by: Karl Albrecht


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Dr. Karl Albrecht is a management consultant, seminar leader, professional speaker, and a prolific author. He has written five other Prentice-Hall books, including Brain power. Learn to Improve Your Thinking Skills.

Brainpower was the basis for the best-selling training film of the same name, starring John Houseman. Karl Albrecht teaches Brainpower seminars to many executives and managers in business organizations.

L OGICAL THINKING IS SIMPLY A MATTER OF ORGANIZING AND MANIPULATING INFORMATION. Problems or situations that involve logical thinking call for structure, for relationships between facts, and for chains of reasoning that “make sense.” When faced with a problem or decision that requires some kind of logical analysis, how do you react? To what extent do you think of yourself as a logical person?

Research into practical thinking processes has shown that there are two contrasting types of reactions that many people have, with relatively few folks falling in the middle. On the one hand, there is the challenge reaction. One person sees the situation as an opportunity for a bit of mental exercise, in addition to a problem in need of resolution. Just as a person who enjoys playing tennis responds positively to being handed a tennis racquet, so a person who enjoys clear, logical thought responds positively to being handed a situation that calls for analysis.

At the other extreme, there is the avoidance reaction. This person sees the situation as threatening, uncomfortable, and involving an unpleasant and defeating experience. He or she experiences what might be called the failure reflex, a snap-reaction feeling of dread, which originates in ancient experiences of having been defeated by situations similar to the one presenting itself. Just as the person who is in very poor physical condition tends to get negative feelings at the prospect of playing a round of tennis, so the person who has trouble with logical thinking tends to shudder at the anticipation of a round of logical thought.

WHY THE DIFFERENCE? Why is it that some people are skilled at logical thinking and enjoy it so much, while others nearly break out in hives at the mere prospect? Why have some people imprisoned themselves within a self-definition as basically scatter-brained, using the disclaimer “I’m basically intuitive” as a cop- out? Why shouldn’t they be able to use their intuitive processes together with their logical processes, rather than instead of them?

THE ANSWER, for the most part, is fairly simple: experience. By various means, the logical thinker has had opportunities to master certain basic mental procedures that work well in a broad variety of situations, and has been rewarded in different ways for using these mental processes successfully. The person with an aversion to logical thinking has found this kind of experience consistently unsuccessful, very defeating, and unpleasant.

Because no one will repeatedly seek out experiences that threaten his or her self- esteem, this person falls into a self-reinforcing pattern of avoiding experiences that would help to develop these skills.

This explains why so many adults suffer from mathephobia in varying degrees. Learning mathematics is a highly sequential process. If you don’t fully grasp a certain concept fact, or procedure, you can never hope to grasp others that come later, which depend upon it. For example, to understand fractions you must first understand division. To understand simple equations in algebra requires that you understand fractions. Solving “word problems” depends on knowing how to set up and manipulate equations, and so on. A person who has trouble with mathematics as an adult must have been, at one time, a child who understood everything that had been presented up to that point.

But sooner or later, the child stumbled over some concept that didn’t make sense. This created a blank spot in his or her learning, and as a result certain concepts that came thereafter never quite made sense either. As the child’s confusion increased and feelings of inadequacy set in, he or she sooner or later concluded “I’m no good at math.” For all practical purposes, this was the end of the learning process. Many people, during their adolescent years, give up on math in this way, and extend their aversive feelings to just about all situations involving the intricate mental processes of logic, sequential thinking, and organizing information.

 Mathephobia is a learned mental process, just as logical thinking is a learned mental process. Please let me repeat Mathephobia is a learned mental process, just as logical thinking is a learned mental process

If you suffer from some degree of mathephobia, or from the more general problem of “logicophobia,” you can begin to erase this self-defeating reaction in two ways. First, stop avoiding or copping out of problem-solving situations that call for logical thinking. Facing up to an uncomfortable situation, and being determined not to feel worthless if you can’t solve it, goes a long way to finally eliminating the failure reflex. Second, you can study the known specific mental techniques used by effective problem solvers, master them, and put them to use on a daily basis in a wide range of experiences. The first of these options is your very own responsibility. This book can help you with the second.

People with logicophobia seem to think the effective problem solver simply looks at a situation, and by some magical act just solves it. They don’t quite realize that the logical thinker has certain fairly specific procedures at his or her disposal, which have the effect of organizing the information, reducing ambiguity, eliminating all extraneous factors, zeroing in on key variables and relationships, and extracting certain findings. This is not done in one fell swoop. It is a succession of mental actions ----a sequence of individual steps that leads to a solution, not a giant leap.

IT HAS BEEN PROVEN THAT SPECIFIC TRAINING IN LOGICAL THINKING PROCESSES CAN MAKE PEOPLE “SMARTER.” Professors in the physics department at the University of Massachusetts created a tutorial program for physics students who were having trouble with their courses. The most common complaint these students registered was “I can do the math okay, but I have a lot of trouble with the word problems.” From this, the professors concluded that the problem students were deficient in a key mental skill they called sequential thought. This type of thought is the ability to take a poorly organized statement of a situation and arrange it in the form of a sequential chain of statements and mathematical operations that will produce the solution . By studying the comments these students made as they attempted to solve physics problems, and by studying the comments made by graduate students who were expert problem solvers, researchers were able to develop teaching techniques to help students increase their skills at sequential thought.

In a similar vein, I have been analyzing both logical and creative thinking processes as part of my research for courses in thinking at the University of California extension, and for “Brain Power” seminars in corporations. I have found that being able to apply a simple label to a certain thought process equips a person to develop it and to put it to use on a consistent basis. The more you think about thinking, the more clearly you learn to think. (MAKES SENSE! ) The more you think about thinking, the more clearly you learn to think.

Come along with me for the next few minutes on an unusual excursion ---—inside the human mind. Let’s listen in on the thought processes of a person who is a clear, logical thinker. We don’t know who it is, man or woman, old or young, well schooled or not. We can just hear the thoughts being expressed as they move along. This person is working through one of those little thinking puzzles that require a logical attack. As you read the transcript of the person’s thought processes, the symbol (!) will alert you to a mental procedure he or she is using to gain control over the information and organize it in such a way as to make the solution easie r to grasp. Let’s go.


If three days ago was the day before Friday, what will the day after tomorrow be?

What’s Going on in the Thinker’s Mind?

“Let’s see, now . . . if three ... hmm . . . (!) the goal is to find out what the day after tomorrow will be—right? . . . Yeah . .It’s worded a little confusingly; wonder if I can (!)rephrase it to make it easier . . Well, I can (!) reduce it to some extent; the day before Friday means Thursday, so three days ago was Thursday. . . . Now, I can (!) count forward in steps to figure out what today is. So, it goes Thursday (three days ago), Friday, Saturday, and today must be Sunday. That (!) narrows it down to finding out what the day after tomorrow means. If this is Sunday, then tomorrow is Monday, and the day after tomorrow is Tuesday. So the solution is “Tuesday.” Let me (!) verify that . . . (counting on fingers) Thursday, Friday, Saturday, today is Sunday, then comes Monday, and finally Tuesday. Yep, it checks out. I’m hungry—guess I’ll go have some lunch.”

If you followed my editorial signals while listening to the low of thoughts, you may have noticed that all of the key steps contributed to one basic purpose: organizing the available information into a useful form and progressively reducing the problem by extracting useful conclusions from what was known so far. This is basically all there is to clear, logical thought—getting the information under control and then using it.

By studying the thought processes of clear thinkers and by analyzing a variety of logical problems and situations, I have succeeded in isolating seven critical procedures that seem to spell the difference between fuzzy thinking and clear thinking.

These seven mental tactics give a person a measure of control over the information in a situation, and make it easier to find solutions. I have given them simple descriptive names to make them easy to learn and memorize. Throughout this book, I will be showing you how these logical tactics work, illustrating ways to use them, and giving you opportunities to practice with them.

The seven basic logical tactics used by effective thinkers are as follows:

1. STEPPING — attacking a problem in simple steps or stages; dividing the

problem up into manageable parts: patiently exploring one thing at a time until you can come up with a logical chain of facts and conclusions that give you the answer you need; drawing simple if-then conclusions.

2. PICTURING — drawing a sketch, diagram, illustration, or other visual analogy you can work with.

3. REPHRASING — stating the problem in a different way by using terms that are more convenient for your own understanding.

4. FENCING — reducing the problem to a smaller scale by making certain

simplifying conclusions or throwing out irrelevant considerations putting a figurative “fence” around it to make it more manageable

5. ITEMIZING — simply listing all of the known options, possibilities situations, arrangements, or combinations that you need to evaluate in finding the solution.

6. CHAINING — arranging a variety of options and suboptions in the form of a logical chain, a time sequence, or a branching tree-type diagram so you can track down and account for all of the known approaches that look feasible.

7. JUMPING THE TRACK — stopping to reconsider the whole course of your

attack on the problem; starting again with a completely different approach or a different point of view; enlarging the range of options to include unusual or novel ones, sometimes by means of a creative leap.

As you read through this book, I will show you how a skilled thinker uses each of these seven logical tactics to overcome problems that look confusing and very intimidating at the start. By listening in on this person’s thoughts, you will have the benefit of a role model for thinking. Each of the seven tactics is treated in a separate chapter. In each of these chapters, I will first show you several simple puzzle problems, give you a chance to work on them, and then take you on an new excursion inside the mind of our expert thinker to see and hear how he or she attacks it.

Then, I will offer several easy practice problems you can use for skill building. By observing a role model who uses the techniques, and then trying them on your own, you will soon become familiar with them and more comfortable in us in them.

Before we study each of the seven key mental tactics in detail in the next chapters, we need to consider one very important issue. This is the issue of your psycho-logical reaction to a logical challenge. As I mentioned previously, people vary widely in the extent to which they feel comfortable and confident in dealing with complex, intricate, or confused situations. Some people, usually by virtue of their early life experiences and formal education, develop a fair degree of skill in logical thinking. Others, unfortunately, again because of their particular experiences and education, develop a very strong aversion toward anything that smacks of logical analysis or logical relationships . Most people are somewhere in the middle, neither extremely good at logic, nor extremely poor. Nevertheless, many people do report feeling slightly discouraged and mildly anxious when confronted with situations that demand a logical attack. So if you consider yourself somewhat logicophobic, you are in good company. Probably the vast majority of people share this problem.

Logicophobia is not a terminal illness, and it can indeed be cured. You may have no desire to compete with the best scientific minds, but you probably recognize that you could benefit to some degree by increasing your mastery over basic logical processes. Here are some suggestions for anyone who wants to become more comfortable with logical thinking .

First, make up your mind to stop fighting logical thinking, and join it. By this, I mean that your own feelings of distaste for logical processes may be ge-tting in the way of your skill because you may be deliberately avoiding situations or problems that call for logical thought. Consider the possibility that you can just deliberately change your attitude you can decide to feel relaxed and at ease with these same situations, whether you can solve them or not. The next time you find yourself in a logic situation, move toward it rather than away from it. Get involved with it to some extent and do as much as you can. If you’re working with other people, don’t let them monopolize the project simply because they may be good at logical thinking. Contribute your part and don’t feel guilty about not knowing the whole answer. While you’re at it, consider asking them to explain things to you, coach you, and help you develop your skills.

The second thing you can do to overcome logicophobia is to learn and apply the specifi,c logical tactics covered in this book. Memorize the names of all seven of them and be able to define them in your own words, even if you may not feel entirely secure about using all of them. Work through every single exercise as well as you can, each time developing more and more of a feel for the processes of organized, sequential thought.

Another thing you can do to help yourself is to pay more attention to the way you talk. People who are extreme logicophobes, bordering on the scatterbrained, tend to talk in a scattered way. They jump around from one idea to another and they neglect to tie their ideas together so other people can understand them . If you train yourself to talk logically, you will begin to think more logically. Form the habit of explaining things to people in complete sentences, using an “A-B-C” sequence of ideas rather than a random “brain dump.” Train yourself to stick to one topic at a time in a discussion, and make sure you have explored it properly before you move on to the next logically related topic.

Work on developing a sense of determination in yourself about dealing with logical situations. Develop an aggressive, energetic attitude, with the feeling that you’re going to attack the problem vigorously, and you don’t care about the fact that you might not be able to solve it completely. You’re going to give it your best shot and accomplish as much as you can.

This sense of determination will help you to deal with the blank wall effect so commonly found in dealing with complicated situations. By this, I mean that momentary hopeless, somewhat overwhelmed feeling you sometimes get when confronted by a problem that looms large and complex, especially if you don’t just immediately see an obvious starting point. Sometimes you just draw a blank, and look at the problem with no glimmer of enlightenment. You feel overwhelmed by the whole and unable to deal with its parts.

The way to cope with the blank wall effect is to simply start somewhere---—by choosing some particular factor and examining it. To mix metaphors a bit, forget about the forest for a while and start looking at some of the trees. Logical problem solving is not a purely mechanical process, with all of the steps clearly laid out and executed. Every problem requires at least a certain amount of “intelligent groping,” in order for you to get enough of a feel for what it is all about. Once you mentally get involved with the problem, you will usually see certain lines of attack that look more fruitful than others.

Teach yourself to jump in with a bit of intellectual bravado, confident that a little familiarity with the nature of the problem and its key features will enable you to decide which of the key logical tools to apply.

The basis of all logical thinking is sequential thought. This process involves taking the important ideas, facts, and conclusions involved in a problem and arranging them in a chain-like progression that takes on a meaning in and of itself. To think logically is to think in steps. People who have difficulty with logical thinking usually have very little patience with these intricate, step-wise processes. This is especially true for those who consider themselves very highly intuitive, for example, and who shudder at the mere idea of having to balance a checkbook or write out a plan for some project.

If you feel you need to improve your logical skills, the best place to start is in improving your ability to handle sequential thinking processes. You must not only learn to tolerate the process of thinking in deliberate, discrete steps, but you must actually develop a certain preference for it. Sequential thinking should be a first resort in those situations that call for it, not a last resort. There are times when an intuitive, flashtype thought process is called for, and other times when a carefully reasoned, linear process is necessary. The mentally versatile person is the one who can do both, and who feels equally comfortable with these two valuable kinds of thinking processes.

The most useful weapon you have for attacking just about any kind of a problem is a pen or a pencil. By drawing a picture, a sketch, a diagram, or some kind of visual representation of the problem, you immediately force it to hold still. You gain a certain degree of mastery over it.

This one factor is probably the most important difference between people who think clearly and logically and those who do not. The skilled logical thinker realizes the value of conceptualizing the problem graphically, putting the various factors down on paper, and organizing what he or she knows so far.

The unskilled or inefficient thinker tends to simply sit and muse, without embarking on any particular course of mental action, as if waiting for some inspiration to strike I call this the syndrome of waiting for the cosmic ray.

Many unskilled thinkers seem to believe that logical thinkers simply “get” the

solution to a problem in a flash — that it somehow pops into their heads fully formed. They have no idea that the logical thinker actually moves into the problem in small, clearly defined steps and develops an organized picture of it.

Very few logical problem solvers neglect the tremendous benefits of pen and paper. The skilled thinker can seldom be found without a pen somewhere on his or her person. Conversely, the fuzzy-thinking person seldom has a very high regard for those two useful implements. He or she will often encounter situations where a pen is needed and will simply shrug helplessly, and be forced to do without, or try to borrow one from someone else. I have even had people show up in one of my seminars without so much as a pen or paper, presumably expecting to spend all day learning something.

Drawing pictures to help you think logically is fairly simple. It is more of an attitude and a habit than a skill. It has nothing to do with artistic ability—it simply involves taking information and putting it down in a concrete form for further study and thought. As before, we will listen in (and, in this case, look in) on the thoughts of a skilled thinker, to discover how he or she uses graphic techniques to get control of problems and solve them.

Often a problem or situation seems overly complex or hard to understand, simply because the words someone else uses to describe it to you are complicated, vague, or confusing. By rephrasing the problem in your own words, you can get it better organized in your mind. You can simplify it and get a firmer grasp of it.

Here is an example of a simple problem.

How much is two-thirds of one-half?

If you recall your junior-high school math, you remember that this problem calls for a routine procedure dealing with the manipulation of fractions.

You say something like: “Two-thirds of one-half.... . . that means I have to multiply two fractions together. Let me see--— what’s that procedure? Multiply the top number of one fraction by the top number of the other and use the product as the top number of the new fraction . Then, multiply the bottom number of one by the bottom number of the other and use that product as the bottom number of the new fraction. So, two times one equals two—the top number of the answer; and three times two equals six—the bottom number of the answer. I come up with two over six, or two sixths. Now I see that two sixths can be reduced to one third. So the answer is: two-thirds of one-half is one-third.”

Fairly simple, yes? Now consider this problem: How much is half of two- thirds’? The answer fairly jumps out at you : Half of two-thirds is one-third, of course. This is exactly the same problem you just solved, simply worded in reverse order. Just by changing the way we stated the problem, by rephrasing it, we have made it simpler, easier to understand, and easier to solve . Rephrasing is one of the most powerful thinking strategies available to you, and it is fairly easy to start using it more frequently.

Resolve right now that you will never again accept another person’s phrasing of a problem situation unless you have thought about various other ways to phrase it, and determine that the other person’s way can help you to think about it clearly. Make it an automatic habit to restate, to paraphrase, to clarify a problem statement until you feel comfortable with your understanding of the problem.

Let’s try another example of rephrasing, this time with a simple problem that invites creative thinking as well as sequential thinking.

A man playing golf drove his first ball so well that it rolled right onto the green. From a distance, something about the ball looked peculiar. When he arrived at the pin, he noticed that the ball had rolled right into an empty paper bag that had apparently blown onto the green. With the ball inside the bag, he couldn’t figure out how to sink the putt for his birdie. Then he suddenly realized how to do it. What was his solution? Think about it before you read further.

How did you make out?

In any case, let’s tune in on the thoughts of our friend the logical thinker, to see how he or she would attack it.

“Hmm .. ... . I don’t want to waste a shot getting the ball out of the bag so I can knock it into the hole. What shall I do? Let me see-----I want to get the ball into the hole. First, though, I want to get it out of the bag. (! )Or maybe I just want to get rid of the bag (rephrasing) .. .. .. I’ve got it! I’ll light a match, set fire to the paper bag, and let it burn to ashes. Then I’ll just blow away the ashes and sink the putt without any hindrance.”

In this imaginary dilemma, we can see that rephrasing the problem helped to find a workable solution. It enabled the thinker to make the creative leap from trying to hit the ball to getting rid of the bag. This is a good illustration of the intimate connections that can and should exist between “logical” thinking and “creative” thinking.

Make it a habit to talk your thoughts out loud in a problem-solving situation whenever possible . If you’re alone, or with compatible people, just start verbalizing different thoughts or fragments of thoughts. This kind of loud thinking gets your mind working in a sequential mode, and helps you start moving toward a solution, however erratic or uncertain that motion might be. It is very important in logical problem solving to get moving and to escape from a dead-center position in which you simply sit and stare at the problem.

This book is available at a special discount when ordered in large quantities. Contact : Prentice Hall Press, Reference Group Special Sales, 13th floor,

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                                                   Copyright © 1984 by Prentice Hall Press

                                                                A Division of Simon & Schuster, Inc.

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