Thursday, May 18, 2017

"Difficult" and "Easy" Are Undefined

This post comes about because in an online forum, someone asked if it is "easier" to heat something than to cool it down. The issue for me here isn't the subject of the question, which is heating and cooling and object, but rather, that the person asking the question thinks that the "measure" here is the "easiness". I'm sure this person, and many others, didn't even think twice to realize that this is a rather vague and ambiguous question. After all, it is common to ask if something is easy or difficult. Yet, if you think about it carefully, this is really asking for something that is undefined.

First of all, the measure of something to be "easy" or "difficult" it itself is subjective. What is easy to some, can easily be difficult to others (see what I did there?). Meryl Streep can easily memorize pages and pages of dialog, something that I find difficult to do because I am awful at memorization. But yet, I'm sure I can solve many types of differential equations that she finds difficult. So already, there is a degree of "subjectiveness" to this.

But what is more important here is that, in science, for something to be considered as a valid description of something, it must be QUANTIFIABLE. In other words, a number associated with that description can be measured or obtained.

Let's apply this to an example. I can ask: How difficult or easy it is to stop a 100 kg moving mass? So, what am I actually asking here when I ask if it is "easy" or "difficult"? It is vague. However, I can specify that if I use less force to make the object come to a complete stop over a specific distance, then this is EASIER than if I have to use a larger force to do the same thing.

Now THAT is more well-defined, because I am using "easy" or "difficult" as a measure of the amount of force I have to apply. In fact, I can omit the use of the words "easy" and "difficult", and simply ask for the force needed to stop the object. That is a question that is well-defined and quantifiable, such that a quantitative comparison can be made.

Let's come back to the original question that was the impetus of this post. This person asked if it is easier to heat things rather than to cool things. So the question now is, what does it mean for it to be "easy" to heat or cool things. One measure can be that, for a constant heat transfer, how long in time does it take to heat or cool the object by the same change in temperature? So in this case, the measure of time taken to heat and cool the object by the same amount of temperature change is the measure of "easy" or "difficult". One can compare time taken to heat the object by, say, 5 Celsius, versus time taken to cool the object by the same temperature change. Now this, is a more well-defined question.

I bring this up because I often see many ordinary conversation, discussion, news reports, etc.. etc. in which statements and descriptions made appear to be clear and to make sense, when in reality, many of these are really empty statements that are ambiguous, and sometime meaningless. Describing something to be easy or difficult appears to be a "simple" and clear statement or description, but if you think about it carefully, it isn't! Ask yourself if the criteria to classify something to be easy, easier, difficult, more difficult, etc... etc. is plainly evident and universally agreed upon. Did the statement that says "such and such undermines so-and-so" is actually clear on what it is saying? What exactly does "undermines" mean in this case, and what is the measure of it?

Science/Physics education has the ability to impart this kind of analytical skills, and to impart this kind of thinking to the students, especially if they are not specializing in STEM subjects. In science, the nature of the question we ask can often be as important as the answers that we seek. This is because unless we clearly define what it is that we are asking, then we can't know where to look for the answers. This is a lesson that many people in the public need to learn and to be aware of, especially in deciphering many of the things we see in the media right now.

It is why science education is invaluable to everyone.


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