Math brains
A nice story by Robert Lucky...
I remember well the day in high school algebra class when I was first introduced to imaginary numbers. The teacher said that because the square root of a negative number didn’t actually exist, it was called imaginary. That bothered me a lot. I asked, If it didn’t exist, why give it a name and study it? Unfortunately, the teacher had no answers for these questions.
As with much of the math that we’ve all studied, understanding comes only much later. We’ve all had the experience of learning mathematical principles before we had any idea what they were good for. If I could go back to that day in high school, how would I have explained matters?
I can think of two approaches, although somehow I doubt that my younger self would have been happy with either. The first is to say that mathematics is beautiful in itself, a study of consistent rules of logic that can be appreciated as an art form, quite apart from any application it may have to everyday problems. The second is to note that this square root of minus one is actually useful (in problems that my younger self didn’t know about yet). It opens the door to two-dimensional thinking—a dimension that gets you off the line of real numbers. So whether or not this imaginary number exists in your world of arithmetic training, it’s useful. In real world problems, it works.
I’m reminded of a famous saying in physics, variously attributed to Paul Dirac and Richard Feynman: “Shut up and calculate.” It was a response to a class of problems in quantum mechanics in which the Shrödinger wave equation often contradicts common perception, yet it always provides the right answers. So don’t worry about it: quit complaining and just calculate. Like using the square root of minus one, it works.
The whole story here
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