+#Q: Ouch! Stop hurting my brain.#
+
+A: Is that a question?
+
+Let's come at it from the direction of arithmetic. Recall that we
+claimed that even `succ`---the function that added one to any
+number---had a fixed point. How could there be an X such that X = X+1?
+That would imply that
+
+ X <~~> succ X <~~> succ (succ X) <~~> succ (succ (succ (X))) <~~> succ (... (succ X)...)
+
+In other words, the fixed point of `succ` is a term that is its own
+successor. Let's just check that `X = succ X`:
+
+<pre><code>let succ = \n s z. s (n s z) in
+let X = (\x. succ (x x)) (\x. succ (x x)) in
+succ X
+≡ succ ( (\x. succ (x x)) (\x. succ (x x)) )
+~~> succ (succ ( (\x. succ (x x)) (\x. succ (x x))))
+≡ succ (succ X)
+</code></pre>
+
+You should see the close similarity with `Y Y` here.
+
+