Static and Dynamic Problems
Understanding "Problem Levels" and why they matter
Greetings! It has been a while since my last newsletter on problem solving. I apologize for my long absence! Thank you all for continuing to support this newsletter, providing suggestions, and offering encouragement! Each reader’s comments, questions, and feedback are truly appreciated as I attempt to make this a newsletter worth your time reading.
Over the last summer and early fall, I was occupied reading books and research articles on problem solving, planning some of the topics I will write about in future newsletters, and organizing the materials I will present in this newsletter. I look forward to connecting with my readers by conveying my dedication to bringing the concepts of problem solving to life in the most engaging manner I can achieve through writing.
An Author’s Note:
Effective communication of teachable information can be complicated for the writer in the modern world where there are so many different mediums available: for instance, video presentations through YouTube offer almost an ideal forum for quickly conveying information of a pictorial/visual quality (and for the receiver of that information, consuming is often much easier), but in many ways a “writer’s voice” is lost in translation to video, where the visual image takes on the superior position (in most cases) to the narrative and commentary. However, I am considering supplementing the material here with online classes that will have a slightly different focus than I have in this newsletter. I have considered Twitter (and other sites) as possible medium for shorter form lessons, but limitations also exist there. Whatever works best for those who want to learn more about problem solving, I am willing to try! Please offer any suggestions in the comments below on additional forums you would like to see this or other related content. But for now, on I write…
What are Static and Dynamic Problems?
As opposed to the activity of problem solving, a problem is a state of being (a problem exists at a certain point in time). That does not mean that a problem cannot evolve. Indeed, a single problem can develop into multiple problems, or the conditions and parameters that defined the original problem change. Therefore, problems can either be static or dynamic.
Static problems generally remain the same; dynamic problems change (evolve) over time. In the next newsletter I will discuss a closely related concept: Problems which can be described as functions of one or more variables (with initial conditions) that change over time.
Since most problems have a core set of initial conditions, the solutions to those problems are dependent on most factors staying reasonably stable, revolving around a few fixed points. Static problems are in many cases much easier to solve than dynamic ones. Complexity ensues when conditions begin to rapidly change, leading to possible chaos; a stable problem can quickly devolve into a disordered state (of affairs), where production of a successful solution becomes difficult, if not impossible.
Closely related to this concept is that of “problem entropy”: the idea that some problems can (and often will) get worse (or more disordered) over time. Most problems rarely resolve themselves…a broken egg does not reassemble itself. If a broken egg is a problem, letting it rest there is not going to fix it. It is a mess that needs cleaning, and no amount of wishing the egg would reassemble itself is going to lead to a solution.
Many problems in life are similar: situations can quickly become chaotic when multiple conditions change simultaneously, as often happens in very “fluid” events. Responding to dynamic problems requires not only quick thinking, but also expert recognition. The nature of evolving circumstances, added/updated information, and chaotic conditions can turn a simple problem into a complex one. That is why flexibility is a crucial component of effective problem solving, and why planning ahead without addressing contingencies can fail (especially when attempting to solve problems of life).
What the heck is a problem space, you may ask? Very simply, it is the sum of all the conditions, parameters, and variables of the problem, along with the domain in which the problem resides and the range of viable solutions. It is where the problem exists in a conceptual form and where all the potential solutions may be found.
For example, say your car will not start. Obviously, you are not going to start researching medical conditions. The domain of the problem in this case is the “space” of the operational and functional components of the automobile. Pretty large domain indeed, but once you have some other basic diagnostic information, the domain shrinks (as well as the range of the solutions).
Problem spaces are crucial in understanding the nature and scope of the problem, because they help you grasp not only how the problem might be framed and defined, but also what potential solutions may exist. These notions may sound theoretical, impractical to apply in real life, overly complex, even needless, but I can assure you they are of immense value when problems become really difficult or murky, when the path ahead toward a solution is blocked. I believe in the back-to-basics approach to problem solving…fully understanding the problem backwards and forwards can save resources down the lane. Basically, know where the problem comes from and where the solution may be located. Even understanding the “history” of a problem can be helpful, as you can back trace it to its origin.
There exists a hierarchy with which we can evaluate the difficulty of most problems. This idea can be described by the idea of “problem levels.” Every problem has an innate, or implicit, level of difficulty, regardless of whether a problem solver can explicitly state the precise difficulty level (some problems appear easy to solve, often by their apparent simplicity of statement, but are fiendishly difficult, if not impossible to solve - some problems appear extremely challenging yet yield to solution easily). Categorizing problems (as has been done in mathematics and computer science) - even the notions of solvability and time needed - is an important method of problem classification: knowing exactly what kind of problem you are confronting and assessing its potential likelihood of solution can offer a reasonable point of departure.
Not all problems are of the same quality or difficulty: this is a seemingly obvious statement but bears reiteration for those who may believe one problem is as good (difficult) as another. Problems vary in their size, scope, complexity, quality, and probability of successful solution.
Every problem can be classified by what I refer to as a “problem level.” These levels are a broad categorization, of course, but understanding where a problem fits into this particular hierarchy may give some insight in to what resources may be required to solve it. My classification is not meant to be all descriptive, nor all inclusive of the many different ways problems may be classified…instead, it is a panoramic overview. A finely detailed breakdown of all conceivable problem types is a future project of mine.
One may wonder why this might matter at all; that is, why is understanding how difficult a problem is or may be a useful measurement)? The answer is that you (as a problem solver) not only need to understand what you might be facing when confronting a problem, but also if that problem is worth the time, effort, and other resources to solve. Additionally, my categorization may help one understand that the problem is not within the problem solver’s ability to solve at that specific time, without further knowledge, skill, insight, or other assets related to the solution of the problem.
Level 1 Problem Solving
Level 1 is the most basic kind of problem solving: Static problems are often the easiest to solve because one is exactly aware of what needs to be accomplished in order to reach a satisfactory solution. Conditions and variables are constant. In many cases, most if not all of the information to be assembled into the solution is available, so piecing together the solution equates to performing the steps, and then the problem is solved.
To be sure, not all Level 1 problems are easy. Often, they require an enormous number of steps that all have to work in unison. Think of the problem of cooking a complex dish that you have never tried before. The problem space domain is cooking (and all the skills necessary for that…quite a lot). The range of practical solutions consists of the dish that comes as close to your ideal as possible. However, this is not such a easy problem, even though you may have the exact recipe in front of you. Many things can go wrong, but as long as you are by yourself or are free to concentrate on cooking (no changes in the conditions or variables), all is pretty much determined except for your performance. Not having the right ingredients or the right tools would take this problem to the next level…
How do you know which level a problem may fall? Well, certain problems are just reasonably easy. When I say “easy” I am NOT trivializing these problems. Easy, in this context, means there is a method of solution that exists (often procedural or step-by-step) and which can be found in a “reasonable” time frame. Given the right approach, method, strategy, technique, time, etc., many problems fall to constant attack or brute force.
For example, say you have locked the door to your office (or whatever) and do not have the key. There are no windows, no spare keys around, no obvious way to get in. What could you do? This can be defined as a problem worthy of solution if you must finish a project on your trapped laptop in the next hour and do not have time to call a locksmith. (Yes, this happened to me). I will leave it as an exercise for the reader to contemplate and comment below on some possible solutions, but I can guarantee there is a solution. The point here is that while a problem like this has urgency, it is straightforward to solve once you become creative. It is “essentially” easy…Level 1 defined.
Reducing complex problems to simpler ones is one of the best qualities of expert problem solvers. Often, one approach is to break a problem apart by creating sub-problems whose solutions may be much more accessible. Then one can reassemble partial solutions into a whole solution. Problems are similar to puzzles; fitting the right pieces together in the right order is the challenge.
Level 2 Problem Solving
In the next level, problem solving takes on an added dimension: Changes in the quality or quantity of information required to solve the problem. Level 1 problem solving contains a problem “space” which is definite, or well-defined, without any (or very little) deviation over time. The problem (type) doesn’t change…there’s no fluidity. However, Level 2 throws information complexity into the “mix.” To successfully attack, and eventually solve Level 2 problems requires adaptability. You may not have all the information at hand to solve the problem, or the information changes over time, so that the problem solver must incorporate a “watcher” function, that is, a separate thinking “channel” to take into account new information to add to the existing conditions of the problem. This requires updating the problem space. It also requires sensitivity to changing conditions and the ability to adapt.
To use the above example of cooking, imagine that now you find out that you do not have all the right ingredients. What to do? This is a problem! To complicate matters, your roommate decides to come home early and begins to distract you with the details of some other problem. The domain does not change that much (except now, in addition to your updated problem, you have to know how to deal with a distraction as you are preparing the dish), but the range of the possible solutions has to be reimagined with the new information (you lack all the necessary ingredients).
This problem may seem trivial, but an analogy here is of that of solving deep problems in mathematics or any other field….quite regularly, one particularly fruitful approach to solving such a problem may be interrupted by the realization that someone has already tried and failed at the approach you hoped to use, or that you simply do not have the right ingredients. What do you do then? Is it back to the blackboard time? Not necessarily, because in changing conditions, or in recognizing another person’s failure to be able to use a particular method to solve a problem, you can update your vision and learn from that, or see another path towards a solution, perhaps even using those changing conditions or failure as a springboard in another direction. It is important to keep an open mind and realize that there are many directions in which to search for a problem solution!
Level 2 problems generally are not problems that will surrender to clever techniques, application of simple ingenuity, or brute force methods. The difference between Level 1 and Level 2 problems is that Level 1 problems have the characteristic of “present solvability.” That means that such problems, once a great technique is employed, can be “broken” quickly without much additional effort. Level 2 problems do not have this quick fix quality, since they have subtleties, changing conditions, or complexities that may be overlooked at first. Because they require more than just ingenuity, most efforts to solve them become complicated by overlooking those complexities, failing to update or take into account current conditions, not seeing the problem holistically, missing pieces of information hidden in a forest of details, falling into “solution traps” (a solution that appears an easy fix but which creates even more problems), and failing to recognize the intrinsic nature of the problem.
In battles and war in general, Level 2 problems are quite common. History is replete with battlefield generals falling for the “easy solution,” misclassifying the conditions and missing the complexities they will face in solving these chess-like problems. Great generals are great problem solvers, either by nature, learning, or experience: they have to be, or the consequences of their poor problem solving (and decision making) results in the catastrophic loss of life. Deep problems rarely have shallow solutions.
And when I say that Level 2 problem will not fall to simple ingenuity, I am not implying that ingenuity is not important or necessary. Ingenious solutions to Level 2 problems are the hallmark of great scientists and mathematicians. Likewise, seeing the “world” in a new way, as Einstein did, or Carl Jung, or any of the other great minds in history, from all civilizations and cultures, is the key to solving difficult problems. Perspective, changing your viewpoint, is often required in producing novel solutions.
Most problems are Level 1 & 2
Seemingly, most problems would fall into the two prior categories. And that assumption is correct…since these are broad categories, I will state (without proof) that about 67-70% of most problems are Level 1, that is, the majority. Most problems (in one “form” or another) have been solved or could be solved with the right technique, even if you do not presently know the exact solution. This should give most problem solvers some comfort: the majority of problems you will face can be solved relatively easily with some effort. Even life problems have this characteristic…most people have gone through, at some point in time, what you may confront in your life. This is not to say that your problems are not unique to your life situation, just that you have company, and that if you have a problem that can be solved, there might be a possible solution that works in your situation that someone has already discovered. Unfortunately, there are just some problems - if they are “framed” in a problem-solving setting or “problem space” - that cannot be solved by any “traditional” method or in any logical sense. Some problems have no positive solution or any solution at all.
Level 2 problems comprise about 25-28% of the remainder. Why are about a quarter of all problems (by my calculation) Level 2? Because we humans still face difficult problems of which there is no easy solution and which are also changing over time. These are dynamic problems. Just look around…if all problems were pretty easy to solve, then most pressing problems would not exist, because almost all problems are cascading, sequenced, that is, they lie atop (or near) other problems (solve one class/type of problem and you often solve them all), building up in layers like a mountain. And there are a lot of mountains of problems that exist. This should give aspiring problem solvers pause…there is much need for super problem solvers in our world, so that no matter the field one chooses to work in, problem solving rests as a foundation on which to tackle problems humanity faces now, or will face in the future. As many problems that exists now, there is nearly an infinite train (or terrain) of them right behind (or in front). We need to get to work NOW! This is a call to action!
Level 3 Problem Solving
What is left then? Level 3 problems have a deepness and structure that make them foundational. These problems make up most of the remaining 2-5%. Mathematics and physics are replete with such problems. For instance, the Riemann Hypothesis (named after Georg Friedrich Bernhard Riemann 1826-1866…Einstein used Riemann’s work in differential geometry in his world changing work on relativity) has roots so deep in mathematics that the proof that is it NOT true (it probably is true) would have profound implications (not just in math). So, the key to understanding Level 3 problems is that their solution opens whole new world of understanding about the nature of existence. Limits of space travel, saving our planet from future destruction from any cause, solving deeply human problems such as sickness, hunger, poverty, war, among many others, are Level 3 problems. Their solution would change the world as we know it. Solutions may not exist, but humanity’s continued search for “answers” helps define what makes us human: the idea that progress is possible, not narrowly defined by any political, economic, or social perspectives, but by the philosophic idea that if we want a functioning place to live, the race to find specific solutions to these pressing problems is paramount and foundational to our mutual happiness and continued existence.
Level 4 Problem Solving
Level 4 problems are transcendental and deal with the very nature of existence of all living beings. Is space and time conquerable (so that we can control it)? What will happen to us as a species in the future and can we prevent our extinction? How can we continue “life” as we know it in the distant future? These problems, and many more unformulated or unknown ones, whether framed by science or technology or philosophy or religion, are beyond the scope of any one person’s ability to solve…or are they?). Do “solutions” to these these profoundly deep “problems” even exist, or have they already been solved for some? Let me know what you think in the comments…
The deeper you dig into a problem, the more layers you see, until the true structure becomes evident…When you reach that place, you have gained knowledge that will help you navigate towards a solution. Value the search as much as the discovery.
I would finally add in closing that my approach to classifying problems by their types (static vs. dynamic) and their levels (1-4) is not meant to be reductionist. The variety and types of problems that exist are approachably infinite. No simple classification system can capture the the diversity of all problems that exist. However, being able to have a broad overview of where your problem resides in a larger sense does provide clarification of its overall importance and scope.
My best problem-solving advice: Solve the toughest problems you can!
Happy Problem Solving!
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