Analogies are how we communicate. They represent a way to relate one subject to another. They can convey emotion or feeling. And they can be used to describe complexity.
“I’m busier than a one-legged man at an ass-kicking contest.” While very few of us know what it may be like to have one leg (much less having one leg and competing in an ass-kicking contest), the analogy conveys a sense of exasperation that many of us can imagine because of the analogy.
Analogies allow us to describe difficult situations. They allow us to make comparisons across boundaries and subjects. And they allow us to compare patterns.
Analogies are gauge symmetry. Analogies are electromagnetics. Analogies are how we identify infinitely repeating patterns… or fractals.
A few months ago, we wrote about gauge theory and it’s applications to the financial markets. The blog post has become one of our most read pieces with many people asking for more information. Today, we’re going to get into another kind of gauge theory… and we’re going to use analogies to describe it.
Electromagnetic theory, or electromagnetism is the study of an electromagnetic force on particles (specifically electrons). This force is carried by electromagnetic fields which include both electric and magnetic fields.
Electrons circulate the magnetic field while positrons circulate in the opposite direction. They interact by “throwing photons at one another.” This process creates a wave with a number of different measurable variables including propagation direction and wave length (direction and duration… i.e. where is the wave going and how long will it take to get there). #analogies.
The origins of electromagnetic theory start with the observations and attempted understanding of lightning in the sky. In the 19^{th} century, it was discovered that both electricity and magnetism were related and thus the independent theories at the time were unified. Perhaps the best known researcher of this field is James Clerk Maxwell who pioneered the study of electromagnetic radiation and the behavior of particles as waves.
Effectively, Maxwell summed up the phrase “let there be light” into 4 separate equations.
In short… a lot.
This can all get a bit complicated… so before we relate this to the markets, let us offer a real world analogy.
Imagine you’re a kid again and you (electron) begin roughing around with a sibling (positrons). For a while, everyone is having fun while mom and dad (electric and magnetic fields) watch over the situation. Sometimes you’re pulling in one direction while sometimes your sibling pulls in the other. A perfectly harmonious wave of back and forth.
But then you toss something (a photon) which lands in just the right spot. You start laughing, your sibling starts crying and mom / dad rush to get everything back under control.
Chaos ensues.
In electromagnetic theory, “the mechanical act of cutting off an otherwise pure sine wave will introduce spurious frequencies differing from the natural one. The actual sharply terminated beam behaves like a Fourier integral of pure sine waves.” (from Mathematical Physics by Menzel).
This event, which otherwise disturbed a harmonious wave (fractal) is now chaos. The perfect wave was disturbed and new spurious waves of more erratic and exaggerated behavior have been created. Only after everyone calms down, your sibling stops crying and you apologize will the harmonious wave resume (until next time.. because we all know there will be a next time).
This analogy is meant to show how electromagnetism analogizes to real life, but the same kind of analogy can be applied to the markets. In our blog about chaos theory, we described how small anomalies or shocks can spuriously impact otherwise harmonic waves (electromagnetic waves). These shocks occur frequently in small ways such as when the “entire Federal Reserve payment system” crashed… or in large ways like when interest rate changes indicate long term policy changes.
These disruptions disturb the otherwise harmonious back and forth waves of the market. Sometimes the buyers win and sometimes the sellers win… causing the markets to move back and forth in harmonic waves in easily forecastable patterns based on direction and duration.
Now, one more analogy.
Buyers are the electrons.
Sellers are the positrons.
The tweets you throw at one another. Those are the photons.
Sometimes the buyers push the market higher. Sometimes the sellers push the market lower. Waves.
Sometimes chaos strikes and things get nutty for a few minutes, few hours or even a few days. But then normal harmonic waves resume. Those are the fractals.
This is electromagnetic theory applied to finance and if you can use it to filter out the chaos… If you can use it to filter out the noise… then, you can identify the underlying waves of the market. The underlying fractal which all data sets have. If you can use electromagnetic theory to find those fractals, real trades can be placed to take advantage of those waves.
We are often asking to recommend books to read. Here are a few (WARNING: none of them have anything to do with finance):
Fourier Series – Tolstov
Mathematical Physics – Menzel
Chaos and Fractals – Peitgen, Jurgens and Saupe