In the sentence “look about the room”, in line 1, about is used as adverb rather than a preposition.

1 I look about the room where I have been at work for
almost a quarter century. Proofs of unread novels
accumulate on the coffee table. I sit at a large table that was
4 in the house when I bought it. Everything since Burr has
been written at this table. Lately we have acquired a
television set to watch the news on CNN and old movies.
7 Videocassettes are beginning to crowd out the books. To the
left of the fireplace, a chiaroscuro Neapolitan painting by
Viola. “Typical of early eighteenth-century South German
10 painting”, boomed the journalist Joe Alsop. As Joe was an
expert on everything, he was generally wrong on almost
everything, particularly his subject, politics. For thirty years
13 we were losing to Communism, according to Joe; he was a
romantic goose, but endearing.

[...].

16 Ordinarily, I don’t think much about the past. A
friend was surprised to hear me say that there was not one
moment of my past that I would like to relive. Apparently, I
19 am unlike others in this. In fact, everyone I’ve put that
question to has a list of times and places and people to be
revisited. I am only at home in the present, and view with
22 dislike the numerous letters from biographers. On my desk
there are now two new requests for recollection — of Alec
Guinness and Terry Southern. Who next? I like both, but
25 what on earth has one got to say about either that will be
interesting? Little anecdotes are not my style. Of course, I
could review their life work, but I charge for writing
28 reviews.

VIDAL, Gore. Palimpsest — a memoir. London: Penguin, 1996, pp. 147-8.