Logic is for the Birds
It is amazing how many people think that getting new ideas is a logical process. If you suggested to the average body who hadn’t thought much about it that inventive genius is a combination of intense concentration and pure logic he would believe you. (Stop frowning. You wouldn’t believe it. Not for a moment. Would you?)
What is logic? Going from one known fact to another until you reach an incontrovertible conclusion. Logic sticks to rules. If you and I are given the same logical problem and all the necessary facts, we would probably reach the same solution. You know the sort of thing: if six and a half men take two and a half hours to dig half a hole, and so on.
Logic sticks to the rules. Your conscious brain sticks to the rules. Even when it jumps to wrong conclusions, it does so in a logical mode. Logic is a wonderful asset. It is the very essence of status quo.
But logic inhibits new ideas. It must do. New ideas break rules. Logic preserves them. So logic inhibits new ideas. That’s logical, isn’t it? Once you get the feel for this concept you’ll be well on the way. It may sound strange—because it’s new—but you’ll soon get used to it.
Innovation is finding a new, creative solution to a problem. Not all problems require such solutions however. They can be solved logically. To demonstrate, I’ll give you two problems. The first can and should be solved logically. The second requires creative imagination.
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Imagine you have twelve billiard balls that are supposed to be uniform in weight and size. One of them is the wrong weight. You have a simple, see-saw balance scale with two pans, each of which holds up to six balls. You have to weigh the balls in order to find the dud one. And you are only allowed three weighings. Aweigh you go … (Remember, you don’t know whether the dud ball is heavy or light; also your system must cover all possibilities. Lucky guessing ain’t allowed.)
One cannot resist the temptation here to point out that logicians appear to like doing things the hard way. The common sense way would, of course, be simply to weigh one against the others in turn, but let’s pass over that.
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This problem was presented by Arthur Koestler in his book ‘The Act of Creation’. Touching my forelock to Mr. K., I offer it to you.
A Tibetan monk climbs a mountain in order to pray throughout the night. To reach the temple at the summit he climbs a winding path. He descends by exactly the same route. Now, he begins his ascent at precisely 8 a.m., arriving at the top sometime in the early evening, having stopped to pick berries and even retraced his steps once or twice. He spends the night in the temple. Then he starts his descent (down the identical route) at 8 a.m. precisely the following morning. He hurries down, reaching the bottom in the early afternoon, wondering, possibly, why the hell they had to put the temple up there in the first place. However, you have to prove that he must have been on one point of the path at exactly the same time on both days.
Nasty, isn’t it? But fun.
What you will discover is that the billiard ball problem, though difficult and tantalising, is a straightforward matter of deduction and permutation. The monk problem is really one of finding a way of expressing what you quickly discover to be the case. You probably won’t have any existing symbols in your brain for doing this so you’ll have to invent some.
To give you another example of problem solving by logic and illogic, compare the skills required for playing chess and those for solving a sophisticated crossword puzzle. In chess, all the facts are before you. It is a matter of retaining complex permutations in the mind. Some people have an extraordinary facility for doing so. However, I am going to suggest that very few chess experts are innovators. Please note, I’m not saying that chess players are not brilliant. They may well be. But very rarely are they innovators. We will examine the reasons for this shortly.
In crossword solving, quite different mentation is required. Basically one is trying to identify unexpected and unlikely relationships. That is to say, you are dabbling in illogical thoughts in order to find new, if somewhat pointless, revelations. However, the analogy with innovation is not as neat as it might be, since the solver is only arriving at what has been devised already by someone else. But the thinking pattern is in many ways similar. And you can see that, other things being equal, the crossword solver is more likely to get new ideas than the chess player, even though both employ sophisticated mental functions.
You might ask: what’s to stop the logical thinker from remorselessly and inevitably arriving at a new fact—because that’s what new discoveries are? One reason is that the logician must always keep solid ground under him. He must use known symbols from his body of knowledge. The new idea has no symbol until it is uttered. In order to arrive at a new idea, a question has to be postulated—What if … ? And that is not logic, it is fancy. It is possible for a logically inclined man to make this postulation but he has to stop being logical to do so.
It is very difficult even to consider this concept of logic being the antithesis of innovation. Our education and upbringing all seem directed at making us believe the opposite.
If you have a reputation for sound judgment, reliability, efficiency, method and loyalty it may be difficult to accept that in developing these qualities you have probably scotched your talent for innovation.
But if you are going to re-awaken it or understand how it works in others you’re going to have to face up to this.
Solutions
The billiard balls
Take balls 1, 2, 3 and 4 and put them on the left hand pan. Place balls 5, 6, 7 and 8 on the right hand pan. Three things can happen. The left side goes down, the left side goes up or both sides stay level. Note what happens. Then, remove balls 1, 2, and 3 from the scales, leaving 4 on the left. Take balls 5, 6 and 7 from the right pan and put them on the left in place of 1, 2 and 3. Take balls 9, 10 and 11 and put them on the right hand pan with number 8. Note what happens. If the same thing occurs, nothing has changed so the dud is 4, 8 or 12. If a different reaction occurs you can account for it likewise. The third weighing will always be one ball against another. I hope that is clear enough to enable you to sort it out in detail.
The monk
One solution is to imagine him descending the mountain, while his ghost of the previous day replicates the earlier journey. At some point the monk must pass through his own ghost … same time, same place.
You see what I mean about illogic? What could be more illogical than that? But beautiful!
Another solution is to make a simple graph of each journey, with the base being time (8 a.m. at the right angle, extending to 12 midnight) and the vertical axis being height. Both lines are drawn at random but the second journey line reaches the top first. Then place the second graph upside down. So that it faces the first one. Through the back of the paper, the lines will be seen to cross. But this, however ingenious, is still not conventional, logical mathematics.