The quotation used

“This is only a foretaste of what is to come and only the shadow of what is going to be”

is from an interview with Alan Turing as part of an article in the Times on 11 June 1949.

The subheading in the newspaper is Calculus to Sonnet.

That is the title of the sonnet below, as indicated acrostically.

The second verse is also a clue to a 10 letter word.

Solution

The clue is in the last line: “These lines twice show a supervisory ending“. It’s a bit like a cryptic crossword clue and you just need to look at the ending of the last verse.

Just as an acrostic starts with letters that spell out something, the final letters of each line spell out something.

Taking the last four letters of each line:

O V E R
E S E E
R I N G
O V E R
N S E E
D I N G

The letters that are doubled are O, V, E, R, S, E, E, I, N, G which spells the solution.
The answer is OVERSEEING.