Pure mathematics and Poetry
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[Formalized discussion with my son, a student of class VI – a victim of maths teaching in contemporary schools ]
Pure mathematics and poetry, in vulgar eyes appear to be useless. People who are exact solutions to “cost-benefit analysis equation” in the most rigorous manner will definitely think so. Pure mathematicians and poet – these two species are most-unprotected in this world. Let us see how :
- Since 300 BC, some people are mesmerized by the property of prime numbers. A prime number is a number, greater than 1 and that is divisible by 1 and itself. For example, 2,3,5,7,11,13,17,19…..They ask the following questions and dedicate their lives in finding their answers.
a) How many such numbers are there ?
b) How are they distributed in the number line ?
c) Is there any “neat” way by which we can tell how many prime numbers are there, say in between 10,0000 and 10,0000000 ?
d) Why is that in between 1-10, there are 4 prime numbers ( 2,3,5,7) whereas between 90-100, there is only one (97) ?
e) If we know a large prime number, when will the next prime number will be ?
f) Do prime numbers appear in number line without any order or pattern or there is some pattern and we are just not able to discover it, since last 3000 years.
Now, prime numbers are not conscious and they do not care if someone turns into an old man from a young man while pursuing them. Failure in this has no tragic consolation as one gets in unrequited love. There is a 50/50 chance that one is pursuing a chimera.
Let us observe the rough sketch of these pursuits with prime numbers :
- Euclid in 300 BC proved by brilliant argument that there are infinite number of prime numbers. How ? The fundamental theorem of arithmetic says that any integer number greater than 1 is either a prime or can be expressed as a product of prime numbers in a unique way. Let us consider now a finite list of prime numbers and P = p1 * p2* p3*p4*…..p(n). Let Q = P+1. Now, Q is either a prime number or it is not a prime number. Then comes a brilliant logical reasoning.
If Q is prime, then we have a number which is greater than P and since this interval [1 to n] we have chosen, there will be always some prime greater than the last prime of this interval and for all intervals. Hence there will be infinite number of primes
If Q is not prime, then we have some prime number p in our list that divides Q. It means it divides both P and Q. But that is not possible because Q-P = 1 and no number divides 1. So there is no such p in our list.
2. Fermat found out a result in 1650 that established a fundamental relationship between the product of 2 prime numbers. It was just playing with the rules of the numbers and no one had any inkling whether this would be of any “practical use”.
3. Riemann in 1888 found out a function called Zeta function that pointed to some remarkable connection with the distribution of prime numbers. Just note that prime numbers do no appear in a regular fashion and as we move to larger number interval, they become less frequent and very very difficult to detect. For example, recent breakthrough research by a mathematician found out an interval of 70 million within which at least a prime can be found in case of large numbers. Now consider that to check this prime in 70 million numbers, any computer will need a finite time. And this finite time is the key antidote for this code to be broken and necessity of this finite time arises, as if it is in the fabric of the cosmos, the way primes are distributed as numbers become larger and larger (128 bit encryption – a 128 bit number in binary will be this one decimal :340,282,366,920,938,463,463,374,607,431,768,211,456). This number in decimal features in the blog that provides a fascinating elaboration of how large this number is.
This property of prime numbers is at the heart of all security of Internet. As a matter of fact, “secured site” means that the site is using 2 very large prime numbers – one is publicly known(public key) but the other one (private key) – being very large prime is so further away and it will take hours, if not days to find this out using the fastest computer and most optimized algorithm. If we use brute force (i.e take a number, check this and go to next number), then the time taken will be so large that solar system will collapse with sun getting off !
Even if an algorithm and machine can make this in 10 mins, the designer of this security code can just use a time-stamp and will expire – “session timed out” in say 5 seconds. This can be used for all communication.
After 350 years from Fermat, we suddenly discovered that his “little theorem” and prime numbers are part of our everyday lives. Like electricity.
Poetry shares this with higher mathematics. If the above aspect of pursuit of mathematics can be considered to be doing something that will be “imposed” on mankind centuries or millennia later . One such poet, Shelley wrote a sentence in one of his essays which is very easy to denounce as “poetic rapture” or “over-speak”. He said, “Poets are the unacknowledged legislators of mankind.”
If we soberly examine the Fermat’s little theorem’s impact on our lives and business today, it is really so. If you run an online business, you must be compliant to the “mathematical legislation” imposed by Nature and first discovered by Fermat while just intimately playing with them and later applied by the designers of RSA algorithm some 350 years later.
Mathematics uses highly specialized language and notation. We are beneficiaries of their work with this language but cannot directly engage if we do not learn the language. And learning the language is not easy or we just cannot pick it up.
Poets use words – used by all and the language is known and we start using this as soon as we are two or three years old. But poets do something remarkable with this commonplace entities using the same rules of grammar everybody use. And the miracle happens.
I am giving an example which connects our native city – Calcutta and a Bengali poet.
In 1856 a French poet Searle Baudelaire published his collection of poetry called “Les Fleurs du Mal” and in 1940s-50s – a leading Bengali poet Buddhadev Basu got so much attracted that he devoted an intense amount of time, attention and care to study, translate, review and spread the poems of this long-dead French poet, almost to his dying day. What is happening here ?
A combination of words, a pattern of words rather become so potent that as if they enter into one’s innermost soul, as if seizes the core of us – call it genetic code, call it consciousness, call it soul, call it “I-ness”, but the effect is remarkable.
Another striking effect is the stability of some of the codes. Some poets are being read over centuries and millennia – the pattern has remained the same – the same old text but thousands of generations have come and gone but few in each generation respond to these codes in an intense way. There is no apparent encryption here – the text is all open – no stated private or public key here but just like our genetic code maintains its stability and integrity over millions of years although using very little matter, poetry – is strangely like these codes which run in our genes.
I think true poetry is also encryption – encryption of our soul – some souls have the private key, most haven’t.
Hence just like large primes do not seem to obey any law or some law of their own choosing which we haven’t figured it out completely but will benefit us as we walk along the time-line, true poets appear in their own choosing and guided by some unknown law.
True Poetry is the encryption for our soul, our private key and people who can create these “keys” are those on whom “eternity casts its gigantic shadows.”