Institute of Semantic Restructuring

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Brief Therapy with Achilles

What is Semantic Restructuring? The best way I can answer that right now is with a story.

Once upon a time I was wandering the hills of legend and myth, when I chanced across this huge man, rippling muscles, ancient armor, fearsome sword, crying. Bawling like a baby. His name was Achilles, and he was depressed because he couldn't catch a tortoise.

Seems friend Achilles had been more or less minding his own business, thinking about what ever it is that mythic heroes think about, when this chap from Elea came by and broke the terrible news. No, not that Achilles would die of an arrow to the heel from the bow of Paris. No, our hero was distraught over the bad news, according to this Zeno fellow, that Achilles had no chance to catch the tortoise that Zeno had set on the path a short time earlier. Even though the tortoise had only covered ten meters in the time that elapsed between being set on the path and the time Zeno told Achilles the bad news, Zeno assured Achilles that he didn't have a chance.

"I know; you're fast, you're strong, you're young," said Zeno, "but logic will show you have no chance. Surely a mighty warrior such as yourself has had training in the finer points of logic and mathematics, haven't you?"

"Of course I have," said stout Achilles.

"Then let us consider the facts and apply the might of logic to them. During the time you are moving to catch up to the creature, it will also have been moving, yes?"

"Of course," replied the warrior, "but not very much, not even one meter to my ten. Why, you should see me do the 100 meter dash; you'd know how foolish your claims are!"

"We'll see about that soon enough," said Zeno, "because no matter how fast you travel, if it takes any time at all --- you don't teleport or travel instantaneously, by the way, do you lad?"

"Don't try my patience. Of course I can do neither of those things."

"I beg your pardon, mighty warrior; it seemed prudent to ask. Well, since you do not travel instantaneously, then during the time you travel to the point the tortoise is at when you start, it too will have traveled, however infinitesimal a distance, won't you agree?"

"Yes, yes, I agree, get on with it."

"Well, no matter how small his movement during that time it is still a distance for you to cover, and during the time required for you to cover it the beast will move yet again, making for yet another distance for you to cover. Surely you see the logic of this."

"Your words carry weight, but do not satisfy me," said Achilles, "and I think I might just ponder what you have said while I jot off and catch that tortoise. You don't mind waiting a second until I come back to finish this talk, do you?"

"Your patience, don't be rash," pleaded Zeno, "if you only will give me another moment or two. If I am right you will never catch him anyway, and if I am wrong the extra seconds travel time will avail the beast little."

"That is fairly put; continue then."

"Not only, mighty warrior, can you not catch the tortoise, you in fact cannot move at all. All movement is an illusion. And here's the proof: every line segment has an infinite number of points, yes? Your teachers did cover that essential matter, didn't they?"

"Practically the first day, but you're still talking nonsense."

"Very good, I will explain. Let us say you desire to walk to yonder tree, a scant five meters away. First you must obtain the distance of two-and-one-half meters, yes?"

"Well, yes, of course," said Achilles, clearly annoyed, mildly confused at Zeno's belaboring of the obvious.

"As you say, 'Of course.' And before you obtain the two-and-one-half meter point you must reach the one-and-one-quarter meter point. And before that the six-hundred-twenty-five thousandths of a meter point, and so on. 'Of course,' as you said. And since there are an infinite number of points on any line segment between any two points there will always be another half-way point for you to obtain before you can obtain the one you desired. As you see, simple logic shows you cannot in fact move at all."

"Oh, my, I suppose you're right. Whatever am I to do with myself now? Not much use for a hero who can't even catch a tortoise, can't move across a room. I guess I'll just sit here and mope for a few hundred years."

And that is just what our warrior did; he sat and moped about his plight. From time to time he had visitors; Lewis Caroll dropped in, Raymond Smullyan, Douglas Hofstadter; they have each reported on their meetings with poor Achilles. But when I ran into him he was just sitting there like a lump, whiny and depressed.

So I said to him, "Look here, if you're going to let a little logic stand in the way of catching that old tortoise you deserve to suffer. What kind of warrior are you anyway, to be put down by mere words. You are a man of action. Act! Go get that stupid tortoise and I'll have my sweetheart make us some soup."

"But what about Zeno?" asked the hero. "He told me it just can't be done. What about those infinite numbers of points?"

"Well," I said, "I see that the direct approach of challenging you to action has failed. It wasn't very compassionate anyway, but sometimes it works. You're feeling pretty glum about all this, right?"

"I sure am. Not to mention I think my keister's fallen asleep while I've sat here moping all this time. And tortoise soup would be great for dinner."

"Well, here's the thing: what's more important to you, being able to do the thing or understanding it? I'm thinking of the old Zen saying, 'Zen does not ask if the glass is half-empty or half-full; rather, Zen asks, "Do you thirst"?'"

"Well," Achilles said to me, with a glimmer of a smile, "I don't exactly know how my invulnerability works; Mum's told me a couple different stories. But arrows don't stick, swords turn. I guess I'd rather be able to do it than understand it. But can't I have both?"

"Gladly. You go grab the main course for us and I'll explain when you come back." And sure enough a few seconds later he was back with the tortoise in hand. "See, that took almost no time. Let me tell you what happened."

"Zeno was a crafty guy, and he was working an agenda, and we all do and we all have the right and that was then and this is now, so let's not get too caught up in Zeno. But let's do take a minute to get caught up in what you did with the words you heard from Zeno."

"Basically Zeno conned you. And his con works as well today as it did way back then, maybe better, for math-talk has taken on an almost holy tone in modern times. Here's the card Zeno palmed: A point has no height, no width, no depth. It has zero dimension, and, in fact, is simply a fictitious entity created to try to describe the action of certain kinds of things."

"Achilles," I asked, "How tall are you?"

"Oh, a good two meters."

"And you are maybe three-quarter meters wide at those incredible shoulders? Perhaps one-fifth a meter deep from your breastbone to your backbone?

"Well, yes, and now that you mention it, I do believe I see where you're going. What the heck do the rules of fictitious entities that have no dimension at all, what do those rules have to do with me, a non-fictional entity that can be measured in all three dimensions!?"

"Exactly. Zeno conned you into thinking the behavior of points was somehow relevant to the behavior of Achilles. And it is; the behavior of points is indeed somehow relevant to the behavior of Achilles. But there are limits. Right off the bat, that thing about an infinite number of points on a line segment---well there certainly isn't room for an infinite number of Achilleses in a ten meter stretch, now is there?"

"Hah. Not likely! Not a big guy like me."

"Well, that's the crux of what went wrong; Zeno cited something that wasn't really relevant to you, but *you* made it come true by believing it rather than testing it. Lots of times the way we describe the world will lead us to certain conclusions, but those descriptions are always flawed, limited, imperfect, and so it's always a good idea to have ways to test the value of a given description."

"Well, that sure makes sense."

Of course that is just a story. But it is a true story in that all too often what holds people back is nothing more than the way they think about the world. Often it is simply a matter of using the wrong analogy to predict the outcome of certain acts, like Achilles did when using the analogy of plane geometry (and that's all it is, an analogy, often useful, but also capable of producing terribly wrong conclusions) to predict the outcome of his behavior. And having come to a dismaying prediction he became depressed. This too is quite common.

Semantic Restructuring, then, is about testing analogies. Literally, Semantic Restructuring is the re-arranging of the building blocks of meaning. Pragmatically it is the pursuit of behavioral change, behavioral excellence via perceptual and conceptual flexibility and agility. There are tools and techniques, but in the end it's the attitude that counts, the attitude of readiness for more and better of the things that are good in life, the attitude of enlightenment, enlivenment, empowerment than can pervade your every act, every thought, every moment if only you will embrace the analogies that make it so.