What a piece of work is man and/or woman

The other evening we went to see The Tragedy of Hamlet, Prince of Denmark at Boscobel, presented by the Hudson Valley Shakespeare Festival with a wonderful young Matthew Amendt as Hamlet, and I could have sworn someone was fooling around with my brain by having inserted the “What a piece of work is Man! How noble in reason!”* speech into Act 2 of Hamlet. You know the speech because it was set to music in “Hair!” and we can all sing it. And I could have sworn, and indeed did swear, that the speech belonged to Caliban in The Tempest. It is the perfect speech for Caliban, poor misshapen & oppressed creature that he is, to express his wonderment at these buff and sweet-talking gentlemen just been washed ashore onto his island.

Then I decided that the director (Terence O’Brien of HVSF) had conceived a clever device to illuminate the plays of Shakespeare: in each play he directed he would insert a speech from another play, but in such a way that it would proceed smoothly and mesh seamlessly with the action. I decided that this was his subtle way to illuminate certain recurring themes. And possibly, so I thought, it was meant as a signature fluke or “error”, in the same way that Native American weavers will deliberately leave one thread awry, so as not to provoke the gods with the perfection of their workmanship.

I may have missed some elegant swordplay in Act V because I was still working out the explanation for this unprecedented insertion of a speech from The Tempest (WS’s final play and a so-called comedy) into Hamlet (tragedy, without a doubt).

But I was wrong. The speech really is in Hamlet. The deeply troubled Hamlet says the words to Rosencrantz and Guildenstern, those perfidious friends.
How could I have been so confused? Is it possible that in The Tempest Caliban makes that same speech, that Caliban in fact, quotes Hamlet?

*What a piece of work is a man! How noble in
Reason! how infinite in faculties! in form and moving
how express and admirable! In action how like an Angel!
in apprehension how like a god! the beauty of the
world! the paragon of animals! and yet to me, what is
this quintessence of dust? Man delights not me; no,
nor Woman neither; though by your smiling you seeme
to say so