# Complex Numbers: Imagination

Hadamard asserted that the shortest path between two truths in the real domain passed through the complex domain. Literally in mathematics this means when we search for real roots we sometimes have to derive them from complex roots after using formulas that give us complex answers. A complex number is composed of both a real and imaginary part. But let us dwell on the statement of Hadamard. It is oftentimes that we have two truths in the real domain and we have to get from one to the other. For example we may know that we want to be with someone and that the person is someone we trust to go further with. Yet we also know once we get past a certain stage a lot of the things we are dwelling on won’t matter. However if we went through the real pathway from one truth to the next, we may meet competition and drag forces that slow us down. So we take a route into the complex domain where imaginary numbers dwell, much like opening up a wormhole portal in science fiction movies to travel faster, and while we are in that complex domain, we must not lose sight in the difficult navigation that a plain real truth is where we came from: that this person was someone who understood and was understood well enough to be an enjoyable partner. Whatever character flaws we may detect in the voyage through the imaginary plane is a consequence not just of getting closer to the destination but also of traveling on another plane.

This plane being inhospitable to competition, is also inhospitable to usual exchanges of human pleasantry and courtesy. Can you love someone devoid of the context you are in before you reach the context they are in? The ultimate test is whether you can love someone if they appear to have betrayed your memory since you were gone as you travel faster than speed of light on the complex plane presumably in the wormhole adventure and while you stay young they seem to have grown old and erased your memories for someone else. But luckily this is phantom as you travel fast enough to arrive at your destination before they grow old unlike if your spacecraft were too slow and then that phantom phenomenon may have become real. A trip through the complex domain back to the real domain which shows us that the final destination is never fixed because there may be one route by fate from here to the final destination in the real domain but time itself bends in the complex domain and there are many routes of fate there so long as we can travel in the complex domain. This is by intuition of imagination. In short, you go on a journey and come back and all the games are still waiting, only you are in a new destination now as you brought the games with you, and now beyond the games, you have an automobile on the information superhighway.

It seems a nice metaphor. All in the imagination though as travel of this sort is impossible without the imagination as the complex domain is by its nature imaginative. As analysis, the study of numbers which leads into the complex domain, is composed of generalities and not exceptions. Thus, the more we analyze, the more our generalities provoke the imagination to generate possibilities in a sort of self defense to shield off the complex domain from the real domain. Little Jackie Paper grew up as little boys don’t live forever though dragons do. His imagination formed a complex domain which shielded off from the real domain eventually while before he probably lived all in the real domain before he began to imagine things as an educated adult that could not possibly be real such as the square root of negative one. And he would travel through it to go from real truth to real truth. Where was Puff the Magic Dragon? He never left the real domain. He could not imagine imaginary numbers as his life was already built around imagination. Much like many artists cannot process the creativity required in fields such as writing for example, because artists already build their lives around creativity. I’m not saying writers have more creativity only they enter other realms. But I suppose an artist could too. My concern here isn’t art though it is economics. What is the real domain in economics? The real economy. What is the complex domain in economics? Finance? No. Finance can be dumb as rocks depending on who does it. The labor market is the complex domain. Think of all the dreams that go in it and imagination into people’s careers. All this disappears the moment you get commands and orders you can’t ignore. What does it all mean then? The labor market is a route from real truth to real truth. It is a complex domain: the labor market. If you have landed somewhere that isn’t real truth, you need to keep navigating through the labor market through the commands which are from your artificial intelligence navigation system keeping you safe. The commands and orders are called the Federal Reserve which has a mandate over unemployment and strives for full employment in the USA. The real truth you may have started from was your family or college. A real truth you may ultimately land on is a promotion or next job, but the promotion itself is not at the bequest of the complex domain or labor market or it isn’t a real truth and wouldn’t be reliable but would just be dangled as a tool of carrots and sticks. The promotion itself is an institutional title in the real domain which is the economy which acknowledges the role you have played: it is like a medallion.

No one ever complained that Olympic medals were made in Switzerland and given out in Sweden. Only if there were irregularities but that is beyond the scope of any athlete to manage. The real domain is sport. Perhaps the corresponding complex domain is music. Suppose the shortest trip between two truths in the real domain in sport is through the complex domain in music. Since I can’t play music for you here, I will just share with you the meaning of a Canadian poem on Flanders Fields: “we are the dead we once saw morning glow, the larks fly above scarce heard amidst the guns below.” The Canadians including McCrae who wrote this poem–he was a physician–were there about the war zone for a soccer matchup on Christmas between Germans and British which produced so much fun the higher command got angry on both sides. The other poem to know is: “the old men of Europe couldn’t work things out so God said to them: sacrifice a lamb instead, but the old man took his son and all the flower of Europe died, one by one.” We can see that when McCrae said the men used to live and see morning glow, he meant they used to be like each other, German or British, but then became something else entirely when the war machine started.

How much are we like each other? We are all on the real domain, most of us. The war machine starts when the walls between the real domain and complex domain fall open and the complex domain becomes more than just a place to travel through but a place to be fought over. That is the warning of McCrae and the Canadians of World War One, that they know how to do it too, to whoever may try to overturn the post world war order. My immediate reaction is scattered as I do sometimes want to debate that world order and where it leads to. Sometimes if you are in a real truth where you must fear nothing, you say it out loud: “I fear nothing!” Sometimes if you are in another real truth, you say out loud: “I see nothing!” But it is not good to see nothing. I prefer to say, “Ozymandias McCrae, you too shall pass.” For as poetry is really on the real space like sport, and music is to poetry what is complex: dating is what is complex to what is real in sport. Dating contains a lot of imagination obviously.

On the real plane, real truths are not faith. Faith is what is required to navigate from real truth to real truth as the journey is rocky. If the faith is a lie you won’t get there so what good is it? I would argue that if there is a way and there surely is, for people to weaponize the complex plane and make it a battle zone in dating or any extension of reality, it is not real, because money is real for example because it buys stuff, and dating is only real for example if it makes you happy. We will save discussion of whether happiness is real for next time.

I said “You shall not ask a french citizen that question” roughly.
Even Canadians conceded I was Canadian confused. I remember. Vive le Quebec Libre!

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