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……

The Balls and Urns Paradox

Start with an empty urn having an unlimited capacity, and a infinite number of balls, labeled “1”, “2”, “3”, etc. At time T minus 1 second, put balls #1-10 into the urn, then take ball #1 out. At time T minus 1/2 second, put balls #11-20 into the urn, then take ball #2 out. At……

Chess and drawing by threefold repetition

Chess is an ancient game with simple rules, so you might think the official written rules would have evolved to be very clear and concise, and to unambiguously cover all corner cases (at least as to which moves are legal, and how the outcome of the game is determined). But I’m not so sure. I’ll……

The finer points of TIFF “ASCII” fields

This post concerns the TIFF image file format, and some related formats: Exif, DNG, and JPEG XR. A TIFF file contains a set of “fields”, each of which contains some sort of data element. Each field has a “tag”: a code number that tells, logically, what is stored in the field. For example, tag #256……

The oldest living former X

Sometimes we can’t have nice things, just because the nice thing is difficult to state clearly in words. For example, the record low daily high temperature for this date is arguably just as meaningful as the record high daily high. But the weatherman never tells us the record low high, probably because it would confuse……

My list of frequently misspelled words

I’ve read a number of lists of frequently misspelled words, and I always end up thinking “Really? That doesn’t match my experience at all. If your methodology says that supersede is misspelled more often than its, then I think you need a new methodology.” Of course, context matters. Professional writers misspell different words than internet……