11-26-2013, 10:32 AM
There is a well-known paradox in philosophy that goes by various designations and takes various forms, but the way it came to me is thus:
A professor announces at the beginning of a semester that there will be a surprise exam each month throughout the period. An inquisitive student asks for a definition of "surprise exam," and the somewhat annoyed professor explains that a surprise exam is one in which the student could not know the day before that the exam would take place on the next day. After some consideration, the student announces that by that definition, a surprise exam is impossible. The astonished professor demands an explanation, and the student replies that an exam cannot take place on the last day of the month, because once all the other days have elapsed, the last day would be the only remaining possibility, and therefore would be easily predicted, and so must be ruled out. Having eliminated the last day of the month, we can apply the same logic to the next-to-the-last day. Once this is so, we can work our way through the entire month, and show that it is impossible to surprise the class on any day.
Intuitively we know this to be wrong. We know that we can, in fact, be surprised by the timing of an event even if we are told to be on the alert for it. Explaining rigorously why the logic is flawed turns out to be non-trivial. I'll leave it for you to work though it on your own, if you are so motivated.
Trust me, this is not entirely theoretical. I've known people who strike me as a walking Xeno's paradox. They set their sights on a goal, but before they can set out to reach their goal, they have to draw a map and make plans to get there,. But before they can draw up their plan of attack, they must research the history and resources related to the project. Along the way, new information may arise that provides new and exciting ways of envisioning the goal. Tactics and strategies must be reevaluated. A number of approaches seem viable, so each must be considered carefully so that the best approach may be selected and meticulously deployed, lest precious time be wasted.
Meanwhile, as with Xeno, the arrow never even leaves the bow, let alone reaches its target.
We see this with prospective students who take the idea of training so seriously that they refuse to rush into it. They ask many questions, examine problems and potentials from all angles. There may be phone calls, emails, dojo visits, interviews, and abundant signs of real interest and commitment. Except they never show up, pay their dues, and bow in.
Other times we see it in the students who are on the mat and ready to train, yet appear to have an assortment of rituals that are required before they can face an attack. Yes, we bow to our partners, we (should) double check to see if they're really ready and paying attention. But even when all seems in order, we grab their wrist and marvel at the inability to move. We may see them take several deep breaths. Maybe they close their eyes and go to their quiet place. Or they shake their hands tekubi-furi style, raise and then lower their shoulders, wriggle their hips, or just make goofy jokes.
Had this been an actual combat situation, they'd be dead several times over.
The problem is not that such people are doing nothing. On the contrary, they're doing a great deal, they spend a lot of energy, and they create a situation that feels to them that actual progress toward their goal is being made. Except by any meaningful interpretation, they're not. They haven't even begun.
They've confused doing with accomplishing.
When I was first introduced in high school Physics class to the definition of work, I was astonished to find out that it had less to do with energy expenditure and more to do with actual distance moved. Now I understand it better, and see it all the time. Lots of sound and fury, signifying nothing. Even if lots of energy is spent, if there is no movement, no work has been done.
The Boy Scout motto is "Be Prepared." I've been thinking about this lately. We all understand that significant enterprises entail a great deal of preparation. No wise general goes to battle without a meticulously wrought plan, with all consideration of tactics and terrain and timing integrating seamlessly with an overarching strategy. Yet there is a difference between being prepared and getting prepared.
In order to be prepared, it's true that we have to have gotten prepared. But getting prepared can involve getting prepared to get prepared, and preparing to prepare to get prepared. And so on.
Before you know it, you are actually succeeding in moving backward in time. You're not moving away from your goal, you're moving your goal away from you by putting an infinite number of sub-goals and milestones between you and your target.
In a way, this is the very thing that defines and resolves such paradoxes. The arrow of time points in one direction -- forward, to the future -- not flying backward into the quiver and into the trees and birds whose parts make arrows, through the arc of evolution that makes trees and birds, the chemical basis for life, and the origin of fundamental particles. No. Nock your bow, draw, let go and let fly. In that order.
When we sequence a complex movement or action, it is useful to analyze it. Tracing it to its utmost root can be most illuminating. But when we act, we must move through the sequence in a way that moves us forward.
Check yourself to see if your are guilty of this, and how often. Check yourself on the mat and in your daily life. Check yourself, but beware of checking yourself checking yourself. Keep your eyes on the horizon and move forward. We must not do things which further our goals -- we must take action to close in on them.
Only by getting closer do we get further. This is NOT a paradox.
Ultimately, every threat and every opportunity is a kind of a surprise exam.
But I'm sure you totally saw that coming.
Still Point Aikido Systems
Austin TX, USA
11-27-2013, 11:04 AM
Awesome post Ross! I love studying logical paradoxes. They are their own little koan of sorts. I also agree that only by getting closer do we get further. I like how you used the word "further", which implies depth and breadth of experience, rather than "farther" which is simply a scalar measurement of distance. A subtle, but important distinction, I think. It reminds me of the old saying is science which says that "everyday we know less and less about more and more."
11-27-2013, 11:49 AM
Ross, I had to laugh at your description of the student standing there, having been grabbed, going through a series of rituals. It immediately summoned images from when I taught CPR and the student (who had just gone through the movie and was often up for recertification) would gawk at the dummy instead of doing or saying anything. The first time I would give a prompt but if it happened again I would basically tell him, OK, she's dead, because you didn't do anything...would you like to start over?
Xeno's paradox only works if you divide time like he divided space. Achilles runs 100 meters in 10 seconds, the tortoise runs 10. As long as you never get to T=12, Achilles never catches the tortoise. Good look with that! Time happens whether you're busy making a map to reach the plan to approach your goal or not.