Teaching an Objectively Correct Robot to Count

Teaching an objectively correct robot to count.

There are two characters in this story; Dave and Pixel.

Dave is a scientist and Pixel is the objectively correct robot he created. Pixel has one arm that he can use to point at things. He’s as tall as his creator, and has wheels to move around.

One day, Dave brought Pixel over to a table in the lab. On the table were several red metallic balls.

Dave: Today you’re going to learn to count using these balls you see on this table.
Pixel: Okay.
Dave: And there’s something special about these balls.
Pixel: What’s that?
Dave: To make counting easier for you, I have made them identical in composition.
Pixel: To the last atom?
Dave: Yes, each one of them. The only differences between them are their locations on the table.
Pixel: Okay. But do these differences matter to us in our calculation?
Dave: Nope. It doesn’t matter where any ball is on the table. It makes no difference. As far as you’re concerned, all balls are similar.
Pixel: Okay.
Dave: Ready?
Pixel: Ready.
Dave: Pick a ball to count as 1.
(Pixel points to the ball closest to him on the table.)
Dave: Okay, now as 2.
(Pixel points to the ball closest to him on the table again.)
Dave: No, you can’t pick that one again.
Pixel: Why not?
Dave: You have to pick a different one.
Pixel: Different how?
Dave: Well, in a different place on the table.
Pixel: Oh okay. But I thought we were going to ignore location?
Dave: We are. We don’t consider it.
Pixel: So… we do ignore the location differences?
Dave: Yes.
Pixel: …to consider all the balls as similar?
Dave: Yes.
Pixel: But you also want me to consider those differences?
Dave: Yes.
Pixel: …to be able to tell the balls apart?
Dave: Yes.
Pixel: Do you see the problem with what you are asking me to do?
Dave: Hmm…
Pixel: What do you really want me to do?
Dave: I mean, can you ignore the differences in location but at the same time consider them as well? Is that possible at all?
Pixel: 0 or 1, Dave?
Dave: Umm… both at the same time?
Pixel: That’s not how that works.
Dave: Yeah yeah, I know. Give me some time to think.
(Several minutes go by.)
Pixel: Dave?
Dave: Yes?
Pixel: Are you sure counting is objectively possible?
Dave: You know what, I don’t know anymore.

Note: The two objects being identical in composition is not mandatory for the implied philosophical argument to be valid. It was chosen as such for convenience. The purpose of this story is not to argue that robots cannot be taught to count (a robot truly incapable of making any similarities wouldn’t be able to recognize the same person from a few seconds ago), but to demonstrate the subjective nature of (our perception of) reality. The way we make sense of reality is by recognizing patterns. And patterns require similarities/ equalities. And all equalities are arbitrary.

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