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I'm making my way through Ologs:




Let C be a set of of all morning stars.
Let B be a set of all evening stars.
Let D be a set of all moving stars.

Arrow g: C->D maps all morning stars to observations of all moving stars.
Arrow f: B->D maps all evening stars to observations of all moving stars.

Pullback A is as set of all moving stars that show up both in the evening and in the morning.

How do we generate a hypothesis that set A exists?

We observe that at least one heavenly body shows up in the sky both in the evening and in the morning. The body is the Moon.

A star is a heavenly body. Therefore, we hypothesize that there might exist a moving star just like the Moon.

Let's check the definition:


How do we find maps f' and g' ?

We try to observe movements of stars day and night. Since we can't observe stars during the day, i.e. from the morning to the evening, we observe them from the evening to the morning*, and discover that there exists a map h: B ->C (diagonal from B to C). Therefore, diagram A -> B -> C commutes. QED.

Now, our theoretical agenda is to discover h': C->B, i.e. a function that describes invisible movements of stars.

* Maybe this is the reason why the day for the Jews begins in the evening. They picked a lot of stuff from the Babylonians during the exile.