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<   Rerun of No. 1068   Originally published 2005-12-29   >

Comic #1068

1 {scene: A filthy starport docking bay. Piles of old crates and barrels and other junk litter the floor.}
1 Iki Piki: So here we are, searching a grimy starport docking bay for flakes of our ex-crewmate's skin. It's the bright future our parents always dreamed of...
2 Spanners: This place is filthy! Look at this decaying crate of mouldy old advertising fliers.
3 Spanners: "A proof that all consistent axiomatic formulations of number theory include undecidable propositions ... which also offers firm slimming control?"
4 Iki Piki: What product is that for?
4 Spanners: "I Can't Believe it's a Gödel!"

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Poll: You need to invent a middle initial to distinguish yourself from someone
else with the same name in a professional field. What do you choose?

Kurt Gödel (pronounced with a vowel sound identical to the one in "girdle") was a mathematician who formulated an important result in formal logic known as Gödel's incompleteness theorem.

The basic gist of the theorem is that for any self-consistent set of rules for doing mathematics (i.e. a set of mathematical rules that doesn't produce contradictions), there will always be mathematical statements that are true, but that cannot be proven to be true.

If you've never come across this before, that may take a minute to grasp. And it may sound ridiculous. But nevertheless, it's true, and the odd thing is that you can prove that this theorem is true.

I'll give you another minute.

Also, not only does Gödel's theorem apply just to mathematics, but also to any self-consistent field of analysis or deduction. Given that the universe is (probably) consistent and non-paradoxical, it's possible (though controversial) to extrapolate this to the result that some things about the universe are true, but there is no way of proving they are true, no matter how hard we try.

What this implies about the pursuit of knowledge and the nature of reality, I leave as an exercise for the reader.

If you want to learn more about Gödel's theorem, I highly recommend the mind-expanding book Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter.


2015-03-28 Rerun commentary: I talk about Gödel's incompleteness theorem a bit more, later on, in the annotation to strip #1845. But I stop short of trying to prove it, as I'm not 100% sure I completely follow the proofs of it which I've seen. At least, certainly not to the point where I can describe them to others. This is one of those things where I have to trust that the mathematicians who do this stuff know what they're doing.

I like that a starport has wooden crates lying around.

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