In trying to find the proper protocol which would give him a chance to find out the secret of the Heavenly Hosts during "Voyage Of The Damned", the Doctor spewed out a series of numbers:
"10, 666, 21, 4, 5, 678. 42, 1"
WHO BY NUMBERS
Why did he choose these numbers? Here are some suggestions:
10 - This is the number of spacetime dimensions in some superstring theories.
But he may have been thinking of himself, as he is the tenth incarnation of his Gallifreyan mind and soul.
Then again, Capricorn is the tenth symbol in the Zodiac, so maybe the Doctor was already thinking in terms of Max Capricorn as being the villain behind the curtain.
666 - Even if he may not be a believer, the Doctor may have figured the Book of Revelations had some kernel of truth behind its prophecies.
21 - 21 grams is the weight of the soul, according to research by Duncan MacDougall, generally regarded as meaningless.
4 - Like the numeral "42" coming up, 4 is part of the sequence of Numbers believed to govern the world. As seen on 'Lost', the sequence is "4, 8, 15, 16, 23, 42". "42" also comes up as a guess by the Doctor. As he probably knew from his friend Arthur Dent, 42 is the answer to Life, the Universe, and Everything.
5 - Could it be that it came to mind after mentioning "10"? Perhaps once he thought of himself and his line of succession, the Doctor remembered his encounter with his own Fifth Incarnation just from a few hours before.
678 - I suppose he just lumped these numbers together because they represent three of the Doctors to precede him. Or he was starting to get desperate with the inspiration.
Back to 42 - The "Ultimate Answer" was probably all he needed if the theory was right.....
And finally he used "1", which meant that he might as well try for the basics - he certainly had nothing else to lose by that point......
And for us watching at home, it might have triggered a response from 'The Prisoner': "Who is Number One?", and that could have led us to pondering exactly who it was behind the plot to sabotage the Titanic.... (And how appropriate that this post is Number Six in today's series!)