If you load this emacs extension (in your init file, etc.), then C M-f will move your cursor forward to the midpoint between the current position and the end of the line. C M-b will move your cursor backward to the midpoint between the current position and the beginning of the line.

(global-set-key "\C-\M-b" 'backward-midpoint)
(global-set-key "\C-\M-f" 'forward-midpoint)

(defun backward-midpoint ( )
"Move backward to midpoint between current position and beginning of line."
(interactive)
(backward-char (/ (- (point) (line-beginning-position)) 2)))

(defun forward-midpoint ( )
"Move forward to midpoint between current position and end of line."
(interactive)
(forward-char (/ (- (line-end-position) (point)) 2)))

This is not the same as binary search, because C M-f, C M-f, C M-b will move the cursor to a position that is before the midpoint of the line. However, it has some properties of binary search and it is practically more useful than word-by-word linear search.