[extropy-chat] Tyranny in place

[nvitamore at austin.rr.com]

From: Eliezer S. Yudkowsky 

>spike wrote:
>>This is a paradox that we cannot solve with our usual tools.  Logic simply
>>fails.

>Heinlein had a sympathetic character say, in one of his stories:  "Logic 
>is a fine thing, but I have seen a perfectly logical proof that 2 = 1."
>(If anyone remembers which story this is from, please let me know.)

>Heinlein was probably thinking of this:
>x = y = 1
>x = y
>x^2 = xy
>x^2 - y^2 = xy - y^2
>(x+y)(x-y) = y(x-y)
>x+y = y
>2 = 1

Proof that 2 equals 1

1) Given:
  X=Y
2) Multiply both sides by X:
  X^2=XY
3) Subtract Y^2 from both sides:
  X^2-Y^2=XY-Y^2
4) Factorise:
  (X+Y)(X-Y)=Y(X-Y)
5) Cancel out (X-Y) term:
  X+Y=Y
6) Substitute X for Y, by equation 1
  2Y=Y
7)Divide both sides by Y
  2=1

  — "Omni"

Natasha


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