symbolism
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Some people think that it is irrational to believe, even provisionally, something that you do not understand. But this is a mistake. Many people who have heard of it will be likely to think that the famous equation of Einstein “e = mc²” expresses something true. Some but not all of those would be able to explain that the respective letters in the formula stand for energy, mass, and the speed of light. But rather few would be able to show that they understand it fully, though they might have been told that it implied that if matter could be converted into energy it would release enormous forces. They might have known: ‘hence the atomic bomb!’ Their assent to what they did not entirely understand should not be considered irrational.

Or again, consider a child learning about exponentiation. It is rather easy to learn that the exponent n means multiplying the number by itself n times: ‘2 to the power of 2 is 2 × 2, 2 to the power of 3 is 2 × 2 × 2, etc.’ But the child faced a bit later with, say, fractional exponents, or even -1 or zero as exponent, or worse still a negative exponent, even when given solid rules about how to deal with them in equations, is put in a quandary. One response could be ‘You can’t multiply a number by itself half a time, let alone no times at all, and definitely not a negative number of times. I don’t understand this at all. I’m opting out.’ Another response: ‘Well, with the rules I’ve been given, it all seems to work. It’s quite neat. So I’ll accept it, though I don’t understand what’s going on. There must be another explanation of exponents out there. Maybe in the next lesson ... ? ’

go on with symbolism
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