I've just been listening to the latest edition of In Our Time. The program concerns 'imaginary numbers'. Fascinating things!
An imaginary number is that which gives a negative result when squared. The square root of minus one - also known as i - is an example. The most astonishing thing about imaginary numbers (though perhaps their name ought to have given us fair warning) is that they don't 'exist' in the real world. One cannot count or measure with them. And yet - when embedded in equations - they have proven extraordinarily helpful in providing verifiably accurate solutions to real world problems. Imaginary numbers are crucial conceptual tools in contemporary scientific models of electromagnetism, fluid dynamics and quantum mechanics for example.
How can this possibly be? How can something that doesn't exist describe something that does? I suppose we ought not to be overly surprised. After all, negative numbers don't really 'exist' either. And that doesn't forestall their use in equations that come out with positive solutions. Imagine a healthy balance sheet. So long as your income (modelled by 'real' positive numbers) outweighs your debts (modelled by conceptual negative numbers), then your bottom line will be a 'real' number insofar as that one could convert it into tangible purchases if one so wished. It doesn't matter that you've used unreal negative numbers to get there. The only difference between negative numbers and imaginary numbers, then, is that the former may be attached to an intuitively graspable concept - debt.
Could √-1 be translated into a human practice analogous to debt? I wonder how that would look. How it would feel.