Compilation errors of humans–while reading

Computers are notorious for interpreting language in an overly literal fashion; a single misplaced parenthesis in an otherwise flawless piece of software code can cause a computer to halt in utter incomprehension halfway through the compilation of that code.

Humans, when reading natural language, tend to be far more robust at this; once one is fluent in, say, English, one can usually deal with a reasonable number of spelling or grammatical errors in a text, particularly when the writing style is clear and organised, and the themes of the text are familiar to the reader.

However, when, as a graduate student, one encounters the task of reading a technical mathematical paper for the first time, it is often the case that one loses much of one’s higher reading skills, reverting instead to a more formal and tedious line-by-line interpretation of the text. As a consequence, a single typo or undefined term in the paper can cause one’s comprehension of the paper to grind to a complete halt, in much the same way that it would to a computer.

In many cases, such “compilation errors” can be resolved simply by reading ahead in the paper. In some cases, just reading the next one or two lines can shed a lot of light on the mysterious term that was just introduced, or the unexplained step in the logic. In other cases, one has to read a fair bit further ahead; if, for instance, the conclusion of Lemma 15 was difficult to understand, one can read ahead to the end of the proof of that Lemma (in which, presumably, the conclusion is obtained), or search ahead to, say, Proposition 23, in which Lemma 15 is invoked, to get more clues as to what Lemma 15 is trying to say. (The use of search functions in, say, a PDF reader, is particularly useful in this regard.)

It is also good to keep in mind that no author is infallible, and that in some cases, the simplest explanation for incomprehension is that there is a typo in the text.

That is Terence Tao, here.

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