Mirrors

Question:

Why do mirrors reverse right and left but not up and down?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Solution: This puzzle continues to totally flummox some very bright people, some of whom have actually studied the question. That’s because a mirror is an everyday object we think we understand. Actually, most of us don’t. Another problem is that this brainteaser is in a class by itself. You can’t solve it with ordinary math. Not even logic can dent it. A solution even evades common sense. It requires the candidate to let go of all assumptions, and that’s what makes the puzzle so revealing. The interviewer wants to see how you react to a puzzle that really throws you.

There are some very ingenious wrong answers. Here is, perhaps, the most creative: “The mirror does reverse top to bottom, but our brains recognize that the shape should be right-side-up, and flips it for us.” Very smart, but why don’t our brains also “correct” left to right reversing?

The critical insight to solving the reflection problem is to realize that the statement of the problem leads to hopeless confusion. Some candidates never recover because they try to answer the question as stated. Besides, normal language doesn’t provide the tools to properly analyze this question. The best response may be to challenge the statement of the question: A mirror doesn’t necessarily reverse left and right or up and down. The puzzle really tests a willingness to reflect independent thinking, even to the point of challenging assumptions posed by the interviewer. One candidate responded to the mirror puzzle like this:

I don’t think the problem is stated quite right. Mirrors don’t reverse left and right; they reverse front and back. Stated another way, mirrors invert front to back, not left to right. An easy way to prove this is to stand facing north with a mirror in front of you. Wave your left (west) hand. The image in the mirror waves its west hand too, so there is no left-right reversal. The popular misconception of the inversion is caused by the fact that when person A looks at another person B, person A expects person B to face him or her. But when person A faces himself (in the mirror), he sees an uninverted person A.

Books have been written about this subject. Resist the temptation to summarize their points.

Extra credit: But if you have to quote someone, quote from Martin Gardner, the patron saint of mathematical diversions. Here’s Gardner’s take on the mirror puzzle: “Human beings are superficially and grossly bilaterally symmetrical, but subjectively and behaviorally they are relatively asymmetrical. The very fact that we can distinguish our right from our left side implies an asymmetry of the perceiving system. We are thus, to a certain extent, an asymmetrical mind dwelling in a bilaterally symmetrical body, at least with respect to a casual visual inspection of our external form.” (From Hexaflexagons and Other Mathematical Diversions, University of Chicago Press, 1988, page 170.) On second thought, don’t.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

w

Connecting to %s