Ken's Blog

I rarely comment on politics these days, but I’m really shaken up by what happened recently in Florida. A seventeen year old boy walking back home from a local candy store was shot dead by a man with a gun. The boy was unarmed. The man was not arrested for killing the boy.

The reason the man was not arrested was that he stated that he had felt threatened by the boy. It seems that under current Florida law, making such a statement is sufficient grounds to avoid being arrested for shooting, and killing, an unarmed boy or girl.

If you are reading this, and you have a son or daughter, you might take a moment to consider that there are places in the United States of America today where a stranger with a gun can legally shoot your child to death while your child is walking down the street, even right in your own neighborhood.

Until these last few days, I had not known that. I’m guessing you had not known that either.

Upon traveling to a new land, it is traditional for an explorer to plant a flag in the soil (or, on occasion, moon dust), declaring, in essence “hey folks, I got here”.

A blog entry is a bit like a flag ceremony. You find a promising place in the rich virgin soil of a new day, and you plant your flag, in the form of a post. Whatever else your post signifies, you are also saying, one way or another, “here is where I was at this moment in my life.”

I have been planting such a flag into each day for well over four years. In a sense, I have been claiming a unique place in my life for each individual 24 hour period. When I think back on any of these little flags, I am reminded of where (and who) I was just then, and what was happening in the strange and ordinary happenstance of my life. Now, as I turn around to look behind me, I see that the trail spans a surprisingly long distance, stretching clear to the horizon.

It’s all good. As Proust understood, time examined is time better than time unexamined. Even now, going back to any individual post, my mind becomes filled with a flood of associations, sense memories, sweet precious moments of pride and regret.

Sometimes it’s good just to plant a flag.

The recent generalization of the popular lit-spoof “Pride and Prejudice and Zombies” has gone broad, with such concepts as “Sense and Sensability and Sea Serpents” and “Abraham Lincoln, Vampire Hunter”. But why not go deep instead? Herewith, some humble suggestions for spinning out Austen’s beloved classic:

“Pride and Prejudice and Wendy’s”:
The imperious and disapproving ways of the handsome Mr. Fitzwilliam Darcy, manager of the local fast food emporium, infuriates Miss Elizabeth Bennet, who runs the joint’s kitchen with a spirited independent-mindedness. The personable and handsome area manager, Mr. George Wickham, alerts Miss Bennet to the possiblity that Mr. Darcy has been skimming profits. Eventually our intrepid heroine realizes that Mr. Wickham was the actual thief all along. Elizabeth and Darcy live happily ever after.

“Pride and Prejudice and Saudis”:
Elizabeth Bennet is an attractive and independent-minded oil speculator traveling through this exotic Middle East emirate while angling to close a major petroleum deal. Mr. Fitzwilliam Darcy, the handsome yet imperious European representative of major multinational corporation Pemberley Oil, at first disapproves of Miss Bennet’s maverick ways. Eventually, over long walks and tea, they achieve a meeting of the minds, and together devise a clever scheme to corner the world’s entire supply of crude oil. The dashing couple’s ingenious plan is uncovered by charming yet dastardly reporter George Wickham of the Washington Post. A major political scandal ensues, which comes to be known as Pemberleak.

“Pride and Prejudice and Falsies”:
While frequenting a hot West Village drag club, Miss Elizabeth Bennet, who maintains a preference for the fairer sex, is delighted to ascertain that a fellow patron by the name of Mr. Fitzwilliam Darcy is in reality a woman dressed as a man. They marry. Alas, Fitzwilliam (nee Fitzwilla), is devastated to discover, on their wedding night, that Miss Bennet is actually a man in drag.

Oftentimes, as I am dashing around trying to get a million things done, I find myself reducing each item on my to-do list to some convenient catch-phrase. The last few days I have caught myself running around muttering “portable fish, must finish the portable fish”.

My friend Sharon, who reads this blog, knows what this phrase means, since it is a reference to a project we are working on together. But at some point it occurred to me that anybody else listening in might just think I’ve gone off my meds. 🙂

I wonder how much of one’s inner focus becomes redacted into such catch-phrases, little mental PostIts that stand in for complete thoughts. If I hadn’t caught myself this time, I would probably never haver realized that I had stuck this particular mental PostIt up somewhere inside my head.

How many others have I got in there? And how long do they stay up after I no longer need them?

Now that I’ve talked in circles for a few days, I thought it would be nice, as a change of pace, to circle back to looking at books as visual maps.

In this next iteration of the interface, you can type in (or highlight by dragging with your mouse) whatever text you want to search for throughout the book. I’ve discovered all sorts of interesting things in the short time I’ve been playing with it.

I’m trying to build up to a more general capability, where you can search for larger patterns, or find relationships between different parts of a book.

But one step at a time.

As Barak suggested in his comment, the perceptible sound quality I was actually referring to in yesterday’s post is sound pressure (the actual pressure of a sound against the ear), rather than loudness, which is a convenient logarithmic scale of perception. Barak, thanks for pointing that out.

Sound pressure — the external phenomenon our ears can perceive — falls off as 1/distance, rather than 1/distance². Why is that?

Well, sound waves consist of regions of air that are acting against each other like little springs. Each air particle is actually spinning in a kind of circle. One dimension of this circle is how rarified or compressed the air is. The other dimension of the circle is how fast each air particle is moving.

When you clap your hands together with four times as much energy, the pressure variation becomes twice as big, and each air particle also moves twice as fast: 2 × 2 = 4. You can think of the energy as the area of this pressure/velocity circle: As particles spin around in this circle with a given frequency, the area of the circle (proportional to pressure × velocity) tells us how much energy the particle has.

By the way, how may times per second each particle spins around in its energy circle is indeed the frequency of the sound. For example, the sound from a standard A-pitch tuning fork makes the air particles spin around in their little pressure/velocity circles exactly 440 times per second.

The energy you cause by clapping your hands indeed drops off as 1/distance², but our ears can only perceive one dimension of this spinning energy — the pressure axis. The other dimension consists of velocity — how fast the air moves as it rhythmically expands and contracts. Our ears cannot perceive this velocity dimension (just as, if you get hit by a baseball, you don’t feel how fast it was going, only how hard it has hit you). The part we can perceive — the pressure variation — which varies with the diameter of the energy circle, not with its area — drops off as 1/distance.

Once you understand that all vibrational energy is actually circular motion, then a number of otherwise mysterious things start to become very simple.

For example, the other day a friend posed the following puzzler: We all know that when you make a short burst of sound (say, by clapping your hands together), the sound impulse radiates out into an ever expanding sphere — since the sound goes in all directions. Logically it would seem that the loudness of that sound, when heard from some particular distance, should drop off as 1 / distance², since the surface of the expanding sphere increases as distance², so the sound should be diffused by that much. For example, you’d think that a clap from twice as far away would sound only one fourth as loud.

But that’s not what happens. In fact, the loudness of the sound drops off only as 1 / distance. For example, a clap from twice as far away sounds half as loud.

What’s going on here? It happens this way because a sound wave is actually a kind of circular motion. I’ll explain the rest tomorrow.

In order to understand the power of Euler’s identity e^iπ + 1 = 0, you need to unlearn some pretty fundamental things you were taught in school.

We are all taught that light and sound travels in waves, that alternating current is described by sine waves, as well as tides, water waves, guitar strings, bouncing springs, pendulums and anything other kind of regular periodic movement.

The problem with this mental model is that it misses the most important thing: None of these things are best described by something moving in a sine wave. Rather, they are best described by something moving in a circle. Deep down, they are all pretty much equivalent to tying a rock to a rope and swinging it over your head in a circle.

I know this seems counterintuitive. After all, we can actually see the bob of the pendulum move left and right. The movement doesn’t look anything like a circle. The problem is that the circle isn’t visible — but even so, it is essential.

In the case of a pendulum, one axis of the circle is displacement and the other axis is speed. Any time you see periodic movement, you are actually looking at something that holds energy by spinning in a circle. Unfortunately one or more of the dimensions of that circle is often invisible to the naked eye.

Once you absorb this idea, Euler’s identity takes on much more significance. It’s the key to understanding light, sound, vibrating strings, bouncing springs, and pretty much everything that sends information around the Universe.

March 14 is Pi Day, and March 15 the infamous Ides of March. Today, March 17, is St. Patrick’s Day.

But what about the orphaned day between — March 16? It seems a shame that poor 3/16 receives no love.

I propose we create a new special day, which combines attributes of the other three days. Maybe we could call it Pi And Irish Day After Ides. Or PAI DAI (pronounced “pay day”). Because everybody likes a pay day!

We could celebrate March 16 by serving Caesar Salad and Irish Pie. It would be truly multicultural!!

One of my favorite of all mathematical statements (and many people agree with me on this) is Euler’s identity:

e^iπ + 1 = 0

 

It’s frustrating that I cannot explain to my “friends who are not into math” just why this simple statement is so extraordinary and beautiful. Basically, it opens the door to understanding why many things in the universe which at first seem complicated are actually very simple and elegant.

In my mind this statement is a kind of litmus test: Once someone gets to the point of understanding the profound idea that Euler’s identity embodies, and why that idea is so profound, simple and lovely all at once, then so much other understanding of the beauty of the universe opens up.

It would be interesting to design a fun and engaging course for “non-mathematicians” that specifically leads to this place of understanding.