My research area is computational astrophysics. This means I use computers to analyze astronomical data or model astrophysical systems. Most of my work is done through an application known as Mathematica, which is a powerful computational program. Like any application, Mathematica has advantages and disadvantages, but it has one property that is absolutely essential: it is Turing complete.
Cosmic Pi
Today is March 14, which many celebrate as Pi Day since the month and day mark 3.14, which is approximately pi.It is also Albert Einstein’s birthday, so it seems fitting to ask whether π can exist in a universe as Einstein described it. Just for fun, I’m going to outline why the answer is no.
Numbers Game
There’s a popular video from Numberphile that shows how the sum of all the integers, adding them up forever is -1/12. If that ties your brain in a knot, it should. How is it possible for 1 + 2 + 3 + … to be a negative number? The answer is that it’s not…quite. It’s not that the video is …
Logs of Nature
We generally think of numbers as a linear progression from 1 to 2 to 3, etc. We also tend to measure things around us on a linear scale. A ten hour road trip, for example, is very different from a one hour trip. In the sciences, however, it is often more useful to look at things on a logarithmic scale.
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