Why does the Placid Platypus function grow faster than any computable function?
The function $PP(n)$ is essentially the Kolmogorov complexity of the number $n$, and is non-computable by standard arguments, which I present below.

Suppose to the contrary that $PP$
is computable. Then so is the function $f:k\mapsto n$ that maps a number $k\in\mathbb{N}$
to the least integer $n$ such that $PP(n)&gt;k$. (Such an $n$ always exists by simple counting arguments.)
If $PP$ is computable then so is $f$.

Now define the Turing machine $M$ as follows:
$M$ prints $f(|M|)$ ones, where $|M|$ is the number of states in $M$.
Thus, $M$ has size $\ell=|M|$,
and it prints 
a string of $\ell$ ones.
By construction, $PP(\ell)&gt;\ell$,
and so
$\ell$ 
ones cannot be printed by any TM with $\ell$ states or fewer.
Contradiction.