Numerical systems across most ancient civilizations developed using similar linear patterns of counting. For primitive hunter-gatherer societies, a linear scale that facilitated counting the number of animals killed or artefacts bartered seemed sufficient. In a more complex and flourishing agrarian society like India, the need to study natural phenomena like rains and floods led early Indians to observe the cycles of the sun and moon, which in turn led them to count along circular patterns.

Ramprasad Soghal deconstructs the process by which ancient Indians arrived at the highly efficient Indian Numerical System, how it was adopted the world over, and how it was erroneously attributed as originating in Arabia.

He further makes a case for the probable origin of the Indian Numerical System in ancient Kannada numbers by shedding light on ancient Kannada notations devised for recording the waxing-waning phases of the Moon, the concept of Zero developed for counting the No-Moon and Full-Moon days, and the unique Placeholder System derived from the effective Kumbha system.

### Transcript: –

Within Europe, different periods how they were writing, it’s not consistent. When did in Europe, How they, then they started calling, its guy as the originator of number system and that’s why they started saying Arabic Number and then there is this Leonardo Fibonacci, who was basically a merchant from Italy and he was positioned in Africa and then he realised Indian system is better because is very easy to calculate. Arithmetic is very fast, all other people when they were counting, they were counting a linear system, I count 1,2,3,4…. But Indians started thinking cyclical system…. cycle. We can explain using Kannada numerals why 3 is written is like this 3. And moreover you can see 3 and 6 they are related. Ok! And 5 is half of full moon day 0 because that’s why it is full half reversed. For example 1 and 2 ok! 1 and 2 is basically what is you cut zero into half. The first part is 1 and second is 2. And that is how we even write in Kannada even today.

Thank you, Padma, So she has introduced me and I will not take more time about me and lets us start with the topic then if there is anything then we will take it in the Q&A. So, my first talk is the numbers. The numbers as you know, we start from our pre-nursery. So what’s big deal. So, I will, we know the numbers. So they are 1 to 9, 0 everything. There is a history and that is also told to everybody, but what is not told, why we write for example ‘1’ like this? Why we write ‘2’ like this? What is the reason? Ok!

So, this question was not properly answered and this is the slide thrown at people. So, the reason is, if you really look at it. There is for example, there is 3, there are three angles and so, it is 3. So, ‘3’ is written because it has three angles. 9 has nine angles, but just look carefully is the sense that the way we write 9. We don’t! So it just made up to show that to have a 9 angles. That’s is not the way it has come. Because if you really see Indians have invented the numbers, but maths has progressed after numbers. So angle should be coming after numbers, so angle should not be the reason to get the numbers. So, these angles are not the answers to the way we get the numbers. And this is just thrown at people. So nobody asks further questions.

OK! So, I am going to talk about it. Little bit I will take you to the history. Because it is to set the context, but some of the things what I will explain later, the information is required then I will purely explain how it has come. Ok!

So, the numbers, the evidences start 30,000 years back, when we have a borne in Check Republic where they had 55 tally marks. So, we know, that’s is the oldest evidence we have and ancient civilisations everywhere we find the numbers of its age. So obviously, you can think about it logically from science how it would have started. So, you have ten fingers, so people started counting with the 10 fingers, identifying each with one-one number. So, people can go upto 10 easily. So, this is nothing great invention. It comes as an intuition everybody followed. All religions followed. And there are different ways people used even horizontally, vertically. So, the representation of hands naturally should have formed into numbers. So single hand is fine but if you really see these civilisations, they were using, they were hunter gatherers. So most of the time they had something in the hand. So, when they have something in the hand, in one hand they cannot represent all the numbers. When they cannot represent all the number, they had to use only one hand. Because this is very very ancient. We don’t know whether language had originated at that time, but something they should be using to identify. They could be using sign languages, so they have invented the next level, the next level something like this to indicate all the ten numbers through single hand. So, they are may be counting 1,2 ,3 4, upto. So that is possible. So even this is used now for counting purpose.

So, we see again for 5000 years, the Sumerians started recording. So, one is counting but for your practical usage it has to be in a recorded format. And what they have done, they have used from single handed instead of using a finger they started using the ribs, whatever the small-small things are there, segments. So, these segments they can count up to twelve. So, 12 in one hand and other we have from. So then this way they can go up to 60. From 10 to 60. And what we see in the recording format also they have not complicated things. They have used only simple, very simple symbols. One symbol, for example 1 is something like a bud, a flower bud and then you multiplied, so you want to write 2, you write 2 times, 3 times, 4 times, 5 times. And you know when they go up to 10 because people where using 10 because of the 10 fingers. They have given a new symbol because from 10 was a big block to go further. So that’s where they doesn’t go to counting of 12. They still use 10, but they have used this mechanism. So, we know up to 60. It’s called sixa decimal system. It’s a Sumerian invention. And then for recording purpose some material is required. So the bone were used first. Then we see in caves people are writing this counting system, so there were no numbers. So, they were still using symbol representation. And Sumerian tablets, mud tablets we can see those every clearly the same pattern of numbers. They are not complicated, simple. And, then, next we see, next Romans using wood and there were using numbers in a one counter kind of thing and they were attaching counters together to derive a number.

So, before we understand anything, we need to go back to the very ancient times and what we see that, what you know, the ancient civilisations that were available. One from this Sumerian, another one we can see from Egypt, another one we can also considered Chinese and in South America we can see Mayans. So, these are pretty old. We know some of their dates. So, we need to look for everybody. Is there a pattern, their thinking, logical, pattern. How they have come to their numbers? Because these were probably were ancient because when you have killed an animal, to count the number of animals you have killed, so you need some counting. So, everybody need not have to wait for some invention to have somewhere, so they had gone ahead independently.

So, we see there the pattern. So, for example, you see here again 1,2,3,4 similar simple number system lies and again, you see 10, they are giving a symbol, then they are jumping to 10. So, after one round when fingers are over, they are repeating. So, same thing is Greek, inherited from Egypt. So, you can see 1 ,2 and 3,4 is written, so there is another invention, probably they have done to cut down by 5,6,7,8,9. So probably they are writing more and more lines. So, they have cut down, so there is one jump. And then Chinese, as you know, they preferred to give symbols for everything. So again, what we see here is, they are writing 1,2,3 again with lines, but then, from with 4 onwards, they start giving different – different symbols. Here Sumerians, I told you, they have only two symbol and then next level we come to Romans and Romans inherits from Greek. And they have 1,V,X,L,C,D,M. So similar, some 5,6 digits so 5-6 notations and combinations of that. So simple civilizations and we can know, we know that till they were using all these things, their civilizations is also simple. It wasn’t very complicated, so we cannot bring any new different kind of technology. Because this act as a posion fill suddenly when we know they were using, they start talking about very complicated angles, then they were talking about some solar system. It is not possible because they cannot even break simple calculations, arithmetic, they cannot go to that higher level. Its a logic we can derive.

So, Mayans again what we see is, again ‘zero’ is in this picture they have added, so again, here again, basically you will see a finger. Instead of finger they are putting a dot. So when you have 4 fingers, they are representing 4 dot and then 5 one hand they are making a line, and so, it continues up to digit 20. So, nothing great. Everybody is following a similar structure, a similar pattern. So, what is missing here till now…, India is missing. Of all the civilizations India is missing. So, these people are thinking in one direction and what was India thinking of this prospective so that’s where we need to see.

So, all these people you see they are all small societies, very few people, fewer needs. Numbers needed were small, the calculations were simple and as long as they remain primitive, they can manage with this. So, at a time probably nobody kills 60 animals may not be required. 60 itself they can do with most of their transactions, day to day activities, they don’t talk any big numbers beyond this. So, we come to India now.

What is happening in India? So, **we know European now, what history tells now** if this is the number, European numbers and then they say this is Arabic numbers, from Arabic numbers, we got into European numbers. And if we really see this, there are two versions of Arabic. And then they map it to Devnagiri and then another example in Tamil, we see a different notation altogether. So, in India, it’s not like other civilisations. It’s not one single formats. Already we see Tamil different, Devnagiri different and we don’t know why same numbers are not used in Arabic? So, we say its Hindu Arabic, then why they are using different notations here? But what the history tells is, it is derived from India. So and of all the civilisation, Indian’s numbers were superior, so it was adopted. I think that’s it. There ends the story of history of numbers. Why do we need to bother about it? Why not we buy it and why not we stop it and buy this argument and close the chapter?

See it’s not the question of numbers alone. Today the whole maths is used to explain Science. So, the whole very big-big things are modelled on mathematics and through maths we are explaining. And what is the common definition of maths numbers. So if we don’t even understand the numbers what are we trying to do? if we don’t understand the foundation and explain the top floor, and **second thing, this** numbers are very very primitive. They are coming from very very early phases and if we start thing why they have come? How they have come? then we know what is their thought process and is there a problem, why they have arrived at this solution. And why and see all over world, all civilisations Indians numbers have become very very good. So how it has become very good? Things will not become very good suddenly. So there must be some cycles, where you have done something wrong and then you improve and then you come out, come to some system. Because what we are talking about is basically a very sophisticated thing. So what crosses in a world. What are the cycle they have undergone? Why they have come to this system? Because we saw already Sumerians were optimised to go for simple very simple just two symbols, 1 and 10. That’s all. Nothing else. When things are very simple why do we need to go per writing 10 digits, 10 different symbols because there is another simple system. Why do we need to go for this? So all these questions we need to ask because it is going to unravel, our culture, our history, our problems and because Indian was the only country which was thinking differently from all other civilisations. That is we need to understand because why India took the leadership position? So, what were we doing differently? And that’s what once we understand all this background factors then probably, we can see because history repeat itself if you yourself do the same algorithm and analogy you can think about it.

So do we have some strength here? That is a question why we need to study these factors and we need to explain it and it should be a motivation because it’s a learning for our kids and it also because this is one of the factors, very big, numbers are very very big. Because if numbers are not invented not like this then probably, we will be still using Romans and we were doing simple Arithmetic not going anywhere. So, this is a very big contribution and something to be feel proud of. So, if the whole world doesn’t care about history further we Indians has to understand and we should be able to answer it. Because if tomorrow somebody can ask it.

Here they say, we know 10 clearly, because the battles of Ten Kings i.e. Daśarājñá yuddhá, that’s is what it is called. That is very famous in Rigveda and there the 10 comes and then 1000 pillars hall they refer. 1000 pillar hall is very big. What we were talking about. The westerner people gave us the picture like Rigvedic people were living in huts. Then why 1000 pillars are coming. Whatever it is. 1000 it is. Forget weather they had or not. Still they were able to think, it itself is a very big matter. 1000 pillar hall. And then again, the slokas says 100 warships. 100 warship means 100 people has to be rowing the boats. Boats, what were the size of boats? The way the picture western has given is totally different than what is existing in the Rigveda.

Forget about all the other things but we need to look at these numbers. All numbers are defined in Veda itself. And then, we have not just in Rigveda, we have Yajurveda. And in Yajurveda we have Shrirudram is very popular and that comes in Krishana Yajurveda’s Taittiriya Samhita. It has two parts. Rudra and Chamka. So Rudra talks about the lord Rudra and basically its names to pray for him and then Chamka is basically requesting to fulfil wishes. So, these are the two things. They are 4.5 and 4.7. And the end of it, we see this is the sloka and where they say, very surprising, they only pray for numbers. And the numbers are in order 1,3,5,7. They are completely odd numbers series. And then they start with even numbers 4, 8, 12. Numbers are missing. We don’t know what it is. And people, there are various interpretations in many many Vedic interpretations. Lots of author have given and they tell what is 1? For example, when 11 comes, 11 rudras. All these things they given, but we don’t know exactly. Because only numbers are given. But why this sequence? One is odd number we understand. But even is not because it doesn’t not start from 2. 6 is not there. So, it’s not really a correct series, but it goes up to 48. But we know we can know these all are multiple of 4. But why 4? And then one odd numbers are given immediately after following by 4 series. But the important thing is, in Vedic times, they also knew this series. That is what is important. And nobody highlights all this.

Then next comes in Shukla Yajurveda. 17.2 and here this is, I have translation of Hindi, not in Devanagiri. This is but what they have talked about is power of 10. They have gone upto 10^12. They are talking about very very big number. Why they went to these number? What are the requirements? And why Indians face this requirement that was not existing in any other religion. This is something we need to see. This is something trigger point you need to question. When we start questioning, you may give one person one answer and another person may give another answer, then another person may give another answer. Then we have to see the points and try to fit in what is the best logic.

And then comes the famous Brihadaranyaka Upanishad. This is Puurnnam-Adah Puurnnam sloka and this sloka what is bring it doesn’t specify infinity but in the end what is say you have some quantity you go on removing things but the quantity remains. So if the quantity has to remain it means its infinity. Otherwise something if I remove, for example, I have 10 litres of water, I remove 1litre of water, then it should become 9 litres. Reduce quantity. They are talking about non-reduce quantity. Of course, they are talking about concept of God here. So, God is infinite and that’s what the idea is. So God is full, you remove anything from him, still he is full God because if God reduces any, for example, from God if I remove some 1% of power will God become 99%? Then it is not idealistic. So, these arguments were happening and they were thinking about God must be idealistic so it must be full. Even if I remove something, he must be full. For example, we have Krishna was reincarnated born, so does 5% God was in on Earth. So was the God 95% there, cannot be. Because he has to be full 100%. If that is 100% then what is this 5%. So, this ideological problem comes, then how do they explain? So that is where comes the question of definition of infinity. Why they were going to be big numbers, we see clearly Hinduism first because this level of deep thoughts and discussions were happening. So and this infinity was not coming from number perspective but from God discussions. Whatever they were trying to define.

Then comes our Jains, Buddhists. They wanted to define we are not less. So, they again, the God has to be infinite. So then to explain what is infinite? It is very difficult because again what is the number? What will be equal? Can you give. Because people cannot comprehend. We know infinity today because we study maths but these are primitive people. How do you explain infinity? So, God they could understand probably, but what is infinity? So they wanted to give an approximation by saying a big number. What is a big number? Then some if you define some number you will become encapsulated. You will become bordered into that. They don’t want that.

Then next guy comes even define higher number. Then even higher number. So that way they started defining numbers. And the first the way they could define is give a name for a number, a bigger number. Then what it is explaining in slokas. 10^54, 10^12 10^24 something like that. And they have three concepts. One is countable, another is countable but infinite, and then endless and not countable. Endless and non-countable for first of our infinity. Concept of Infinity. And then countable but infinite is some concept for example. For example Rama is reincarnation, but he died. So, something like that. It has some purpose, but it’s big but has some purpose.

And where it is coming the references. So, the references I am giving, this is explained in a book the same thing. In Buddhist Lalitavistara, they have defined as I explained to you. They were going 10^53. And this is I already explained in our Yajurvedas. We are going up to 10^12 and it is extended up to 10^ 19. They were broadening the numbers and then comes the concept of Yuga concept. Again, they started defining. As I said the **limitations of what number** so you need to define. They all are very big numbers. So, the big numbers comes not because our day to day transactions but because of this religious discussion. There is no practical usage otherwise, because they couldn’t able to map it and identify with any specific item, materialistic items. So, what is the, this is little bit of history.

But what is a feature of Indian numbers. One we see is a decimal system, and second is very very important, that is, place holder system. This is where our Indian system and all other culture, whatever they followed, this decimal number. Because decimal number system comes because of our 10 fingers, but place holder system is very unique. It comes from India. So that is what I am going to explain why we have come to this Place holder System. Because numbers is not the biggest contribution from India this place holder system is. This is unit, this is 10 and this is 100. That is out something of the box thinking. And then it is simplest form of writing again. Not why I mean if you ask some artist, they will give you different, they can give you fantastic beautiful pictures why they are not used. Because for numbers, repetitions doing very quick transactions, it has to be very simple. So that is our number system is our efficient and effective also. And that is why it was adopted all over the world, without question. Because today just think about It. I say something, it is very difficult to convince people and propagating our number system in those old ages and why would others would buy it. And unless otherwise there is a huge benefit, then people will adapt it, otherwise there is a penalty. If you don’t use it there is a penalty. So obviously they will come to this. That is the meaning of effective and efficient. When your system when your things are very effective and efficient, that is something like we have in maths, the concept called global minimum and global maximum. So global minimum is the very minimum point, very optimal point. This is the optimal point and that is why everybody adopted it.

Another important question comes here. Okay, the number system are effective and efficient, but why do we need to use Indian numbers? they had their own notation why not use it? What is the problem? I mean we need to see that. I am adapting because the people are already use to some writing. For example, I write in Tamil. When I want to write to something, I can write in Tamil letters because you see that people now want to type in whatever mobile they prefer to use their language. Same thing you type in English for example English typing is easy, the typewriter the facilities are easy. You type your language in using English alphabets. So many things they do so. Here also we should logically expect those people should be using their own notations and not Indian notations. But that is not the way we see.

Today we see they have adopted Indian system only. So, there must be some strong reason to adapt these number the way it is written. And its huge very lot of years, lot of years since we are using it, no more innovation because that is a best. That’s all. That is the answer. So, this is the… I am coming of answers because this is again my question. So, I have to find out some answers, whatever answers I have found, I am trying to explain here. And so, this slide, that data is coming from Karnataka.

In Karnataka, we have Karnataka Itithasa Academy. They are basically an organisation of historians. So what they have done? They have published lot of things of inscriptions and how the letters have move from one age to another age. Similarly, they have published numbers also. Data they have published nobody analysed. So here I am presenting it. I will explain. So here are our English numerals, English numerals. The second column shows 3BC. This is how Ashoka has used in his inscriptions. So basically, this explains the history, how the numbers have evolved within India. This is the data. Then this is Satavahana period and this is the number you can see in the inscriptions. These are dates which our current history has accepted. So that dates, we will get into the discussions. But let us take right now, these are the dates. Then we have Kadamba period, then we have Chalukya period, then we have Rashtrakuta peiod, then we have Kalyana period, then we have Hoysala period at 12AD, then Vijayanagara period, then Mysore, very recent 18 century AD, and then we see how it is written in Kannada. Because here I see nearly 3^{rd} century BC and 21^{st} AD, nearly about more than 2000 years, and just look at the number ‘1’, nothing has changed. And we write in Kannada exactly it was 2000 years back.

And only in the Kannada we write like this. Now again In India people don’t follow these numerals. Telegu similar is basically a branch of Kannada. So, some numerals are same, but closest or ancient to Karnataka or closest to Karnataka is Tamil Nadu. Tamil Nadu we have totally different numbers followed. So only in Kannada we have these numbers. This is one set of a data. I will come to this slide later. Then I have this slide. So, when I was looking at it, there was one book in Kannada and that is called Siribhoovalaya. That’s a book. 50 years back it’s published. That is lot of controversy around the book. In this book and they have written the whole in numbers. There are no letters. The story is written in numbers. Maybe it is the only book in the world where they have used numbers to express, solve and, not some pages are found, and some pages are found, and there is lot of discussion at very top level also to research and this all, these things, but it controversial. **But in that book, they have published this, the Kannada numbers, this number, the way it is published and talked was not there in any of the earlier, the columns I showed, 2000 plus history** also, this is not there.

And these people, the Siribhoovalaya book is again, Jains and they tried to give very very old dates claims. It claims. So we don’t know and the thing is, this book, you can read it in different ways. Because it’s like a Matrix and you can read in columns and in rows. The book itself claims that you can the book you can interpret in 33 or may be 1000 languages. So one you can read like a Kannada, so another row you read it becomes a Sanskrit text something like that. **And there is a… you will get** in a sequence and then in the sequence you need to interpretate, so but important is this. We need to understand how each and every number it is written here.

The first is in Kannada what it says is Kuilu. Kuilu means the correct today, what Kuilu is explained basically as when you cut your crop. That is Kuilu beginning. So Kuilu means beginning. And then we have numbers. The second row is expressed in our existing fashion. Then again you see that they are all very very closely matching. Closely matching and then below we have the numbers. This is the number which has been derived from Bakshali script in Northern India and there is a beautiful video from Oxford and that is subscribed from 4 to 5 century. So here also you can see 1 is matching with Kannada 1. This is in North India and this is Karnataka. You can see ‘3’. ‘3’ and ‘3’ and then you can see, for example, 0. They are representing like this. Some other numbers they have changed, but the thing is, this is another set of data.

Now we need to connect the dots. In Kannada, why they are using this. See the question is very primitive. Why the ‘2’ is written like this? Why is written like this, because today our new number, English number 3 has come very very similar. So, if we go through these numbers, so we may not be able to go back to the originals. So, it has these numbers are transformed over a period of time. So, this is the earliest reference we are getting, again similarity in the way it is using in Karnataka. So, let us see, look at the logic. We have come to this number, then we can see whether there is link between Kannada numerals and then weather we can even relatively because the dots connect probably it originated comes from Karnataka. So that is my argument.

These are the evidences and then I will explain the logic. Next slide I will explain the logic. So, I asked the first question. Why India was taking differently? Why all others, all other civilisations, they were similar fashion of coming to the number. India was the only one which it is coming differently. See this is where it explains our culture, our civilisations everything. All others, normally, all other cultures were hunter gathers, very natural, in all the forest hunt for an animal, kill it, eat it, over, problem is solved. But India, they started thinking differently. They went for agriculture. They thought hunting gathering is anyway risky. They thought why kill an animal if we can grow and eat an agriculture. Let us form and so they settle and found the better food security with that and because of that, the culture has flourished. That’s where they started making the cities. All these things, we can explain. So, when you are hunter gatherers you are bothered only about your family, so there are also fights. So, today I got a killed, but my neighbour didn’t get a killed, then for his food he will fight, for his food he may steal. So, it’s all individualistic. So, there is no question of coming together and forming a society, collaboration, cooperation; all this is won’t come. So, when you have come to our agriculture, the dimensions changes because you cannot go in fight. For example, I have to clear a forest to get the land to cultivate. I cannot cultivate alone. I need people support. So, people have to come together. That’s why they are becoming society, then cities everything.

So, what is the problem? So, we need to look that the problem, so if we understand the problem correctly, then solution is very easily to explain or to come to the solution is also very easy. So, what is the problem? You want to do farming, what is the problem? They make some village and the easiest thing what you can think is of water is required for agriculture. Where will you get the water? You will get a water near a stream or a river so you may even make your habitation, even close to your river, so when you have made habitation close to river, so what is the problem? So, what is the problem? The problem at that time is floods. So you don’t know at a time you cultivated. You put lot of efforts, suddenly floods comes. Everything is gone. So again, you have to go back to hunter gatherer. You don’t know what is the alternate? So, floods were very very troublesome for them, and second flood did not come, but there is a water shortage, then again you are depending on rain because again either you are close to a river, you are for, who will bring the water. There was no channel concept or draw extensive irrigation projects to take water to all your irrigating lands.

So that is not there so then how will you get water? So, the problem is rain, so rain and our floods, so these two are major problem. And when you repeatedly hit then what will you do? you will start thing about manage it? How will you manage it? Then they started absorbing the data. Then they realised that floods and rains are repeating. So while when you get the floods because all these people when settling, they were settling in our Punjab – Haryana areas and rivers they were banking was on snow fed rivers, snow is coming from Himalayas. Some are you know, snow melts suddenly, you find the floods in river locality, and so melting of snow is again is repetitive because some are snow melts you get the floods. Then they started realising ‘ok, ok now I understand, it comes after some time’. What is that sometime? I don’t know I have no calendar system. I have no number system. I cannot benchmark one year or one month. All these things, but very simple, they have realised that last sometime this has happened and then again, for example, maybe you have 3 kids in your family when they were born first kid when he was born it flood hit, second kid born it flood hit, third kid born there was no problem. You can easily remember and these kids are born in some periodic period. So, you know very easy to find out that it is cyclic. Now then they start thinking when my 3^{rd} kid born I was fine, what is the reason? Why flood did not come. First two kids there were problem, so they realise it is cyclic.

All other civilisations they did not have this problem, never existed because it was not their area. It was not their direction, so agriculture is the main root problem and to address this root problem they started looking out. Looking out or a solution and when you start looking out for a solution something is found, so what they found and these people were not dumb people like. Like this is one representation of Harappa city, very very big, very big and you can see its very close to river. So when the floods comes so your city is flooded, huge problem. And then you can see it’s a multi-storey structure, very well organised, just think about it because flooring and your roof is not so easy because when water, heavy rains comes how sewage are managed. Why will they go for this kind of roof? They are sophisticated, they start thinking how they arrive? Even all these things also question because in west you have snow, rains, they go for slanted roofs, but here they have gone for our normal todays the way we have our roofs and so they are, they are already sophisticated.

They have made so much of system and out of it, so much of system, they have evolved all these things, for example, standard weights all these things. So this is where it comes. All other people when they were counting, they were counting a linear system. I count 1,2,3,4, number of animals killed, but Indians started thinking about cyclical system cycle. When you get into your cyclic repetitions this is where you get, all this starts differing, that’s why India was different. That’s why our number system what we gave is also different. So, what it did, for example, here you start your to identified you floods easy thing they started counting on moon. Moon is easily visible and it is also cyclical. So, they were trying to benchmark with anything related with moon. We know now that it is a snow fed river and snow melts and we are hit. But at that time it was not snow fed, they have to they were thinking celestial bodies is there any link so first they started counting the moon then they started counting sun so you see here we have the names of all the days and then if I start for the whole month, if I pictured it today is easy, the traces of Moon I get this picture. So here there is a calendar for the entire year. So how the moon was mapped was the traces of moon and how we write in our traditional system and do we need, for example, for this moon, to count this moon do we need individual symbols? No, because 15 days, after 15 days the moon repeats and here you see the black portion totally becomes reversed in Shukla Paksha and Krishna Paksha means moon is growing and moon is coming back.

So you don’t need for different notations, what you need basically is a count of 14 because there are 14 phases of moon plus you have one full moon day and one new moon day. So there are 16 items and then you need Shukla Paksha and Krishna Paksha, you need some differentiator because here the way we write is Bhadrapada Shukla Chauti. So chauti is used both in Krishna Paksha and Shukla Paksha. Chauti numbers is same, but differentiator is Shukla and then, for example, Deepavali Karthika Amavasya.

Karthika denotes months and Amavasya denotes day whatever. So how these people just look at it, how just look at full moon, full moon is this, and then Krishna symbol is a dit. They have just used it. So how will you write 14 is basically they were counting a year rain from King. For example, my son is born. I start counting from that son’s date of birth and that year is what they were writing and then and the dot are the Symbol. So then these are the notations which will explain this thing in a further form.

Then what we see is, there are two another, two concepts – one is Kumbha and one is Zero. See zero is also we have understood very very wrongly. The way we learn in our maths is different. So, what is Kumbha. Kumbha has a significance in our religion. We all know it’s used in temples, even houses, everywhere. So basically, when you are filling earlier merchants or whoever is bringing, what they were doing, they were trying to transfer into pots or whatever in a storage format, and then once the one pot is filled that is Kumbha. So, if you really see there were this bigger pots and transfer pots to transfer. There are bigger and smaller. If you got to village side, in fact I have experienced when I was small guy, even if you can go to villages, you can see that the way they have, they don’t use your weighing scale, they use this this kind of utensils. That’s basically called Litre for our oil, but they used it for measuring solid items also, and what they say is, when they count, their count start 10 and then at 10, they will say Kumbha, and what they do is, they count only the Kumbha. If you count 10 Kumbhas, it is equivalent to 100. So basically, it’s a reduction of complexities. So, that is traditionally followed even villages follow it. So, why I am saying this Kumbha because this kumbha explains our decimal system, our place, placing units tens places are there, you know, that’s what it explains. So when you finish feeling one that is unit, then when it becomes Kumbha, Kumbha are basically represented in a second place. That’s where you jump from one to 10. So ten to 100 may be 10 Kumbhas, you put it in one cart and you count the cart, that is third place.

So that’s how we get into 100 decimal, hundred tens units like that and then again zero. So the problem is, what is problem with zero, actually there are two. The way Indians have thought at that time are two. One is zero behind the number, one that’s is the beginning zero one, then the number what you raised next to 10, next to 0, that is 10, that is Kumbha and the beginning zero is represented with our, this dot, not zero. This zero is used because of Kumbha that is full moon. Full moon is basically a Kumbha and then its beginning is dot because they were counting from Amavasya. So, Amavasya was the beginning and to represent Amavasy,a so it’s very intuitive, very natural. Then so, this is already explained, I skip this.

So, there is another problem. See, all these people, they were using other civilisation’s, they were thinking number line, what is zero, somewhere it has to begin, where is beginning and if you start zero, then again people can ask before zero what was it. For example, I say from when my child was born zero, before that what was there. So already there are negative numbers start coming and its very complex, but Indians, they went for cyclical and once you say centre is a beginning, you don’t complexity, don’t come what is behind, that you are getting. So, this, I say this is dot, this is dot and then there is cycle and cycles, so only positive numbers. So, we think only about positive number, so this is an abstraction, so this is the briefly explained the history.

So, there is a guide called AL-Khwarizmi. He was an Arab guy who has translated our number system, and the way we write zero places of 10, places of 100, these are all basically called algorithm. Algorithm comes from this guy, so and then there is a description, how it translated into Europe. How it went into Europe, how they then, they start calling it, this guy as the originator of the number system, and that’s why they start saying Arabic number.

And then there is a Leonardo Fibbiocani, who was basically a merchant from Italy and who was positioned in Africa and then he realised Indian system is better because it is very easy to calculate, Arithmetic is very fast. So the Romans numbers are not so good and then he realised because of the efficiency factor we should start adopting it, and there is a Hindu article, Hindu paper by CK Raju, and he has explained beautifully all these things. You can go through.

These are the number evolution from Brahmi to Indian to Sanskrit to all these things, to all these things. So again, you see, there is no two similar number copied they were confused totally confused. They don’t know how to write why to write because this logic is not known to anybody. They know this numbers are very efficient very good and even people were so they were thinking that some magic behind it. So they should represent write it properly. Dor example, now you write Om symbol or Swastika. Can I write right swastika or left swastika? Which is correct? If I write wrongly what will happen? So, all these problems were there, whatever. But the thing is, there is a fear factor not writing properly because when you associate some mystery to these number, this problem comes.

So, again zero they had the problem because they were not understanding. They heard stories beginning of Amavasya and all. They were very hesitant to use it. So, Europeans were ready to use other numbers, but not zero. They first have adopted all numbers but not zero because they don’t know number it is. So this magic of add 10, so if you add one next to 10, one is next to that, you write 0, now If I write simply another 0, it becomes hundred. The value is raised by 10 times. Why it will happen like that? So, they were not able to understand all this logic. They were confused and again they invented this Abacus.

Abacus basically is a method for Roman thing. You don’t need Abacus to for maths using Indian numbers and calculate, but they we retrying so many things. See all these things again there is boo,k where they have written how within Europe different periods, how they were writing. It’s not consistent. So, they were writing some numbers from Arabic, then somebody came to India, and said that is not the way Indians write. Then write way is this, so they started changing this. Some places they start changing it. But some people they continued it with old style. So totally we can see full, not they were clear. They were not able to understand it and they were very fearful to use it. It took nearly 5 centuries for them to realise, there is a benefit, this is the way to use, let’s just use it. There is no problem. There is no mystery behind it. We can use it for normal transaction.

So, there are the notations so we see there are so many notations for a single number. You can see for everything, there is no consistency and as I said that first another question I asked. Why should I write 3 like this only? They were also not sure. They were writing different patterns. But they know it is not correct, they have fall back to Indians. You can see this zero, you can see this, I showed you the way our Kannada number started with the Kuillu. The beginning, this is the same they were using for zero. They were confused. Even today Europe has confused, that’s why we write beginning zero, and decimal zero, same zero because they don’t, they didn’t understand the concept of Amavasya and Full Moon. So that notations, they have confused. You can see here numbers were used but not zero. Zero were empty. They were hesitant to use numbers. So, I have written little more in detail.

So, my argument is my final concluding argument is this. We see in Kannada numerals, so I will go back to slide just a minute to conclude. Our Kannada numerals, so here what you see is basically a combination of the moon. How you write the first day of the moon. Basically, this one. So, if we really go back here, what you are doing. You are showing increasing phases of moon. First day, Second day, Third day. So, this is the way, so the moon, of the moon how this is, how it is represented and they were writing for 4, 5, 6. But then it is very difficult to represent. So, they optimised and when they optimised, they optimised using the same curves to represent all the numbers. So, we see, we can explain using Kannada numerals why 3 is written like 3, and moreover you can see 3 and 6, they are related. And 5 is half of full moon day Zero because that’s why it is because it is full half reversed. So, we can explain why 5 is written like this. 6 is written like this. 7 is written like this.

They were using instead of complicating, they were using the symbol of one. For example, 1 and 2, 1 and 2 is what you basically cut zero into half. The first part is 1, second part is 2. And that is how we write even in Kannada numerals even today. So using Kannada numerals, I can explain why the numbers are written and how it has come. So now I can have one answer, a better answer than the first picture, where I showed the angles. So how Indians have come? Indians have come with logic with reason. It is not some random number suddenly has popped up. Not some numerology at that time something somebody said, let us use this. No, It’s not like that. There is a reason behind why they have come and they have come to this conclusion and that is why it is effective and efficient and how we have came to this decimal places.

So, the advantage of how we come to the Indian system, I can see all the proofs here for everything. Decimal system, zero system. Why we write beginnings zero number dot. Everything we can explain. So, this is one of the explanations. I saw this is missing in our history. I can see that still used in Karnataka. so probably it should have originated from Karnataka. So that’s where u conclude my argument.

You should start increasingly using the word Hindu, rather than Indian. Because Indian includes much more now. So therefore, the origin of all these things have Hindu origin, they are not Indian origin. Indian is only territory, but Hindu is much more than. So therefore it would be appropriate if you start consciously using Hindu in place of Indian when talking of these things. This is one. These are observations. The second one is, notations are representation of numbers. As the close connection with the developmental scripts so what you have explained may be true, but then various scripts. Most of the scripts have come out of Brahmi and so therefore whether this would really explained how the numbers were visualised and whether if that is, has happened. Let’s say in Kannada and Telegu and what about the North India, Eastern India. So, whether this gives a complete picture or it only gives one aspect.

Third one is the cyclical nature that you have explained, but that cyclical nature has been there every civilisation throughout the world. Why is it that only because of the cyclical nature we have come of this kind of thing? That doesn’t explain much of this. There is much more than the cyclical nature of that. How Hindus have visualised cyclical nature. It has not just come from floods or from rains or these kinds of things. Is there something much more? This is at a level don’t affects, it’s a primitive level explanation. I will answer that.

See first of all the outside world they were using in history books, the school books, Arabic numerals. They were no Hindu, Indian connection at all. So it’s not a question of, for example we have lot of things in History, now we are unable to convince our Government to correct it, but here, it was included even in Foreign Governments. It is more even difficult to convince them, but when things even started coming out, then they realise because there is awareness among public, then they cannot go on giving a different explanation. Now all over the world, it is written as Hindu Arabic, so Hindu has come because of the awareness among public. So when we create awareness about this among public, I want to call it as Hindu numbers. There is no question of Arabic. For example, I get a car from Japan, for example my apple phone maybe it is made in China, but it has originated in USA. Do it call it as Made in US China? No right. It is manufactured in China, but it is fully attributed to US right. Why Indian invention is attributed to Arabs. They are also saying that it is completely acknowledge, it is from India. There is no reason to use Arabic at all.

And second question again for word Hindu again. There is lot of controversy because Hindu is not a word even by ourselves, we never use a word Hindu. There is proof. The earliest proof for the word Hindu comes in Rajatarangi that comes from Kashmir history where they used Hindu but that is in 12^{th} century. But I can show you in slide, also that is already there. The Christians were using book called Indo. The Arabs write as Hind. A book of Hind and when it is converted to Christian in 12th century, I am talking about the 12^{th} Century, so when in 12^{th} century, when India was also coming from 12^{th }Century, when the, what proof Hindu is also give from 12^{th} Century. So Hindu is not a word from India at all. No No I agree. We should use it, completely agree. Little confuse about numbers here. 3^{RD} century BC in one slide you mentioned is the origin of the Brahmi script and then we have Rigveda. It says the 3^{rd} Century BC the origin is the number is that correct. 3^{rd} Century BC we know Ashoka is 350BC right. That’s why we write it. That’s right. Ya. but if Rigveda is talking about 10^19, so obviously they were writing something or, no they were. See… the problem is we have no records. We know the earliest records in Indus Valley Civilisations. They have written. So, we know, there is a script. Indus Valley Civilisations.

Right now, people have decoded it and says it Brahmi. Same Brahmi similar local version of Sanskrit only because the word, for example, Vimshat, we see the same as Vimshat, we see today even in Sanskrit, that’s in RigVeda, but the problem is Rigveda is all words, right. There is no numbers. So we cannot say how Rigvedic people were writing unless otherwise we can decode Indus Valley Civilisations and attribute something as numbers. There again whatever is decoded they are all words not numbers. They may get 20, but 20, how they were writing, we don’t know. And I think he has another question. Because of the time limit, I skipped it about the cyclic nature. you asked an important question. See the point is they were using, they did not use the cyclic thing for numbers. Numbers normal people I think I have explained in the slide; also, normal people were using like other civilisations only. They were counting from 1 to 10 and they were all linear only. But some people started thinking about Agriculture they started looking at cyclical level and that’s how even our Astronomy developed and they did not develop from 1 to 10, because it was 50. So it is basically base 50, so they were using from 1 to 50 and then when writing came they wanted to harmonize, they applied the principle of that in today’s decimal system. So that’s how, it has become, actually if you see the notations are upto 50 not just 10. I have shown here 9 because they started mapping up to 9 and then write zero as Kumbha as Kumabhayagiri, so Kumbh is basically a full moon. Same notations they have copied and that’s how they got 1 to 10 and from 10 onwards it’s a repetition because that’s how we thought about, it’s a repetition. It’s a cyclical thing and that’s why we went into all other algorithm, whatever we call algorithm our decimal calculation out algorithm. For example, I has 8 plus something and there is a carryover, so that’s is a algorithm and that is an invention of Indians. Nobody else started like that and all those things came because of our counting moon, and then it also developed in originating calendar system, and then calendar system is also exactly 30 and then 30 repeats. For example, 12 months although 365 days, they know for 5 days they were intercalary months. They were addling intercalaridous months, they were adding and correcting it. But it was cyclical, may be if you are not satisfied, I will answer it later. Just one thing cyclical. Is monsoon the reason? or because I think India is the only country where monsoon is a yearly phenomenon, for rains and anything happens anywhere, so may be, that can explain cyclical part.

The other thing is the number system, you said the number system, the place system. Does India have any other system like second place after 9 or second place after 12, like we can have 12 different character for 12 and then repeat. That’s what I understand, that is what I showed you, none of the civilisations went for more than 10. They did not count 11 and 12 with different symbols. So why there is number 30. No up to 12. See… they are cutting at 5. See 5 is a symbol, then we see a symbol, that’s is because when you say 5, you make a one full hand. So you get a symbol you are trying to consolidate again.

Then they were consolidating, they did not go because again it was intuitive or natural, why we came to see actually in our maths you don’t have to do decimal only, you can go to hexadecimal systems . Hexadecimals is even more affirmer actually, but it is not intuitive, it is very difficult for us to understand. If you go to our computer works bits and 16 bits. 16 digits works like hexadecimal, they say binary, but strictly speaking when you are design your chip, that is basically a hexadecimal. Hexadecimal is more optimal than decimal, but we go for decimal because of our intuitive hands of 10. Not just in India. Indians actually went up to 50, then they adapted to 10 because normal people were using decimal system. Did I answer you question?

Mayans went upto 20. I had a slide on that. No, recently we had a year of 2012 or something that is 10^3. As you told about value place system, right value place. Yeah, place value system, that’s what I told about. So, place value system, you say, originated in India only. First you count from 1 to 10, then treat 10 as a unit. Put it here and then again you start counting from there, but treated as a collection of 10 only, right correct. Now unity should be considered as collection of 10, that means any number can be written as infinite series on left or right series both because on left every place will be multiplied by 10 on right, every place will be divided by 10, right? So it’s like infinite series on both ways. Correct?

So my main question is, in European mathematics the historical development of that naming the infinity was basically, you can say, a very important movement to break into this modern method of calculus. Right? So, do you think, that is concept of infinity and naming of infinity was already existing in India? See, I see, infinity bringing into maths, they are disconnected, actually. I showed you. In the concept of infinity is from religious background for Indians. It never came to maths to thinking to begin with. The problem is they ended up the explaining of when they wanted to calculate the circle, they calculate the circle the way if you look at how they come to pi, they wanted high precision of pi and there they ended with infinite series. So, you can write, go on infinite series and it will increase your precision and in fact the concept of calculus came from infinite series. In fact, basically that’s a way to express in fractions. And the concept of calculus like I think, if you look at the prof. Raju, you will understand it better, he explains it there is a different of infinity. infinity is not really required for our practical purposes, getting into the infinity. You can go up to whatever is required approximation and that’s good enough. In one of your slide, you mentioned of the data from the Lalitavistara , The Buddhist text the number goes to 10^, something I guess 420, the maximum number goes up to that unit. So, see, this number is so big that even modern science doesn’t really care about it. Right? Modern science hardly goes about, you can say, 10^50 or 60 right and then you talk about the size of the universe or even in the main concept of plank length. So, in plank length, you go up to – 10^34. So, when talking about something 10^420 and still making some physical sense out of it, how is that possible if you are not talking about infinity? That’s what I said actually there is also a story in that slide, how they were talking, basically, In a discussion it was a challenge to explain why 10^20 only, then they went into our Yuga kind of thing, cycles and cycles and when you explain cycles and cycles, it basically a multiply. So, there is a 10^20, that’s cycle of 20. Then it becomes 20* 20 that’s when it lands up with 400. So that’s an explanation of why only 20 cycles and that’s why 400 is coming and moreover all these things were conceptual things. There were no physical requirement there is nothing to correlate or explain what is 10^200.

So until the things evolved into the concept of, may be in my next talk, I will talk about it, like distance between Earth and Sun, Earth and Sun are beyond star. What could be the distance when they are able to measure something concretely, they are able to get into bigger numbers till that time, it was all conceptual. They wanted to explain for example what is a number of stars? Somebody ask and you are an intelligent guy, he will tell 10^400, you go and count. No, I am just giving a simple reason so that’s is a concept of infinity, closer to infinity. That’s all. The total number of electrons and photons on scientific argument is about 10^ 88. So, anything beyond that it doesn’t make sense. I am coming to this, in Mathematics and Science when we break this normality and entering into this domain which is beyond our perception, metaphysics, yeah metaphysics. So I am talking purely in terms of numbers.

So as a human being we can say 10 km, 15km, 20 km. This distance can be measurable or in a way can be understandable but if somebody say 3 light years or 300 light years suddenly, that is not we are not able to comprehend how big that distance is, but still Science talks about and it doesn’t talk about in a hollow manner, but with concrete evidence. For example, when we talk about a number of atoms in this mole or may be in 10 gms of iron, how many atoms are there. So we talk about 10^20 in terms of that, again the number of stars or number of galaxies. Number of galaxies are to be considered something around 10^11 and in every Galaxy there are around 10^11 stars so the propose number is 10^22 may be we can go beyond that. In tradition of Science, there is always, you know, some fundamental rationality involved that why we are saying this.

See all these arguments are after 20th century. See I am telling you, Europeans had a problem in even adopting our Hindu system till 17th century. See these people never, till they adopt that, if you were using Romans system none of this maths is possible till 17th century, forget about it, nothing is possible unless otherwise you can count you do some normal counting system, nothing else is possible. All these talks now it makes sense because we have evolved and Science has advanced and I am talking of primitive people, bigger number doesn’t make sense.

yeah last question. Sir, if you don’t mind the book of numbers and how do you make sense of that. The book you mentioned in that. It’s already decoded and how do you make sense of those numbers. No I ,I mean you just Google that word. What is the word sir? That The slides I will be sharing with them you can also take it. So if you Google it you will get it. So the pages are also available. There are English books, Hindi books . Hindi also it is written , Kannada also it is written but its a Kannada book.One very unique book.