The new powerful technique of
zero-based problem solving
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| Zero based solving |
We tend to start a problem solving process with previous biases.
Admitting that we can’t be totally free of biases, it is of great importance to
start a new problem solving process from as much neutral a standpoint as
possible. It will enable me the problem solver to analyze the new problem in
its own merit. After this analysis, if need be, old known techniques, methods,
principles and approaches I will use just as it is required to be used for solving
the specific problem.
At the very beginning, before analyzing the problem well, I should have no
opinion regarding how I will go about solving this problem.
I will start with a clean slate,
a zero base and an alert and bias-free analytical mind, prepared for anything. As I proceed
towards the solution step by step, gradually I will start forming rules and
patterns that I think will be effective in solving this specific problem.
This is what I call the Principle of zero based Problem Solving.
We know what is zero based budgeting and some of us have heard about
zero based thinking. Here we have used the abstract idea of zero based
approach in problem solving to form a useful principle. The important concept
here is the idea of zero based approach. It simply means, start fresh.
It is a powerful approach and can be used in situations in our lives
when we are in dumps, want to forget the past but cannot escape remembering.
The link below possibly contains some useful insights:
Now we will discuss solution to our Four Square Problem. I hope you have solved it
already.
Learning from
solving Four Square Problem
Problem
restatement:
Question 1: Divide the light grey unshaded area in square A into two
equal pieces.
Question 2: Divide the light grey unshaded area in square B into three
equal pieces.
Question 3: Divide the light grey unshaded area in square C into four
equal pieces.
Question 4: Divide the light grey unshaded area in square D into seven
equal pieces.
The original square is shown below for convenience.
Answers to the first two questions are easy.
The red diagonal line divides the unshaded area in square A into two
equal pieces and it is immediately visible to you.
While looking for the second answer, you perhaps imagined or visualized
the empty area as a collection of three equal squares. Basically in this case,
you have imagined square B in terms of a square made up of four smaller
squares. For this answer you didn’t have to wait long. By visual inspection,
the answer comes easily.
Perhaps the third question gave you some trouble. At least it gave me a little
trouble. By previous bias I tried to think square C as a square made up of four
squares – no, that won’t do – within a few seconds I found this. Basically the
unshaded portion here consists of three equal squares. We need to divide it into
four equal pieces.
How can we divide a three unit piece into four equal pieces?
Can we break down each part of the three part piece into four smaller parts?
If we do that we will get 3x4, that is, 12 smaller parts. These parts are equal
squares. Oh yes, we have got the solution now. Take three such adjacent squares
each. Do it suitably three times and you will get your solution (when you do
three, the fourth will automatically be created). The breakdown of the three
small squares is shown below.
And now the final solution.
I don’t know how you have got the solution, but
if you look at this method, don’t you feel this is a more sure and systematic
way of solving at least this problem?
Which principles did we use? In the question 2,
we straightway divided the empty space into three equal parts. That method we
can’t follow here we have tried and found out. This learning was through
analysis and application of Principle of Fresh Start.
This step of problem analysis is vital in
learning the nature and anatomy of the problem. At this step we have also
discovered that we need to divide a three unit area into four equal pieces.
As we are not using any fraction concept here,
the new derived requirement implies that we need to breakup each of the
three units into four equal smaller units. Do you find any similarity of
this concept with anything you know? Think over.
As soon as we know what is needed to be done,
we examine the smaller squares, and decide that it is easy to break each up
into four still smaller squares ending up with 12 small squares.
Now it is easy for us to get to the final
solution. First we combine three squares together four times to get four
collections each containing three equal squares. And last but not the least:
you need to actually implement this abstract solution, which is in your mind,
into the physical square domain.
Does it remind you of any school level knowledge?
Remember the concepts of divisibility and factorization. This is nothing
but application of those early basic concepts into another domain.
This is beauty of using abstract principles and
concepts in problem solving. A school level basic concept you have now used for
solving an entirely different kind of problem. Here division of space was the
core activity and required ability.
In the same way, in future if your MPSF finds
some similarity in a different problem situation, it will recommend use of this
abstract principle and will lead you to the solution.
By the way, can you say which is the abstract
principle we are talking about? Give it a thought.
We have used two highly powerful principles
here:
First we have used: Principle of Segmentation (or dividing or
fragmenting), and
Next we have used: Principle of Merging (or combining similar
things).
These are two of the leading principles in the
set 40 inventive principles of TRIZ which we will discuss in later sessions.
These principles have very wide applications.
Let us come back to the four square problem again. First we
finish answering the fourth question.
What was your experience in answering the
fourth question? Either you know the
answer instantly or you find it difficult. If you get the solution instantly,
you have used your intuition. Intuition is also a powerful mechanism towards
problem solving, no second thoughts about it. Intuitive problem solving is
fastest.
In emergent situations such as fire-fighting,
front-line battle in a war split second decision making is the necessity and
that kind of decision making is mostly intuitive based on experience and
training.
Unfortunately for me, I was stalled for about
10 seconds trying to segment the totally empty square D using complex methods I
had used in question 3. That was bias. This is one example of the need to start
fresh without any bias. The more you move along the earlier path, farther away
will you move from the solution.
In about 10 seconds I recognized my mistake and
started to think fresh from a zero base. It became immediately apparent
that I can divide the fully empty square into any number of equal pieces by
just dividing one of its sides into equal portions by drawing side length lines
parallel to its perpendicular sides.
This is another kind of segmentation. It is
segmentation, but used differently. You are segmenting a space by segmenting a
length.
This is more versatile, as by applying this
concept you can actually divide the square into any number of equal portions.
We say application of this concept here is more general in scope.
Now notice how we have used the same concept of
Segmentation in four different ways to answer the four different questions. In
the first question we have used simple observation. In the second question, we
have mentally broken up the space into three equal pieces straightaway at the
first attempt itself. To answer the third question we faced some difficulty,
but finally we reached the solution by first segmenting the squares into still
smaller squares and then merging them into required number of collections. In
the fourth question we have not used any of these techniques but took resort to
segmenting a side to segment a space.
Before anything let us see the fourth solution.
Concepts and
Concept structures
How to segment is an abstract concept. We may
think of this as a standalone concept. It can briefly be described as: a process of dividing something
into smaller pieces of same something.
This process of segmentation can be applied on
practically any physical thing that can be segmented without breaking it and destroying
its property. But before going down to a physical object we might discover that
the characteristics or properties of physical things form an abstract concept
layer higher than the physical things but below the concept of segmentation.
What are the physical characteristics on which
segmentation principle can be applied? What did we segment here? We segmented
space in the four square problem. From a general abstract concept of dividing into smaller pieces
we became more specific and learned how to divide space into smaller pieces. The four
different questions led to four different ways to segment space. Each of the
ways forms a specific variation of the concept of segmentation.
The following shows the relationships between
various layers of the concept segmentation in the form of a structure.
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| Concept structure of segmentation - in four square problem solving |
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But in addition to Space, we may further
consider applying the concept of segmentation to Distance (divide a distance in
kilometers), Time (divide a day into hours), or Weight (divide a quantity of sugar
into kilograms).
We segment many characteristics of tangible or
intangible things during our daily lives. Think of some examples.
How do we segment? In many cases we
have units and measuring instruments that help us in segmenting, but in many
other scenarios, we need to use our estimation.
For example, we may need to answer the following
questions with respect to an empty room.
How
many students can be accommodated in this room if used as a lecture room?
How
many workstations can be put here to form a computer lab?
How
many office desks can be placed in this room if used as an office room?
To
answer these questions, we need to estimate space requirement for students,
workstations and office desks with sitting chairs respectively. For each we
will use the concept of space segmentation, but suitably modified according to
the problem. Carrying out the actual segmentation, we need to estimate, each a
different type of estimation.
Thus
from the abstract concept of segmentation we become more and more specialized
and specific in segmenting as depth of level increases. Following is a
representative concept structure.
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| Versatile Concept Structure of Segmentation |
This
is a vertical segmentation starting with the abstract concept or principle
Segmentation at the Level 0. At the next level 1 we become more specific with
the idea of Segmenting Space. It could have been, Segmenting Time or Distance
as well at this stage depending on the problem model. At the next level 2, we
become still more specific with the concepts of Segmenting an office room, a
class room or Segmenting a lab room depending again on the problem definition
at hand. If I know how to segment Space, with a little more thought I should be
able to segment any kind of space. I would need the capability of estimation to
effectively do that.
This
is what we call Structure, rather a hierarchical structure. We will just state
here that Structures
are the skeletons that hold all knowledge. It is sufficient to know
here that clearly defined concepts and their inter-relationships form a
structure. When solving a problem, the very first thing that you may do is to
form a problem model in the form of a structure. It may not be explicitly drawn
on paper, but nevertheless forming such a structure in your mind makes the
problem solving much easier.
Interestingly,
most real life problems are inherently ill-structured. It depends on the
problem solver to create some kind of structure of the problem after due analysis
of the problem.
Isolated
concepts are of little value
When
we start learning about a concept, we may learn bits and pieces of it in the
form of concept components. At the very start, these constituent concept
components may not have many relationship links between them. At this stage of
unrelated concept components, we cannot use the components well. Once we start
relating the components and gradually establish a structure (it may be
hierarchical or a network or of other forms), it becomes highly effective and
usable knowledge. This form of inter-related concept structure makes retrieving
the whole structure from memory and using it effectively much easier. Load on
your memory decreases as well as power of knowledge increases.
Cramming
facts about a subject creates unrelated pieces of concepts of little overall
value, whereas well structured and connected concept structures represent
effective and usable knowledge.
Why are
these ideas on concept structures important for our purpose?
The
reason we are discussing concept structures at length is: to solve real life
problems of any new type, not only you have to use well-formed already existing
concept structures in your mind, but also you have to create such structures by
analyzing the new problem and only then you will have proper control on the
problem.
Building
powerful and effective concept structures is a continuous process and this
process speeds up if you are aware of existence and importance of such
structures.
Look
where we had started and where we have finally landed. This is again a process.
We call it Idea linking and Exploration. We discover new areas of knowledge and
new possibilities by consciously using idea linking and exploring and Problem solving needs continuous learning and
exploration.
Read my other blogs
on Innovative idea generation and its basic principles and Get smart, get innovative usingTRIZ
