After talking to Pooja, I felt it necessary to mention the great mathematician G. H. Hardy on my blog. Hardy is most famous outside of mathematics for his "A Mathematician's Apology". The book, written in later in life by Hardy, talks among aother things about how mathematics is young man's game. He is also somewhat know for his association with Ramanujan and for being the person responsible for bringing him to Cambridge where his greatest mathematics unfolded.

Quoting one of the mathematicians, C Snow, that Hardy worked with:
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hardy.html

A mathematicians apology is, if read with the textual attention it deserves, a book of haunting sadness. Yes, it is witty and sharp with intellectual high spirits: yes, the crystalline clarity and candour are still there: yes, it is the testament of a creative artist. But it is also, in an understated stoical fashion, a passionate lament for creative powers that used to be and that will never come again. I know nothing like it in the language: partly because most people with the literary gift to express such a lament don't come to feel it: it is very rare for a writer to realise, with the finality of truth, that he is absolutely finished.

Hardy was a sort of purist mathematician, one who did his mathematics not for the sake of its applicability to anything, but for the sake of doing great mathematics. Hardy, along with Littlewood and Ramanujan,  is also mention in Apostolos Doxiadis' "Uncle Petros and the Goldbach Conjecture". The link above gives a short summary on his life.

Some quotes:

Asked if he believes in one God, a mathematician answered: "Yes, up to isomorphism".

http://en.wikipedia.org/wiki/G._H._Hardy:

It is never worth a first class man's time to express a majority opinion. By definition, there are plenty of others to do that.

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

Aaargh.... Its shaped like a card but its not to be carried in you wallet. Otherwise the top layer just comes off! And guess what, that's the layer with your name and number and photo on it. Seriously, would it have killed them to make these cards of a slightly better quality? What did they save by creating the cheapest possible kind of card?

Now before you ask me why I cant use the license as an Indian government issued id, let me tell you - that's because its cracked too. It cracked within the first month of my getting it. And no, all the other cards in my wallet are just fine. The govt issued ones are just cheap manufacturing quality.

Its fun to play with light. Light has so much color and "texture". I bought this strange looking glass bowl at an antique shop. They were selling it as an ashtray. I figured I could use it to hold candles. 

This Tuesday I finally got my driving license in the US. Well, I technically don't have the license itself yet - it will be mailed to me eventually. Since I had a rental car at my disposal, Kyle and I decided to take a little photography trip. We drove to Lake Lemon, a few miles from Bloomington.

We reached the lake a little before sunrise. It had been years since I saw a sunrise, and the quality of the light was just fascinating. Its true what professional photographers say - there is quite nothing like the morning light. Also, wild geese make lovely subjects.

I usually don't shoot in black and white. Kyle almost always does. Here is my attempt to look vaguely Ansel Adams-ish. The picture below looks a lot better in full resolution. So the hi-res version of the picture is uploaded, you just need to click on it.

Finally, to add a bit of color, here is Lake Lemon a few minutes before sunrise. This too is better hi-res, but in the interest of server space I am uploading only the little version here.

Most photographers I talk to, who are hobbyists like me, act a little strange when the topic of post processing comes up. A manner that is rather reminiscent of a stupid friend letting slip something in front of your parents. They look a little squeamish and then they start to feign innocence. "I never post process my pictures", "Oh! that's how it came out of the camera", "I want my photos to be *real*", "Only minimally, just yadda yadda yadda..." etc.

What?

What are you all uptight about? What's the big deal? Do you realize that when you take a digital photograph there is a lot of software in the camera making choices for you already? I haven't done much (if any at all) post processing so far, not because I have anything against it, but because of (1) I don't have the tools and (2) It takes too much time. I do have Picasa on my machine and every now and then I have tried boosting saturation on a picture or cropping out an annoying detail and have felt good about it.

The problem with Picasa is that it doesn't allow much control over things and I still end up wasting a lot of time if I ever start playing with it. Many many years back I had access to a copy of Photoshop and that program simply made me feel stupid - I couldn't get it to do anything. I remember Abdul Rafeeq who was in my undergrad engineering class and was a wiz with Photoshop. Rafeeq used to design all our posters and such, so I had first hand evidence of the fact that the tool was powerful in the right hands. (The only image manipulating program I felt good about was Gimp - the fact that I never installed it and that I never really used used it, made me feel really good about myself. Once in a while I'd find some poor soul struggling with it and feel a deep satisfaction that it wasn't me.)

Enter Adobe Lightroom. Lightroom is a post processing tool designed primarily with the interests of photographers in mind. The tool is designed to let you select and organize pictures, do a decent set of color corrections, tone fixing etc type operations that most photographers are interested in.

I downloaded a copy a few days back on the 30 day trial period and I like it. Its a bit slow, not as responsive as Picasa, but is otherwise rather nice. After playing around with it a bit, I must say I like the added power to fix the color settings of my pictures. Being able to boost color in your pictures (or de-saturate them) is an added dimension of power. Of course, it cant make a bad picture good, but it does compensate for the color of the light, the white balance settings, the nuances of your cameras sensor etc. As a matter of fact, once I get comfortable with this I suspect I will be able to get the look I want without much trouble as well.

Comparing the detail of someone's forehead. Which one do you think came out of the camera and which one is the post processed version? The odd looking reddish hue, the one on the right, is the version that came out the camera.

The downside? The several hundred dollar price tag. Its cheaper than Photoshop but its a bit too much for what the PhD program pays me.

I have started liking groups so much, that I think its worth spending some time drawing out these beautiful things with some care. These mathematical abstractions have some really nice corresponding pictures.

This is the dihedral group D3, produced by
s^3 = i
(st)^2 = i

The quaternion group.

Quaternions are a generalization of complex numbers. I am a little fascinated with the above group because a long time back before I had known of Group theory I had constructed the above diagram in my attempt to understand quaternions and multi-dimensional geometry.

The discovery of quaternions is credited to the great mathematician Hamilton. Story has it that Hamilton had been pondering the issue for a quite a while and fundamental equation of quaternions came to him when he was taking a walk with his wife. It is said he carved the equation into bridge where he was at that time. The bridge, now has a plaque to this effect. So here is the fundamental equation:

ijk = -1

From this we can also derive i^2 = j^2 = k^2 = -1

The group produced by
s^3 = i
(-s)ts = t^2

where "-s" is to be read as "s inverse".

Here is a slightly different rendition of the same group:

Here is a different group:

This is the group generated by:
s^4 = i
(-s)ts = t^2
t^15 = i

This is the group generated by a variation of the above equations:
s^4 = i
(-s)ts = t^2
t^5 = i

Many years back I worked full time at Microsoft on one of the many projects related to Vista (or what was then called Longhorn). Last December I was visiting friends in the Redmond area when one of the jokingly observed how the code I had written for Microsoft still hadn't seen light of day, while two and a half years later, I had moved on and completed my Masters and had started on my PhD.

This wasn't a sort of accidental slip, but I remember we were told at that time that if we had any ideas to suggest for Vista, they better be ideas that will be new and interesting 3-4 years later when the OS actually ships. This is a tall order for any sort of idea, much less for the volatile world of "software project" ideas.

While this seemed like very ironic humor at that time, over the past month or so, once in a while I thought about what that meant. After all, I had spent a year writing all that code. A very busy year at that - I had spent 15+ hours a day, I daresay, that was my average day, struggling with the turmoil of the massive engineering effort that was Vista.

I wasn't a *great* programmer by many standards, but I'd like to think that I was better than many I had encountered. 15+ hours of my time for about a year, took a lot of out of my life and it didn't seem to have amounted to anything! Sure I was being paid a handsomely, but one one like to think that one's efforts contribute to the world in some way as well. After all that year was full of deadlines and things being rushed to be completed and such. What came of all of it? If it came to nothing, what a waste of life that was...

A few weeks back, I got a call from Steve who works with Google (who has a fascinating blog btw), about coming back and working with them on some stuff. I casually asked what happened about the last thing I had worked on, when I was there last summer. I had made some extensions to the Rhino compiler, the largest part of which was adding the yield control operator to it. Steve said that they were using it. Somewhere in the back of my mind I said "What?!".

Maybe my programming has matured over the years. Maybe the ~6 hrs a day I spent in office as an intern produced production quality code. I somehow assumed that it wouldn't see any real world use. Was it really that special that it was ready for real world use? Don't get me wrong, it wasn't bad code. But it was code that only written, not "baked" for years.

Maybe there was another reason. Maybe, it wasn't a property of the code at all, but of the fact that there was something radically different about the outlooks of both these companies. There are many thing one can say about this "difference in outlook", positive and negative things things about both. But a shift that causes developers to feel effective by default as opposed to feeling ineffective by default, is an empowering thought. "If I build it for you, what will become of it?"

Maybe mine was an isolated case of wasted engineering effort and this is nitpicking. If that's so, I'll be happy for it.