Among very few of my pet peeves, one of my most long-standing ones is my mild repulsion towards scientific descriptions being boiled down to words, devoid of any underlying mathematical strata. In a world full of contradictions and misinterpretations, I was and still am to a degree, a firm believer of mathematical rigour — any scientific discussion should have mathematical underpinnings, or it shouldn’t be done at all. But unfortunately, the older I get, the more I get aware of the limits of my mathematical privileges — more often than not I am hitting the edges of my knowledge of mathematics in attempts to interpret the world around me; I am finding myself resorting to prose, poetry or music. I suppose it was bound to happen. But in retrospect, I see some chapters of my mostly-science-driven education, broke the boundaries of tenacious mathematical juggling and spilt over into my and by extension our, reality so dramatically that I can’t help but regret my pet peeve. One of those chapters is about information theory.
Information theory is essentially a set of principles that allows us to quantify information like we weigh a bag of potatoes, or purchase gasoline for a road trip to Prague. Before you groan in dismay in my description of a potentially dry subject, I should say that this theory also allows us to understand how tihs borken peice Enligsh txet is smoewaht readalbe but this gsqtpixi hmwvikevh sj wermxc is unreadable. Not only that, but these principles also gave us the tools to build ambitious radios on spacecraft that relayed back photographs of distant planets — quite literally connected the world from one end to the other with the advent of the internet — and in a convoluted way, made sure that the lit-up signs over a highway are readable on a foggy day. It’s one of those theories that I can express my profuse admiration to endlessly as it spills on reality all around me; I would gladly write prose about it instead of mathematical cruft.
My admiration, however, was abruptly paused when I stepped out of my bubble only to learn that Claude Shannon, father of information theory is not that well known! The Wikipedia page about Claude Shannon is shallow, to say the least, with a depth of a mere three scrolls, compared to Albert Einsteins’ at least ten scrolls of depth. I can’t imagine how a genius like him has flown under the radar of celebrity-dom while living to a ripe old age of eighty-four. But he was, as a biographer puts it, excessively modest. His work, however, speaks for itself. In his seminal paper, “A Mathematical Theory of Communication” texts, telegrams, photographs everything gets distilled into mere mathematical blobs, shedding all context leaving merely a collection of bits. If I may dare say in my naivety, his “idea of information”, treads a mild parallel to what Kurt Gödel walked on in mathematics. Being fortunate enough to have been given the time & privilege to study his work in all its glory, I can say that after almost a decade of introduction, I am amazed by a man so “meta”, as the pop-lingo goes, that he figured out the absolute limits of our communication. Even when poets might not be very enthusiastic about this realisation, I take every opportunity to sew threads from his work in my life, day in and day out.
To illustrate one aspect of his work, let me take you back to the broken sentences that I had written before. If we step back a little now, it is qualitatively obvious why you could read
tihs borken peice Enligsh txet is smoewaht readalbe but not
gsqtpixi hmwvikevh sj wermxc even when both contain information; the latter is just a bit more obscure. But in terms of information theory, the first chunk is more readable because it has more of something called redundancy compared to the second chunk. The second chunk is a very primitive form of cipher, commonly called a shift-substitution-cipher, and it is quite readable — even by a 16th-century code-breaker as Queen Mary of Scots had figured out with her life. The beauty of Shannon's work and subsequent works is that it spurred a whole host of mathematical and scientific inquiry that answered questions similar to the one I have just asked, all the while blurring the lines between what we consider tangible reality and mathematical description of it. And not only that, thanks to such rigour engineers can ensure you get to watch a YouTube video without missing a beat – scientists could get excellent photographs of Saturn's rings and mathematicians, they made sure there's some redundancy in every piece of human communication. But that's a story for another time – that started with a reply from one of my favourite mathematicians.
P.S. In case you want to, to decode
gsqtpixi hmwvikevh sj wermxc, all you need to do is shift all the alphabets towards "A" four times, as in G becomes C, S becomes O, Q becomes M and so on and the original words will come out. And if you really want to learn how you or a 16-th-century code breaker could have decoded it without any hint from me, I have two words for you – frequency analysis.