Category Archives: Wobble

Feline Amplifier

A tiny motion induced in a cat’s epidermis, or an even smaller vibration induced in its eardrum, will produce a reflexive reaction in the cat’s nervous system and that in turn will be amplified into muscular contractions involving a quantity of energy several orders of magnitude larger than the energy of the input. The reaction manifests every time the stimulus impinges on a living cat. The magnitude of any single reaction is the result of an unknown function ranging from barely perceptible up to the maximum muscular exertion threshold of the cat. An effective amplifier would be rated according to the accuracy of the system, measured by the span of time required to achieve certainty of the correctness of any output for a given input, and the simplicity of the system, measured by the number of cats involved.

War on Terror: Cult?

The nation must defend itself from threats foreign and domestic and I’m very glad that my country, not any other one, has the most powerful military forces on the planet. This article carries the hope of our continued prosperity as a great nation.

(The title is inflammatory hyperbole. In writing it, I borrowed the style of Fox News so you will believe me when I say I’m fair and balanced. To keep with proper form, much of this article will be composed of irrelevant and misleading statements. It is my hope that you will be capable of distilling something worthwhile from the morass—good practice for when I’m not around and you have to watch Fox News.)

I am writing because in response to two Rolling Stone articles (The Fear Factory and Truth or Terrorism? The Real Story Behind Five Years of High Alerts) my discontent congealed into a desire for new movement of conscientious objection.

Starting movements is not my thing, so I’ll just scatter some ideas here and leave it to more zealous people to organize and undertake. Indeed, it is too late to found such a revolution in this country. The movement is already under way. Even so, let’s set about dissecting it so as to better understand it.

In order to start a movement, one must first locate a controversy and then inspire others to lend support to the weaker side. It wouldn’t be a movement if its efforts merely reinforced the status quo.

For the sake of academic exploration let us take as a controversy the War on Terror—the term itself should elicit an unpleasant emotional reaction—with the weaker side held by the people who want to stop it. Let’s be very clear and establish that nobody believes the United States should stop defending itself. This is an academic exercise.

There are three parties in this controversy and you should evaluate your own position in one of them. They are the leaders, the followers, and the opponents.

The leaders are few and difficult to pinpoint. They include politicians, financiers, and military advisers and strategists, though some of the people in such positions are opponents.

The followers are the largest of the three parties and only by the power they lend to the leaders does the War on Terror march on. They include all levels of military personnel, government representatives, corporations in the defense and security sectors, mainstream media outlets, right down to the American voters who elect pro-War politicians.

The leaders being so well distributed and the followers being so many are the reasons assassinations don’t happen in this country. You can effect unimaginable change by killing a great mind but when the juggernaut is steered by hands so hidden and pushed by devotees so numerous and the great minds are nowhere to be found…

The opponents are the weakest group not because their premise is weak—they alone base their effort in truth and not lies—but because the majority of Americans do not demonstrate their full intelligence when confronted with pictures of violence.

To argue for continuation of the War on Terror by saying that we must be ever-vigilant, that to disagree is unpatriotic, etc., is to misunderstand the controversy. Those who wish to stop it are not mujahideen trying to subvert our government. They are trying to wrest our government from the control of American politicians who they believe have taken it hostage, to put an end to needless spending and killing and dying, and to restore American civil rights.

The undecided and the inactive always fall in the second camp because inactive parts contribute to the momentum of the whole. If you could ask Isaac Newton or Albert Einstein they would agree with me: an object in motion tends to stay in motion unless acted upon.

Opponents gain support by taking followers away from the established leaders, converting the leaders, or removing them from power. In a peaceful movement, this would be done by working within the system according to its own rules. I do not think the situation is bad enough to justify a military coup or a civil war. Let’s hope it never is.

Naturally a movement should spend a portion of its effort on weakening the bastion of the status quo which it opposes. However, whereas it is simple to consider members of the establishment as objects to be destroyed, the opposition would be most wise to see each one as an undernourished opposer and only provide the sustenance needed to effect a recovery.

Each type of follower is best converted in a different way and each tactic could be the subject of many books. The main ones are: swing the undecided by handing them the truth; spur the inactive by showing them the evil their inaction condones; split the followers from their leaders by shedding light on the differences between them.

An effective revolution, even a peaceful one, must: depose the leadership with the democratic support of the newly enlightened majority; deal graciously with the ousted villains; resist corruption just long enough to be remembered as a hero; retire and let the next administration pervert reality to favor their hijacking of the public mind, thus beginning the cycle again.

And now the part you’ll wish you hadn’t read, the scene where the gleaming trestle set to underlie the majestic railroad across the divide to universal liberty explodes into slivers with a blinding flash, the unbelievable news that the captain will not be going down with the ship as planned, final hope succumbing, once again provided by Rolling Stone: Kurt Vonnegut Says This Is The End Of The World.

There, I wrote it. It’s nothing like what I had in mind when I started—originally it involved retraining and mobilizing young Scientology protesters against their local reservists—but hopefully it can help me remember what I was supposed to buy at the hardware store.

Politics Zero

Politics always made me tune out. From my earliest memories of adult conversations at table, the pattern that emerges is a series of blanks. My parents and their friends spoke of far-away things and none of it had any bearing on my small world. Could I please be excused to play outside?

Later I made a stab at formulating political opinions of my own. Having paid so little attention to any issues larger than my own small world, all I could do was restate what I’d read or heard. Analysis hadn’t begun for me yet and so I forwarded hearsay to fill the vacuum with beliefs I pretended were my own.

Inevitably there is talk of politics. Digging around for something to add to the conversation, all that appeared had already been said. In my better moments, I remembered that it was wise to remain silent rather than advance an opinion that I could neither justify nor defend.

Very recently I struck something solid: I actually believe something! I’ll write about what it is when I have a clearer idea of it.

[Update: I don’t believe in anything after all.]

Carry the one

I’ve been nibbling through Douglas R. Hofstadter’s Pulitzer Prize-winning book, Gödel, Escher, Bach. In Chapter XVII he mentions the mathematician Srinivasa Ramanujan (1887-1920) who had a talent for extremely fast mathematical analysis. This class of mind (including so-called idiot savants) he called lightning calculators. In this passage he discusses the unlikelihood that such minds have access to resources or processes outside of general recursive functions:

One could probably make a nice plot showing how the time taken by a lightning calculator varies with the size of the numbers involved, and the operations involved, and from it deduce some features of the algorithms employed.

This got me thinking about my own mathematical algorithms. By that term I mean the series of atomic steps taken to produce a result such as the sum 14 + 38 = 52 or the quotient 39 ÷ 3 = 13.

I vaguely remember being taught to add two-digit numbers in grade school. The process begins with the numbers stacked so that the ones and tens places are vertically aligned. A horizontal line is drawn to separate the stack from the result below. Starting with the right-most column, we sum each column and place the result below the stack. If the result is two digits, place the “ones” numeral below the current column and the “tens” numeral above the next colmn to the left. (“Carry the one.”) Here is the final product, showing the work done:

  1   ← carry the one
  14
+ 38
  52

That is the most basic algorithm in my mathematical toolbox. You probably have a similar algorithm that you use to add a column of numbers. Maybe you visualize the stack and proceed consciously through the steps or perhaps you have trained your mind to produce mathematical results at a subconscious level. Hofstadter’s point was that everyone’s result must be produced, at some level, by a series of simple steps he called a general recursive function (Church-Turing Thesis).

Reading about this, I realized that my own addition algorithm proceeds not from right to left but from left to right. Whereas the standard method begins with the least significant digits, my method begins with the most significant digits. (Lets leave the Freudian isomorphisms out of this discussion, interesting though they may be.) Here is the way I add numbers:

Stack the numbers as before. Sum the left-most column and write the result below. (Begin loop.) Sum the next column and if it exceeds one digit, increment the previous result and append the new result. (End loop.)

I wonder whether my algorithm can produce results with fewer operations on average. I guess that if the likelihood of column sums exceeding one digit is less than a certain threshold, my method will be faster (completing in fewer operations). Perhaps one method is easier for minds having a specific learning preference, i.e. visual or auditory or tactile.

Here’s homework for the curious: write a program that compares these algorithms in terms of number of operations to sum every possible set of two, three, and four numbers having two, three, and four digits. If my method is faster for some class of sums, such as those having an instantly recognizable feature like a low occurrence of digits greater than five, would the extra steps of recognizing such a class and selecting the most appropriate algorithm improve the overall speed of doing sums?

My hope is that somebody can produce objective proof that my summing algorithm is not always slower than the right-to-left method taught to me in school. If not, I might be afflicted with mathematics disorder—an actual diagnosis in the DSM-IV. Pfizer?