Wow, I'm glad I asked, since that is interesting. I think I can see how the computation could be automatized and regulated to subconscious components of your brain through practice, but its neat that your brain can keep track of those products (8 .. 16 .. 14 .. 2) and their place value (8 .. 160 .. 1400 .. 2000) and add them.
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.