January Question – Zipper around the World

I make zippers for a living. Every few months we produce enough zipper to go around the world, which is 40,075.16 kilometers at the equator.

One day I’m bored. I haul out 40,075,160 meters of zipper (over 700 tons) from the warehouse, and make a perfect, tight wrap around the equator.

I smile in satisfaction. Upon inspecting my work, I find that the zipper is on the ground and on the surface of the ocean, getting dirty and wet, which is obviously unacceptable. Being the fickle person I am, I decide to haul in more zipper from the warehouse, and raise the entire zipper loop one meter above ground level (and sea level).


The math is relatively straightforward.  However, before you work out the answer with some pencil and paper, based purely on your intuition, estimate roughly how much more zipper I need.

To help out, here is a quick guide:

1%: 400 kilometers

10%: 4,000 kilometers

100%: 40,000 kilometers

You have 10 seconds to make a guess. Ready?




Note: Illustrations from WHAT IF?: Serious Scientific Answers to Absurd Hypothetical Questions by Randall Munroe. Copyright©2014 by xkcd Inc. Used by permission of Houghton Mifflin Harcourt Publishing Company. All rights reserved.


Afterword: As you can see, I have taken the time to ask for permission from the publisher before using someone else’s work, even if they are only stick figures drawings. Sometimes all you need to do is ask (click for full image).

Answer to December Question – Man in the Mirror

The first, and rather difficult step, is to realize that the mirror doesn’t care about direction, and realizing that the problem is with your brain, not the mirror or anything else. To illustrate this, point to the right, and the image will point in the same direction. Point up, same thing. However, point towards the mirror, and the images points back at you, in the opposite direction. The key observation is that the mirror inverts not in the left/right or up/down, but the front/back direction.

The second step, is to realize what you are actually seeing in the mirror. Imagine a cone pointed towards a wall. As you push the cone into the wall, imagine a cone growing on the other side of the wall, growing as you push, in the opposite direction. You end up with a cone, pointing towards you, on the other side of the wall. Now put a red dot on the left side of the cone and a blue dot on the right side of the cone, and do the same thing. You end up with an inverted cone on the other side of the wall, with a red dot and a blue dot, on the same corresponding side. Now, imagine a human face being pushed through the wall nose first, just like the cone, with the colored dots as eyes. You end up with an image of a face on the other side, inverted front to back. The left eye is still the left eye, just flipped front to back. Although highly counterintuitive, that is the correct interpretation of the image in the mirror. Still having problems? Another way to look at it, is to take a latex glove and put it on your right hand. Now, take off the glove by inverting it, so it is inside out. The inverted right-hand glove is the analog of the image in the mirror, even though it looks like a left-hand glove.

The question now becomes, why do we so instinctively see a person swapped in the left/right direction, to the point where you cannot help but see it that way? The reason, simply put, is that it requires the least work from the brain. The correct interpretation (inverting), requires an incredible amount of work, as evidenced by the effort it takes simply to imagine it. There is no existing brain circuitry to do an inversion, because there was no need to do so when the brain evolved. It is far easier for the brain to treat the image as “someone” facing you rather than an inverted meaningless image. The agent detection circuitry in your brain is where the problem is, not the mirror.

Once the brain treats it as a “person”, it needs to orient the “person” in space to make sense of it. There are two main ways to mentally turn objects around in space, around a vertical axis (turning around), or around a horizontal axis (think foosball). Technically speaking both are equally valid (as are any diagonal axes), and our brain will use the existing evolved circuitry, which is to turn around the vertical axis and spin the “person” around to face you. Interestingly enough, if one were to mentally flip around the horizontal axis, one would see the image as flipped in the up/down but not left/right direction, further showing that the problem arises from a hardwired preference in your brain.

This example shows that something seemingly so real and veridical, is no more than an erroneous representation concocted by the brain. The explanation is readily verifiable and probably enough to change your mind, even though it is counterintuitive and doesn’t “feel” right. More importantly, it should deeply challenge our beliefs about how we acquire knowledge and its validity; after all, if something that seems so real and taken for granted is in fact just an illusion, what about knowledge acquired on much shakier ground?  Another salient example is #dressgate, in which people are absolutely convinced that the dress they see with their own eyes, is either white and gold, or blue and black.  It is almost inconceivable that others may see it entirely differently.

Bertrand Russell once said “The fundamental cause of trouble in the world today is that the stupid are cocksure while the intelligent are full of doubt”. Undeniably, the will to doubt requires far more than the will to believe. Doubting others is comparatively easy; far more difficult is the will to doubt yourself and carefully examine even your most cherished and emotionally invested beliefs.

“Some things you need to see to believe; some things you need to believe to see”