Imagine that you have four people standing at the corners of a square field that measures 100 meters by 100 meters. On your command, they will all start walking in a clockwise motion toward the person in front of them. (The one who starts at the top left—the northwest—corner initially walks eastward toward the one at the top right, while the one at the top right initially walks south toward the one at the bottom right, and so on.) Each person must keep his/her eyes focused on the person they are following and must make any course corrections needed to stay lined up with their person.
If done correctly, what will each person's path look like? I'll give you a little bit of time to think about it because it's actually kinda hard. Okay, time's up. Each person's path would resemble a logarithmic spiral, which follows the formula Θ = (1/b) ln (r/a), where theta (Θ) is the angle, b and a are arbitrary positive real constants and ln means the natural log. The logarithmic spiral is also known as "Spira mirabilis" (miraculous spiral) and was so named by Jacob Bernoulli. It appears all over the place in nature, but most people would recognize it as the shape of a Nautilus shell.
Poor Jacob Bernoulli. He was part of what might have been the smartest family of all time. If you had a list of the Top 37 mathematicians of all time, at least eight would have the last name Bernoulli. Jacob was so taken by the properties of Spira mirabilis that he insisted that one of the spirals be inscribed on his headstone upon his death. Unfortunately, the guy who made the headstone inscribed an Archimedean spiral (one in which the distance between the various arcs remains constant) instead.
Can you imagine going through all eternity looking up at a headstone with a mathematical misprint on it? That would suck exponentially.
I've always joked with my kids that I want my headstone to say simply "Tom: He Never Wore Sandals." That's actually true. Never wanted to wear them as a kid; refuse to wear them as an adult. I don't want something yucky between my toes and I don't want to wear the kind with straps for fear of being mistaken for a vegetarian.
Anyway, back to the logarithmic spiral. I thought of it the other day while pondering the question of our age, that being whether the internet, with all its infinite possibilities and equally infinite shortcomings, is actually a net (no pun intended) positive or negative for our society and our world. Is your ability to file your taxes online outweighed by the fact that some jihadist a half a world away can use the net to try to convince the knucklehead kid from down the street to make a bomb?
It's an argument that's going to continue, unabated, at least until 2063, when Zefram Cochrane invents warp drive and we make First Contact with the Vulcans who just happen to be cruising past Earth in the survey ship, T'Plana Hath.
Sorry. Wishful thinking.
Back in the old days (like eight years ago), people would read newspapers and magazines. They would take in solid information gathered and then disseminated by solid professionals, meant for educated readers who actually cared about knowing things and getting stuff right. But then, as the influence of the internet became more and more pervasive, people began trading cogency for convenience. The thought process (such as it was) became "If I can read it online, why should I bother buying the paper?"
But then, as the shouters took over the net, that degenerated into, "If I can read all kinds of stupid stuff on the Internet, why bother caring about what's actually truthful?"
Which, in turn, leads to today's self-appointed pundit, who spouts, "Hey, I'm going to say something outrageous. It's loosely based on what somebody told me that they had heard from another person who might have read it online."
That's how we get the people following each other in a logarithmic spiral down into the pit of inanity. It's very discouraging.
The other day, I witnessed it firsthand. I've always known that there were online chat rooms on a variety of topics, but I had always avoided them like they were overweight Salvation Army bell ringers in front of Walgreen's. Now I know that it was wise to have done so.
The University of Arizona football team suffered a slew of injuries and then lost a couple games to good teams. The online maggot went nuts! Fire Coach Rodriguez! Change the defense! Change the offense! Change the mascot!
It's kinda scary that these people have access to electronic devices. It's as though we rounded up all the idiots in the world and put them all on one big Idiot Island. But then, social stratification set in and there emerged a subset of people who were, in relative terms, considered to be idiots by the main body of Idiots. Those are the people in some of the sports chat rooms.
On the plus side, at least they're not engaged in revenge porn, going online to post naked pictures of their ex-girlfriends. For obvious reasons.