Does Hick’s Law Apply to the Moon?

decisions signWhen I'm in a bakery, I often stand transfixed by the many rows of donuts. They all look so delicious, I can imagine myself eating most of them. After a few moments, I narrow down my selection by deciding which one or two elements I really need to have (sprinkles, glazing, chocolate…). After that, I compare prices and sizes of the available choices. Ultimately, I make my choice and try to live happily with it.

Other times I remind myself that I'm trying to eat as little sugar as possible, and walk out without buying anything at all.

Most of us are fortunate to have these moments of abundance in our lives. But the real crux of this tale is the decision time it takes to make a selection. If there were only 3 or 4 donuts to choose from, certainly my process would be much simpler and quicker, even if it resulted in me not wanting anything.

The burden of selection and it's effects on the brain is a long studied phenomenon…longer than many people realize.

In the 1950s, a gentleman named William Edmund Hick performed an intriguing experiment. He utilized computers and humans to test how the amount of choices affected decision time.  In fact, he boiled it down to a logorithm:TR+a+b{Log2 (N)} (read the wikipedia entry for more on that). Through his studies Hick concluded that IQ and choice quantity were heavy factors in determining the ability of a person to react quickly to external stimuli. In fact, as choices continued to rise, reaction time would increase logarithmically.

Hick Invades the Martial Arts

He couldn't have predicted it, but Hick has made a real splash in the martial arts world. Britain in the 1940s and 1950s didn't have the same kind of martial diversity as we see all over the world today. In fact, traditional arts like karate, taekwondo, jujitsu, etc were just starting to make appearances outside of their native homelands. Had they been as popular during his time, he might have seen the obvious connection.

One of the biggest (legitimate) complaints surrounding the traditional martial arts is the focus on technique quantity and visual appeal over quality. While there were many brilliant westerners who helped spread martial arts in meaningful ways, there were far more who treated kata like currency and were more interested in developing large schools and successful tournaments than truly learning how to use the skillsets handed to them.

The result of the early boom was a lot of half-learned concepts taught in unintegrated fashion. Instead of learning "better", many instructors just learned "more". Before too long styles were cropping up that boasted thousands of moves to defend against any attack.

Some practitioners (both traditional and modern in background) have spoken out against this kind of training, frequently citing Hick's Law to support their argument. They state that the hastily collected techniques and myriad of kata relied upon by many traditionalists will increase their needed reaction time beyond any semblance of usability.

It's a compelling argument. Unfortunately, it's not quite complete…or original.

Hick's Law – Not Complete

Since Hick's time there have been many studies in the realm of neurobehavioral science, many of which dispute some of the direct assumptions made by Hick.

"New tests on skills like driving vehicles, flying, sports and psychology, have created so many layers of fresh information. Larish and Stelmach in 1982 established that one could select from 20 complex options in 340 milliseconds, providing the complex choices have been previously trained. One other study even had a reaction time of .03 milliseconds between two trained choices! .03! Merkel's Law, for example, says that trouble begins when a person has to select between 8 choices, but can still select a choice from the eight well under 500 milliseconds. Brace yourself! Mowbray and Rhoades Law of 1959, or the Welford Law of 1986, found no difference in reaction time at all, when selecting from numerous, well-trained choices. " – W. Hock Hochheim

Mr. Hochheim's work goes on to explain further studies in deeper context. I recommend you read his study if you have the time.

It turns out, there are a bunch of other important variables that can affect a person's reaction abilities other than just pure stimulus-to-reaction-choice quantity. One of the most important aspects is how well trained each choice is inside the person's neural pathways.

Gary Klein (also sourced by Hochheim) explains that the brain actually possesses a dual track. When stimulus enters the brain through the eye, it is transported to two sections. The first (System II Cognition) can be likened to my donut quandary as stated at the beginning of this post. In System II, external stimulus is transferred to the frontal lobes of the brain, where the consciousness analyzes, assesses, and comes to a conclusion about the best course of action.  This is a rather slow and deliberate process.

The second location is located in a more primitive part of the brain – the amygdala. Here in System I Cognition the stimulus flashes against pre-existing sensations similar in sight, sound, smell, and essence. The amygdala bounces a response back based on pre-conscious patterns that are not under deliberate control.

And, according to researchers Martin D. Topper, Ph.D., and Jack M. Feldman, Ph.D…

"Even though these two tracks are complimentary, we know that some people seem to be much more skilled than others at integrating System 1 and System 2. These especially competent individuals seem to resolve critical situations and also adapt to rapid changes in those situations. They invent routines they have never before performed and act in a fluid, seamless manner without employing full focal awareness." – Unconscious Competence

When taking more modern research into account, it can be concluded that the brain isn't slave to a single reactionary track that enlongates reaction time exponentially as stimulus increases. Instead, the brain can utilize different responses depending on how well trained it is. If the amygdala can sense recongizable stimulus as ingrained during training, it is then more likely to respond in kind. It can also utilize conscious decision making while responding in order to create new and more appropriate solutions.

Hick Back In!

While's Hick's ideas have been built upon since his original studies, he still has more to offer. One of his most useful ideas was that of Stimulus–Response Compatibility. In essence, he was suggesting that the closer the stimulus and response are in character and kind, the shorter the needed reaction time.

For example, it's easier for a person to hit a red button (amongst other colors) when a red light illuminates. Similarly, a person can more easily drive a car if turning the wheel left is connected with moving the tires left.

This idea works with the natural connections already established in our brain. The body and mind have built-in connections that allow us to function normally in every day life. They also allow us to protect ourselves instinctually. If something flies toward our eyes, our hands automatically raise up and turn palms outward. If something swings passed our groin area, the hips will instinctively lurch backward.

From a martial arts perspective, it could be considered wise to work WITH those bodily reactions and enhance their effectiveness. Furthermore, instincts can be used as launch points, connecting other methods of self defense from them, utilizing and sculpting the amygdala while providing it with trained pathways that connect it to a few structured solutions in the frontal lobes.

The Hick Argument – Not Original

The sophistication behind neuroscience is increasing every day. Our technical understanding of the brain's functions has never been better, and we stand to improve radically in the next few decades.

Would it surprise you then if I said the Japanese were making the same Hick-like arguments a couple hundred years ago?

Kenjutsu is an art with limited real world application. Anyone caught carrying a katana in day-to-day life will be quickly escorted to jail. Because of that, it's value in the martial pantheon is often overlooked by individuals focused on practicality. But consider this brief story…


In the early 1600s, a powerful man named Muso Gonnosuke roamed the Japanese countryside while engaging in musha shugyo, the practice of challenging other warriors to test one's own skill. One fateful evening Gonnosuke happened upon Miyamoto Musashi. His fame preceding him, Musashi found himself challenged by the brash Gonnosuke. Attacked suddenly, Musashi was able to easily evade and defeat Gonnosuke, leaving him alive after the duel (a rare occurrence).

Gonnosuke, thoroughly defeated, retreated to a Shinto shrine near Mount Homan where he meditated and trained for 37 days. It's said that he received enlightenment there and invented the Jo in order to finally defeat his rival Musashi. Armed with a weapon of increased length and an enlightened mindset, Gonnosuke eventually found Musashi once again and either fought him to a draw or defeated him (as the story goes).

The duel itself is not critical to our exploration of Hick's law in the martial arts. Instead, we need to analyze one of Gonnosuke's enlightened theories:

maruki o motte, suigetsu o shire – with the round stick, know the strategy of the moon on the water.

The round stick of course refers to the Jo. However, the idea of "the moon on the water" is a bit more slippery (pardon the pun).

When you observe the reflection of the moon on a still pond, you can see it's true nature. However, disturb the water and the image becomes distorted. Try to grab the moon, and you'll reach through it to the water.

moon water

The movement of the moon, subtle as it may be, is always reflected on the water. They are attached, not by any physically measurable property, but inescapably nevertheless.

The Moon and the Mind

This Japanese concept is very esoteric. In fact, many Japanese concepts are esoteric.

Japanese culture has long been steeped in oral transmission, frequently mixing fact with fanciful embelishment. In addition, their desire to hide real knowledge from one another has been deeply ingrained since the time of The Warring States Period.

In the old days, a good kenjutsu instructor transmitted wisdom to his students using artful story telling as well as thought provoking analogies and metaphors.

Despite all that, what the samurai were trying to impart is clear – The mind, when like still water, can reflect the truth of the moon. If the moon moves, it does not escape the water's notice and yet the water remains unperturbed. Should something disrupt the water or should it's surface become muddled, the image of the moon becomes hazy and unfocused.

This concept is often related to the idea of mushin – the uncluttered mind; free to act or respond.

To draw things out a touch, we can correlate the idea of disrupted water with that of a mind that is burdened by decisions. Think of dozens of techniques as being like dozens of reeds tossed on the water's surface. The clear path to the moon (as in, the opponent) is now slowed down as you attempt to push through the reeds and once again reveal the reflection. Continue the metaphor by analyzing the perpetual connection between any change-of-state between the moon and water. If a practitioner is connected to the opponent with such unencumbered clarity, they can move and act even before the opponent attempts anything of their own since the opponent's intent is at-once revealed.

When looking at the practice of kenjutsu, such a principle is apparent in every movement. The core of sword work is based off of 8 cuts. Everything that happens can be created from and returned to these cuts. Waza as performed by kenjutsuka are stark, simple, and effective.

Kenjutsuka realize that their lives can be ended with the smallest mistake, and a mind that is burdened by excessive choice and stimulus-overload would be quickly defeated by a better prepared warrior.

One Case Among Many

Gonnosuke's idea of "maruki o motte, suigetsu o shire" is hardly unique. All of the major sword styles have some way of building a foundation that can be relied upon in times of high stress with minimal choice conflict. They may not have known what an amygdala was, or that the frontal lobes are responsible for conscious thought, but they saw what worked on the battlefield. A few brilliant minds like Yagyu Munenori were able to communicate their ideas through the language of the time. Had they been able to grasp the science behind studies like that of Hick and Topper/Feldman, they would likely have concurred with the logic.

So, what of traditionalists that are fighting their own natural instincts in an effort to collect more techniques? Are they lost forever?

That depends. Each of the major classical arts (kenjutsu, karate, taekwondo) have roots based in true violence. The progenitors of those styles knew about things like unconscious competenence. Falling short of their high level can come from a wide variety of causes, including desire to make profit, grow business, form new systems before the old ones were understood, incomplete teaching, cultural miscommunication, lineages moving away from effectiveness (you get the idea – a WIDE variety of reasons).

Personally, this is why I find modern investigations so valuable. The scientific, research-based understanding of conflict can prepare us in ways that we might have missed while trying to navigate old esoterica.

And what of modernists who consistently blast traditional artists for being backward and blind to real conflict? Should they keep raging on?

That also depends. There will always be martial artists out there who spout nonsense and rely on parlor tricks to seem impressive. But perhaps modernists can also take a moment to realize the brilliance of some of the old masters, and what they were trying to impart through generations of artful study.