Change is inevitable and all pervasive
All things change. This is nothing new. But the change itself may be considered an important entity to be used as resource for efficient problem solving in various areas of activity and thought.
Global warming
Rise in temperature worldwide is of great concern and studied in details regarding what can be its effects and how much the damages might be. From management perspective, temperature is one of the key parameters in understanding climate behavior.
Change use in Organizational environment
In every operational environment we identify key parameters to measure their change at regular intervals, effects analyzed, causes identified and actions taken to keep the operational environment at desired state.
In organizational context Change management is an important topic of interest.
Use of change in health domain
In medical diagnostics, temperature is a key parameter in many illnesses. At home when my child catches cold, I check for fever by placing my palm on her forehead to judge the change in temperature from my experience. Physicians prescribe suitable medicines and observe the change in temperature to see whether the medicine is effective in killing the cause of fever.
Temperature though is not the only key parameter in health domain, there are myriads of others. Measuring changes in these parameters, identifying and removing the causes form the backbone of the efforts in keeping humankind in good health.
Change used in R&D
In life science research, change in state is closely monitored by inducing the change artificially through different types of stimuli to the entities of interest and the bio-environment involved.
Change as an independent element of study
The more we know about change as an independent element, what causes the change and by how much, what are its effects and how the harmful effects can be minimized, the more powerful would be our usable knowledge.
Study of change in itself is a subject.
We would highlight here only how you can solve your problems faster using Change analysis technique as a powerful problem solving resource in real life and academic life.
We would use two case examples drawn from two different domains to understand how the technique can make a difference in totally disparate areas of activity.
This characteristic of multi-domain applicability is of course a crucial requirement for a resource to be a member of the overlay abstract discipline of Problem Solving not dependent on any other discipline.
Applying Change Analysis Technique in Maths
Case example 1
Problem: A group of students stood in rows with equal number of students in each row. If number of students in each row were increased by one, the number of rows decreased by 2, whereas if the number of students in each row were decreased by 1, the number of rows increased by 3. What was the total number of students?
Usual conventional solution
Let the students be imagined in a formation of rows and columns. The number of columns and number of rows are assumed to be $x$ and $y$ respectively, so that total number of students will be $x\times{y}$.
From the first problem statement we have,
The number of columns increased to $x + 1$ resulting in a reduction of number of rows to $y - 2$, so that their product, the total number of students would be,
$(x + 1)\times{(y - 2)} = xy$, in whatever row-column formation the students are arranged, the number of students in all rows are same and total number of students remains unchanged.
Or, $xy -2x + y - 2 = xy$,
Or, $y - 2x - 2 = 0$.
Similarly from the second statement, the number of columns decreased to $x - 1$ resulting in increase of number of rows to $y + 3$, so that their product, the total number of students would be,
$(x - 1)\times{(y + 3)} = xy$,
Or, $xy + 3x - y - 3 = xy$,
Or, $3x - y - 3 = 0$.
Adding the two last results,
$x - 5 = 0$,
Or, $x = 5$, that is, the number of columns originally was 5.
And so, from the first equation,
$y - 2x - 2 = y - 10 - 2 = 0$,
Or, $y = 12$, that is, the number of rows originally was 12.
Thus total number of students is, $5\times{12} = 60.$
Answer: $60$.
Problem solver's solution using Change Analysis Technique
Same as before we assume $x$ as number of columns and $y$ as number of rows.
In the first case,
Number of students remaining unchanged, Change in number of students in horizontal direction (from left to right: increase) due to increase in number of columns by 1 is,
$1\times{(y - 2)}=y - 2$, and this must be equal to the change in number of students in vertical direction (from top to bottom: decrease) = $2\times{(x)}$,
Or, $y - 2 = 2x$.
In the second case, similarly equating changes in the number of students in horizontal (a decrease) and vertical (an increase) directions, we get,
$y\times{1} = 3\times{(x -1)}$,
Or, $y = 3x -3$.
From these two simple equations we get $x=5$ and $y=12$ quickly.
Answer: number of students = $x\times{y} = 5\times{12} = 60$.
Aside: It is normal to find change analysis a bit difficult to conceive at first. This is because of the need for abstraction of the entities to visualize, identify and extract the change relationships, while we are not used to think in abstract terms. That's the reason behind the initial discomfort with the idea. In this case, just make two simple drawings to reflect the change situations in pictorial form. This would make the concept crystal clear.
There are other solutions to this problem filling up a complete page opposite to the direction of our efforts.
In contrast, our focus is always to assimilate, formalize and apply a problem solving resource that would solve a problem quickest and most efficiently, that too in more than one domain of activity. Resources are getting more precious by each passing day. Saving and optimizing the use of resources is now one of the most critical activities.
Scope of Change Analysis Technique
This is only one of the numerous math problems that can be solved much faster and hence more elegantly using this powerful problem solving technique. This technique can be applied with great effect in a number of other problem areas of math as well.
But again, math is only one of the areas where this broad based problem solving technique can be applied. There are other real world activity areas of application of this problem solving technique not related to maths at all.
For long I was interested in using change as a resource to make improvements around, unaware about the fact that I was applying the Change Analysis Technique in various forms only. The following effort is something I won’t forget in a hurry because of its unexpected positive results in a very short span of time and that too with minimal efforts.
Case example 2
Teaching editing to my writer friend
Sometime back I was involved in editing and publishing a magazine. Authors were my friends who were just like any other normal people. I mean, they were not professional or even amateur writers.
Editing their first time literary creations, composing the pages and publishing in a short time all by one man was hard.
Layout and composing were not such a burden but editing was. I had to keep the flavour intact while polishing a piece to its shining best. It took a lot of my intense time.
That’s why when I looked at the first paragraph of one of my budding writers’ piece, I got a shock. She had a good flow and powerful expressions but each line of her eight page long write-up had three or four glaring errors on an average.
When all the tasks got somehow completed with unexpected success, I decided to talk to this most promising author of mine, “Listen carefully. You have with you now your fully edited story in the published mag. What you have to do is – Compare your version of the story you sent me with my edited version word by word. Identify each change that I have made. Evaluate and understand reasons behind each and learn how not to make those mistakes next time onward.”
To make the deal clinching, I further clarified, “If I find more than five errors in a page of your next piece, I will mail you back the piece immediately without any more edit.” That was my half-cooked managerial expertise in action.
To the great credit of my friend, her next piece two weeks later was self-edited to near perfection and my labor was minimal. She had learned literary editing, at least up to my limited standards, at one go just by comparing my edits with her original.
Later she wrote a few of the best stories I have ever read.
Change is a powerful resource of problem solving on occasions.