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.
We use words to solve word-problems. Before words, people thought without words but not about word-problems. Asking for techniques for solving word-problems without words is like asking how to create potteryware without pottery. There might be some sort of isomorphism that would allow you to think about words without words, but you would mainly end up with an encipherment. That is why I asked, "Has anyone developed techniques to do math without symbol manipulation?" We use words precisely because we need to know and use their systematic properties, in a similar way that we manipulate symbols to do math.
I am not saying that we are not able to understand the meaning and referents of words without words.