The observable universe

[I suggest reading my earlier post, The Big Bang, before this one.] The observable universe (OU) is the part of the universe that we can, at least in principle, observe, from a designated vantage point at a given place and time. This post is my attempt to figure out in more detail exactly what the OU……

A puzzle about a Fibonacci-like sequence

I’m thinking of a mathematical sequence, $latex S$, whose terms are all nonnegative real numbers. It is infinite in both directions. Like the Fibonacci sequence, it satisfies the relation: $latex \displaystyle S_n=S_{n-1}+S_{n-2}$ And we are given: $latex \displaystyle S_0=1$ What is the value of $latex S_1$? Surprisingly, you have enough information to figure it out. Note……

The Big Bang

In cosmology, the term the Big Bang has several subtly different meanings. It means the moment in time, it means the “explosion” event, and it means the all the events and states of the early universe. How early is early? Could be lots of things. Maybe just the first fraction of a second, maybe the……

Preview images in old CorelDRAW files

CorelDRAW is a popular vector graphics program. Its native .CDR file format has gone through many different versions. I want to focus on the files written by CorelDRAW version 2. These are the .CDR files that begin with “WLl” or “WLm”. Even though it dates from 1989 or so, and has been obsolete for most……

Bismuth became radioactive in 2003

I know this is nitpicking, but the definition of a “stable” vs. a “radioactive” isotope seems a little silly to me. The usual definition of a stable nuclide (or isotope) is one that humans have not observed to decay. A radioactive nuclide is one that humans have observed to decay. A stable element is one……

Hill Spheres and apparent radii

Suppose you are a passenger in a spaceship, you look outside, and you notice that, from your vantage point, the Sun and the Earth appear to be almost exactly the same size. Question: Is it possible that you are currently in orbit around the Earth? Suppose instead that it’s the Earth and Moon that appear the……

Comments in WMF files

Windows Metafile (WMF) is a vector graphics format native to Microsoft Windows 3.x. It was succeeded by Enhanced Metafile (EMF) in 32-bit versions of Windows, but it seems to have remained in use, alongside EMF, long after Windows 3.x became obsolete. It was often embedded inside other file formats, such as PowerPoint (.ppt) or Write……