Winter Is Here!

I wanted to call this post “Instant Winter” but I used that title eight years ago. Pity given that, as of yesterday morning we had no snow, and by 5 pm it looked like the picture above.

It would have been a good title.

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Fourier Geometry

Last time I opened with basic exponentiation and raised it to the idea of complex exponents (which may, or may not, have been surprising to you). I also began exploring the ubiquitous exp function, which enables the complex math needed to deal with such exponents.

The exp(x) function, which is the same as ex, appears widely throughout physics. The complex version, exp(ix), is especially common in wave-based physics (such as optics, sound, and quantum mechanics). It’s instrumental in the Fourier transform.

Which in turn is as instrumental to mathematicians and physicists as a hammer is to carpenters and pianos.

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Circular Math

Five years ago today I posted, Beautiful Math, which is about Euler’s Identity. In the first part of that post I explored why the Identity is so exquisitely beautiful (to mathematicians, anyway). In the second part, I showed that the Identity is a special case of Euler’s Formula, which relates trigonometry to the complex plane.

Since then I’ve learned how naive that post was! It wasn’t wrong, but the relationship expressed in Euler’s Formula is fundamental and ubiquitous in science and engineering. It’s particularly important in quantum physics with regard to the infamous Schrödinger equation, but it shows up in many wave-based contexts.

It all hinges on the complex unit circle and the exp(i×π×a) function.

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The First Snowfall!

We got our first snowfall of the season today. It melted immediately, but it was really pretty while the big soft flakes were pouring down.

Snow “pouring” was the topic of a small controversy once long ago…

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Rovelli: Reality Lessons

Sunday I breezed through Seven Brief Lessons On Physics (2014), by Carlo Rovelli. It’s a quick read of only 96 pages that still manages to touch on some of the key aspects of physics.

His much longer book, Reality Is Not What It Seems: The Journey to Quantum Gravity (2014), covers the same territory in greater detail (and greater length: 288 pages). After I finished what amounted to an appetizer, I tucked into the main course. I’m about 30% through it and am enjoying it quite a bit more than I have his work so far.

Both books, but especially the longer one, explore the theory of Loop Quantum Gravity (LQG), of which Rovelli is a co-founder.

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Old School Viral

Remember when “going viral” didn’t mean hospitalization and possible death? (Obviously if we go back even further to the original meaning, it did.) I had an old post go briefly and mildly viral last week. Big traffic spike with a very rapid tail-off. Most bemusing.

I’ll tell you about that, and about a spike on another post, this one weirdly seasonal — huge spike ever September for three years now. I have no idea what’s going on there. Most puzzling.

There is also a book about the friendship and conflict between Albert Einstein and Erwin Schrödinger that I thoroughly enjoyed despite it not being my typical sort of reading (I’ve never gone in much for either history or biography).

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A Better Debate

Our next VP? I sure hope so!

I thought Kamala Harris did very well last night and that the debate was a welcome return to almost normal politics (to the extent politics can ever be said to be “normal”).

In particular, she showed more signs of life than Joe Biden did, and she showed some appropriate emotions towards her opponent.

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Karma

The thing about facts is that they always win in the end.

(Must resist urge to wallow in schadenfreude…)


More Multiplying

At the beginning of the month I posted about a neat Japanese visual method for multiplying smallish numbers. Besides its sheer visual attractiveness, it’s interesting in allowing one to multiply numbers without reference to multiplication tables (which, let’s face it, typically require rote memorization).

As I mentioned last time, my interest in multiplication is linked to my interest in generating Mandelbrot plots, which is a multiplication-intensive process. But for those learning math, digging into basic multiplication has some instructive value.

With that in mind, here are some other multiplication tricks.

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Agatha Christie

Shakespeare talked about the ages of man, and it’s well known that age seems to revert us to our youth. The last handful of years that’s been true for me with regard to mystery authors. For the first time in many decades I’m reading (or rather re-reading) Dorothy L. Sayers (Lord Peter Wimsey), Rex Stout (Nero Wolfe), and others from my past.

This month I’ve been enjoying Agatha Christie and her Hercule Poirot novels. I got into them after finishing a collection of 51 short stories starring her famous Belgian detective (with his “egg-shaped head” and giant mustaches). Reading those put me in the mood to revisit the novels.

And I must say I’ve been thoroughly enjoying them!

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