I have two delightful daughters, now aged eight and 10. Just for fun, we have been trying to see how many digits of pi we can memorize. Our efforts are pathetic compared to the real pros out there, who can memorize tens of thousands of digits.

We are just starting out, however, and I’m only able to recite about 80 digits by memory. I’ve been employing several mnemonic tricks, and this experiment has helped me to see how it might be possible to eventually memorize several hundred digits if I worked at it hard enough (I doubt that I will). So far, my main trick has been arranging the digits of pi in chunks of five on a grid containing lines of four chunks each. This allows me to assign a physical coordinate for each chunk. From there, I’ve been mentally walking through my grid, trying to memorize the chunks by associating a story with each chunk or setting up a simple ” song” for each chunk.

As I’ve been working on this memorization game, I’ve appreciated, even in light of my meager memorization skills, the power of the human mind to internally represent the external world. I physically set forth my 5-digit chunks on a physical grid on a piece of paper, but while I’m reciting the chunks, I am doing all of the “work” in my head on an imaginary grid of imaginary numbers mentally footnoted with imaginary stories or songs to trigger each chunk to spill out.

This mental ability (not just mine, but this human capacity generally) is well worth stopping to contemplate. The human mind is able to replicate (to greater and lesser degrees) the external world and to make it available to us so that we can  silently and internally manipulate its component parts, sometimes with great effectiveness.

We employ our representational abilities in many other ways other than memorizing the digits of pi, of course.  It’s probably happened that you’ve lost your keys but gave up looking for them. Then, only while you were away from the house, you employed your representational powers to re-create your house and imagined where you last had the keys, or where you might have placed them. Perhaps you’ve successfully “located” your keys using only the representations in your own mind, mentally looking in the pocket of a mentally represented coat. This is truly a phenomenal capacity.

When it works well, there is nothing more impressive than this human ability to re-create external reality and to manipulate its component parts in one’s head. The fact that it works so well so often perhaps explains why many people fall prey to believing that their representational capacity is infallible.  There are many people who have convinced themselves that the representations in their heads completely and accurately duplicate the external world.  These are the smug people who have little use for real world evidence.

Here’s what I am suggesting: when they are not careful and humble, many people make the mistake of thinking that anything that they perceive in their heads is an absolutely true copy from the external world and, in fact, that their mental representations of the world might even be more accurate than the external world itself.  Is this the move that gives credence to supernatural worlds for so many people?  Are they so dazzled by the representational powers of their minds that they overlook the frailties of their representational powers?

I suspect that some people combine the confirmation bias with their admiration for their own mental powers.  Many people (those who are mentally fatigued or simply not careful) tend to filter out evidence that conflicts with their own representational systems. They begin to make their permanent homes within their representational capacities rather than making sure that they stay anchored by the real world.

I realize that this is vague food for thought, but this problem is a real one: How is it that so many people who are so certain (but so very wrong) about basic facts have no use for evidence?