# Feynman on quantum mechanics

An amazing lecture on the quantum mechanical world, especially the double slit experiment and its ramifications:

# Comma

For those who are regular visitors to this blog and who are disappointed by its increasingly infrequent updates, I apologize to the both of you! I have had quite a busy last month and I expect this hectic schedule to extend into March but when the dust settles beyond the horizon I hope for the advent of a new spring in its wake. I hope then to have the time and the experiences to, as Ezra Pound rallied, 'make it new'. For now, here's the frozen Niagra which I visited recently, thereby accomplishing my life's purpose as far as being an Indian in America is concerned (having already visited the Grand Canyon):

# Death of a motorcycle

5 years, 30000 miles and the motorcycle that I have come to refer to as my noble steed has decided it quits. Since I have had relatively few material possessions during my time in the US, I have grown fond of the few that I did have. And the 2003 blue-white yamaha yzf600R is perhaps the one that I have cherished the most. In the company of a certain yellow suzuki sv 500, it has taken me through the stunning mountains of Utah and to the incredibly desolate deserts of Nevada in the North and Baja in the south. On it I have scaled the beautiful Southern California shore under its mild cold Sun an innumerable number of times. I have crisscrossed across the myriad neighborhoods of San Diego, from the affluent north to the seedy south and the surprisingly diverse east. I have ridden it in the sweltering heat of Calexico and the cold damp of Flagstaff. I have ridden it on ribboning mountaneous roads with nary a soul to be seen and on the suffocatingly clogged freeways. I have taken it to its limits, to speeds which would be imprudent to mention and I have slipped it through exceedingly tight tolerances. And it has always responded with vigor and has made me feel alive on those sweeping curves where I had to bend it low, very low, with the asphalt a small distance away and the world frozen in an amber drop of serenity: the Sun reflecting in the visor, the rippled jeans, and the incredible drop a few feet away. Well it has been an absolutely great run and hopefully there are bigger and better things ahead!

# Mural

My friend Natasha who is an awesome singer, pianist, painter and a thoroughly interesting person got a contract to paint a mural in Ocean Beach. She asked me if I'd like to help her paint it, obviously unaware of all the immense painting talent that I do not possess. Although I jumped up at this amazing opportunity to contribute to something new and different, being her friend, I duly warned her against asking me to paint anything which required any semblance of artistic creativity or deft handling of paints and brushes. Having established this, we met up one Saturday morning in front of the mural site with a huge scaffold, long paint rollers, buckets of different paints, and more brushes than I knew existed. I helped her paint the background with multiple coats of white, orange, yellow and blue and the huge whale and she reciprocated, very gracefully I must say, by consistently maintaining that I hadn't screwed up. I worked with her on Saturday and Sunday and she worked through the week to complete the rest of the mural. And just for those 2 days of work, she asked me to put my name in the corner. So there, I now have my name (in Hindi) on a public work which is probably going to be there for years to come. Thanks a lot Natasha for giving me this awesome opportunity to do something different and fun and to add to that eclectic bank of memories and experiences which I value so dearly.

Location of the mural: Intersection of Sunset Cliffs blvd. and Narragansett.

# Some truly great writers

Leo Tolstoy, Anton Chekhov, Nikolai Gogol, Vladimir Nabokov, Franz Kafka, Gustav Flaubert, Marcel Proust, James Joyce, Charles Dickens, Pelham Grenville Wodehouse, Joseph Heller, Jane Austen, William Shakespeare, Lewis Carroll, Oscar Wilde etc.

Pick a book written by any of these and you would be enriched. And Dostoevsky is not in the list not by mistake.

# Superfluidity by Alfred Leitner

I came across this awesome youtube video by Alfred Leitner where he is showing some fascinating experiments involving supercooled liquid helium. Helium turns into a liquid when cooled to ultra-low temperatures (<-268 degrees C) but when it is cooled further to -270 degrees C it turns into what is called a superfluid. In this superfluid phase, it has zero viscosity and flows through extremely fine pores without any resistance. It climbs up glass walls and has zero entropy (perfect order) but what I find most fascinating is that heat travels like waves through this phase. It hits boundaries and gets reflected, just like sound or light do!

# Prime numbers and encryption

I have just completed reading the code book by Simon Singh and was immediately struck by the elegance of our current encryption technologies and their pervasiveness. The book clarifies how the very fundamental concept of prime numbers lies at the very heart of all our Amazon purchases and our banking transactions.

The fundamental problem of encryption is the following. Person A wants to transmit a private message to person B. This message is vulnerable to getting intercepted by person C but even if it gets intercepted A wants the meaning of the message to hidden from C. The fundamental way in which it can be achieved is by changing the form of the message (encrypting) and transmitting the encrypted message. B receives the encrypted message and if he knows how to decrypt it then he can reverse the process of encryption and gather the original message. If C happens to snoop in on it and doesn't know how to decrypt the message then even though he has the communication, he would not be able to make sense of it. As a very simple example, A might want to transmit two numbers 15 and 20 to B but he adds, let's say 50 to each and transmits them. The encryption in this case is the addition of the number 50. If B knows the encryption function (addition of a number) and the key (the number 50) then he can retrieve the original two numbers. If C doesn't have the ingenuity to figure out the encryption and the key, then he would not know the original numbers. There are, therefore, two distinct problems here. The first one is deciding upon an encryption algorithm and the second is deciding upon a key with which to encrypt the message. Ideally one would want to encrypt a message with an encryption algorithm which is complex enough to render decryption impossible without the knowledge of the key. In essence, the encryption algorithm may be public knowledge but it should be impossible to break it without the knowledge of the key. The simple encryption described above doesn't suffice obviously. If A is trying to transmit something meaningful like say the Fibonacci sequence and if it's known that he has merely added a number to all the entries, a mere trial and error would reveal the original sequence. Precisely because A is trying to transmit something meaningful, the simple encryption would be rendered useless. The second problem is how does B know what the key is? A can also transmit the key but then the key may itself get intercepted. A can personally meet B and give him the key but in the real world where billions of messages are being exchanged every day, personal meetings between senders and receivers are frankly out of question.

A solution to both these cryptographic problems was suggested in 1976 and goes by the name Diffie-Hellman-Merkle key exchange. The first idea is to use an encryption algorithm which is very difficult to undo without the knowledge of the key. The second and more revolutionary idea concerns the distribution of the key itself. The encryption algorithm is a modulo function.  c = a(mod b) gives the remainder c when a is divided by b. 8(mod 2) is 0, 9(mod 2) is 1 etc. As it turns out, if one only knows c and b, it is very difficult, if not impossible, to figure out a. The modulo function, therefore, is a one way function and a good candidate for encryption. The second idea was how the modulo function was utilized to solve the key distribution problem. 'A' chooses 3 different numbers let's say 3, 7, 11. He transmits the encryption function as being $7^x$(mod 11) where $x$ can be any number. He keeps the first number 3 secret. 'B' also decides on his own secret number, let's say 6. Now C, who is snooping, may get to know the encryption function which is public but he doesn't know the private numbers 3 and 6 which were never transmitted. Now A transmits the result $7^3$(mod 11)=2 and B transmits back $7^6$(mod 11)=4. Upon receiving 4, A calculates $4^3$(mod 11)=9 and upon receiving 2, B calculates $2^6$(mod 11)=9. Both have come to the same number 9 which is the key. C which knows the encryption function and the numbers 2 and 4, cannot figure out the key 9 because he doesn't know the numbers 3 and 6. It can be seen that the key depends upon the secret numbers which were never transmitted and yet, both A and B come to know this key.

The next major development in cryptography was the RSA encryption which is the mainstay of all secure communication today. The above key exchange process still suffers from the fact that there needs to be a two way exchange of information between A and B. RSA does away with this by another neat usage of the modulo function coupled with the headache that is prime factorization. A prime number is a number which is only divisible by itself and 1. While it is very easy to take 2 prime numbers p and q and find r=p*q, given r it is extremely time consuming to figure out p and q. The RSA works by having a public and a private key. 'A' chooses 2 very big primes p and q and multiplies them. He keeps p and q secret but publishes r=p*q. If 'B' wants to transmit an encrypted message to A he uses A's public key (the number r) and uses a modified modulo function to encrypt his message. The function is such that even if r is known, it is extremely difficult to decrypt the message. As long as r is large enough, there is no way to decrypt the message unless p and q are also known (and hence A can do it).

The strength of RSA encryption basically boils down to the difficulty of prime factorization then. As all public knowledge stands currently, the encryption is unbreakable. Despite the tremendous amount of research in the problem of prime factorization there is no fast solution yet. The day the problem is solved much of our daily activities would grind to a halt! I find it fascinating now to think that every time I buy something on Amazon and provide my credit card information, the data is encrypted by what would be Amazon's public key (just a very very big number which is a multiple of 2 very big primes) and the current theoretical understanding assures me that decryption by a third party is beyond all human capabilities.

# Bookstore

There is a bookstore in the neighborhood which I ended up walking into today. I do not remember the  name of the place but it's just as well. The place is stuffed with arbitrarily crammed bookshelves which rise up to the ceiling and one has to tiptoe around them for the fear of making one wrong move and bringing the whole place down in an academic tumult. There does not seem to be any rhyme or reason in the arrangement of the books on the shelves either. So while Joyce is found jousting with Zola, art history blends effortlessly into biographies with nary a seam to be seen. The air columns separating the gray ones have the unmistakable smell of stuffed paper and they are colored in sparkling gold-dust as a lone sunbeam finds its way inside the shop and illuminates the suspended dust particles in streaks of yellow. I move my hand through it and the dust is perturbed. A little part of the mighty Sun, which continues to burn away aimlessly in a void, is captured in the contours of the liquid dance of dust. The solar shaft ends on Huxley and a brave new world is prominently called up on stage. Although purely coincidental, a romantic must dream! I stood there wondering if the time of the bookstore is finally up as the brave new world takes over. '21 years,' said the owner when I asked him how long has he had the place. I mentioned that during these 21 years he must have seen a tremendous amount of change. 'Yes,' he said adding, however, that it's merely transitory, as if to imply that the good old days of yesteryear are bound to come back as the wheel of time inevitably complete its rotation. The wheel may be broken now, I thought, as I saw him selling a used book for 54 cents.

Ours is a time of short attention spans and slick surfaces, a time in which the rough and antediluvian presence of bookstores is fast becoming anachronistic. It's a little sad, especially to a nostalgist like me but it does seem inevitable. I do not remember the name of the place but as I said, it's probably just as well.

# First few lines from Pale Fire

I was the shadow of the waxwing slain
By the false azure in the windowpane
I was the smudge of ashen fluff--and I
Lived on, flew on, in the reflected sky,
And from the inside, too, I'd duplicate
Myself, my lamp, an apple on a plate:
Uncurtaining the night, I'd let dark glass
Hang all the furniture above the grass,
And how delightful when a fall of snow
Covered my glimpse of lawn and reached up so
As to make chair and bed exactly stand
Upon that snow, out in that crystal land!