Q:

What does the naked man signify?

While watching The Draughtsman's Contract written and directed by Peter Greenaway, I was surprised to see a naked guy that appears on and off in the film mostly in the garden. One particular scene is when the Talman's, Mr. Neville, Mrs. Herbet and company, that naked guy removes the monument, stands with torch, and pees. I find it rather perplexing and shocking.

A:

As with all of Greenaway's movies there's layer upon layer of symbolism and structure going on in TDC.  My take on most of his films, though, is grounded in the general idea that Greenaway's attitude towards filmmaking is a painterly one.  He favors carefully composed imagery over plot; there's plenty of the latter, but it's usually through the former that the real meaning of his films comes forth.
The Draughtsman is an idealist who believes that he can impose an order on his surroundings both directly through his work (he claims that his drawings reproduce exactly what he sees) and through the contract with Mrs. Herbert (whereby he's allowed regular access to her entirely on his own terms).
But the goal of perfectly representing reality on a piece of paper is fruitless; the Draughtsman's output is static, orderly, and enclosed, while real life is messy and complicated (and ultimately inflicts itself on the Draughtsman as a messy death).  The appearance and disappearance of objects like the ladder and washing from day to day frustrate Mr. Neville's goals, and I believe the "living statue" is a similar symbol of the unpredictability of the real world.  A classical statue should be a prime example of the Draughtsman's attitude towards reality and art---the statue captures an ideal form, a fixed reproduction of humanity with none of humanity's imperfection and unpredictability---but Greenaway instead plays a joke on the Draughtsman and the viewer by having the "statue" live, breathe, move around, and amuse itself with juvenile bathroom humor.

