FAQs about Self-Reference

Q: What is a self-reference?

A: It’s a statement that refers to itself.

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Q: So, like… is this question self-referential?

A: Yes.

 

Q: And this question too?!

A: You can stop now.

 

Q: So why is self-reference important in mathematics?

A: Because mathematics is built on logic, and self-references unravel logic.

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The Number Line: A Journey

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Everybody thinks they grew up in the most boring neighborhood on the whole number line. But trust me: you’d rather spend seven eternities in your home than a Saturday night in mine.

I don’t need to describe my home interval; you know it already. Neither terribly close to an integer, nor terribly far from one. No famous constants for miles around. No crossroads, no bustling port, no frontier town: just an anonymous suburb of an unseen city, a faceless stretch on the long gray road that runs from one infinity to the other.

Nothing to do? Understatement. There was nothing to think, nothing to feel, nothing to say. I gathered stories wherever I could, scavenged for tales of distant realms where something, anything, was happening.

Somewhere, a trillion covert sequences spiraled towards pi.

Somewhere, a mirror reflected the negative image of every number I knew.

Somewhere, the integers climbed beyond trillions in an Icarus flight to infinity.

Somewhere, somewhere, somewhere…

Adulthood came without sentiment or fanfare, like the bell at the end of third period. I simply gathered my things and made for the door. I’d like to say that I hugged my parents a half-decent goodbye, but the truth is that I left without a word.

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I traveled first to the hub, the nexus, the galactic center around which everything else swirled.

I went to zero.

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