Author: Menzonius

I am a huge fan of , which is a document preparation system. While it does have a steep learning curve, it has a number of advantages over word processors, one of which is typesetting of mathematical symbols. And now this feature is also available for blog people such as myself, thanks to a delightful plugin called ‘WP QuickLaTeX’.

I would like to illustrate its use by demonstrating the solution to a puzzle I encountered recently. The puzzle is stated as follows:

 “Four years ago, Jane was twice as old as Sam. Four years on from now, Sam will be 3/4 of Jane’s age. How old is Jane now?”

The key to its solution is to recognize that it’s a linear algebraic problem involving a set of simple linear equations. Let Jane’s age be equal to and let Sam’s age be equal to . Now the sentence can be rephrased as follows:

“Four years ago, . Four years from now on, . What is the value of now?”

Now we are getting somewhere. But these equations are still incomplete, because they do not yet take into account that the statements are only true four years in the past or four years into the future. So let’s travel in time by adding or subtracting 4 from and in the equations.

(1)  

That’s better. We are almost there now. But first the equations must be put into standard form, i.e. . Like this:

(2)  

Now finding the solution by elimination of variables is the most straightforward way to proceed, although the row reduction method would also work just as wel. We simply multiply one of the equations by some scalar such that the variable we are not interested in () cancels out and we are left with an equation with only the unknown variable for which we want to find a solution (). You could for example multiply by to obtain the form . And now we can eliminate the variable, like so:

(3)  

Finally, we are left with an equation that is trivial to solve: , thus and we are left with the conclusion that Jane must be twelve years old.

I don’t know if I will use this plugin more often, but it’s nice to know it’s there should I need it ;).

It is my observation that most of the movies that have come out in recent years tend to be classifiable in one of the following two categories. On the one hand there are movies that rely entirely on computer-generated special effects to captivate their audiences, whilst on the other hand there are movies that don’t use CGI effects at all and instead rely on a decent performance from the actors who play in it. It is unfortunately rare to find a movie in which good acting is combined with spectacular CGI effects. And perhaps it is just as rare to find a movie in which both convincing CGI and good acting are entirely absent, which I think is just as well.

But if for some reason you happen to be looking for an example of this latter sort, then ‘Seeking a friend for the end of the world’ will certainly not disappoint! For this movie contains neither the grand computer-generated special effects you might expect from a movie based around the imminent extinction of mankind by the pending collision of an asteroid with earth, nor any of the good acting that usually compensates a more limited production budget

This is a thoroughly boring movie. Unsurprisingly, the trailer for the movie turned out to already have all the funny parts in it, so I would suggest saving yourself a lot of time by watching that instead.

P.S.
I really enjoyed the outdoor theater in Greece where I watched this movie, you can find its location on the map below ;).

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