Once upon a time there was an alien trapped in a ship floating high above reality. The ship had no windows or cameras. The alien couldn’t leave. The only way to catch a glimpse of reality below was through the labeled blips on a radar screen.

One day, the alien noticed your grandfather’s axe. The alien never got to actually see the axe. It couldn’t touch the axe or hold it or feel it. It didn’t really have a clear idea of what an axe was – it only saw the little dots on the radar screen. Two red dots, labeled The Handle and The Blade, and one big blue dot labeled The Axe:

The alien watched as the axe moved around and began to notice that the blue dot always stayed precisely in between the red dots. It seemed that The Axe could never leave The Handle and The Blade. The alien wondered why this was.

For the alien could easily imagine the blue dot leaving the red dots. The radar screen need only look like this:

Such a readout was obviously imaginable (for the alien often imagined it) and seemed consistent: the radar screen was quite capable of such an output. And yet, the situation never occurred.

The alien built little robots and sent them down to the surface of reality to probe the axe. Through these robots, the alien learned much about the axe. The alien learned that the reason the red dots always remained the same distance apart is because they were fixed together by tiny nails, too tiny to show up on the radar screen. This made sense. But the alien simply could not determine how the blue dot (the axe) was connected to the red dots (the handle and the blade).

Try as they might, the robots could not separate the blue dot from the red dots. No matter how they twisted and turned the handle and the blade, they could not remove them from the axe. In a desperate effort to get the blue dot to break out of its confines, the alien had the robots remove the little nails and separate the handle from the axe. The alien hoped to judge how the blue dot averaged the distance between the reds, hoping to glean some knowledge of the nature of the blue dot. And yet, to the alien’s dismay, as soon as the red dots were disconnected, the blue dot disappeared!

The alien hastily had the robots re-assemble the handle and the blade, and the blue dot popped back into existence. Then the alien sat down to ponder. Truly, it seemed that reality conspired to hold the blue dot in place. Everywhere the red dots went, the blue dot followed, exactly between the red dots. If the alien tried to separate the handle from the blade, and see which one The Axe preferred, then The Axe disappeared completely.

The alien seriously wondered whether it would ever be able to understand the strange rules governing this obstinate reality. The alien wondered why reality was so determined to hide the true nature of the blue dot.

Yet, this alien was not one to give up quickly. The alien devised tests in attempts to foil the pesky blue dot. The alien had the handle and the blade swiped in the dark of the deepest night, but the blue dot followed. The alien built a chamber and doused the room in liquid nitrogen before sending the robots in to grab the handle and the blade, hoping that the axe would be pacified by the cold – but the blue dot followed.

Experiment after experiment, reality thwarted our alien friend. The blue dot refused to be separated from the reds.

No matter how swift or clever was our alien, it never did manage to separate the axe from its handle and its blade.

Axe