I'd waited for too long..

This is John Connor. If you are listening to this, you are the Resistance.

Thanks to Christian Bale's peculiar accent and the ambiance of the movie, these words etch in your memory. Watched it (the latest Terminator movie) yesterday. Our original plan was the 9AM show at E-square but we could not get tickets. It was overflowing, and I imagine all were there for T4. So that became the 10AM show at Rahul. As I said, I was waiting for this one since long. Maybe because I am a fan of Christian Bale, maybe because it's a Terminator movie, or maybe because I hadn't watched a good action/sci-fi since long. Or maybe because all of the above. Anyway, the point is I had huge expectations, and they were fulfilled. Not as much action as I would have liked, but enough. And what there is is awesome. I think there are some moments that a Terminator movie can not not have. Like a Terminator smashing a human skull under foot, or an appearance by Mr. Schwarznegger, no matter how tiny. This one has both. Some nice, touchy moments too, like the LA branch of Resistance. I mean, these two kids.. A most poignant lesson about the human spirit. A real must watch, I'll probably watch it again. Let me end terminate this post with my favorite line from the movie

This is John Connor. There is no fate but what we make.

Today is 28th of June..

So 28/6. The interesting thing is that they are both what are called perfect numbers. Now you might already know what perfect numbers are, or can read the earlier wikipedia link, but let me try to explain, just to increase the length of this post. The idea is to first collect all the divisors of a number (except the number itself, these are called Proper divisors). Why, you might ask. There are many answers, because we can (from TBBT), or because I chose to (from Neo). So Just do it (Nike :p). To take an example, let's say the number is 10. So the divisors are 1,2,5. Add them together. So 1+2+5 = 8. Now this sum is less than our number. Such numbers are called deficient numbers. It also happens that in some cases the sum exceeds the number. For example, 12. Divisors of 12 are 1,2,3,4,6. So sum of divisors is 1+2+3+4+6 = 16, which is greater than 12. Such numbers are called abundant numbers. But a third possibility exists, and you might already have guessed it. A case where the sum of the proper divisors of a number is equal to the number. This is the thing we were after, the perfect numbers. See for yourself.

For 6, proper divisors are 1,2,3. Sum = 1+2+3 = 6
For 28, proper divisors are 1,2,4,7,14. Sum = 1+2+4+7+14 = 28


Enjoy!!

World through classic goggles!

I clearly remember what I was thinking when I spotted an omnibus edition of three Jules Verne novels on one of my crossword trips. I said to myself, "I want to see what science fiction looked like a hundred years ago". Having had this wholly remarkable thought (yes, I am all for self admiration :p), I purchased the book, set it in an obscure corner of my shelf and it just stayed there, gathering a good amount of dust in the process.

That was a year or so ago, and it reappeared a few days back, when I could not find anything to read (despite those stacks I keep mentioning). Started reading Around the world in Eighty days. I had watched a movie with the same name, starring Jacky Chen, and remember not liking it. The premise is simple, a man (in 1872) decides to go around the world in 80 days and the story revolves around how he goes about it. If you want a sophisticated story, with intricate plot development and complex personalities, this might not be the right book for you. But if you want a simple, enjoyable story, that makes you keep reading, this is the very thing. That, and it's an interesting look at how the world was in late nineteenth century, like the modes of transport and the routes, the customs and political scenarios, seen through the eyes of an European. Mr.Verne seems to have been intimately familiar with the geographical world, giving exact distances, times for journeys and so on (Did you know he had ran away from his home as a cabin boy on a trading ship in his youth?). To use one of his own expressions, he must have traveled everywhere, at least in spirit. There is very little in the story to qualify it for the label science fiction, but that doesn't stop it from being an enjoyable read. And you learn a thing or two, like what Cisco meant before it referred to the networking giant.

It is available online through Project Gutenberg.

Enjoy!!

Today is 26th

26 is the only number that sits between a perfect square (25) and a perfect cube (27). Fermat proved this.

Enjoy!!

Some idle comments

I became a Jeffrey Archer fan relatively recently. Thirty seven days ago, to be precise. And all this time I have not been idle, despite what impression you might have :p. I have been trying to read some of JA's work and what follws are some idle comments about what's gone so far..

The first book I read was Paths of Glory. It came on the back of a lot of non fiction, and the simplicity of the story appealed to me. But some plots appeared overdramatic, which constantly remind you that it is fiction.

Next I read Prisoner of Birth. I had heard mixed reviews about it, and so thought a bit before starting it; an exercise I rarely do. But the reviews were justified. It's a good book, may not be JA's best. And I think the book has everything a Bollywood movie needs, is story me emotion hai, action hai, drama hai.. (Ok action thoda kam hai, par chalega). The plot development is good, especially the courtroom sequences. I found the pace lacking in some places though.

Next came Not a penny more, Not a penny less which I finished yesterday. Reviews in this case were unanimous and raving. The thing I liked most is the pace. It continiously keeps you on your toes. And the hero is a mathematician, now that happens rarely :p. And if a Bollywood can be made on POB, there is a Marathi movie based on the this one. Aamhi sare sajjan, starring Prashant Damle. The movie even has something about how the heroes return the money ;-). It also appeared to be the most well researched of the lot.

Next on my list is Kane and Abel, for which again, I have heard much praise. But maybe not immediately..


[Thanks to Abhishek for sharing POB. Thanks to Zarin for sharing NAPMNAPL.]

Today is 24th

Here is an interesting fact about 24. The sum of first n squares for n=24 is a perfect square, the square of 70. In other words,
1² + 2² + 3² + ... + 24² = 70²
What's more, 24 is the only integer, except 1 of course, for which this is true.

Enjoy!!

A thought

We deal not with people but with their abstractions. Created and revised over time, but imperfect nonetheless for the simple reason that we are not perfect. And which means law of leaky abstractions applies (you should consider reading that essay, if you haven't already). Here's how Joel puts it, "All non trivial abstractions, to some degree are leaky". And just like in software, it causes trouble when it happens. I've seen people fighting it, but it seems to me there is no escaping it (because reality is so complex) and so a more fruitful course of action would be to expect it and then (try to?) deal with it, just as in software. And that begins with acknowledging that you are dealing with an abstraction.

Impossibility

Man is not a circle with a single center. He is an ellipse with two foci. One is facts. The other is ideas.

-Victor Hugo

Take a good look (Image Courtesy: Wikipedia). The object you are staring at is known as Penrose triangle. And it is an impossible object. Now what do you mean by that? Well, you might already have guessed. The object cannot be constructed. Hence the name. It's just that our brain interprets the image as a projection of a 3 dimensional object. And this is one of the topics dealt with in John Barrow's Impossibility.

Let me start by saying that it was impossible for me to understand some parts of the book :). [But you know my opinion of Mr. Barrow, so you (and I) know whom to blame :p]. As for the rest of the book, it was a delight to read, informative and sometimes illuminating. The subtitle might give an idea of it's contents, The limits of science and the science of limits. It is a rather different kind of popular science book. Generally they focus on what Science has achieved, and tend to give the impression that the march of progress is unstoppable. Here we get to see what kind of constraints to our investigations of nature might exist, along with a look at the history, because the question is clearly not new. They might take many different forms, like limits of economy because information clearly has a cost, limits of technology of how small things can get, limits because the universe is the way it is (like the finite speed of light), limits of our ways of reasoning (those of mathematics), and finally limits of our minds, because we clearly have not evolved to do science, we have evolved to survive and so our minds might have preferences for certain kinds of patterns which may not be ultimately adequate or appropriate for describing the universe. There is an interesting discussion of Arrow's theorem towards the end, which states that under a few reasonable assumptions, it is impossible to rationally convert multiples individual choices (like votes cast by people) into an unambiguous social choice. Another interesting tidbit that I just can not not share is the financial proof of why there are no time travelers (given by Reinganum). Here's how the argument goes. If there are travelers visiting us from the future, they can use their knowledge to make huge profits in futures markets, which will drive the interest rate towards zero. The fact that we see positive interest rates means no time travelers are visiting us. Fundoo.. :)

It took me more than usual amount of time to finish this book, because as I said earlier, I kept getting stuck. But those moments got me thinking about impossibilities on a more mundane, personal level. I mean it's very easy to say Sky is the limit in an exalted moment, but it would be foolish to ignore your limits, if only for the reason that you must identify them before you can transcend them.

Enjoy!!

Haskell: First Impressions

I first heard of Haskell while in college. I learned that it is a functional programming language, like Lisp. And that was the end of the story. Later, when I started working, I kept hearing a lot of praise of Lisp and even played a little with car and cdr and cons (Scheme in particular), but that was pretty much it, and a long time ago (Go here if you want to know how those names came to be). Recently (OK, yesterday) Haskell reappeared on my radar. Maybe because I discovered this online tutorial, and liked the look of it. I mean, cartoons!! So started reading. Haven't finished yet, but I already think it's quite good. Here's a program to compute the pairs of amicable numbers (OEIS: A063990).

answer = [(a,b) | a <- [1,2..], b <- [sum (proper_divisors a)], a < b && a == sum (proper_divisors b)] where proper_divisors n = [x | x <- [1..(n-1)], n `mod` x == 0]

The thing I find impressive is, it reads almost like the definition written on paper. And while I am sure I've coded it in the most inefficient way possible, it took only about 10 minutes and 168 characters to write. Think about it, by trimming a few unnecessary whitespaces, I can send it over SMS. Bwuhahah :p.*

Cutting the long story short, I am enjoying Haskell. I don't think I get the functional thingy yet, and I am not sure if I'll ever use it professionally. And while we are at it, I am also not sure how deep I will go. But one thing for sure, I am having fun, and that is pretty important.

Enjoy!!

[For the interested, there are quite a few good online resources for learning Haskell. In addition to the tutorial I mentioned above, there is The Haskell Tutorial, Haskell wikibook, and a series of posts by MarkCC whose writing I generally admire. Please let me know if you know anything else which is good].

Update:
Just discovered this. O'Reilly's Real world Haskell is available online. I don't know how good it is, but it was the Winner of Best Technical Book, Jolt Awards 2009, so it probably is.


* To whom might be a question ;-)

Oppie

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite.

-Paul Dirac

That is a pretty famous quote. In fact, I think I've used it before. Ohh yes, in this post. But of course remarks are not made with the express intention of creating quotes. So today I provide some context. It comes from a letter Dirac wrote, and reads in full, "I understand that you are writing poetry as well as working at physics. I do not see how you can do both. In science . . ." And that letter was addressed to J.Robert Oppenheimer, the legendary director of Los Alamos during WWII, and a tragic figure by any count.

I read a biography of JRO (affectionately known as Oppie) by Abraham Pais recently. First a fact, the author passed away while in the process of completing the book, so this book reads more like a collection of essays than a coherent biography. And like any collection of essays, some are good and some I found boring. I had expected details of his Los Alamos days, but there is surprisingly little of that. The author felt there were other good books that covered those and decided to focus on other facets of JRO's life (I should probably get one of those books). Also there is not much about his personal life, but there is a lot of material on JRO's post Los Alamos political career. One important thing to note is that the author, himself a distinguished physicist, personally knew many of the players in the unfolding drama and there's a wealth of his personal observations and opinions. There are also sections about JRO's scientific contributions, and the important role he played as a mentor to younger generation of physicists. There are little interesting digressions too, like the history of the Institute, where the author was a professor and JRO became the third director. The biography is very extensively researched and draws heavily on original sources, so if you want to study these topics, this is the place to go. There is a lot of supplemental material about Oppenheimer trials by Robert Crease towards the end, but I did not read that. I felt the earlier parts gave a reasonable view of the man's life and work, and did not feel the inclination to find out exactly how the man fell.

The lesson to be drawn from JRO's life is about the great uncertainty of life. The man who became a legend in his own lifetime survived to see the dramatic fall of his public stature, to see former colleagues and friends turn into hostile enemies, or at least useless bystanders. Not that he did not make any mistakes, but the impression you get is he paid more than he deserved. As for the book, it was not everything I had wished for, but still, worth a try!

I can't tweet this link..

It MUST be on a blog. :-)

Enjoy!!

First meet with the Monster

Everything should be made as simple as possible, but not simpler.
-Albert Einstein

Recently I finished reading Symmetry and the Monster by Mark Ronan. It was a chance find on my last Landmark trip, I happened to have read something about it on the net and picked it up. It is a history of Group theory, right from the time when E. Galois pioneered it in demonstrating the unsolvability of general quintic in Nineteenth century up to the present day. Galois, despite his genius (or was it because of it?), led a very tragic life and died in a duel at a very young age. The account of this tragic event presented in the book (which differs from Bell's) is very.. let me say senti. Significant theorems were later discovered by Langrange, Cauchy, Burnside and Feit-Thompson, including others.* [Please go and read the footnote in case you missed the last end-of-sentence marker. Thank You]. Simultaneously continued the discovery of all the finite simple groups (the atoms of symmetry), their classification (there are 18 countably infinite families), and discovery of exceptions that won't fit in any family (there are 26 of these). The Monster in the title is the largest of these exceptions, and exists in 196,884 dimensions. [Someone proposed the name 'Friendly Giant' for this beast, but it never caught on. Does it tell us something about human psyche? ;)]. It was a huge undertaking, spanning centuries and contributions came from many directions. The book captures the excitement of this endeavour well. Plus it explains how symmetry groups are related with leading edge physics like String theory (most of that stuff went over my head, but I can't blame it on Mark). There were other things that I did not understand as well, but I guess that can be a virtue for a book. If you think you understood everything too well, you might stop there. This book whets your appetite, and so at least a possibility exists that I'll look up some of these things elsewhere (not necessary that it will be realized though, at least going by my track record :). But that aside, if you want to meet the Monster, let this be your first step.

Enjoy!!

* I might give the impression that I understand this stuff. I want to assure you that I really don't. This is the first book I read about Group theory and it is a popular science book. But again, the following quote by the great John Von Neumann might be in order. "In mathematics, you don't understand things. You just get used to them."

Why do people leave?

Well the title appears a bit misleading to me now that I have written it. That question might not have a satisfactory answer, and I don't feel qualified enough to tackle it, but what I actually have in mind is a very specific instance of that question, why do people leave blogging? I am not talking about people who did not quite get started, and their one or two posts stand there to pay testimony to this fact. I am talking about good bloggers (at least in my opinion), who had interesting things to share and readers to prove this, but consciously decided to quit at some point in time. The question popped in my mind while reading Stevey's latest post. His blog is very popular and I enjoy it, but he's about to leave. And let's not forget that it was his post, why you should write blogs that encouraged many, many to write their first post. And he's not alone. In my short life as a blogger, I've seen this happening more often than once. So what is it? Does it take too much energy, or you run out of things to share? Both of these reasons seem unlikely to me, but they might be true. Or is it that after a certain stage blogging starts turning into an obsession, interfering with the way we experience the world? (this was related to me by a friend, xkcd is as always helpful in making the point). Or is it that you lose interest, stop seeing the point, in a way? But if so, why? Or is their some other reason that I am too naive to see right now? I don't know. Myabe I will find out one day. But another question now pops into my mind, will the feel-like-leaving thingy ever happen to me?

Rains

Rains are here, fellas! Now many of you just absolutely love rains, but I have a love-hate relationship with the season. I hate the chik-chik, I hate having to carry around a raincoat (one more thing to take care of), I hate having to be extra careful while driving; well, that's a long list; but again, can't say that anything beats sitting by the window on a stormy evening, a hot cup of tea in one hand (and bhujiyas nearby), and listening to nature's dance. Seasons are one of those few predictable things in life; you want it or not, remember it or not, when the time comes, they are there to say hello. But life keeps changing, you keep changing, and you end up with a store of memories, united by just a single theme, Rains.

The first memories of rains I have are from my school days. It was when the academic year used to start. I distinctly remember the fresh scent of new books. I was a story lover even then, and you could pretty much treat your language books like story books. That made it more special. This was accompnied by the usual activities like putting covers on new books, deciding how many pages a math notebook should be, and demanding a new compass box from papa. Even today, the cloudy sky invariably brings that scent back.

Then I moved to Kolhapur for Junior college. Spent two years there. The thing you won't forget if you've lived in the city is the constant pouring. It's happening all the time!!. To make matters worse the room had leaks, but the kindness of the landlord and his family more than made that up. I can say I've met few kinder people.

Then I moved to Pune. In rains, Mulashi was our favorite destination. Arranging bikes, fights over who drives with whom, the unending fun, and in the end, coffee at Relax, always! And five guys trying to fit inside one umbrella on their way to canteen!! (The sixth guy pretends to be enjoying the full fury of nature). And let me skip over all the fun of protecting journals, b'day bumps with muddy shoes and plans over which teacher deserves to be the first one to drown in VIT boat club :p (though I really don't want to).

Then came the first workex. I won't forget the first 3/4 months, constant rains, and I had to change two buses to get to the workplace. If you have any experience with PMT travel, you know the kind of pain what I am talking about :). But it was fun nonetheless, I think those first days always make an indelible impression.

And that brings us to this year. Who knows what it would be like? Maybe a year from now I will be writing about this time, maybe not. Becuase though seasons are predictable, life, for better or worse, is not. Happy Pawsala!!

Enjoy!!

Something about The Search

John Barrow is one of the best popular science writers we have. I was quick to pick his New Theories of Everything on my last trip to Landmark. I had expected a discussion of the current candidates for TOE, especially string theory. The book has that, but rather than focus on particular theories it takes a broader approach. It begins with the concept of 'Laws of nature', how the idea came to be, how we discovered some, and are they really there, or as some philosophers (especially Kant) would have us believe, are just constructions of the human mind. Then it ranges over Godel's incompleteness theorem and its possible implications for Physics, the relationship between Mathematics and Physics, the role of initial conditions and symmetry breaking (which is essentially random) in the birth of the universe, the emergence of complexity and a lot of other relevant stuff. It's more of a sketch of how a TOE might look like and whether it could be really present. And Barrow is remarkable not only in the breadth of the material but also in the lucidity of explanations. Let me give you an example. Conservation laws (notably the one for Energy) were discovered in Nineteenth Century. It's a standard scientific fact. What Barrow adds is it lead to a growth of Atheism among the scientists because earlier they all had believed that some divine control was required (at least periodically) to keep the world from going astray. What conservation laws showed was Nature has measures of her own. To take another example, at the beginning of the twentieth century it was discovered that the conservation laws can be expressed as invariances, like the conservation of angular momentum as invariance of the laws of nature to orientation in space. But it also lead to the deemphasis of the nature of time, with a revival of Parmenidan Philosophy from some two thousand years ago, because the focus shifted from studying change to studying invariances. Barrow has written entire books about some of the topics discussed here eg. Infinities (The infinite book) or fundamental constants of nature (Constants of Nature), so the discussions here may serve as useful summaries of those more detailed works.

If you want a readable view of the current search for TOE (with a lot of stuff about how that reflects upon other areas of enquiry, like philosophy or theology), you should read this book.

Enjoy!!