## Sunday, April 18, 2010

### On Communicating with Aliens

Popular belief has it that whatever intelligent life from outside of our solar system that we encounter will be so far removed from us that we will be unable to communicate with them. It is often said that we will need to demonstrate our intelligence to them by showing knowledge of mathematics. Most specifically, by using universal constants such as the value of π . This bugs me a lot, firstly because mathematics is not a universal language (It’s principals may be universal, but to assume that the way in which they apply is universal is completely ignorant. If you disagree, go try to find the similarities between Mandarin and Icelandic), and secondly, because we assume that this intelligent life will also make use of 3.1415... as their magical constant to map circular geometries into linear ones.

Speaking of mathematics, I did promise many months ago that I’d have a warning when I went off about that sort of thing, but then I never made use of it. So, as promised:

WARNING: HIGH MATHEMATICAL CONTENT.
If you wish to remain socially functional, do not pay
to much attention to the technical details.

More importantly, the number π , the so called “universal constant” is starting to become extremely popular amongst the sort of people that like to think of themselves as part of the “geek” or “nerd” stereotypes. As a person who is often considered to fall into these stereotypes, I am ashamed that this number is held in such high esteem when I see π as an embarrassment.

π is essentially defined as the ratio of a circles diameter to its circumference, which is all very well. But what mathematical significance does the diameter of a circle have anyway? Well, the sad truth is, very little. I mean, a diameter makes perfect sense when you are talking about a circle, but when you get to more complicated, non-symmetric shapes, how would you define the diameter? A meaningful radius can be defined, even if it varies around the shape, but a meaningful diameter does not exist.

A far more meaningful constant to use would be 6.2831853... i.e. the ratio of the radius to the arc length of the circle. I’ll refer to this as Π . Then you’d be able to write a single equation which contains every single mathematical constant:

Which, in all honesty, makes -1 a far cooler number than π could ever be...

But I do admit... I have absolutely no dislike for pie.
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