This entry was inspired from a post by talented Mrs Ray.
And it is part of my introduction to the “imaginary numbers”. I love their philosophy since they have that title opposed to the “real” numbers.
Suppose there is a problem in maths… Something you can’t solve. Or, better yet it is impossible to solve. The healthier approach would be “ok, can’t do this, lets go out for a drink”.
But in my “modest logical mind” there is another approach. I have no idea if its healthier and since it is mine I suppose it is not. But It is fascinating.
You invent something. In the title posted by Ray you “invent” a number that does not exist and you name it “i”. The basis or imaginary numbers. This number is special because it has a quantity that is impossible in maths. The square root of dear old “i” is minus 1. And this is impossible. But you assume that it can be done since you must continue and base all your theory in that tiny quantity.
This is an “axiom”.
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) ‘that which is thought worthy or fit’ or ‘that which commends itself as evident.’
The second step to that give that “i” a reason of being. Give him characteristics that worth building an entire theory on him. I’m not going to bore you with fancy maths trying to be smart and distant. It is not my point.
And the third and most important step is strip “i” from its original quantity, give him an everyday use, let him compete with real numbers and see how does it do.
And there’s the magic of “imaginary”. It blends with “real” and it works. In most of the times it works better because it has that certain quantity that allows it to get a bit further than its adversary. It is more useful in “radical” and “outside-of-the-box” thinking since it lacks the boundaries or “real”.
Sometimes this is how the “I” works.
When facing some tough or impossible situation, it stops, it seizes and the it reinvents itself. This time with a quantity that wasn’t there before. A quantity that seems impossible at first. But necessary to get over the wall that is placed opposite of it. The wall that was impossible to get over.
And when that wall is behind at las (most of the times it doesn’t even realize that the wall is not there anymore), the “I” still works.
And if we’re lucky and we can come in terms with the process and not just “go out for a drink” we can see it works better.
I can see the wall.
I can see the new “quantity” given to me.
I can’t decide if the wall is no longer there.
to be continued