Fully homomorphic data encryption

May 28, 2010

In this day and age of free-flowing information everywhere, cryptography is a very hot topic. There has always been demand for better ways of encoding sensitive messages, but it is only really since the advent of the internet that this has taken on great importance in everyday life. Now that it looks likely computing will be increasingly outsourced to “cloud servers” in the future, a whole new form of encryption is necessary, and recent advances which have been made in the subject look set to make this kind of internet-based computing possible.

Phi

May 15, 2010

One problem mathematicians constantly struggle with is that there are just not enough letters in the world: we long ago exhausted the entire Roman and Greek alphabets (and even some of the Hebrew one), and as a result many letters are used in a bewildering number of different contexts. Well, I will straight away put your troubled minds to rest by stating that, continuing my occasional series on important mathematical constants (am I allowed to call two posts a series?), when I say “phi”($\phi$) I mean the number$\phi ,$otherwise known as the Golden Ratio, or the Divine Proportion. But first, here are some numbers:

$1,1,2,3,5,8,13,21,34,55,89,144,...$

This is the Fibonacci sequence, and it pops up all over the place.  It is generated by a very simple rule, which I won’t reveal in case you haven’t seen it before (try to work it out).  Now, before I start enthusing about the prevalence of the Fibonacci sequence and the golden ratio in nature, first a disclaimer: one problem with looking for appearances of these sort of things is that people can end up getting a bit obsessed and start seeing them everywhere.  I don’t doubt that some of the claims are little more than a mixture of conspiracy theory, coincidence and approximation; and I have tried to filter out the more wacky theories.  Some things are clearly more than coincidence though!

A Serious Man, and A Beautiful Mind

May 6, 2010

You may have noticed that I am not exactly diligent about referencing the pictures and diagrams  I use on this blog.  In fact the majority of them come from google images, and I usually have no idea where they were originally used (one of the good things about writing a blog is the lack of academic rigour required).  However, last night I saw a Coen brothers film called “A Serious Man”, and am pleased to be able to reveal that the header above is actually a screenshot from that film.

As you might guess from the picture, the film itself is not really all that serious, and how Larry Gopnik – the physics professor depicted –  managed to write on a board that size is left to the viewer to ponder.  Larry’s brother Arthur is also a mathematician, although a rather less functional one.  He is quite a strange man , and spends most of the film lying on the couch writing what he calls his “Mentaculus”, which is supposed to be a “probability map of the universe”.  This may or may not be a serious endeavour; we are only given a brief glimpse at its contents, and it appears to be no more than a collection of very intricate doodles.

The Mentaculus

Writing a probability map of the universe is a noble but rather misguided aim; the notion itself doesn’t really make sense, and it would clearly be impossible to pull off.  But the urge to explain the workings of the world around us is a major drive for mathematicians.  Unfortunately, the real world is messy and chaotic, and there is very little that we can do to accurately describe how things work in practice outside of rough models.