12 Tone Equal Temperament

On a standard piano keyboard, one octave is divided into 7 whole tones: A, B, C, D, E, F and G. In between these tones are 5 further notes which can be called either sharps or flats: A# (Bb), C# (Db), D# (Eb), F# (Gb), G# (Ab). (whether it's a sharp of a flat doesn't really matter, the note has the same frequency, just a different name). This gives us a grand total of 12 notes in one octave. If you were to measure the frequency of a note, then measure the frequency of a note exactly one octa...

 The Meaning of "We" in Science and Mathematical Texts

I request a last indulgence from the reader. The introductory material, thus far, has been written in the friendly and confiding first person singular voice. Starting in the next paragraph, I will inhabit the first person plural for the duration of the mathematical expositions. This should not be construed as a “royal we.” It has been a construct of the community of mathematicians for centuries and it traditionally signifies two ideas: that “we” are all in consultation with each other...

 Santa Clause and God

It’s hard to even consider the possibility that Santa isn’t real. Everyone seems to believe he is. As a kid, I heard his name in songs and stories and saw him in movies with very high production values. My mom and dad seemed to believe, batted down my doubts, told me he wanted me to be good and that he always knew if I wasn’t. And what wonderful gifts I received! Except when they were crappy, which I always figured was my fault somehow. All in all, despite the multiple incredible improb...

 The Borg and Ants

"Restless aggression, territorial conquest, and genocidal annihilation ... whenever possible.... The colony is integrated as though it were in fact one organism ruled by a genome that constrains behavior as it also enables it.... The physical superorganism acts to adjust the demographic mix so as to optimize its energy economy.... The austere rules allow of no play, no art, no empathy." The Borg are among the most frightening, and intriguing, species of alien creature ever portrayed on the t...

 Herschel Compares Scientific Discovery to Columbus' Explo...

Herschel prophetically implied that electricity and electro-magnetism still hid many secrets, and that their investigation would become the leading science of the new age. This would indeed be Faraday’s coming field of triumph. He summarised (paragraph no. 376) this pursuit in the image of a great and noble sea voyage of exploration. ‘There is something in this which reminds us of the obstinate adherence of Columbus to his notion of the necessary existence of the New World; and the whole ...