The notion of hishiryo as discussed in the school of Japanese Soto Zen should not be understood to mean "not to think" when taking up the practice of zazen (lit., sitting Zen). Under this view it would then be paradoxical. One would be thinking about not thinking so as to think non-thinkingly!
Hishiryo (S., ashraya-paravritti) really means to transcend thought so as to be in the absolute—being thus thoroughly anterior to the carnal mind and body. For us, this is the animative source of figurative thought and body.
If zazen practitioners are engaged in thinking (J., shiryo) and/or not thinking (J., fushiryo) they haven't got a good grasp of what Zen and sitting means, i.e., zazen. The Chinese character for sitting, according to Wilder & Ingram's book, Analysis of Chinese Characters, is "Two men [the character] sitting on the earth [character] t'u, face to face to talk." This character can also mean contemplation (zen) into one's ultimate nature or the same, the sitter looking (zen) at Rinzai's "true man of no title" which is a metaphor for the animative pure Mind.
In the context of hishiryo the highest zazen is the return (paravritti) to the foundation (ashraya) or pure Mind. It should be mentioned that Bodhisattvahood commences with a brief return to pure Mind and culminates with a final return to ashraya which is inconceivable, abundant, in the sense of good, eternal (dhruva) and blissful ((sukha).
However, for the beginner engaged in the practice of zazen there is no cognition of hishiryo. To be sure, beginners vacillate between unbridled day dreaming and its suppression (fushiryo). Thus, beginner’s zazen only serves as an introduction to the mental state conditioned by samsaric life. Indeed, the beginner under the weight of bad habits and beliefs has for their immediate foundation (ashraya) the transitory, the disturbed (duhkha) and what is not the true self (anatman).
Any breakthrough in zazen comes, not by being in the dilemma of figurative thinking and its suppression, but by the seeing of one’s original face, to use Hui-neng’s marvelous expression. This is the medium from which our figurative thoughts are made, so that even the suppression of such thought becomes unnecessary. This is authentic hishiryo not the kind in which a Zen master instructs the student thusly, “When you are sitting in zazen, don’t think. Don’t use your frontal lobe.”