| Author | Message | ||
     Thikka_sankara Hero Username: Thikka_sankara Post Number: 17332 Registered: 02-2012 Posted From: 49.207.179.70 Rating: N/A |
so, arguably the best mathematician in the world today, is trying to saffronize mathematics @ princeton keka link: fikileaks, | ||
| Thikka_sankara Hero Username: Thikka_sankara Post Number: 17330 Registered: 02-2012 Posted From: 49.207.179.70 Rating: N/A |
Mathematics is often taught like a science but a lot of people don't know that its origins, especially in India, is in the arts, and we shouldn't forget that interesting aspect. We should be using both sides of the brain to understand mathematical problems. NDTV: There is some mathematical basis to music as well., tabla, what is the connection? This is very tough for me to understand, maybe others do, but what are, what is the connection? Prof Bhargava: Tabla. Tabla is all about rhythms, time cycles, trying to fit various pieces into a rhythm cycle and so, the arrangements that one practices as a tabla player uses a lot of mathematics. One example that I always start with in the class that I teach, just to get people to realise that mathematics is connected with poetry and music, is an example of Hemachandra. That is always one that I start with because it brings in tabla and poetry and mathematics right away. So, in Sanskrit poetry, there are two kinds of syllables, there is a notion of laghu syllable and guru syllable, how many people of heard of laghu and guru before? NDTV: That's about 5 percent, 10 percent. Prof Bhargava: So, yes, that's one thing I feel should be there in mathematics. The notion of laghu and guru is something that led to some of the most fundamental breakthroughs of mathematics, believe it or not, in ancient times in India. So this notion of a laghu syllable and a guru syllable, a short syllable and a long syllable, so in any kind, every kind of poetry in the world, there is a notion of stressed syllable or unstressed syllable. And you see poetry, some syllables are stressed and some are unstressed. In Sanskrit, it goes a step further. Stressed syllables are long and unstressed syllables are short and short syllables take one beat of time to say and a long syllable takes two beats of time to say. So what's peculiar about Sanskrit is that a long syllable takes exactly twice as long to say as a short syllable. So when you recite Sanskrit poetry, all the syllables will be like this, some will last one beat of time and some will last two beats of time. The short are one beat and the long are two beats, and so this is very peculiar about Sanskrit, and as a result of the set-up of Sanskrit poetry, lots of ancient poets considered lots of mathematical questions that related to this one-beat, two beat-up set-up of Sanskrit poetry. So one basic question that would come up, if you're writing poetry and you have 8 beats left in your stanza and you need to fill it with long and short syllables, where a long syllable takes two beats and a short syllable takes one beat, how many ways can you fill in 8 beats with long syllables and short syllables, where long syllables are two beats and short syllables are one? NDTV: Don't give us the answer, does anyone know? Prof Bhargava: What would be your guess? NDTV: Oh wow, come on. Audience: Communication combinations? Prof Bhargava: Yes, it is about communication and combinations, but it's still beyond what you learned in school. What would be your guess, 8 beats filling it with longs and shorts, long two beats and short one beat? NDTV: How many variations can you make? Prof Bhargava: How many ways can you do it? So you could do long, long, long, long or you could do short, short, short, short, short, short. NDTV: 8 times. Prof Bhargava: Or you could do short, short, long, short, long, long, long, short, short, long, so I actually clap these rhythms with my class and we try to figure out how many there are. NDTV: Sorry, say it again. Student 4: 34 times Prof Bhargava: Yes, so he knows the answer. NDTV: So it just went straight above my head. Prof Bhargava: So the answer is 34. So most people when they first hear this question, they think oh maybe there are 8 ways, 10 ways, the answer is actually 34, which is more than what most people expect it to be. And in this ancient Indian work of Hemachandra, which I read to the class because it's written in poetry, the answer, so it's a poetic question, it's a question about poetry and the answer is written in poetry. So it's something that really excites people, it excited me when I was a child so I like to share it, and it's really easy. So Hemachandra's answer was as follows: write down the numbers 1 and 2, and then every number you write down subsequently should be the sum of the previous two numbers that you wrote down. So 1, 2, then 1 plus 2 is 3, then 2 plus 3 is 5, then 3 plus 5 is 8, then 5 plus 8 is 13, then 8 plus 13 is 21 and then 13 plus 21 is 34 and so on. The 8th number that you write down will give you the number of rhythms that have 8 beats, which is 34. NDTV: Wow, that's amazing actually. Prof Bhargava: And this goes back to the year 1050, so these numbers may be familiar to many people, right. They are called the Fibonacci numbers in India. Even though in India they were discovered pre-Fibonacci, by Hemachandra in this work on poetry, which I find very amazing. So when we are taught Fibonacci numbers in school, maybe this is true in India as well, I've definitely seen it in some Indian schools, they teach it the way Fibonacci came up with it, which is about the problem about rabbits. This incestuous problem about rabbits where brothers and sisters are mating, and it's a very unnatural act, but the real place that it actually came up is in poetry, and the reason that it came up is a very natural one. You need to know the answer, if you want to know how many ways you can fill in the rest of the poem. So that's an example of the kind of way mathematics came up in poetry in ancient times and still comes up today. When people compose Marathi poetry or some Kannada poetry, this type of poetry is very similar in those languages as well. NDTV: And it came in India a long time before this, right, so how important or how relative to other parts of the world? I know you have quoted maths, historically in many other parts of the world how important was India in developing some of these concepts in maths in ancient times? Prof Bhargava: Oh very important. I mean in this example I just gave of course the fundamental, the fundamental concept, the Fibonacci numbers, the Hemachandra numbers as Sanskrit is called, it was important for the world of mathematics and science and art. So that's one example, but there are many. Pascal's Triangle we learned at school, with something that also came up in context of poetry, in the work of Pingle and by 2000 years before Pascal's NDTV: Really? Prof Bhargava: Yes, these were all the things really known in India, except that the Sanskrit is; so there are lots of contributions in India, mathematics is really a global subject. Every ancient of these nations have contributed NDTV: Which is the other center that contributed? Prof Bhargava: Egypt was a great center. Mesopotamia was a great center, China was a great centre and then Greece was the great centre NDTV: So India is in context of equivalent to all of these, a little bit, like it's difficult to... Prof Bhargava: Yes, all are equally important in development of mathematics. You know in India I have been seeing lots of debates, India contributed nothing to science versus India contributed everything to science. But the truth is that, I would say I have read a lot of mathematics work of India, the truth is India contributed really key ideas to geometry, lays some of the foundations of trigonometry, foundation of calculus were done in India in the Kerala school. So, all the major subjects of mathematics have lots of the key foundations from India, that's the true fact. It's not nothing it's not everything, but it's really important keka link: fikileaks, | ||
| Thikka_sankara Hero Username: Thikka_sankara Post Number: 17328 Registered: 02-2012 Posted From: 49.207.179.70 Rating: N/A |
One thing that I have been doing at Princeton University for the past years, I developed a course, for freshmen, so first year, where we teach mathematics through poetry, classical music, classical Indian music, magic tricks like you said, and games; so those are the four ingredients of the course through which I get to teach fundamental mathematical concepts. So make classes begin with a card trick that's based on a mathematical concept and when you see this card trick, there's nothing you can do but want to know how it worked. And for the card tricks that I do or for the rope tricks or for the various other kinds of magic tricks that I do, there is a fundamental math concept that you have to learn in order to know how it works, and everyone is so immediately excited about knowing how did it work. And so, while they learn how it works and while they learn how to do the magic trick, they can't avoid but also learn in the process the fundamental mathematical concept. And when you learn it that way, there's no way that you'll ever forget it because you have that visual of the trick, the memory of the trick of how it worked and there's no way you'll forget the mathematical concept keka link: fikileaks, | ||
| Thikka_sankara Hero Username: Thikka_sankara Post Number: 17327 Registered: 02-2012 Posted From: 49.207.179.70 Rating: N/A |
http://www.ndtv.com/article/india/india-questions-math-geniu s-professor-manjul-bhargava-full-transcript-651924 keka link: fikileaks, |
