First Blog

Often I get questions about math. Some tell me they like math but just can't solve the problems. What I always say is this. Life is solving problems. If you can’t solve problems, your life will be one speed bump after another, one crisis after another, one brick wall after another. Learn how to solve problems. First you learn at home from toys and your parents. However, school is the first place you learn this formally. Others are experience, reading, management, parenting, teaching, hunting, sports, carpentry, and many more. All teach applicable lessons for life's problem solving. As John Daly on What's My Line , would say about everyone. "My line is problem solving." Now a word about math... All that said, you may like math, but you cannot say you’ve learned it unless you can solve related problems. Otherwise, it would be self-deception.

The  late, great mathematician George Polya has advises all (math) problem solvers to begin with a guess. What the? Really? This question was recently posted on quora.com.  Here is the response I gave. For any and every problem you face, if you haven’t experience with the problem, you first think about and then guess how to solve it. Based on this guess, you try to solve it. If it fails, you use this information and guess again. Life doesn’t usually give you a road map. Well, not quite. The chef has a recipe. The judge has procedures. The accountant has principles. Hence, the consultant.  However, the hunter, the parent, the student, the president, the citizen, and most others do not. They guess, at first. You must start somewhere. Hence, the guess, hopefully the educated or experiential guess. You begin life with no methods; your journey through life adds experience which helps. Polya’s guessing mandate is little more than common sense.

Your brain is nature’s first attempt to manage big data. a. Too much and it dysfunctions. b. Some brains get filled but get cluttered like a dump. c. The best examples are those who can tease out what's needed when it's needed.  d. Some have the power to discard the irrelevant. e. Many keep working, always working on a problem.   f. Problem solving ability?  Use it or lose it.  g. Solving the hypothetical is like working out. It is possible that newer developments and needs by humanity to survive in the age of data, the next step in evolution has begun. It will favor a brain with adaptive, algorithmic sensibility.  It may be a rapid transition. In a previous evolutionary step, the brain with abilities to seek different food was favored. The hunter was born. To make and use tools to kill was another step to favor the hunter. The tool maker evolved.

There are two ways to solve a problem. A. You can either get what you want, or you can want what you get.—Ralph Barton Perry B.More graphically, you can shoot your arrow at the target, or you can move the target to where you shoot your arrow. However, in politics you never get what you want, but always hope to want what you get.

We most often talk of the evolution that occurred.  Yet, some evolutionary steps that could have happened never did and never will. This is a story of one example. Evolution that doesn’t happen.  I thought of this years ago, but never had a really good example.  Thanks to the BBC series  Blue Planet II – Coasts , we see the story of a bachelor sea lion that  discovers a way to trap yellowfin tuna.  Normally, any sea lion could never catch the very speedy tuna. But our bachelor thought up his method to herd the tuna into the dead end of a very shallow coastal region in the Galapagos.   When it first tried, the tuna escaped though the sea lion herded them into the shallows successfully. The problem? He could herd and close the trap at the same time.  Then he recruited some “friends” and they worked together to trap the tuna with one of them closing of the escape route.  Each enjoyed their own 60 kilo tuna – big meal-deal.  The creator of this trapping tuna scheme is no doubt a sea lio

Proposition .  Students should learn to solve problems in multiple ways.  Can this be so or are we asking yet again our students learn even more than what is needed? The short answer is "yes." Let me explain.  First, the math teaching community has embraced, I think correctly, the idea of multiple representations.  This means looking at data and functions in multiple ways graphs, tables, formulas, and the like.  In fact, I've written on this. See http://disted6.math.tamu.edu/newsletter/newsletters_new.htm#current_issue for the three articles. Second and more generally, the more facets of the same thing a person is familiar with, the better is his knowledge of it. When it comes to problem solving, the same rule applies.  If a person can solve a problem in two or more different ways, this is an indicator of their understanding of the problem and techniques to solve it.  If they can solve it in only one way, this is an indicator that they have a single method in their mind. 

Problem solving with rational and emotional choice theories. The heart has its reasons that reason knows nothing of. - Blaise Pascal (1623-1662) French mathematician, physicist and religious philosopher We all need to solve problems, daily and constantly. There are the more-or-less clinical methods of applying beliefs, programs, instinct, intuition, emotion, analysis, and just plain random choice. (See, Allen, 2013.) However, it is not as though one can simply turn on or off any of these methods. We want to believe we use appropriate methods at appropriate times. However, there must be some underlying guidance a person uses to select the methods used to construct solutions. Naturally, we are not discussing simple problems that demand a particular method. Math and science problems are among them. Note, it is not that such problems are simple to solve, but rather are simple to state with unambiguous clarity. Use accepted methods or you lose marks. Yet, man made climate change is. W

Problem Solving – the pathway to the impossible Life is problem solving.   From work to school to religion; in love in pleasure, in strife, we are always solving something.  Some problems are simple, some tricky, some poorly defined, some complex.  Many are impossible. We have not set about to discuss school math problems.  In a sense, these are the simplest of all because much of the toolkit needed for solving them have been presented in the course.  These problems are those with the greatest clarity, a unique solution, and for them there is always a final resolution.  You get it or you don’t.  We have an array of problem solving methods, from logic to emotion, from instinct to intuition, from random to programmed, and more.  These methods are applied individually or in combination, often generating intrinsic conflicts, resulting is partials solutions, no solution, personal solutions, new problems, new situation, and impossible situations.  Results can be satisfying or frustrating,

The End of Computing.   We put forth the question as to the end of computing.   That is, we ask when will computing and computers come to their end of innovative applications, though this is not a discussion about bigger and faster machines.   Sure, bigger, faster computers can and will push to new limits ordinary and well explored topics.    They have this, and will so continue.   We are entered into a discussion about the use of computers to solve new, even revolutionary, problems   of this world.  Examples of innovations now at the end of their road .   Of course, these examples may simply reveal this author’s lack of futuristic insights.  ·          Watch making – long the epitome of machines, the watch is now engineered with precision and at least mechanically do just about everything ever desired – extremely accurate time keeping.   Even still there has evolved a new technology for this task. ·            The horizontal milling machine - Just about everything a m

Impossible Problems by Don Allen Impossible problems are everywhere.   They are in your life, your friends’ lives, your work, your family, your dreams, your future, and your expectations.   No matter what you do, no matter what you try, you can’t avoid them.   Impossible problems come in many flavors. ·          Problems you can’t solve ·          Problems than change when you try to solve them ·          Problems solved on the basis of past knowledge ·          Problems involving a change of scale ·          Problems about systems exhibiting memory In this note, we take up the nature of impossible problems.   We will illustrate some, but naturally we cannot solve them.   We’ll consider these topics, though the last one is problematic. ·          Definitions ·          Categories ·          Sources ·          Creating ·          Solutions But we should begin with the nice problems – those that actually have a solution, and not only that a unique so