I end up knowing the answer (or some subanswer of the algorithm) in some subsymbolic way
Do you mean you have a subsymbolic concept of 3,568 or that you seem to arrive at it in a subsymbolic way?
I'll normally double things starting at the right and going left. So first 4*2=8, no problem. Then I need 8*2. As soon as I think the number 8 my brain instantly returns the number 16 as its double, but I still feel like I need to consciously think to myself "What's eight times two? Sixteen". Then the same thing happens for 7*2=14. Now I feel like I need to add up the work I've done so far. At this point my brain instantly returns the number 1568 (The number 1568 appears in my mind as a sequence of digits, not visualised visually, but just the co...
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.