Before language, people must have thought without words. I often have the impression that I have a thought fully-formed in my head, yet I wait to listen to it unfold in words before moving on to the next thought. Perhaps I could think much faster if I weren't addicted to words.
Has anyone developed techniques for thinking without words?
This would have a little in common with Buddhist practices of emptying your mind, but wouldn't be the same thing. For one thing, Buddhists also try to empty their minds of images. More importantly, they are trying not to think, while I'm trying to think - just not unpack everything into words.
I've found that when I try and do basic arithmetic in my head (like 1784 * 2), I end up knowing the answer (or some subanswer of the algorithm) in some subsymbolic way but then feel the need to carry out the calculation with the symbols. I can calculate quicker by jumping straight to the answer I already know, although it feels like making a leap of faith. It sounds like you want to do a similar thing with words.
Do you mean you have a subsymbolic concept of 3,568 or that you seem to arrive at it in a subsymbolic way?