I have a challenge for people who understand imaginary numbers (if that is indeed possible).
Now, I have seen how imaginary numbers can be useful. Just as negative numbers can.
For example, what is 4-6+9? 7. Easy. But your working memory may well have stored ‘-2′ in its mind’s eye during that calculation. But we cannot have -2 oranges. Or travel -2 metres. Oh sure, you can claim 2 metres backwards is -2 metres. I say its +2 metres, the other way (the norm of the vector).
What about a negative bank balance? I say that’s still platonic, a concept. In the real world it means I should hand you some (positive) bank notes.
We use negative numbers as the “left” to the positive’s “right”. Really they are both positive, just in different directions.
Now for imaginary numbers. I have seen how they allow us to solve engineering problems, how the equations for waves seem to rely on them, how the solution of the differential equations in feedback control loops seem to require them.
But I argue that they are just glorified negative numbers. The logarithmic version of the negative number.
So what is my challenge?
Well, the history of mathematics is intertwined with the history of physics. Maths has made predictions that have subsequently helped us to understand things in the real world. Maths models the world well, such as the motion of the planets, or the forces sufferred by current carrying wires in magnetic fields.
But the question is: is there any basis in reality for imaginary numbers? Or the lesser challenge, negative numbers?
Is there a real world correlation to “i” ? Or is it a mere placeholding convenience?
Or perhaps positive numbers also lack this correlation?