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I'm looking for a source to cite. I'm working on mathematical expressions that re-use the same subexpression multiple times. Intuitively someone reading such an expression only needs to understand a subexpression that is re-used once and can then apply this knowledge multiple times. In computers one could cache the output of a re-used subexpression and then call the cache whenever the same subexpression is queried again instead of recalculating the whole subexpression.

I'm sure something similar happens in the human brain, or at least this is how I read mathematical expressions myself, but I'm unable to find a source because I lack the terminology. Could someone help me out?

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  • $\begingroup$ In the longer term, one might say the subexpression's sense enters muscle memory, which more likely is the introduction of a System 1 reaction. See dual-process theory. In the shorter term, I imagine expression abstraction is handled by the verbal system, like with grammar. $\endgroup$
    – Michael
    Dec 17, 2021 at 21:04
  • $\begingroup$ You could look at research on algorithm-retrieval shift. I.e., the first time you solve a problem (e.g., a multiplication problem), you might use an algorithm like repeated summing. But with repetition, you are able to recall the answer from memory without applying the algorithm. Some theories of skill acquisition heavily emphasise this process. $\endgroup$
    – Jeromy Anglim
    Dec 18, 2021 at 2:57
  • $\begingroup$ I think (and the comments so far seem to support) that this question is primarily opinion-based because there are many ways to interpret the question and find analogues in the brain, such as memory, practice effects, heuristics, etc. For the idea that the brain can be treated as a mathematical expression or computer program, see this question. $\endgroup$
    – Arnon Weinberg ♦
    Dec 27, 2021 at 18:34

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