SERF, Thoughts

The Butterfly & The Arrow

Damn I really have a hard time finishing large blog posts, but I’m creating this new one in parallel just to keep a trace of an insightful idea.

A bit of Context

I was watching the unaffordable foldable phablets and was surprized to see the Huawei Mate X had slightly better features and design than the Samsung Galaxy Fold.
Historically, the latter was the innovation leader, especially regarding hardware, while the former used to be noticeable by a good cost-quality ratio and quality softwares to compensate the hardware limitations.
After trying to reach the leader, they finally passed him.

In the same sense, that’s why startup don’t want to go public too early. If execution is still ongoing, a larger company could focus on reaching the same goals, with a different approach, and propose a better service; as they’re organized, efficient, knowledgeable, while startups are still trying to figure out what they’re doing.

But what does it show is that Samsung had the same behavior. As the leader, having Apple in the back copying every device with delay (even buying the components from Samsung), they didn’t had incentive to push towards novelties and kept looking around for ideas, prototypes and profits, while being risk savvy and not assertive for execution.
In the mean time, Huawei had its focus not on finding its way but on, first, reaching the lead level (which can be considered recently accomplished when you compare the Mate 20 to the S9) and then beating him on its own innovation; which they seem to have done on this first wave of the new generation of foldable phones.

The Duality in Companies

I really see 2 behaviors here: one was focus on finding the right way to execute a will, the one of bringing an innovative generation of smartphones, fluttering around ideas, analysis and decisions to make. This means the goals have to be determined from the will; I call this the Butterfly behavior.

While the other already had the goals in mind and focused its energy on execution. If your employees are specialized and focused towards well-established goals; all your forces are going efficiently towards the same target. While fluttering around means you might be more inclined to switch directions and find a better target, but you’re consuming resources in prospecting instead of producing. Though no company, either established worldwide or in a garage, can fully behave in one way.

Every company needs to find a balanced behavior between The Arrow and The Butterfly. Every company needs to both prospect and execute; the remaining is management. Should we foresee big plans? Should we improve design? Should we produce more? Should we increase investment in R&D? etc.

Using The Butterfly & The Arrow as a Tool

The behavior of a company, is a balance between the Butterfly and the Arrow behaviors. How to represent it? How to get a feeling of this?

Setting the Analogy Scene

Let’s say we have an infinitely long rolling sheet of paper. On top of this paper, you put a pen. If the pen stays still, it has no behavior. On the sheet, this is represented by a flat line; the paper keeps rolling but the pen stays static so a horizontal line is drawn.

This gives us the time as a horizontal axis; then we’ll suppose the vertical axis is another metric, like how well a company is doing at reaching its goals at a given time.
If it stays still, it doesn’t do good at reaching its goals, if it goes down it’s doing worse than nothing and, if it goes up, it gets closer to it.

That’s a simple plan defining a continuous function that serves fitting purpose (but with a pen and an infinite roll of paper, don’t think about bringing deep neural nets yet!).

The Arrow Behavior

There it defines its goals by pointing at… points in the future of this rolling paper sheet. And, as close it gets, as good it made it. It also means that a goal is to be at a defined value at a given time; so the pen is a micro-agent.

We could extrapolate to an agent if we had multiple states the system should reach as a goal, while using complex behavior in complex spaces and blabablah. We’ll keep it simple: a pen evolves on a rolling sheet of paper and sets its goals to reach points.

From its position, defined by its vertical coordinate at a given horizontal coordinate that keeps incrementing,  to its goal point, we can define a vector translating the pen to fill its objective. This embodies the concept of The Arrow behavior.

In a perfect world, where goals are well-established and reachable, this is it. The pen just has to follow the vector and gets to its point, the management just needs to push the team to deliver it, the spaceship just has to accelerate to reach light speed, etc.

In a true world, if the pen needs to reach a coordinate to, let’s say, 3 vertical-km higher and 1 sec away, where 1 sec = 1  horizontal-meter; then the pen needs to get to a point so far in such a short time that it won’t. Not because it’s breaking relativity, it doesn’t fall short, but because the paper will burn and the pen will break before it reaches its goal.

The Missing Behavior

What can we say besides; That was a stupid goal ?

There’s no magic potion, no healing the wounds, no alternative path. Trying to launch a pen at 11.000 km/h over 3 km on a paper translating at 0.001 km/h; that just doesn’t make sense as a goal. No company should try to confront a GAFAM company while being 2 guys in a garage; that’s not a realistic step, and none sensible would try this.

Does it mean we have to limit the goals? Should the vector only points to reachable goals? What kind of goals are reachable ?
Then we start implementing goals classification at a given time, establish constraints and reasonable delays; we grow on knowing how to behave regarding certain goals and disregard what is not reachable.

Though this is a complex social construct that requires time, resources and knowledge gathering via trials & errors. What if I’m just a disorganized startup? What if I’m an explorer discovering a new land? What if I’m just an ant trying to behave in a unlabeled environment?

Although it doesn’t require to be a well-organized expert to be certain when you claim “I cannot build a spaceship”. People have naturally more sense than what a goal-oriented vector would do with or without complex expertise.

The Butterfly Behavior

If our pen is expressing a metric, it should convey the will for the Arrow behavior, but we don’t expect it to have extreme goals. This has to be tempered by reality and capabilities, in order for the pen to become a metric of real values.

In reality, companies will have to work around their problems, have good or bad surprises in their results, determine their image, get resources delay, rework their goals in a lean fashion, etc. They really don’t go straight to their goal, though they point at it, but they might change it; in density, in direction, in multiplicity,… The Butterfly behavior acts upon the Arrow behavior it also inflects its goal in such a way that they have a symbiotic coexistence.

The Butterfly expresses the fluttering as the pen oscillating around its path due to noise, delays, constraints, research of better path, etc.
By making the Arrow varies (in intensity, direction,…), the expression of both is setting the goals. And what is really reached, from what is expected to be reached, is the product of both behaviors.

You can therefore think of the pen point as having 2 behaviors attached to it; an Arrow that is willing to reach its goals asap, and a Butterfly, that adjust the Arrow behavior while propelling it.

I personally pictures it as a pen trace in a plane with the Arrow pointing at a location and the Butterfly introducing nondeterministic noise.

  • With no behavior, the pen is still at its origin
  • With Butterfly, the pen flutters around its origin
  • With Arrow, the pen gets to target location
  • With both in the same amount, the pen gets to target location in random path

But the rolling paper helps gets things moving (in a plane, everything is static) so the make seeking goals more relevant, and as to already project myself in the Agent modeling I’m developing for my current project.

Extension to Other Domains

Then, what hits me, is how frequently this pattern is found.

In Humanity

In investment, you have the Bull & the Bear similarly; when profits are easy on some domains (let’s say companies, or crypto-currencies) everyone is already willing to buy it as it makes a good deal. Plenty of growing interesting opportunities; the will of the investors is there and they rush towards the goal. It’s a Bull market, it’s an Arrow behavior.

As the market becomes less profitable, subjective risk increases and people limit themselves and carry long-term investments; they are more hesitant about what they do with their capital and try to find new safe opportunities. This is a Bear market, or a Butterfly behavior. It changes once the new profitable opportunities are found, back to an aggressive behavior towards the new target.

We can also see more fundamental behavior in it; just like human introverted/extroverted behavior switch. As the context becomes clearer, the situation is safer, the goal is better established, the people around are getting known,… a human will move from introverted to extroverted. As everything is clearer (just like the dark; not clear is not safe), a person can start affirming his goals and know which can be filtered or emphasized (e.g. finding things in common).

In Nature

This pattern can also be applied successfully in nature. If I take a simple case; the Sun is going through the Universe towards one of its lost corners. It has an Arrow behavior towards that place and, around it, many bodies are orbiting, like the Earth. Forcing the path of the Sun to be shaky through space and time. This is similar to our pen not getting straight to the target point.

The exact mechanisms are, of course, quite different from our pen as the context is also. But there’s noise and inflected trajectory though this might be harder to picture. If you take the Moon and the Earth, then the Arrow behavior is much less significant compared to the Butterfly behavior; the Moon acts upon seas and bend the Earth orbit.
But to see really in large scale interactions where the Butterfly behavior is significant, you might want to live next to a binary star system.

In a smaller scale, you can see the exact opposite is happening: it becomes common for the Butterfly behavior to be order of magnitudes more affirmed than the Arrow behavior.

A simple example, as everyone had seen its planetary model, are atoms. You have the kernel at the center, it is the essential of the mass so it determines the speed vector; and, therefore, the Arrow behavior as traveling will be the metric.
But it doesn’t travel straight, because it is surrounded by electrons that react to another type of cause (the electromagnetic field is not our metric) and our kernel reacts to its electrons movement.
Actually, the electrons are so strong that they are, at scale, waaaaaay further from the atom’s kernel than the Earth is from the Sun. So the Butterfly is much more important than the Arrow, in this example. In this case, erratic movements around the same place will be proportional to the orbitals states; as it gets more excited, it gets more “turbulent”.

In the Limits of Our Knowledge ?

At a larger scale, for molecules, we have the Brownian motion. But, at smaller scale, I’d like to refer to a concept I had quite an interest in by the past: the pilot wave theory.
In this approach, quantum weirdness is interpreted by a duality similar to the Butterfly & Arrow behavior, which is why I took the time to write this down (I kinda found half the examples on the way; pretty sure there are plenty).

I won’t trick you in telling you the following is an incredible theory unfairly ignored, unlike some others do, but it’s a promising approach from some to reinterpret an elegant theory, as old as Quantum Mechanics, but in a modern valid way. Because mathematical and physical theories are just like software products; they need to grow and validate new and stronger constraints.

There already exist quite a lot of great resources on the web. I’ve been storing papers that I can barely read for years (some with baiting names, damn!) but, to get you a stronger insight than my summary below; here’s some videos vulgarized videos from physicists :


In my non-physicist vulgarized way;
Think of electrons as 4D particles bouncing up and down on the thin sheet of our 3D world. What determines how they will bounce is the wave under them, produced by the sheet wrinkling under the directed bouncing. Both the waves on the sheets and the bouncing particle are adjusting each other during movement.

From bouncing against obstacles, the wave already knows the ideal path for the particle to translate to. From bouncing on the electromagnetic field, the electron maintains the wave. This is an effect that can be mimicked at larger scale (using a high-power speaker and non-Newtonian fluids, for instance)

In Conclusion

What I find really interesting by thinking about this Butterfly & Arrow dual behavior, is that this pattern seems to be quite everywhere though it’s quite an abstract one. So it’s interesting to name and point to it to better determine and observe it.

Maybe there’s some truth behind? Maybe an intelligent system should start by having both behaviors and the capacity to orchestrate their alternate use… Maybe that’s what could better mimic real agents?
Maybe this pattern has a deeper truth that I cannot grasp yet…