Viswanathan K's Thoughts

In his book, Ignorance: How it Drives Science , Stuart Firestein wrote: “In science there are so far two well-known instances where knowledge is shown to have limits.” He was referring to the famous Uncertainty Principle from quantum mechanics and Gödel’s Incompleteness Theorem in maths. The former says it is impossible to know both items in certain pairs of properties of objects. What does Gödel’s Incompleteness Theorem say? Simply put, it about any system of axioms (statements taken to be true, as being “obvious” without a formal proof) and proofs built using those axioms. No matter how you much progress you make with this system, the theorem says that there will always be true statements that cannot be proven . Aha, you think, but does this just mean that one needs to add another fairly obvious axiom to the list? Would that then make all true statements provable? Go ahead, said Gödel, add another axiom to the list. I’ll then find a different true statement that can’t

In recent times, my 6 year-old daughter has shown signs of being aware of the existence of other countries and the distances between them. In astronomy, the unit of distance is light years; for her, the unit of distance between countries is the number of connecting flights! One time, I showed her a video of the Aurora Borealis (aka Northern Lights) and told her that unfortunately it can only be seen from countries far north. Later, when she overheard us talking about (possibly) going to Maldives some time, her ears perked up. “That’s a different country from India, right? So can we see the Aurora Borealis from there?”, she asked. I realized it was time to get her a globe so she’d be able to see where countries are located. I am already finding the kinds of things she notices and asks thanks to the globe amusing and interesting. Wow! There are so many countries? So China is bigger than India? Which is the biggest country? Oh, so America is really on the other side of the world?

Richard Feynman’s dad gave him an excellent example of confusing knowing the name of something with having knowledge about that thing: “The general principle is that things which are moving tend to keep on moving, and things which are standing still tend to stand still, unless you push them hard. This tendency is called ‘inertia,’ but nobody knows why it’s true.” In other words, “Inertia” is a term to describe observed behavior: it is not an explanation of the observed behavior. And yet most of us walk out of our physics class thinking we got an explanation! Next, take this example of how terms we coin can then mislead us when we continue to use those terms beyond their original context. In his book, Climbing Mount Improbable , Richard Dawkins cites one objection that many throw at the theory of evolution: if evolution is so gradual and happens incrementally rather than in big jumps, why don’t we find fossils corresponding to the gradual change? Why do we have fossils of o

As a kid getting ready to go to engineering college, I am ashamed to say I barely knew the difference between science and technology (engineering) back then (they don’t ask such questions in the IIT-JEE exam). It took me a few years of being at work to finally get the difference. Or so I thought. Well ok, I was right about the parts I knew but turns out there are other aspects as well. I learnt all this after reading a few excerpts from the book, Radical Abundance , by Eric Drexler. First the part I already knew: “Scientific inquiry expands the scope of human perception and understanding; engineering design expands the scope of human plans and results.” Ok, that’s it: that’s all I knew. Drexler goes on to point out that in real life, the two fields often mix: “Engineering new instruments enables inquiry, while scientific inquiry can enable design.” and it is because of this intertwining of the two which can often “obscure how deeply they differ.” So what is this

Sherlock Holmes asked Watson in A Study in Scarlet : “What the deuce is [the solar system] to me? You say that we go round the sun. If we went round the moon it would not make a pennyworth of difference to me or to my work.” Continuing in that vein, Holmes even announces his intent to unlearn this bit of information, “I shall do my best to forget it”. Are Holmes’ remarks the reason why even very knowledgeable teachers struggle to teach their students? Because the student is thinking, “So? What do I do with that new bit of information you hurled at me?” After all, most people think of teaching the way Nobel-Prize winning physicist and professor Carl Wieman started: “When I first taught physics as a young assistant professor, I used the approach that is all too common when someone is called upon to teach something. First I thought very hard about the topic and got it clear in my own mind. Then I explained it to my students so that they would understand it with the same clarity I

I’ve always been happy that we engineers don’t have to get additional degrees beyond the B.E. or B.Tech., and that we don’t need to recertify ourselves periodically. 4 years of college and we are done. At the same time, I’ve felt sorry for doctors who (at least in the West) need to get themselves recertified periodically. My mom felt everyone does update themselves, even if it’s not always via a new degree. Surely, she said, all professionals read up new stuff and stay upto date, especially when their job demands it. Don’t engineers learn new programming languages and ways to speed up constructions, she asked? I think I found the answer when I read this Farnam Street analysis about the book, “ The Half-life of Facts: Why Everything We Know Has an Expiration Date ”, by Samuel Arbesman. Here’s the theme of that book: “Knowledge is like radioactivity. If you look at a single atom of uranium, whether it’s going to decay — breaking down and unleashing its energy — is highly unpre

What does it mean to know something? More specifically, what does a person mean when he says that he has knowledge of something? In science, the answer to that question involves 3 parts (the Tripartite Account ): 1) Belief : You should believe what you claim to know. After all, if you don’t even believe it yourself, how can you say you know it? 2) Justification : You should have valid reasons for your belief. 3) Truth : What you claim to know should, in fact, be true. This seems very tame and oh-so-obvious at first. Until you consider cases that violate one or more of the items of this Tripartite Account: So the Tripartite Account sounds like a good way of defining knowledge, right? Unfortunately, no. There is a whole class of counter-examples called Gettier counter-examples that shows the inadequacy of these 3 conditions. Here’s an example: it’s afternoon, you look at your watch and it says 3 o’clock. So you believe it is 3 with valid reason (your watch says so) and let’s say it is i