Continuous as the stars

No computer stuff today. Martin Gardner – writer, skeptic, recreational mathematician – died recently. As a teenager I would scour the back room of Casablanca Books looking for back issues of Scientific American for interesting Mathematical Recreation columns. Martin Gardner was one of the people whose work got me interested in mathematics, science and computing,…


Absence of evidence is not evidence of absence

Today, two more subtly incorrect myths about C#. As you probably know, C# requires all local variables to be explicitly assigned before they are read, but assumes that all class instance field variables are initially assigned to default values. An explanation of why that is that I sometimes hear is “the compiler can easily prove…


What are the horns for?

(Technology of a different sort today, just for a change of pace.) The first time I saw a picture of the Falkirk Wheel — the world’s only rotating boat lift, in Scotland — I thought that it must be a really nice computer-generated landscape. It looks like something you’d see in Halo. But it’s real;…


Talking About The Weather, Part Two

What we’re missing is a phenomenon that probably was described correctly by your high school science teacher, namely, the phenomenon of “latent heat” (which is what I was taught, though “enthalpy” would be the more modern term.)  I said that the temperature of a substance is the average amount of energy in it. I lied;…


Talking About The Weather, Part One

No technology today; just talking about the weather. I love talking about the weather. I mentioned the other day that I had just returned from my ancestral homeland on the shores of Lake Huron, the great inland sea of southwestern Ontario. We got some rip-roaring thunderstorms this year. I love thunderstorms on the lake. They…


Through the Looking Glass

I’m back, I’m married, we had a fabulous time, and now I’m setting up new machines and figuring out what the heck I’m doing on the C# team. Today, we’ll get back into it with some non-tech fun. A regular flat mirror seems like it ought to be perfectly symmetrical in its operations. So why…


Desafinado, Part Five: Getting Down Without Hitting The Bottom

Back in the 1960’s a guy named Shepard published a paper which described a way to create a descending scale of twelve notes such that every consecutive pair was perceived as being two notes, the second one lower than the first. That’s not hard — every descending scale has that property! The kicker is that…


Desafinado, Part Four: Rolling Your Own WAV Files

We’ve established why every just about piano in the world — in fact, every concert-pitched musical instrument in the world — is slightly out of tune. No one actually plays perfect fifths; every fifth interval is slightly flat. Why don’t we hear the difference? Is the difference even perceptible? It is very hard to hear…


Desafinado, Part Three: Too Many Fifths

Last time we established the diatonic scale which has the nice property that there are five tone intervals and six fifths: Note Frequency A 220.000 B 247.500 C 260.741 D 293.333 E 330.000 F 347.654 G 391.111 and then double for the next octave up and so on. But it’s a little weird in that…


Desafinado, Part Two: A Perfect Pythagorean Tuning

Last time we talked about the Pythagorean’s discovery that sounds with vibrations in the ratios 1:2 and 2:3 sound consonant to the human ear. Let’s explore the consequences of that a bit. Suppose we’re building a stringed instrument from scratch and we want to tune it so that it sounds good to human ears.  Let’s…