Solution Methods of Last Resort

 

Solution Methods of Last Resort

G Donald Allen

1. Introduction.

You and the team can't solve the complex problem. All the engineers, all the accountants, and all the plant managers can agree on nothing definite. Every tentative solution you’ve offered has been rejected by the higher-ups as flawed. Call this a Humpty Dumpty problem[1].  When up against impossibility or at least complexity, the problem-solver looks for any clue to help. Just a trace of inspiration may do.

When you’re trying to move a mountain, only
a morsel of information can help.

What is singularly important here is that these notes are not confined to normal propositional logic for consideration or resolution. They work with any problem-solving tool you may prefer, from beliefs to faith to emotions, to all. To this point, we’ve already discussed dozens of solution methods. In this chapter, we add on the final bunch, dominated by dream states and thought experiments.

2. The Usual Suspects.

You can't even think of any possible pathway or even how to make a first step toward solving the problem. You're completely stuck. What to do? The regular answers include just giving up. Don’t do this just yet. Taking a break from the problem sometimes helps, but more often simply confirms the difficulties, now with a refreshed viewpoint.  In the list below other of the usual methods are suggested, and methods probably you’ve already tried. So, little discussion is given.

A.    Be certain all your terms are precisely defined and even measurable. For example, many economic theories have undefinable variables.

B.    Avoid the use of vague terminology. For example, good, big, and healthy are vague.

C.    Take risks. Mostly we want to be careful, and even conservative, as money and lives may be at stake. Risk often leads to error, but when nothing else is working…?

D.    Take a different perspective. But how to do this? You are locked into your thoughts, ideas, and processes. Talking through the problem with an outsider sometimes helps – if you're allowed. Another method is to read materials related to your problem. Read different materials connected with aspects of what you’re doing. This forces a different perspective if you can adjust. Yet, it comes with no guarantees. One could say that the application of knowledge from many sources may lead to positive results – if you can do it. It is no simple matter to be facile, meaning “at ease,” in multiple knowledge bases.  

E.     Be open to feedback – for example, call in a consultant, or give a talk. With respect to consultants, note the wide variation of expertise is a caution flag. Consultants tend toward formulaic or prescriptive solutions. They may not help with complexity issues, even if the consultants understand them.

F.     Reasoning backward. As mentioned earlier, this is the method of assuming some solution and trying to work back to the original problem with the full set of conditions and constraints. This method takes practice and rarely works – at least in my experience.

G.    You know or suspect what the solution should be, but can’t prove it. But you must at least justify it. One approach is to assume it’s wrong and see what the implication might be. Sometimes they lead to a contradiction of some fact. This gives a weak justification you can use to convince. It is not a solution per se, but it supplies further information to the solution process, at times true inspiration toward establishing it. This is akin to the method of contradiction. (To prove that proposition P implies the proposition Q, is equivalent to proving not Q implies not P.)

H.    Visualization: Tree diagrams. Diagrammatics[2], Flow charts. Figure 1 illustrates a diagrammatic, sometimes called a spider web. The visual mind seems to process information differently helps to see alternative relations both between concepts, processes, and text and numerical information.

I.       Art. Using art to represent a complex or impossible problem often requires “seeing” connections not previously recognized.

J.      Storytelling. Many a complex problem has been revealed in stories and novels where symbols of evil, good, love, et al. are in the characters. Aesop’s Fables is an ancient form of problem-solving through stories.  

3. Dream States. At this point, with most of the well-defined problem-solving techniques explored, we delve into the great known unknown, the mind’s secret weapon, the dream.  Therein lies a power most certainly unknown, and scarcely studied. Let’s begin at the movies.

What happens when you watch an intense movie late at night?  Your mind is absorbed in the pictures, dialogue, and sounds of the film.  Your mind still dwells on these, computing, digesting, and ruminating on all of these even into sleep. In your dreams, your subconscious mind recalls all these thoughts but convolutes them as only dreams can. Maybe you wake up with yourself a part of the distortion. Maybe, you make it through the night of restless sleep but you wake troubled. Dreams fade quickly, happily.  Has this happened to you?  To me, many times. As a pre-teen, my dad took me to the movie, The Man with the Atom Brain.  The imagery and plot of that movie stayed with me for years. I know this was a childhood fantasy, scientifically unrealizable even now, but a remake of the movie titled, The Man with the AI Brain, seems just as scary even for us adults. Even now, chips are being implanted in people and in the brain – for the good of course.

Welcome to one aspect of creative thinking, invention, and conceptual revelation.  How’s that? Let’s reshape the movie episode. Let’s consider you’ve been working on some issues/problems/situations intensely for days or weeks – right up to bedtime. Haven’t we all? It’s the same story. Your thoughts before bedtime weave their way into your dreams. You wake up the next morning.  This morning you resume your work, but something different happens.  There appears a new idea. It might work, you think! Where it came from is best described as “out of the blue.”

Welcome to the world of discovery! What is described does happen. It’s happened to many, me, and maybe you. This is the power of the incubation of thought and the dreaming mind. It is not by formula, and it’s not by logic. It reveals powers of mind unquantifiable and unqualifiable. It happens rarely, but it happens.  Alas, more often than not, your new idea is no better than any precedent. But how many ancient hunters woke up one morning with a new approach to their craft? Even the great Joseph Marie Jacquard (1752-1834), a Lyons weaver extraordinaire, perhaps woke one morning in 1852 with the concept of the punched card programming of looms. It revolutionized weaving, surviving to this day. (Looms are now programmed electronically, of course.)

Nonetheless, the mind is far more powerful, though decidedly unpredictable, than any assessment has yet shown. The marvel of insight, even through dreams, is essential, fundamental, and without valuation. Logic is but one solution tool, often transcended by the full powers of your mind. Dream-state solutions are so difficult to classify as a method, they cannot be put into our general categories.  Yet, it is a modern research subject[3]^,[4]. They are an essential part of the mind’s toolkit but are rather unreliable. Different from Albert Einstein’s thought experiments, they enjoy no controlled intellectual guidance.  But when nothing else is working…?

Remarkably, a recent MIT study showed that quick naps can enhance creativity[5]. Imagine that, a nap is a creativity pump. It is well known that naps reduce stress levels, increase energy levels, improve cognitive abilities, and enhance mood. Even fifteen minutes will do. Caution: naps can be habit-forming.

4. Thought Experiments.

A thought experiment is a mental scenario one uses to consider and explore some idea or concept. They are used in math, physics, and other sciences. As well, all professionals facing difficult problems use them just to run through possibilities. Even teenagers with a pending hot date do small mental experiments.  They are used to explore their personal understanding, test their knowledge, and explore outcomes of all varieties. As well, they are used to explore the deepest ideas of the universe[6]. Though appearing in the literature hardly more than a century ago[7], they have no doubt been used even in prehistory, where there was no other method for thought expression.

The format varies, from narratives created for personal or interpersonal relationships to recounting events and what might have been said, to preparing for trial, to considering deep conceptual scenarios and thinking of the world in new ways. Sometimes they involve imaginary characters and simulations. Anything goes. In your mind, you may use taboos, maxims, allegories, fables, or anything that resonates with the problem.

Our purpose here is to use them to consider complex and impossible problems and how to solve them. Thought experiments help break down complex and impossible problems into more manageable pieces. This always helps.  They help both see and challenge assumptions. Working on smaller pieces can yield new insights and possibilities which then enter a formative stage. It is important to accept most ideas or solutions arising from thought experiments are worthless. On the scale of importance, discarding bad ideas is on par with passing good ideas.

Thought experiments are used everywhere for everything. They are used to interpolate and extrapolate, identify logical flaws, refute assertions, predict, forecast, retrodict and predict, make decisions, evaluate risk, study causation or blame, solve problems, assess culpability, and challenge the status quo. They are especially used to consider possibilities. Basically, thought experiments are used to examine all manner of problems – all in the privacy of your mind. This anonymity is a blessing, for there you can make crazy mistakes, correct them, and move on. And nobody knows. They can also create locks on your outlook, though false solutions you are unable to identify or shake off. The familiar expression, “Lost in thought,” illustrates the notion.

What is significant, but rarely mentioned, is that thought experiments as used by a problem-solver of considerable experience are that bad ideas can be quickly rejected. This is opposed to doing a full paper-and-ink study, which could take days or weeks to reject. Also, to mention again, the thought experiment is a principal tool of the highly intelligent as they can consider and reject (bad) ideas far more quickly than most of us.

Hazards abound with using thought experiments. Foremost among them are results that can be misleading, imposition of ideology on solutions, possible bias, assumptions that can be forgotten, problem oversimplification, not to mention frustration, confusion,  and excessive time expended. Thought experiments require mentally absorbing the whole of a problem, and that takes practice. Once, a professor told me he didn’t understand anything unless he could contain its entirety in his head all at once. Tough criterion, yes?

Examples of Thought Experiments. Not all thought experiments solve problems. Some create problems, vexing, horrible impossible problems requiring serious thought. We’ll consider just a few special types out of history and science. While we’ve been constant on problem-solving methods in this chapter, most of the more famous thought problems have no realizable existence or solution. In my student days, they were the grist for evening conversations over pizza and beer. About what students consider grist these days I am uncertain, but a shame if they miss this important part of their intellectual development.  Our first example is a classic of science but applies to all organizations.

Maxwell’s Demon (1871). You have a box full of air with a divider in between creating two compartments, called left and right. In the divider are two weightless doors. Atop the box is a demon who opens the door when a fast-moving air particle (i.e. hot) approached from the right and lets it into the left box. Similarly, when a slow-moving particle (i.e. cold) from the left approaches the second door, it opens the other door to allow it into the right box. After some time, the hot particles will be in the left box, and the cold particles with be in the right box. 

This violates the second law of thermodynamics which states that any closed system moves from order to disorder[8]. The measure of disorder is called entropy and the second law states that entropy always increases. So, this thought experiment needs work to make it right. But it’s not right, partly because the demon is part of the systems and all that door opening takes energy. This entropy-increasing law has a place in business through the following, “In an organization that doesn’t consistently monitor and improve processes, entropy manifests as decreasing quality [disorder] and eventually self-destruction[9].” This means an organization must infuse (human) energy and thus make money to survive. Entropy is an interesting subject and plays a huge role in modern information theory.

The Lady and the Tiger (1882). In an ancient land, the accused was punished through a trial by ordeal. He was placed before two doors. Behind one was a beautiful woman he would marry, and behind the other was a hungry tiger that would eat him.  Before the trial his love found out which door was which. She understood that she would lose him no matter what hint she offered her love. What did she do? Quite the conundrum. This thought experiment is similar to the famed Trolley Problem, discussed earlier.

The Ship of Theseus (ancient): This thought experiment of identity asks whether a ship that has had all of its parts replaced over time is still the same ship. Again, a physical realization of this situation is unlikely, and thus it is a pure thought experiment. And again, as in the previous case, there is no clear answer. The problem of identity applies even to yourself. Are you the same person at age 6 as at age 36? If yes, what does identity mean? If no, ask the same question. Identity is quite the problem, especially these days.

Hundreds of thought experiments are on record. Mostly, to achieve prominence in the literature they need to have a paradoxical or enigmatic quality. Impossible alternatives, contradictions to principles, and meanings of definitions are the mainstays. However, we use them, police detectives use them, diplomats rely on them, generals would be lost without them, and Presidents mull on them all the time. They are the ever-constant back chatter of deliberate thoughts deep in our minds. Finally, for problem-solving, uncertainty is sometimes the driver to look inside, to find more within.

5. The Impact of AI.

Artificial Intelligence (AI) is not a thought experimental tool, though it can help find information and establishment viewpoints. It is unlikely to offer you much-needed and unique nuggets of information, as it is trained on volumes of similar information. It can regurgitate what is known about any particular topic. It’s hard to stump. But it is not a problem-solving code. Questions you pose must be carefully worded, and sometime you must coax out what you need.  I use it often to fill in background information, but it furnishes nothing original. Sometimes it can substitute for reading, though it only furnishes summary knowledge. It can furnish items you haven’t considered, although others have, but always at an informational level only. However, when you’re totally stuck, any data point may offer a catalyst for a positive step. What most of us, like me, have trouble understanding is these chatbox codes have ingested a full university library with almost instant recall. Their ability to communicate in the local language is almost (but not) a sideshow.

6. Conclusions.

Of the usual suspects, Section 2, thinking or reasoning backward, while difficult requires a different view of the problem. As well, just the preparation in giving a talk on the problem usually yields some benefits, if even to show the problem may have no solution. Consider which is preferred: no solution is possible vs. can’t find any solution?  Dream states may be new to some. They confuse probably more than help. Yet, they are available if you can harness them. They are most helpful when just before waking, you are semi-awake and can “engineer” your dream on your own topics. Thought experiments, on the other hand, are serious problem-solving tools, particularly for creative thinking. They are not dreaming or daydreaming. They are solid thinking structures. Indeed, thought experiments are essential thinking for many problems, not just complex or impossible variety. Thought experiments are similar to thinking but often used to explore rather than contemplate.

Corporations and institutions have equivalents of CEOs, CIOs, CFOs, and the like. What is also needed is a CPO – Chief Problems Officer. This is a “guru-like” person, of great experience, who is entrusted to guide subdivisions in solving difficult problems, and even impossible ones. Problem-solving is a skill; it can be taught, and it can be learned. Yet, it is not a rigorous discipline. For personnel problems, many companies have an ombudsman to mediate. Why not a CPO? In any event, all institutions should cherish their best problem-solvers. You can’t do without them.

 

[1] Remarkable it is that nursery rhymes anticipate impossible problems before there were impossible problems.

[2] In the film, Game of Shadows (2011), Sherlock Holmes uses such a diagram to identify his arch enemy, Moriarty. Holmes called it a spider web.

[3]  Barrett, Deirdre. The Committee of Sleep: How Artists, Scientists, and Athletes Use their Dreams for Creative Problem Solving—and How You Can Too. NY: Crown Books/Random House, 2001

[4] https://news.mit.edu/2020/targeted-dream-incubation-dormio-mit-media-lab-0721

[5] https://news.mit.edu/2023/sleep-sweet-spot-dreams-creativity-0515

[6] Brendal, Elke, "Intuition Pumps and the Proper Use of Thought Experiments". Dialectica. V.58, Issue 1, p 89–108, March 2004.

[7] Mach, Ernst (1897), "On Thought Experiments", in Knowledge and Error (translated by Thomas J. McCormack and Paul Foulkes), Dordrecht Holland: Reidel, 1976, pp. 134-47.

[8] More intuitively, with a Maxwell demon on board, you can create a perpetual motion machine.

[9] Shawn Roades, The Business Journals, online at https://www.bizjournals.com/bizjournals/how-to/human-resources/2017/04/how-to-leverage-the-laws-of-thermodynamics-to.html#:~:text=The%20second%20law%20of%20thermodynamics,quality%20and%20eventually%20self%2Ddestruction.