In response to my criticism, Arnold writes:

I do not think that central banks control nominal GDP any more tightly
during a hyperinflation than at other times. That is, in normal times,
if nominal GDP wants to grow at a 5 percent annual rate next quarter,
the central bank cannot hit a 10 percent target. In hyperinflation, if
nominal GDP wants to grow at a 10,000 percent annual rate next quarter,
the central bank cannot hit a 10,005 percent target.

Question for Arnold: Could the central bank hit a 20,000% nominal growth target, plus or minus 1000%

If Arnold says yes, then he’s deeply conflating central banks’ power over nominal GDP with the precision of their power.  So instead of saying that the Fed couldn’t have raised nominal GDP growth in 2008, he should say that it could have, but it would have run the risk of sparking 5 or 10% inflation. 

Furthermore, if Arnold does say yes, I’d add that the precision of the central bank’s control is obviously going to be far less when nominal GDP growth is roughly 10,000% than when it’s roughly 0%.  If you’re currently at 0%, it’s pretty easy to add 5±1 percentage-points.  If you’re currently at 10,000%, adding 5±1 percentage points is going to be tough.

If Arnold says no to my question, then I’m still dumbfounded.