Viswanathan K's Thoughts

In an earlier blog on why the number 1 is not a prime number, I’d quoted these lines from Steven Strogatz’s The Joy of x : “It pulls back the curtain on how maths is sometimes done. The naïve view is that we make our definitions, set them in stone, then deduce whatever theorems happen to follow from them. Not so. That would be too passive. We’re in charge and can alter definitions as we please.”   I found another such instance of this “(we) can alter definitions as we please” power in Jordan Ellenberg’s book, How not to be Wrong . It involves a topic everyone encounters at school maths – what is the value of the infinite series: 0.9 + 0.09 + 0.009 + 0.0009 + … (the ellipsis means infinite terms) Common sense tells the sum keeps getting closer to 1 (0.9, then 0.99, then 0.999 and so on). Such examples led mathematicians to a deeper question: “What is the numerical value of an infinite sum?”   This is not just a silly, only-mathematicians-would-care query. It i...

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...

My niece’s class discussion on free speech concluded that free speech does not mean limitless power to hurt. It’s understandable for school or college kids to come to such conclusions. After all, that sounds so reasonable. But, and this is a huge ‘but’, in the real world, the immediate question we have to consider is who decides that limit? Can there even be a single rule to demarcate that line? And if not, would we have different limits for different groups/topics? Would such differences in limits then trigger accusations of bias, caring about some and ignoring the rest? If those accusations get ignored for too long, would it trigger a backlash later? Is the implementation so impractical that we will just tie ourselves in knots? If it was me, I would have set up Round 2 of that class discussion with these questions! At least kids can be excused on their stance because of their idealism, inexperience and lack of practical world scenarios. But adults, what’s their excuse? Lik...