# Why is a constant plane of ones added into the input features of AlphaGo?

In the paper Mastering the game of Go with deep neural networks and tree search, the input features of the networks of AlphaGo contains a plane of constant ones and a plane of constant zeros, as following.

Feature       #of planes Description
Stone colour  3          Player stone/opponent stone/empty
Ones          1          A constant plane ﬁlled with 1
Turns since   8          How many turns since a move was played
Liberties     8          Number of liberties (empty adjacent points)
Capture size  8          How many opponent stones would be captured
Self-atari size 8        How many of own stones would be captured
Liberties after move 8   Number of liberties after this move is played
Ladder capture 1         Whether a move at this point is a successful ladder capture
Ladder escape 1          Whether a move at this point is a successful ladder escape
Sensibleness  1          Whether a move is legal and does not ﬁll its own eyes
Zeros         1          A constant plane ﬁlled with 0
Player color  1          Whether current player is black


I wonder why these features are necessary, because I think a constant plane contains no information and it makes the the network larger and consequently harder to train.

What's more, I don't understand the sharp sign here. Does it mean "the number"? But one number is enough to represent "the number of turns since a move was played", why eight?

Thank you very much.