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Complexity

Power of NOT

Last Updated on July 2, 2021

Warren Buffett Says this 1 Simple Habit Separates Successful People From Everyone Else:

“The difference between successful people and really successful people is that really successful people say no to almost everything.”

It seems more important to know what you DON’T want, than what you DO. And it makes sense, really:

  • If you focus all your efforts on just what you want, you will probably miss opportunities that may otherwise grab your attention;
  • You are also more likely to take on tasks that you really don’t want but you think will get you closer to what you want.

One of the first things I learned when I started working as an engineer, that I never was taught in school, was that the purpose of calculating probabilities is not to predict the exact value of a variable at any given point in the future, but rather to eliminate the much bigger space in which the variable is not expected, in order to define the narrow “cone” of possible values in which it might be found in the near future. Of course the base of this cone and the space of possible positions increases the farther you go in the future with your prediction, but it still retains its cone shape that eliminates a huge area where whatever you are tracking is not expected to show up.

So, it seems logical that there is more benefit in any given situation or condition to focus on the negatives or inverted assumptions than on “positive thinking” and affirmative statements. Some times ago I went through the thought exercise described below that may provide some more insight into why I make such a suggestion.

Logical vs. Causal Conditionals

The well known “if/then” statement can be either used as logical conditional statement or as a statements of causality.

The statement: “If A is a square, then A is a quadrilateral” is a logical statement, while “If switch S is thrown, then bulb B shall light” describes a causal relationship similar, for example, to an engineering requirement.

Causal relationships are easy to disprove because the stated condition is usually not sufficient for the effect to materialize, because inmost cases there are other necessary conditions that have to be satisfied in order for the statement to be true. In other words, there are several things that can go wrong to prevent bulb to light up when the switch is thrown. A connection to the power source might be loose or the bulb might be broken …

Logical statements, from the other side, are harder to disprove. If the bulb does not light, we are not justified in concluding the switch was not thrown, but if A is not a quadrilateral, we are justified in concluding that A is not a square.

We can, however, say for sure that if the switch is not thrown, then the bulb will not light (regardless of the state of all other necessary conditions); but we can not say that if A is not a square, then it is not a quadrilateral, because it could be a rectangle, rhombus or some other type of quadrilateral.

It is immediately obvious that he difference between these two types of statements is the fact that a logical statement is about a particular entity (e.g. the square) and one of its class attributes (it is a quadrilateral), while a causal statement is usually about an entity (the switch) and the effect that its change of state (“is thrown” method) has on the state of another entity (the bulb will light).

So, my conclusion here would be that if a conditional “if/then” statement is used for defining a class relationship between an object and its container class, the statement is most probably logical, but if the statement is used in the definition of a functional working relationship between two objects the statement is causal !?

If this is true, we can then represent logical conditionals with a hierarchical organization chart (or tree) and causal conditionals with a linear branching (flowchart) configuration and identify all possible relationships between the elements of each statement.

When looked at this way, another difference between the two statements comes out. The original two positive statements were:

  1. If A is a square, then A is a quadrilateral (Always True) – because the mapping is N to 1 (the structure is stable with a sink attractor)
  2. If the switch S is thrown, then bulb B lights (Maybe True) – because the state of other necessary conditions is not known (the working structure is missing an input)

However, when presented in their inverted form the statements will also invert their properties compared with the previous case and will look like this:

  1. If A is a quadrilateral, then A is a square (Maybe True) – because the mapping is now 1 to N (the structure is a fan with no attraction)
  2. If the bulb B lights, then the switch S is thrown (Always True) – because the state of all other necessary conditions must be OK if B lights (the input now must be applied)  

Another difference that also pops up from the original discussion applies to negations (counterfactuals?) of the two original statements which (as expected) results in the same truth scheme as in the inversion case:

  1. If A is NOT a square, then A is NOT a quadrilateral. (Maybe True because of N to 1)
  2. If switch S is NOT thrown, then bulb B will NOT light. (Always True) (All conditions must be fulfilled for the final outcome to happen)

And finally the inverted negations (or negative inversions?) have properties identical to the original two statements:

  1. If A is NOT a quadrilateral, then A is NOT a square (Always True because of 1 to N)
  2. If bulb B does NOT light, then switch S is NOT thrown (Maybe True) – (the cause of failure may be some other necessary condition)  

It is obvious that, inversion and negation have the same effect on both logical and causal conditionals, but the interesting thing is the fact that the two kind of statements are behaving differently:   

One immediate conclusion from looking at this table is that the best way of describing causal statements is by formulating them as inversions (If effect then cause) or negations (if NOT cause then NOT effect).

Effects of Discrimination   

So the final outcomes of the above exercise was a proof for a “hunch” I had for a long time that negation (discrimination) is a much more powerful explanatory mechanism in engineering for causal relations than positive affirmative statements.

Discriminatory statements are always unambiguous. Saying that if a condition is satisfied something shall happen does not provide as much information as the statement that if a condition is not satisfied the thing shall not happen. In the first case there are always possible open issues about what are all the other necessary conditions for the thing to happen. As the switch/bulb example clearly shows “throwing the switch is definitely not a sufficient condition for the bulb to light” (there are other necessary conditions that need to be fulfilled) but “not throwing the switch is a sufficient condition for the bulb not to light” (in this case all other conditions are irrelevant).

If the above is true, why is it that at any course on writing “effective requirements” the first thing they will teach you is to use positive statements? The pressure for “positive thinking” today is so great that even such problem solving methods like cybernetics and systems thinking, probability, information theory and operations planning are all often misinterpreted and neglected (discarded as useless) because they are not able to provide a definite answer (prediction) about what will exactly happen as a consequence of any given cause in an experiment. Having a definite answer about what will not happen seems not good enough even if it clearly eliminates a much larger space of all impossible outcomes.

Determinism, Predictability and Probability is often vilified in “new” postmodern, chaotic and complexity thinking. The futility of all efforts to get a definite (deterministic) answer about the exact outcome of an experiment or prediction of some future event, seems now clear to everyone. But, from one extreme we suddenly found ourselves in another.

Today all (even negative) predictions are considered futile. The prevailing attitude is that if everything is driven by chaos and thus unpredictable, the best (or only) thing we can do is perform the experiment and see what happens. So we now have “edge organizations” with a “just do it” attitude, with no place for any, not only strategic, planning, no risk/opportunity management, no end vision of what (or not) the future may bring us or where are we heading. All of that is part of an ancient “command and control” attitude and the best thing is to let it be forgotten.

No point in planning because circumstances will change anyway. Let’s do it and we’ll see how it works. Things will evolve somehow, and if such blind experimenting was good enough for natural evolution to bring us where we are now, we also don’t have (and don’t want) to know in which direction we may “evolve”.

The only problem is that the “blind watchmaker” has no favourites and doesn’t care who dies in the process, so it may be us who are next in line for extinction.

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