To Solve a Problem

To Solve a Problem
Don Allen
September 10, 2013

Life gives us problems, relentlessly, one after the other.   All of us are so blessed, though dubiously.   Some are economic, some social, some political, some financial, some family, some of power, and some of just everyday living.   We need to solve these problems, or at least resolve them to some end.  Long ago, and in many talks, I advocated the entire schools’ curriculum, from history to math, from English to cooking, be problems based.  So important is problem solving, those that cannot construct problem solutions are almost totally lost.  More simply, those that cannot solve their problems are at a disadvantage. 

There are many problems for the many people.  All have their unique signature and style.  All have their own techniques for solution.  This accounts for the fact that the physics genius may be fully incompetent at everything else. 

The problem with problems is just how many there are, and more importantly how different they are.  You may be a math whiz, but if you can’t figure out how to “fit in” to a social situation, you are relegated as something of a geek.  If you can dance through social situations but cannot understand simple political ruminations, you are something else – a geek of another color.  No matter what your vocation or avocation, you live through your problems and how you solve them.  Many do not even consider their lives as a series of problem solving events, but in a brief reflection it is certain they are there, with you constantly, requiring your time, requiring your consideration, and all requiring some sort of action.

When there is a problem at hand, there is a usually a method for solution. But what are the rules for the solution? The consummate lawyer may simply be unable to solve a problem of human relations; the mathematician may not be equipped to solve a problem of the law; they psychologist may not have the tools to even consider new zoning ordinances.  You need to know and understand the rules of engagement, and that is but one factor.  Another is that you need to know what information is in play.  Still another, you need to know how to apply your knowledge.

We come to the concept of “geekness,” which implies you have skill at one set of problem-types but relative incompetence at others.  I suppose most of us are “geeks” in this measure of the word.   Many of us consider ourselves to be problem solvers, though our skills are often applied in situations where our methods do not work.   We have computer geeks, social geeks, political geeks, auto geeks, and geeks of every type in the mix.  

What kind of geek are you?

Problem solving is many things, particularly in what it means and to who is solving the problem.  It is loaded with self-negating factors.  It is a subject well beyond critical thinking as currently regards, though less taught.  Problem solving is not a pure discipline. it is a philosophy, an art, a method, and more.  Problem solving involves …

·         Logical aspects

·         Analytical aspects

·         Complex scenarios

·         Contradictory knowledge

·         Multiple solutions

·         Contradictory solutions

Indeed, finding one solution often leads to new problems requiring further problem solving.  It may lead to the discovery of a better solution.  The discovered solution may be unsettling; it may reveal there are underlying unknowns not previously considered.  This gives problem solving an iterative nature.   

Merely considering what problems political leaders must confront exemplifies the multi-faceted nature of problem solving.  Problems confronting our leaders transcend anything we see in school classes, where there are usually a sensible solutions – even in English literature classes.   Problems are so diverse as to obscure a simple description, much less a method for solution.

Components of the Problem – that is, what you have and what you don’t.  We briefly recount the known and unknown facets of any problem or situation.

·         Known knowns – These are the “facts” of your problem.  You know them and work them to the best of your ability.  When the problem is so limited, your problem solving skills are paramount.  Analyze and solve.  Easy!

·         Known unknowns.   These are those facets of your problem you do not know.   They are there, but you don’t know the details.  Problems involving social situations loom huge here.  You have a situation; you know some of the facts but do not know others.  You know there is more to the story, but don’t know it.  What should be done?

·         Unknown knowns – These are tricky.  There are known facts, known paradigms, but you just don’t know them.  For example,  if you are attempting to resolve a social or political situation on the basis of your information, but there is more information you do not know, you make a delimited conclusion, knowing well it may not fit well.   I have seen so many students instructing me that “I will learn this theory (aka stuff) when I need to know it.”  But if they don’t know it is there to learn, they cannot carry out their program.

·         Unknown unknowns – These are most difficult.  You do not know what is unknown.  You are faced with a problem having unknown factors and cannot know them.  Strikingly, you know this, but are powerless to affect any resolution on their basis.   You must make a purported judgment, and this may be incorrect. 

Whenever one considers some aspect as “known” there is compounded with the simple fact that what is known is more-or-less a flawed evaluation of the true situation.  The legal, political, and social worlds are confounded by, let us say, those knowns associated with a particular opinion.  Now we are delving into beliefs – and we try to avoid this at all costs. You may have thought we were working toward how to solve mathematical problems.  In a way, these are the simplest of all problems.  All the data is known, all the methods are understood, and all the procedures accepted.  Even if you can’t solve them, you can believe in the solutions.  But why can’t all of us solve them, given all information is available?  Of course, it depends on your skill set.

All communities have wrestled with methods for problem solving.  Machiavelli’s famous book is in many ways a recipe book of problem solving for political and military leaders. A current method in education is to teach “critical thinking.”  This is good. It is good because mostly it applies to high information settings where all facts are at hand.  But critical thinking is seriously diminished when intuition and other factors are involved.   In this context, we consider just what the givens of any problem solving situation.  What are the variables, knowns, and unknowns?

To Solve a Problem - Solution Information

1.      High information – This is happiest of situations, wherein we know almost all of the facts of the given problem.  We simply apply our school-given logic.   Math and science problems are exemplars.  (Example.  Show that every third Fibonacci number is divisible by three.  Total information is given; just solve the problem.)

2.      Low information – Though we may not so regard a problem as so, often there is little information upon which to make an assessment, much less a solution.  In many of life’s problems, low information is the “status quo” of what do know.   We actually know little of the “knowns” though we happily make conclusions and even generalization.  (Example, Why is there a God, or not?)

3.      Mixed information – This one is most difficult.  We know well some of the aspects of the situation but not others.   Our solution depends on what we know and to a much lesser extent on what do not know.  How many problems offer us mixed information, and we ask how many solutions offered are based on what we do know, subtracting or diminishing what we do not or perhaps cannot know?  Mixed information solutions are the bane of problem solving.

To Solve a problem - Solution methods

A.    Logic  - the quintessential method of Aristotle.  One applies the known facts to infer and deduce an unfailing conclusion.  This is the preferred method.  Solutions are often claimed on an errant basis owing to “logical” deductions.

B.     Analysis – One analyzes the problem as to facts, situation, and the rules of the problem arena.  From this a logical conclusion is derived.

C.     Intuition – One applies an internal wisdom about the problem, not making obvious or analytical conclusions at any step.

D.    Experience – One applies personal  experience toward the problem at hand, what has worked  previously, and will it apply to the current problem.

E.     Expectation – One wishes a certain outcome to the problem, and applies the history of similar situations to make a conclusion of that which might occur now.

F.      History – Using history and similarly to what is now to what was then.  Conclusions are made on these bases.

G.    Authority– A favorite of the church and courts to apply what has been considered the solution to be the solution in the current circumstance.

H.    Brain storming – This may be new to many readers.  It involves stakeholders to jointly consider a problem or pre-problem to make possible scenarios toward a solution.  Low, high, or mixed information problems are included.  Often there involve serious but ignored unknowns.

To Solve a Problem – Exceptions
These issues and qualifiers concern real-life problems, those non mathematical problems for which no clear solution is available, evident, or deductible.   Most mathematical problems do not fit within the spectra of items below.  Yet, for most of life’s problems these are critical.

A.    Knowing that something is missing – In solving a problem it is known that some factor or factors are unknown to you.  You guess at what those factors may be, but can never be assured.  This is the quintessential problem of political, military, and social situations.

B.     While you may believe you have the full situation in hand, you suspect there is something missing.  Usually, except possibly in the antiseptic world of mathematics, there is some fact or event missing from consideration.  The reference here is to a significant one. 

C.    Believing complete information is available - This is a dangerous situation.  You believe you have all the bases, all the factors, and all the contingencies covered.  You have analyzed everything.  You have made a decision.   All of this is upon belief.  Other factors are there. They are not only unknown unknowns, but they are unknown unknown unknowns.  That is, you do not know that you do not know – that you do not know -  there are unknowns to consider.

To Solve a Problem - Flags

A.    Novelty – One aspect of problem solving is novelty.   The solution of a difficult problem may involve just that, something outside the proverbial box.

B.     Distrust of obvious – When making a solution, one is often cautioned about whether the solution is too simple, too obvious.   This flag is not exactly noticed by all problem solvers.   On the other hand, simple problems may offer the only and obvious solution.

C.     Subterfuge and Traps – Let us conclude that in dealing with an opponent,the “natural” solution may not be the correct solution, or as we may say the successful solution. 

D.    Bluff – In many problem solving situations, the opponent offers a bluff, something purported will happen if and when something else happens.  The bluff offers false “facts” into the considerations of the problem solver that transcend most normal methods. 

Needed for most.  Many problems in real life involve decidedly un-rational and illogical factors.  Even mathematical problems involve many such factors.  Almost all problem-solving methods involve the knowledge of non-analytic factors, or cleverness, but most transcend normal problem solving methods.

A.    Information – Needed is as complete information about the problem at hand.  If incomplete errant conclusions can be derived.

B.     History of the situation – What is exactly the history of similar problem types?  Can we study solutions offered and how to modify or correct them to the current situation?  Military leaders study assiduously the history of military conflicts, learning what is available and modifying their tactics accordingly.

C.     Rules of reasoning -  In most problems there are the rules of the road; that is what types of arguments are allowed to make conclusions.  “Out of the box” conclusions are often rejected no matter how correct they may be in retrospect.  Science is loaded with such rules, and often serve as a deterrent to new science.

D.    Capacity, desperation, or greed of the opponent – In this category, we consider alternate factors transcending facts and rules. They play a large role in problem solutions.  It the opponent has a diminished capacity, but this is not known, a solution to a problem using this plays a role.   Discerning this is key.  The same may be applied to a desperate opponent, or one overly greedy.  Both of these may influence any problem solving considerations, even though they may not be among the facts of the situation. These are not meta-factors, but rather they are ancillary factors 

E.     Power – The requirement for power often eclipses the strategies and tactics of many players in a problem solving situation. 

There is no recipe for problem solving

  

To solve a problem - Discussion Questions

1.      Consider this recipe for problem solving.    a. Determine what the problem is.  b. Relate the problem to your sphere of knowledge.   c. Apply combinations of that knowledge toward finding the solution.  You have applied it faithfully, but cannot solve the problem.  Give three reasons why this may be.

2.      Give two personal road blocks above and beyond logic that often prevent you from successfully solving a problem.

3.      The concept of unknown unknowns, as described above, seems to indicate an external world of knowledge about which you are unaware.  But you can.  How?

4.      Give those characteristics of a person that thrives in a low information setting. 

5.      Carol likes Ted, while Ted is dating Sally.  Bob kind of likes Carol, and Sally thinks kindly of  Bob. Can we make these four people happy?  Analyze this problem on the basis of this essay.

6.      The President is pondering going to war with a foreign power.  What are his/her unknown knowns?  Known unknowns?

7.      Give a situation where you needed to solve a problem, but knew something was missing in your considerations.

8.      Of the solution methods offered in this essay, Logic, Analysis, Intuition, Experience, Expectation, History, Authority, and Brain storming, rank them in order of importance.  After that explain why each possible ranking depends on the problem at hand. 

9.      What kind of geek are you?