A stitch in time

A stitch in time, saves nine, they say. To really appreciate its meaning, one needs to have a root canal performed though.

Take good care of your teeth.

Facts and Meaning of Logicomix

Facts:

A. It is a graphic novel about the 'foundational quest' in mathematics, an endeavour to put mathematics on a secure footing in the first half of the twentieth century. The story is told via Russell's life and in Russell's voice, a central character in that story.

B. It counts noted computer scientist and author Christos Papadimitriou as a coauthour.

C. It was on my reading list for a long time.

Meaning:

I (in fact) made a number of beginnnings under this section, but found none of them satisfactory. The essence always seems to escape, much more so than for most other books. Read the book and make the meaning for yourself.

Notes from a math lecture

Public lectures have a distinguished history going at least as far back as Faraday, but I hardly have any history of attending them. Call it new year fervor that has not subsided yet (or whatever), something did prompt me out of my laziness when I came to know of a public lecture to be given by Prof. Schmid from Harvard last week. My thinking was, more or less, it's a public lecture, How hard can it be?

The topic of the lecture was 'Riemann's continuous, nowhere differentiable function'. As it happens, before Riemann it was thought that a function that is continuous everywhere but differentiable almost nowhere could not exist. Weierstrass was the first to publish such a function, though Riemann (second hand reports claim) gave an example of such a function earlier, but without giving proof. Working that out took a while. G. H. Hardy showed in 1916 that the function is not differentiable at irrational points, while Gerver and Smith showed in 1970s that it is not differentiable at rational points either, except those of the form p/q with p and q relatively prime. Prof. Schmid worked on this function himself, which is intimately related to fractals, a topic which came to prominence much later. The area is important and broad enough to have its own book.

That is the summary, and I am afraid I cannot go in more detail. The lecture was obviously intended for students who are learning related stuff and was full of details and formalism, though the key ideas (like the ones mentioned above) were clearly  brought out. I remember reading John Derbyshire's Prime obsession with great interest, and those who have read it (or are otherwise familiar with the history of Riemann hypothesis) would not fail to notice a parallel here. One minor quibble on the personal front is that I was interested in getting a view on, of the six remaining millennium problems (which include both Riemann hypothesis and P vs NP), which one we are closest to solving, but ended up squandering the opportunity to ask. 

Overall it was a good learning experience, and sitting in a hall surrounded by an overwhelmingly young crowd brought back memories of my own college days, turning it into a refreshing one as well.

Wild ride

Wild ride is the story of Uber. Now to anyone who reads news, at least parts of that story would appear familiar; the strength of Wild ride is it gives a highly readable, balanced and insightful account in a remarkably small package (just over 200 pages). It is worth mentioning that the author went beyond the usual research tools (interviews etc) while preparing for the book, working as an Uber driver himself for a while. I thoroughly enjoyed it, and to those who are interested in startups, it would make a pleasant and instructive read.

First few days with Pixel2

This is not a systematic review of Pixel2. Many of those exist, and in any case, interest in such a thing would be low because Pixel2 is not that new anymore. Instead, what follows is a bunch of impressions, in no particular order. Note that my previous phone was the first gen Moto G. While an excellent phone when I bought it, over time it grew many warts, making me spend a lot of energy in cursing (being able to curse in three languages was a boon here). Undoubtedly my impressions are tinged by that experience.

The first thing I noticed after opening the box is, it's light. Cross that, it is surprisingly light.

It charges fast, but also seems to discharge fast, especially when data network is in use.

The backside gets a bit warm with extensive use.

This was the first time I really used a voice interface, and I continue to be astounded by the accuracy of Google assistant. I find it quite uncanny too, e.g. the first time I asked it to play a song, it came up with ye jo des hai tera from Swades.

Much has been said about its camera, so I'll just mention that I have replaced an iPhone owner as the chief photographer at office birthdays.

I don't have a VR headset yet, but did use it once on a relative's Pixel2. The roller-coaster demo gave me a very real dizziness.

I had pretty much stopped trying new apps, and the ones I used formed a close-to-immutable set. Now I am (much more) likely to be found with my head buried in the phone. 

I restarted using Twitter, and (as evidenced by this post) am more likely to blog. I check Facebook more often, and the same applies (probably to a larger degree) to Quora, Stackoverflow, HN, LinkedIn, Medium, TechCrunch and more.  Which brings me to the next point.

Information overload was already a problem, and it grows worse with a better phone. Same goes for the distraction angle. Thankfully relief (so to speak) is not far away; the play store has a number of Meditation apps too :-) So Headspace joins my trusty Insight timer  (but I am yet to try it, being busy writing this post).

The EMI is pretty high (had to say it)! :-p

The fabric of reality

The fabric of reality by David Deutsch is certainly one of the most delightful books I have read. Now I would rate a good popular science book along the axes of being informative, readable, comprehensible. Very few would qualify as being delightful, so let me try to say why this one does.

A popular science book is, in general,  intended for the person who is curious about some field of science, but lacks the time and/or brainpower to undertake a thorough study.  While by design it can't get into the details, the good ones provide an understanding that is not wholly superficial. Generally they talk about a specific area of science. The fabric of  reality distinguishes itself, firstly, by not being about any specific area of science as such, but about the worldview that emerges when we take our best theories seriously, and treat them together. The theories in question are, namely, quantum physics, evolution by natural selection, theory of computation and Popper's theory of knowledge.

Is it possible for one person to understand everything that is understood? The book opens with this question and Deutsch answers this in the affirmative. Knowing all the facts is clearly  impossible, but understanding comes from explanations. The deeper the theory, the more it explains and you understand more even while having to know less. Science is fundamentally about explanations. This last is an important point, and (at least) I have not seen it made with such force and eloquence before.

Quantum physics has pretty good coverage of its own in the popular science category of course. As far as I can tell though, most of it makes a virtue of the counter intuitiveness of the quantum, which befuddles the nonexpert. The many worlds interpretation of quantum mechanics makes the same predictions as the standard Copenhagen interpretation (which is often implicit in the popular accounts), but Deutsch argues powerfully that it embodies a better explanation. Part of the argument comes from quantum computing, especially Shor's algorithm for factoring. Factoring is an intractable task with currently known classical algorithms, but quantum computers can factor in polynomial time using Shor's algorithm. Deutsch asks, where does this factoring take place, if not in the multiverse? I know that the case for choosing one interpretation over another is not settled among the experts, but (as someone whose entire knowledge in this area comes from reading a few popular science books), I can say at least that I find Deutsch's explanation to be much more comprehensible than the alternative. In other words, I now believe in parallel universes :-) [I plan to revisit this bit some time later and see if I still believe in them. I also plan to read more on this topic]. Another related point is whether we should believe in parallel universes though they are not directly perceptible except for interference phenomenon in special situations. To this end, Deutsch develops a criteria for reality, viz, if something behaves in a complex and autonomous way needing independent explanation, it is real. And so are the parallel universes. Another important point, but not addressed elsewhere.

Inductivism is a theory of knowledge, which says that theories come by way of generalizing observations and are justified when their predictions are confirmed (more times the better). Deutsch points out that no amount of confirmation can give sureshot confidence, and theories in general come by way of good explanations and not from generalizing observations. In Popper's scheme, problem solving within the context of existing theories and their perceived deficiencies is of the essence. There is no ultimate source of justification for a theory (in the form of a principle of induction), but we are justified in acting on them because their rivals have been refuted by rational argument and/or experimental failure. This does not mean a better theory would not appear tomorrow. Parts of the book dealing with epistemology were a major source of the delight that I alluded to earlier.

There are of course, so many other things worth mentioning. Real quickly; how replicators survive by embodying true knowledge about their niches and how their  adaptation means their structures would be identical across the multiverse; how the concept of a flow of time does not make sense, but that of free will does and that too without letting go of determinism; what are the limits of virtual reality and why it is fundamentally important (instead of being just a new form of entertainment); how Turing was mistaken in thinking he 'undetstood paper' (as Feynman once put it); is time travel possible and if so, are paradoxes possible; what is the relation between mathematical existence and mathematical proof; and so on and on. But I see this post is already quite long and my point already quite clear.

There are very few books which made me want to reread them as soon they were finished, this one is one of those few  (I ended up ordering Deutsch's Beginning of Infinity in this case). One reviewer has compared Deutsch to Russell as a stylist and I could not agree more. As I said after finishing Russell's autobiography, it made everything else seem schoolboyish. This one, to a lower degree of course, certainly did too.