gravity.
    ” Indugaladu andu ledani sandehambu valadu. Endendu vetikina andande galadu”Which interprets a dialogue told by Prahlada to his father Hiranyakashyapa telling that Sri Hari is anywhere and everywhere in this universe. That adds up to my thoughts. This can be contrasted with modern inventions and Einstein’s theories of relativity and gravity. ”Gravity is Everything. We are none without gravity”

    Space (Lord shiva himself) is a platform where all this universe works. Probably that was the reason why Lord shiva doesn’t completely/usually take part in any epic directly/partially. He just sets up platform where Lord Vishnu plays all the things ( The gavity plays a vital role in this universe where the space just responds to it).

    I don’t know much about Brahma.I wildly guess that Brahma is something related to motion. The motion is the third and the major part in this universe. We move through time, the objects move through space and aeroplane move through air. These are the things which has got nothing to do with Space or gravity. They just move, but under the influence of Gravity and space, in an unpredictable manner decided by lord Brahma.I just wanted to share What I know, learnt, read and thought. Comments are welcome for any part of my view. I have no proofs, unlike modern technology, and more like our ancient texts. Its just what i understood about the working of this universe.I think we should concentrate on our part in the working universe, rather than trying to know how universe works. Kudos to our ancients who knew this fact thousands of years ago and written an Ancient text called “Manu Dharma” which describes the role to be played by Everyone in this universe.

    • Anonymous

      A very good one Sheshank. Way to go. Keep digging.

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  • Kaz Maslanka

    Here is a mathematical equation created around the year 1800 by the philosopher Friedrich Schlegel which addresses this absurd idea of dividing by zero.

  • Kaz Maslanka

    Its very interesting that you discovered that relationship about ego and dividing by zero … I think it may be more common than people would think. Here it is again (link)


  • Gurudev

    Really cool Komila, perfect :)
    Soul is nothing, yet present in everything.. just like zero..
    Universe/world is that everything which contains infinite nothing, which is the definition of God/universal consciousness, which is again nothing but the soul itself! Advaita!

  • Komila

    Fantastic is quite philospical & absolutely, logical !!

    Multiply : World x soul/atman = soul/atman
    Divide: World/Soul = God or Soul/World = God
    Add.subtract: World +/- Soul = World

    where, world being ne number and sould being nothing/zero…inifite results relates to GOD..

    it took me lot of time to get results, but it was fun interpreting the same…

    Thoughts/corrections are all welcome.

  • Gurudev

    Well said Apsara, philosophical math :)

    Kislay, dont worry about somebody writing wrong things, truth cant be hidden for a long time ;)
    As for 0/0, it is ‘undefined’, there is nothing more to worry about it. It simply means, how many times can we remove nothing, out of nothing, so that nothing is left!!

    Thanks Viji and Phani :)

  • Phani

    The best post by far… i have forwarded this post to all my friends!!

  • viji

    Another nice article.

    Division by zero can be said this way also,
    6/3 means, how many 3′s are there in 6.
    so for 6/0 it can be.. how many 0′s are there in 6. This statement is absurd and so is infinity.

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  • Kislay

    This is an established fact that Ancient Indians invented the zero , right ? Recently I read a book called Holy Cow by Sarah MacDonald , and in that book the author says that zero was invented by Indians but somebody from Damascus . I tell you it really pissed me off . And regarding 0/0 , George Cantor went mad trying to find the value of infinity , so I guess the question is not that stupid . Watch the documentary Dangerous Knowledge if you got time . Its about George Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing .

  • Apsara

    Hi GD, excellent philosophical math post!

    Now, am intrigued here. You said:
    Division of any number by zero = infinity.

    What about if I translate it into this:
    Cut your ego till you are gone (nothingness), then ‘you’ will get the Infinite. Call it the Universe, the Multiverse, your true self, whatever.

    And about 0/6 = 0 or 0/1 million = 0…

    It seems to me that the Grand Nothingness remains the same, whatever you do to it. Take anything from it, add anything from it the Grand Zero is the same.

    Mountain is still mountain. Rose is still rose, as you said somewhere :-D

    It’s intriguing how basic maths can actually explain some basic stuffs of spirituality.