Create Your Own Sliderule

There's a neat article in Scientific American's May issue about the history of slipsticks. You can download a template and make your own. I realized that you could make one without knowing about logs. If you take a two rulers, label the left edge '1', and then each regular tick mark with ascending powers of a number, e.g. 2, 4, 8, 16, 32, 64, you can multply the numbers just by adding lengths--a primitive slide rule. To add other numbers, you'd have to do the same with powers of 3, 5, 7, etc. and be able to shrink or expand the scales in order to reconcile where the numbers properly go. For example, 3 squared is 9, which should be greater than 2 to the 3, but less than 2 to the 4.


Graduation Adventures (now with flashbacks!)

The best moment of the whole school year was graduation. What, you say? Sitting in a black robe for three hours in the Carolina sun? That doesn’t sound like the twitchy Dave I know. Yes, let me explain.

I finally got booted off the faculty island this year, ostensibly because I only teach one class per semester, but it’s really because I’m a member of the Opus Duh society. Another story that. So I went to graduation and sat in the shade with the Economist to read during the boring bits. Wished I’d brought Scientific American too by the end of it. But my glee at not roasting in the sun like those other poor buggers did not go unnoticed by the mysterious fates that rule the universe and steal socks from the dryer.

My punishment was that I had to go to another graduation. Since I’m on the board of Krista’s school, it’s expected that I show up. Anyway, so I finds myself tonight sitting in another graduation ceremony. This one was inside, but the mysterious fates that rule the universe and cause squirrels to change their minds frequently decreed that the air conditioning should fail. I sat near the exit.

They piped in the national anthem. It took me a moment to find the flag. About the time I did, the lady behind me launched into song. It was precisely pitched, well modulated, and LOUD. I squinted against the pain, but resisted actually sticking my fingers in my ears. I steeled myself for the bombs bursting in air, but she mercifully dropped to a lower register just as my skull was about to shatter. I thought I was out of the woods. But no it was…it was …

[wavy lines indicate flashback to...]
…1980, and I was delivering drugs. For Lon’s drug store, I should hasten to add. All my other friends were delivering other kinds of drugs. The DESTINATION in Murphysboro was not high on my list of fun places to see. These were serious cases—no way they could function normally. I ran the drugs in, trying not to dwell on all the mistakes that the intelligent designer had made. But this one chick (that’s what we called girls in 1980) followed me. She couldn’t put her arms down, or wouldn’t, so she looked a bit like a T-rex ambling after me. It seriously creeped me out having a special fan, so I hastened. (This reminds me of the time I had a psycho stalker at the College, but that’s another story.) If you’ve seen The Ring, that’s her to a T. So I did the paperwork quickly, dotting the tees and crossing my eyes. Almost home free—I could see the door. Just gimme three steps toward the door. Then she SCREAMED right behind me—not a long wailing ghosty scream that might give you a goosebump or two, but a short piercing SHRIEK like a Freon bath. I quickly discovered it’s very hard to get traction when you’re three feet in the air. I remember the nurses saying in that soothing voice “no more screaming now, calm down,” but I kept right on. The horror. We buried the pants, and Lon never let me drive his truck again.

[/wavy lines]

So anyway, the bombs burst in the air but our flag was still there. I hadn’t counted on a grand finale, so it had double effect when the voice behind me rose to a high loud pitch for HOME OF THE BRAAAAAAAAAAAVE! It was like panzers coming through the Ardennes in the dead of winter. Worse, she had chosen an unfortunate note to dwell upon for her extended vocal comment on courage. It wasn’t the melody note, nor could it easily be identified as a third, fourth, or fifth interval harmony. Honestly, I think you would have to search for a culture unfamiliar with Western tradition to find such a musical scale as this. But to her credit she stuck to her guns. No sliding into an approximately correct note for this lass. She held that sucker to the bitter end. We got some stares, I tell you. People probably thought she did it to protest the situation in Tibet or Sudan or Murphysboro. I took a quick glance to make sure her arms weren’t held up to her chest.

Things calmed down after that for a while. The speaker was interesting—a state representative who told a cute story.

[cute story attributed to Jay Lucas]
Kid wants a pet, so dad weighs the options and gets a box turtle. It says on the bottom that they only live six months. But this one lives for years and becomes as much a pet as a turtle can. The kid’s now four when dad comes home to find him crying. Points at the turtle, which isn’t moving. Says his pet is dead. Dad consoles him and tells him sometimes death is cause for celebration, if it’s a life well-lived. Says the kid can invite his friends over the next day and see Mr. Turtle off into the next world in style with cake and ice cream and tales of great deeds. The kid really likes this idea, smiles for the first time, and starts listing all the friends he wants to invite. But then Mr. Turtle wakes up from his nap and starts walking around like he’s not even dead. Kid looks at turtle, looks at his dad. “Can I kill him, dad?”


One final point of note. This was an 8th grade graduation, and near the end, a young lady from the 7th grade introduced her classmates as the class of 2007. She called out the names, pausing dramatically between each. The students stood in turn. When she got to her own name, she paused, read the name, and then looked a bit bewildered. I could see why. All the other students were standing as their names were called, but she was already standing. What to do? So she hopped. Like a little bunny bounce, just to let us know who she was, then proceeded.


Real Estate Theory

I'm on a roll with these theories. See how you like this one. In Freakomics, the authors show how real estate agents' own homes tend to sell at a higher price than their clients'. They theorize that the difference may be due to the fact that the extra effort in getting a better price for one's own home nets the agent 100% of the increase, while the same deal for a client only nets 3% or so of the difference. This may not be worth the effort in time and chance expended.

That caused me to wonder today (a friend is looking to buy a house) about relative pricing of homes. Suppose a home is priced lower than market value. This would make it not only attractive to potential buyers, but also to the agents trying to sell. The reduced price won't bother them, because 3% of the reduction won't amount to much. But the fact that it'll move quickly means that they don't have to invest as much energy, and can sell more houses in less time. Therefore one would guess that these houses would be shown to potential buyers more often than average or above average-priced homes. In fact, you'd think that there would be a correlation between the relative pricing of the house and the amount of attention it gets.

This would be a great project for an undergraduate research paper. Maybe next semester.


A Theory of Wisdom

In my previous post I described the theory of theory. Now show its usefulness with an application—another theory. The central question I want to address is why do we do things that we will regret? Have you ever ate too many potato chips, drank one beer too many, or bought something that you later wished you hadn’t?

First of all, let’s rule out circumstances we couldn’t possibly control. Like if you walk out to get the mail and a stray dog attacks you. Since you didn’t choose, with full knowledge, to put yourself in that situation, it doesn’t count.

On the other hand, if you eat a whole carton of ice cream and then have a belly ache, that does qualify as what I will call a failure of wisdom. Let me define it.

Wisdom is knowing how you’ll feel afterwards.

Notice that acting on it isn’t necessarily part of the deal. You can be very wise and not act on the wisdom in this definition. If that’s not a useful definition for you then change it (see previous post).

So a wise person would fully understand that a bellyache is going to follow when the ice cream carton has been scraped clean of its last spoonful. If said glutton goes ahead anyway, we can say that he or she acted unwisely. You can be wise and act unwisely.

So we’re talking about a simple skill here—just understanding your own emotional makeup enough so that you realize before you send that flaming email to your boss, that you’ll regret it tomorrow. The positive aspect of this definition is that wisdom is then something that can be developed. In fact, I use these ideas all the time to vet courses of action. But you need a little more to actually have a useful tool.

To appreciate the role of wisdom, it needs to be distinguished from imagination. Let’s take an example.

Tatianna likes to fish. She stops by Bubba’s Big Boats one day after work and admires the sleek bass boats. She imagines herself whizzing across Lake Dioxin in search of the perfect fishin’ hole. And because this is just fantasy—she hasn’t invested anything but a bit of her time—there are no negative thoughts to intrude. In her internal movie, the boat doesn’t spring a leak, nor the engine sputter and quit. So in this state of isolation from harm, her emotions are bound to be good ones. Thus she’s likely to think positively about dropping 12 grand on a boat.

Notice the role imagination plays. What wisdom does is add to the picture a truer sense of the emotions we feel after making the decision. Although Tatianna can’t force her mind to alter its emotions, she can analytically think about them. I guess you could call wisdom a kind of emotional imagination. I’ve done no testing whatsoever, but I imagine some people are better at it than others.

So if Tatianna takes a moment and searches her memory for other times she’s spent a big chunk of money, and remembers how that felt. Or perhaps remembers what it’s like to own a boat. These bits of information are important to distinguish between the NOW emotional setting and the AFTERWARDS one.

If you apply this technique consciously, you may be able to avoid doing something unwise. It’s saved me countless times. I guess I should be embarrassed to admit that—I’m not quite sure. Anyway, that’s the theory. It might be useful to you or it might not. I don’t claim that it says anything at all about the objective universe (if there is one).

One last note. A wise person can be helpful to someone else, under this definition, by helping the other understand his or her own afterwards-emotions. This is something that parents can do for their kids, for example.

My Theory of Theory

I’m teaching a half-day class in June to a group of teachers as part of a character academy. I’ve set up their tech for a few years (DVD, LCD, etc.), but this is the first year I’ve proposed to teach a class. I picked game theory as the topic. In case you don’t know, that’s a mathematical theory of conflict and cooperation. It has applications in economics or any other subject involving decision-making.

I figure that my first problem is to briefly describe what a ‘theory’ is in a non-threatening way. I have my own way of thinking about it that probably isn’t standard, but should be useful in this situation. Namely, a theory is a set of ideas. A good theory is one that you find useful.

This simple definition isn’t what you’ll find in the dictionary, and for good reason. Its implications would be controversial to most scientists, I suspect. But it’s good for putting people at ease. A theory is just a tool that you can pick up, look at, try out, and if it’s useful put in your toolbox. There’s no obligation to believe the truth of the theory. That is, a theory is not an empirical statement about the world—it’s a statement about ideas.

Using this definition, you could perhaps generate discussion between people who are different sides of the evolution battle. A believer in a literal genesis story can call that his theory and a biologist can call Darwinism her theory. The former is useful to the believer by providing some emotional comfort (I imagine), and the latter useful to the biologist because she can understand why antibiotics weaken over time. So rather than the fundamentalist trying to disprove or supplant Darwin, he can simply declare it not useful to him as a theory (so it’s not a good theory for him).

The problem some would have with this is that the worth of a theory is relative. But isn’t that the case anyway. I’m sure the standard model of quantum mechanics is a great theory for those in the field. But the equations don’t mean that much to me, despite trying to read Penrose’s new book, so it’s not a good theory for me. On the other hand, my theory of theory, which you’re reading, has been very useful to me, so it’s a good theory (for me).


A Squared Plus B Squared is Half a Million

It was an odd phone call. I was told by our VP for advancement (i.e. the guy who raises money) to call a certain Dr. Moyd regarding a math problem. A few hours later I was at the good surgeon's country estate looking at a swath of ugly mud and stumps that ran through his woods. He explained that the power company had asked for permission to put a natural gas line through his property, which he had granted. But they had come back with a request to run a high voltage transmission line--towers and all--straight through his favorite woods. A clear case of "no good deed goes unpunished." He declined their offer.

The power company claimed eminent domain and put in the line anyway. To add insult to injury, they had (he suspected) cut far more trees than they actually needed to. My job was to verify this using none other than the Pythagorean Theorem, and do so in a court of law. I suggested that perhaps a civil engineer would probably know more about trees than I did, but Dr. Moyd assured me that he already had that covered. He just wanted to nail down that one fact for the jury--as asserted by a genuine math PhD--that right triangles still worked the way they ought to.

He showed me the model he had built. It had cute little transmission towers, about 10 inches tall, and "wires" hanging from them. For a while we discussed the details of the problem, and in particular the arc that the wires make when they sag. This is known as a catenery, although it looks like a parabola. It would be absurd to bring such details into any discussion of pine tree heights and electrical lines, though. We conference-called his lawyer. I agreed to do what I could to reinforce the perception of Euclidean geometry on the jury.

A few months later I gave Dr. Moyd a call. I hadn’t heard from him, and assumed he’d given up. No, he assured me—it was still a go. But he didn’t call, and I forgot about it. Until yesterday when I saw the Hartsville paper.

Hartsville physician wins $540,000 verdict against Progress Energy
DARLINGTON — Dr. Pickens Moyd said he hopes a jury’s decision against Progress Energy in a condemnation case involving his family-owned farm sends a message to small landowners around the state to stand up for their rights and for what is fair.
[link to article]

I reckon it's time to present my consulting fee, seeing as how effective I was!


Faster pdf Downloads

If you're tired of waiting for Adobe Acrobat to load up when you click on a .pdf link (I used to actually cringe), head over to www.foxitsoftware.com and get their reader. It's free and a whole lot faster.

Time Trouble

There's a great article in the May 6 Science news called To Leap or Not to Leap, which is about the problems in keeping clocks lined up with the Earth's rotation. Because of friction, the big blue ball is slowing down, but because of the melting icecaps it's also speeding up. It's therefore hard to predict how long a day will be in a few months. The really interesting part to me, though, is that the most precise clocks will soon be so good that they will have to take into account the gravitational field they're in very precisely. The altitude needs to be known within a few centimeters, and the tides could throw the clock off a tiny amount. That means that it will be very difficult to synchronize these to within their precision.

Gravity affects time because of the general theory of relativity. I recommend Lewis Carol Epstein's book for a very readable introduction.