### Calculating the value of \pi

As part of a course on computational physics, one of the questions that might appear on our final paper is regarding the estimation of \pi using monte carlo methods. It was puzzling when I read this question at first.

The method is pretty straight forward. Take a square of side 'a' in which we inscribe a quadrant of a circle of the same radius 'a'. The ratio of the area of the quadrant to that of the square is \pi/4. Now, if we choose a point at random within the square, the probability of that point lying within the quadrant of the circle is equal to the ratio of the areas which is \pi/4.

Looking at this problem computationally now, let's discretize the square into unitary squares, denoted by the x,y coordinates of their center. Now, let's choose x and y values within the square i.e < 'a'. If the value x**2 + y**2 is less than or equal to the value of 'a' i.e it lies within the circle, we raise the value of a counter . If it doesn't, well drat! We keep track of the total number of such iterations. The ratio of the value of the counter to that of the number of iterations is now the value of \pi.

If one tries implementing this code, it will become obvious that the larger the value of 'a' within which we x and y, the better the estimate of \pi is. Or the larger the number of values x and y can be chosen from, the better our estimates. This is inherent to the fact that we are sampling the space within the quadrant or the square better. I'm speculating here since I haven't read up enough about this but I think the reason the error decreases because the ratio of the number of unit squares that lie exactly at a distance of 'a' reduces in comparison to the total number of unit squares in the square! These unit squares that lie at a distance of 'a' are the problem as part of their area lies within the quadrant and part lies outside! I will implement this and get back to you regarding how fast the value converges to \pi, the error and it's dependence on the value of 'a' and how the estimate grows towards the value of \pi over the course of multiple iterations. Hint : the initial estimate of \pi will either be zero or 4.

### Animation using GNUPlot

Animation using GNUPlotI've been trying to create an animation depicting a quasar spectrum moving across the 5 SDSS pass bands with respect to redshift. It is important to visualise what emission lines are moving in and out of bands to be able to understand the color-redshift plots and the changes in it.
I've tried doing this using the animate function in matplotlib, python but i wasn't able to make it work - meaning i worked on it for a couple of days and then i gave up, not having found solutions for my problems on the internet.
And then i came across this site, where the gunn-peterson trough and the lyman alpha forest have been depicted - in a beautiful manner. And this got me interested in using js and d3 to do the animations and make it dynamic - using sliders etc.
In the meanwhile, i thought i'd look up and see if there was a way to create animations in gnuplot and whoopdedoo, what do i find but nirvana!

In the image, you see 5 static curves and one dynam…

### on MOOCs.

For those of you who don't know, MOOC stands for Massively Open Online Course.

The internet is an awesome thing. It's making education free for all. Well, mostly free. But it's surprising at the width and depth of courses being offered online. And it looks like they are also having an impact on students, especially those from universities that are not top ranked. Students in all parts of the world can now get a first class education experience, thanks to courses offered by Stanford, MIT, Caltech, etc.

I'm talking about MOOCs because one of my new year resolutions is to take online courses, atleast 2 per semester (6 months). And I've chosen the following two courses on edX - Analyzing Big Data with Microsoft R Server and Data Science Essentials for now. I looked at courses on Coursera but I couldn't find any which was worthy and free. There are a lot more MOOC providers out there but let's start here. And I feel like the two courses are relevant to where I …

### On programmers.

I just watched this brilliant keynote today. It's a commentary on Programmers and the software development industry/ecosystem as a whole.

I am not going to give you a tl;dr version of the talk because it is a talk that I believe everyone should watch, that everyone should learn from. Instead, I am going to give my own parallel-ish views on programmers and programming.
As pointed out in the talk, there are mythical creatures in the software development industry who are revered as gods. Guido Van Rossum, the creator of Python, was given the title Benevolent Dictator For Life (BDFL). People flock around the creators of popular languages or libraries. They are god-like to most programmers and are treated like gods. By which, I mean to say, we assume they don't have flaws. That they are infallible. That they are perfect.
And alongside this belief in the infallibility of these Gods, we believe that they were born programmers. That programming is something that people are born wit…