And congrats to the First Dogs (elect), Very Good Boys Champ and Major.
How great to have four-legged furry friends back in the White House! (I’ve long thought a love of dogs and a good character are correlated. Guess which POTUS hates dogs.)
Stay with dogs, my friends! Go forth and spread beauty and light.
Fell asleep reading a Nero Wolfe novel and woke up to a new world. Pennsylvania and Nevada called, Arizona still breaking for Biden/Harris…
Pretty nice thing to wake up to!
Well, we kinda knew this was going to happen, but it’s still a pretty damn dark day for Our Democracy.
There seems reason for optimism, but in these crazy times, who knows how this all shakes out.
It’s official: Based on available data, the resolution to the Fermi Paradox is simply that intelligent life does not exist in the universe at this time.
Life that thinks it’s intelligent does, though. But based on our observations, it has a long way to go. The universe can relax; Earthlings aren’t likely to be a problem to anyone but themselves.
Well, here we go on Mr. Toad’s Wild Ride. I’ve said it many times: That this is even a contest says a great deal about the changes in our society in the last score or two of years. I think it’s tragic, but obviously (yet astonishingly) mileage varies.
Funny how so many of us already have. My vote’s been in for weeks.
Last week I read a science fiction novel I’d seen in a number of “must read” lists: The Long Way to a Small, Angry Planet (2014), by Becky Chambers. The title certainly appealed to me, and, along with the book’s cover, it seemed like it might be fun, funny, or even zany.
I like to let things unfold, so I usually avoid trailers and reviews until after I’ve seen or read for myself. A few months ago I wrote about Axiom’s End, which I really liked. I was anticipating a similar ‘great new author’ experience. (I’ve also mentioned the S.L. Huang Cas Russell books. I kinda liked those, too, so I’m definitely feeling favorable towards new authors.)
Unfortunately, I didn’t like this book at all.
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.
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.
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.
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…