Mental Action

Chapter 4
Quantifying Difference

We've taken the first step on the road from helplessness to mastery by noting the difference between reacting to change and confronting change. Without cognitive self-regulation, my pet can only react to change. It cannot deliberately focus awareness on this rather than that. But I can. With cognitive self-regulation, I can confront change, search out differences—and take the next step.

The next step is in fact a giant leap. It is, as shown by Dr. Binswanger, the transformation of difference into similarity. It is the quantification of difference.

Ready for more research? Here are the colors we compared before:

Are they still in the same place? Or are they now in different places?

The answer, of course, is yes.

That is, the answer depends entirely on how you decide to confront difference—what kind of comparison you choose to focus on. Compared one to the other, they are in different places on the screen. Compared to other web pages, they are in the same place: this page.

Depending on what use you want to make of it, you can regard them as in the same place, or in different places. Your consciousness can self-regulate to the standard of usefulness.

Right now we are talking only about position, so we ignore the difference in color. If they differed in shape and size, we could ignore that too.

Let's picture some different colors:

The picture represents ten separate, different objects. But no adult sees it that way. The human mind grasps a relation of the objects called similarity. Then the picture is of the same shape in ten colors.

Can you imagine a world without sameness? Can one think of a world in which nothing is like anything else? No, because thought requires some degree of order, some way to organize perceptions, some way to sort things out. If every difference had just the same importance as every other difference, so that nothing could be called the same or similar to anything else, even memory would be useless. It would provide a jumble of past perceptions, with no clue about which ones were important and which ones were trivial.

What's out there to be perceived are differences. What we have to work with is the ability to regulate attention—to make comparisons. What we need is to quantify differences, so that some things can be called alike, the same, or similar.

How do you make similarities out of differences? The same way we put our colors in the same place or different places.

Here's our color again:

We put with it something different:

Then we compare with something more different:

Notice how it pops out at you: similarity. You're comparing square shapes to round shapes. You long ago acquired the habit of focusing on the bigger difference and renaming as similarity the smaller difference. It's a way to sort things out. You can group the square shapes together because they are similar. Likewise the round shapes. What about another grouping?

Now you're comparing blue shapes to black shapes. You're using the similarity of color. The groups are different, but they still look right, because there is an obvious reason for each way of grouping them.

Note that this grouping is not as good:

You don't have obviously similar shapes on the left and on the right; you have arbitrary groups. You could compare all the shapes as a group to all the text near them, because the text is visually similar as text, and the pictures are similar as pictures. But you can't group things together by whim and just declare them similar. Similarity provides an orderly way to group things together, because it has rules. The rules are given by what Ayn Rand identified as measurement omission.

Look around the room you're in. Note that, by habit, you pick out some things as similar and other things as different. You do know rules for similarity. You learned them at an early age by making comparisons. Later, you learned a fancier word for comparison: measurement.

You have a pencil, a ruler, and a stick. You compare the pencil to the ruler, and find that the pencil is 7 inches long. You compare the stick to the ruler and find that the stick is 13 inches long. You're focusing on length, which is different in each. Now you compare a coffee cup, a mug, and a demitasse. You focus on capacity, which is different in each. You could measure the exact capacity of each, but you don't, because you can see that they are similar, and different from the first group of similar things. Knowing that the measurement is possible is enough; they must all have some capacity, but it can be any capacity. In order to see similarity, you must be aware of the possibility of the measurement, but you omit making it.

If you wanted to find similarity between a cup and a ruler, you couldn't focus on capacity, because the ruler doesn't have any. You couldn't focus on length, because the cup doesn't have any. You'd have to find some common measurement which could be made, even though you wouldn't have to make it. In other words, you'd have to find a commensurable characteristic.

The essential of similarity can be called measurement omission, because in order to omit a measurement, you must be aware that it can be made. In fact, you must be aware of the range of measurement: a cup will not look similar to an oil storage tank.

So the rules of similarity turn out to be mathematical. To see similarity, you focus on commensurable characteristics within an appropriate range, but omit the actual measurement. If it sounds complicated, remember you were doing it as a baby: looking at things, comparing things, grouping things—learning to exercise your faculty of cognitive self-regulation. What you learned to do then by trial and error, you can review now with all the advantages of hindsight.

We began by noting animal consciousness in which there is no mental action, but only reaction. We are progressing toward adult human consciousness which is capable of full mental action. The half-way point is similarity.

When you found as an infant that you could wave your arms and wiggle your fingers, you had no thought of learning to play the piano; you were just exploring your capabilities. When you found that you could kick your feet, it did not make you think of walking. When you saw similarity, you were not trying to think deep thoughts, but just to avoid confusion. That's the point of understanding what similarity requires: you don't see it by just looking. Your eyes don't register similarity; your mind does. The instant you make an effort to see similarity, you have gone beyond the capabilities of your pet. You are at the threshold of conscious mental action.

Crossing that threshold is something you do fully on purpose. It is an act of will.