Not every true thing is conveniently obvious. And even so, large numbers of people may well operate on the assumption that all true things are—or should be—obvious. It is a common overestimation of human capability, often based on the assumption that what can be detected should be detectable without effort—and more particularly, detectable by our natural human senses.
The four-year-old in this video will tell you what he thinks, not knowing that when he does, he’s revealing that has has some “missing mindware”. And my point in this post is that adults will do quite the same thing. So let’s talk about the boy first.
The lady in the video is surveying the boy on Piaget’s conservation tasks. She expertly asks him questions to determine how he’s thinking about what he sees. For example, when the blue water is poured from one of two identical glasses (equally filled) into a new, taller-but-narrower glass, he judges that the new glass has more water than the old glass did, even though he saw the transfer of the water with his own eyes. It appears that his reasoning is based solely on the fact that the height of the water has increased, and ignores the fact that the width has decreased. (He doesn’t know that both the height and the width are factors in determining volume.
He lacks the “mindware”, then, to account for these two factors. Nor does he know the more-sophisticated resulting principle that under normal circumstances, the volume of the water would be conserved, even if its shape changes. To you and me, these things are intuitive, but to the four-year-old, they are not. (Intuition is nothing more than understanding that is powered by memory.)
So, he happily answers the questions, normally with only one consideration in mind. And you should know that this is normal for a child of his age. The human mind is born without a grasp of these things, but typically grasps them in the early years with enough real-world experience.
Missing Mindware in Adults
Kids aren’t the only ones who can be missing mindware. Adults can do it, too. For example, many adults will miss this problem because they either don’t know the proper way to figure it, or don’t take the proper care in the moment to reason through it well:
In a certain pond one day, a certain lily pad begins to double in size every day. On day 30, the lily pad has covered the entire surface of the pond. On what day was the lily pad half the size of the pond?
Many lacking a sufficient grasp of certain mathematical principles will answer Day 15, while the correct answer is Day 29. To arrive at the Day 15 answer, they’re not just guessing, but doing math, but it goes wrong simply because they’re doing the wrong kind of math. When they see the word “half” in the word problem, they decide to half the total days (30), which yields the answer, 15.
But this way of approaching the problem ignores some of the information given in the first sentence of the problem: “…a certain lily pad begins to double in size every day.” That is, it didn’t just double its size on the first day, but on the second day, it doubled the enlarged size of the first day, and so on until day 30.
Reframing the Problem
Suppose we had asked this related question instead:
If a certain lily pad has been doubling in size every day, how many days ago would it have been half the size it is right now?
This problem gets at the same principle as the original problem, but does it without mentioning any number of days. And it may be that when the original problem mentions “day 30”, it provides a stumbling block for the ignorant or non-careful mind. That is, it’s as if presenting the original problem to the subject excites the brain thus: “Ooh, boy!—a division problem!—I can do division!—I just need two numbers, and I’ve got a 30 already—oh, and I know that to half something, we divide it by 2—so, 30 ÷ 2 = 15. Yay, I’ve solved it!”
To keep this brief, I’ll fight off the temptation to do a full analysis of the lily pad problem. Instead, let me just say that right principle to have in mind for this problem is this:
Every day moving forward in time, the lily pad doubles in size, and every day moving backward in time, it halves in size.
Solving the Wrong Problem
The issue at hand, then, is not halving the 30 days, but halving the size at 30 days. And the size is never explicitly stated by way of numbers in the original problem. So, a brain seeking numbers to perform operations on will immediately find the 30 explicitly stated, and can rightly infer that there must be some halving that needs doing, but the number 30 is not the right thing to be halved; it’s the size at Day 30.
And for the record, let me briefly point out just two more things about the the lily pad problem before I move on to the ultimate point of this post:
Someone could know exactly how to solve this problem, and still make the Day 15 mistake simply by not paying attention well enough before answering. That is, the mindware for the problem wasn’t missing, exactly, but it wasn’t accessed!
Another way to look at this problem is with the question, “How am I setting up the problem?”. That is, do I think this lily pad problem is about an additive process where the same amount of new area is added every day, or do I think it’s a multiplicative process instead, where there’s geometric growth involved?
It Happens with More Than Just Lily Pads!
Adults can have problems with missing or unaccessed mindware in many ways, such as in moral behavior. For example, when a person feels mistreated by another, he may turn the tables and mistreat the mistreater if he has opportunity—as if mistreatment were only wrong when done to him, and not when he does it to someone else.
And it could be that the adult simply has not yet learned the principle of the Golden Rule, or that his mind is simply not engaging this already-learned principle in the way it responds in the moment. But whether it’s a missing mindware problem or an unaccessed mindware problem, it’s still a problem!
In the case of the four-year-old, we’re pretty sure that he has simply not learned the conservation mindware at that stage in his development. But what about the adult who has some mindware and simply doesn’t isn’t careful enough to use it in the moment? Or what about the adult whose will is habitually opposed to applying some certain principle to his own behavior?
This is so often a moral problem, and it may be one of the biggest moral problems this world has. Among other things, we call it hypocrisy, which is a particular form of double-mindedness or cognitive dissonance. And there’s so much more to be said about it, but this post will have been a smashing success if I can simply get you to be on the lookout for it—not only in others, but particularly in yourself!