The Magical “All Possibilities”:

When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth. – Holmes

Imagine that you have a coin in your hand, and you are throwing it up in the air. How would you assign probabilities for the outcome? Generally, we are taught that a coin flip has a 50% chance of tails and 50% chance of heads, assuming that we are using a fair coin. The reasoning is that there are only two possible outcomes (heads, tails). Therefore, the probability of either one happening is 50%.

I have written about Bayesian epistemology before. If we evaluate the coin flip example, there is more going on here than meets the eye. The basis of all this is – from whose perspective? In Bayesian epistemology, probability is not a feature of the phenomenon such as the coin flip. The coin is not aware of the probabilities with which it should fall. The probabilities that we assign is a feature of our uncertainty, and it has nothing to do with the coin. In the example, only two outcomes were considered. Depending on the observer, this could be expanded. For example, we can consider the coin falling on its edge. Or perhaps, the coin may not land at all if we can imagine a bird catching it in midair and swallowing it, or it could be that the coin is being thrown in space. Based on our experience, we may conclude that the last two scenarios are unlikely. But the key points here are:

  1. Every description requires a describer. Every observation requires and observer. In science and in general language, we ignore the describer/observer. We engage in conversation or studies as if, we have access to objectivity. The science we have is a human science in the sense that it is a version that we have generated based on what our human interpretative framework affords.
  2. We need to be aware of how we made our observation, and be open to modifying it. Whatever we say or do if based on the current state of our knowledge/belief system. This needs to be updated based on the feedback from the environment.
  3. Any attempt at an experiment or study is to reduce our uncertainty about something. Going back to Bayesian epistemology, any expression in probability is an expression of our uncertainty. The phenomenon that we are studying are not following any rules. They do not have a mind of their own. We are projecting our “certainties” as rules onto them. A great example is the often-quoted scenario of birds flocking together to explain complexity. The birds do not know these rules. They exhibit a behavior that got reinforced through natural selection. The rules are our merely a projection of what we think is going on. In other words, the complexity of the flight of birds coming from the simple rules is just our construction.

The idea of “all the possibilities” is made quite clear in the Arthur Conan Doyle quote at the start of this post. This quote is often touted in TV shows and movies alike. However, the quote represents a fallacious idea, the root of which stems from an incorrect assumption. The assumption here is that one can eliminate ALL which is impossible. Similar to the coin toss example, this depends on the observer and their ability to know ALL that can happen, which requires omniscience. Additionally, one has to disprove every one of those possible outcomes. Only after this can one truly look at whatever remains. Aptly, this fallacy is termed as “Holmesian Fallacy”. We simply do not have access to ALL possibilities.

In Cybernetics, a key idea that is relevant here is variety. Variety is the number of possible states. This was put forward by one of the pioneers in Cybernetics, Ross Ashby. For example, we could say that a coin has a variety of 2 – heads or tails. Or we could say that a coin has a variety of 3 – heads, tails or its edge. As we can see the variety is dependent upon the observer. Being aware of this dependency is part of second order cybernetics. If we could restate the definition of variety in second order cybernetics, it would be – variety is the number of possible states as perceived by an observer. Variety is tightly linked to the concept of entropy.

Ashby noted that the initial variety that we have perceived will tend to decay over time if nothing changes. A great example that Ashby gives is the example of a wife visiting a prisoner. Let’s say that the wife wishes to convey a message to the prisoner using a cup of coffee that she can send to him. The warden is smart and he foretells the wife that he will add cream and sweetener to the coffee, and will also remove the spoon from the coffee. In addition, the coffee will always be filled to the brim. The warden has removed a lot of variety from the cup of coffee. The wife realizes now that the available variety that she has is to do with how hot the coffee is. She perceives the variety as 3 – HOT, TEPID or COLD. However, the warden is able to block this with time. If the warden is able to delay giving the coffee to the prisoner, then this variety is also lost. As Ashby put it, as time progresses the variety in the set cannot increase and will usually diminish.

On a similar note, Ashby also spoke of the law of experience. He noted that when we impose a change in a ‘system’, we tend to reduce its knowledge of its initial state or variety. The example he gave is that of a group of boys who have been to the same school – it is found that a number of boys of marked individuality, having all been through the same school, develop ways that are more characteristic of the school they attended than of their original individualities.

If we are including the idea of observer here, we see the “system” as the “system” that also includes the observer. This brings in a self-referential nature to this. If nothing changes, then our useful information regarding a phenomenon will either stay the same or decay over time. The useful variety that we have perceived will remain a constant or will decay over time. In addition, as the observer, we ourselves tend to fall along a line or conform to whichever tribe or community we belong to. We lose our original variety with time. The first step in overcoming these is to be aware. Be aware of our blindness; be aware of our limitations and biases; be aware of our shortcomings. We have to be aware that we do not have knowledge of “ALL possibilities”. We have to be open to challenging our worldviews. We have to evaluate and error-correct our beliefs on a regular basis. We do not perform error-correction on a continuous basis, but on a discontinuous basis.

I will finish with an anecdote on the apparent randomness of quantum mechanics that prompted Einstein to say that God does not play dice. As noted Italian physicist Carlo Rovelli wrote:

When Einstein objected to quantum mechanics by remarking that “God does not play dice,” Bohr responded by admonishing him, “Stop telling God what to do.” Which means: Nature is richer than our metaphysical prejudices. It has more imagination than we do.

Einstein was worried about the uncertainties he faced with quantum mechanics and he noted that the metaphorical God does not play dice like that. In a similar way the late Stephen Hawking noted:

So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion… Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can’t be seen. 

Stay safe and always keep on learning… In case you missed it, my last post was The “Mind Projection Fallacy” in Systems Thinking:


6 thoughts on “The Magical “All Possibilities”:

  1. I agree. Thanks for posting this.

    Laws are human laws; nature doesn’t obey laws. I like to say: “there’s no gravity police”. Nature is, as the title of the book, “Out of Control” ( Natural laws work, regardless of the law.

    Human beings tend to make their enacted and then invented Baysian beliefs into habits, repeating “what worked”. What works, works. (As I told you, in Dutch and German, the word for reality is “what works”: werkelijkheid, Wirklichkeit). Habits become rituals, rules for behaving. Rules made into laws. “Habit is ten times nature.” – Duke of Wellington

    Then law enforcing kicks in, laws. Beliefs made into a system of law induces more rules, because rules cannot cover natural reality. Laws becoming a self-sustaining system- as Luhmann noticed. Systems get an existence, an identity of their own.

    Like a biological cell, our systems can only sustain themselves behind self-made boundaries, requiring reducing variety. “Our beliefs are ours!”; they may not be questioned. Even when things are blatantly impossible or lies. They have to be protected against outsiders, heretics and schismatics. Ambiguity, uncertainty, doubt (inclusive) or paradox have to be eliminated.

    Real laws are paradoxical. They’re true, and cannot be proven. Like the laws of thermodynamics. (The concept of energy conservation requires a concept – energy – which is conserved. If it’s not conserved, it’s not energy. As it happens, the word energy has been derived from the Greek “erg” or “work”. Energy is what works).

    This also holds for Ashby’s Law of the Requisite Variety. Knowing his background and his time, I can understand his formulation, which doesn’t look like a paradox. At the same time, this law hides a paradox – variety requires variety. There’s no “variety police” – that’s why I consider it a “good”, natural law.

    I tend to use a different formulation – also by Ashby. The development of a system is constrained by the variety of its communication channel. That’s also Von Foerster: act always so as to increase the number of choices.

    Liked by 1 person

    • “I tend to use a different formulation – also by Ashby. The development of a system is constrained by the variety of its communication channel. “

      Perfect timing. This was going to be one of my future posts.

      Liked by 1 person

  2. 🙂 I’ve written a book on facilitating groups (in Dutch, I’m afraid, because I needed to use ambiguity – variety – present in language and in one’s mother tongue this is easiest). I paraphrased Ashby’s formulation as my motto:

    The Law of the Requisite Variety for a Facilitator (F) prescribes that F’s capacity as a facilitator cannot exceed F’s capacity to communicate with various reality perceptions.

    My work is based on Will McWhinney’s PhD “Paths of Change”, who shows how every change can be understood as moving through four complementary and opposing reality perceptions. (Sensory, Unitary, Social and Mythical, like earth, air, water and fire).

    As you’ll know, one constructs one’s reality. In constructing a reality – “objectively” – one also constructs ways one perceives reality – “subjectively”. People develop habitual use of one or two of the possible six “modes of change”.


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