The author of the blog post raised a few points that I thought were interesting and that I'll provide my own answers to here. Feel free to comment if you disagree with me.
> Why would anyone prefer Python, given that there is a much faster, free alternative in Julia, which is just as easy a language to program in?
I've used Julia a bit and the lack of libraries was frustrating. It is getting better now, but you'll still have to write a lot of stuff from scratch if you decide to use it.
> What justification is there for preferring R to Matlab, other than cost?
R makes it very easy to perform exploratory analysis on a dataset. Matlab might be similar, but I don't have experience with it.
> Why does anyone bother with Java? If speed is the critical issue, there are faster alternatives. If you like the relative simplicity of the syntax, Julia is cleaner, simpler and just as fast in execution.
I agree with this. I've never enjoyed programming in Java, but some people seem to like the large number of libraries available.
My impression is that the primary problem domains for these two are pretty different.
Matlab is pretty heavily targeted at folks doing numerical analysis [1], e.g. solving differential equations related to physics/engineering/economics, and has its origins as a wrapper around existing fortran implementations for numerical linear algebra. Engineers, especially, use Matlab all over the place.
The R project explicitly is interested with statistics [2], and as someone earlier pointed out, make is pretty easy to do analysis on a dataset. Though, I have pretty limited experience with R, so I could be mistaken.
[1] Cleve Moler. Numerical Computing with MATLAB. http://www.mathworks.com/moler/chapters.html This is the guy who wrote the first Matlab implementations, and founded Mathworks.
[2] The R Project for Statistical Computing. http://www.r-project.org/
Python also has a much more mature ecosystem (read: more pre-written libraries to do what you want to do), and delivers some of the UI benefits of Mathematica if you take into account ipython notebooks and packages like Bokeh.