
Tupper's formula - agumonkey
http://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula
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tobinfricke
The problem with "Tupper's self-referential formula" is that it's not actually
self-referential at all. It's just a method for encoding a bitmap that's
encoded in a constant value. That constant value is external data.

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omaranto
Here's an actually self-referential variant that does include its magic
number: [http://jtra.cz/stuff/essays/math-self-
reference/index.html](http://jtra.cz/stuff/essays/math-self-
reference/index.html)

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mathieuh
The always excellent Numberphile's video about it:
[https://www.youtube.com/watch?v=_s5RFgd59ao](https://www.youtube.com/watch?v=_s5RFgd59ao)

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agumonkey
That's how I found out actually. I don't like the bias into self reference too
much, the formula being re-encoded into K (IIRC). It seems like an algebraic
encoding of a bitmap. Anyway, pretty neat find.

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darkmighty
At least it seems reasonably efficient. The bitmap is composed of 106 * 17 =
1802 bits, while the digits contain 543 * log2(10) = 1803.8 bits; not bad,
disregarding redundancy in the image.

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agumonkey
Great point.

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jlas
How would someone even go about figuring this out? Maybe Tupper was incredibly
bored?

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Sharlin
The formula simply interprets the big magic number as "pixels". Then you just
pick your magic number to encode an image that looks like your formula.

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amelius
I would have been more impressed if that number k was also depicted in the
image.

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omaranto
Someone did that too! [http://jtra.cz/stuff/essays/math-self-
reference/index.html](http://jtra.cz/stuff/essays/math-self-
reference/index.html)

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amelius
Wow, that is very cool!

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msane
Now that, is cool.

