### Computing the non-zero, independent components of the Riemann Tensor

The Riemann curvature tensor is a rank four tensor and it is used to describe space-time. $R_{abcd}$ has some peculiar properties i.e

i.e it is anti-symmetric in the pairs $a,b$ and $c,d$ but it is symmetric upon the interchange of the pairs $ab$ and $cd$.

which is referred to as the first Bianchi Identity.

Using the above constraint equation, assuming that $a,b,c,d$ can take values between $0$ and $n$, one can compute that the total number of non-zero and independent components of the Riemann tensor are $\frac{n^2(n^2-1)}{12}$. In (3+1) space-time, there are twenty, in (2+1) space-time dimensions, there are 6 and in (1+1) dimensions, there is only one.

Now that I have introduced what the Riemann tensor and it’s properties are, my question is how does one go about computing these independent, non-zero components i.e what are the different combinations of a,b,c,d!

for a = 0,3
for b = 0,3
for c = 0,3
for d = 0,3
if a != b
if c != d
print a,b,c,d


to get the combinations of a,b,c,d for which we get a non-zero Riemann tensor. But the problem now is that we have a lot of redundancy i.e

I am not able to figure out how to weed out the dependent components of the Riemann tensor and get only the independent ones. If you have a solution, hit me because I haven’t been able to find one online. So far…

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### 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…