Category Archives: Cognitive Science

What Is This Brain?

The Human Brain. Credit.

What is this brain, this living machine,
Ever striving to make sense of things,
Even when working unsupervised?

And who is this idiot that has charge of it—
Morally stupid beyond what he is
Willing to admit, and clueless as to
The great value of well-regulated
Good sense and reliable reason?

Let us all suppose that he should
Someday take a notion to become
The better steward of this treasure,
And put it at last to better use.

“If That Were True, I Would See It”

See photo credit.

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.

Here are a few ways it happens:

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“Missing Mindware” Makes a Difference in Children and Adults

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?

Lily pad. Credit.

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:

  1. 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!
  2. 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!

Reasonability Bias: The World May Be Worse Than You Think

When you put forth a reasonable argument to someone, you’re pretty much assuming they are going to care about reason, and assign some authority to it, submitting themselves to its authority. Frequently, though, we get responses that don’t fall in line with that assumption. And what do we do? We get frustrated, of course. But more than that, look how often we continue to expect people to yield to reason!

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Triggering, Neurodiversity, and Jesus

We’re all different from each other—to some degree. And we’re all like one another—to some degree.

OK, I get that.

And special attention is being paid to this in cognitive science these days, the idea being that most of us are somewhat “neurotypical”, while others of us are “neurodiverse”—the particular idea of which being that we are somehow, to put it in everyday language, “wired differently.”

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An Inclination Deeper than Words, Thoughts, and Feelings?

In a way, the human will seems to underlie so many of our cognitive processes—and even so, it is not always unified within itself.

I’m going to do my best to keep this short, as I just want to put a couple of thoughts out there without composing the volumes of supporting ideas that should eventually go with it. So here’s my main point: I think that in our complicated selves—somewhere amid that thingor groups of thingsthat we sometimes refer to with words such as mind, heart, soul, spirit, or being, there’s an important part that underlies the parts of which we are more often aware. The parts we more commonly “see” in action—that we are more routinely aware of—have to do with mental functions or features like thoughts, words, actions, feelings, plans, decisions, and actions. Though probably none of us are fully aware of all of these things when they happen, most of us are at least generally aware that such things are indeed doing on inside our selves. That underlying part is what I will (today) call “the will”; it’s our set of desires (wants, wishes, inclinations)—and the important feature of it that I’d like to draw attention to in this post is that not all of the desires that reside there are pointing in the same direction; sometimes they are at odds with one another. And when this happens, it can sometimes make us miserable. I’ve lately taken to describing this misery by use of the metaphor of a horse having a burr under its saddle.

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You Could Fill an Ocean

I suppose you could fill an ocean
With the things I don’t know.

And I should explain that
I say I suppose because
I don’t know that for a fact
But I confess it seems at least
A reasonable stab at
The aggregate volume of
The things I don’t know—
When attempting
To be unbiased in response to
My general experience in this world
And my study of philosophy and cognitive science—
Except that I must further confess
For the record that I realize that an ocean
May indeed be too small a basin
To hold the things I don’t know.

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Being “Neurotypical” May Not Be Something to Which We Should Aspire!

Most people are said to be “neurotypical”—meaning, more or less, that the way their minds work is “normal”. And then, in contrast to that, there are the “neurodiverse” people, who are “wired” differently in one way or another, we are told—and who, as a result, may have different aptitudes and life habits to some extent.

The world is still trying to get its head around this idea, and so am I. And there may well be something to it, but the question is “what exactly is that something”? That’s the question, right?

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