How our brain seem to understand these two syntaxes.

I just finished to read Mathematics is a language of is own pointed out by MathForge. “A team of scientists led by Rosemary Varley at the University of Sheffield, UK, studied three people who had extensive damage to the left hemisphere of their brain, the so-called Apollonian half that includes linguistic skill areas”. They observed that those people were able to understand the difference in mathematical sentences of the type “7 – 2” and “2 – 7” but were not able to understand differences in language sentences like “The boy chased the girl” and “The girl chased the boy”.

The experience is really interesting. It seems that the brains zones involved in the understanding of basic mathematical sentences are not the same as the one of the traditional, written, languages. Good; but what about more complexes mathematical sentences? Everybody who tried to demonstrate theorems of any sorts in algebra or set theories know that this is not just a question of syntax understanding but more a question of imagination.

By example, if you work in the field of computer sciences, you know what formal specifications of software are. This is a method used to prove that your software is consistent with himself, it help to clarify, without ambiguities, the specifications of your software (it help for many other things but I’ll not discourse on the subject of software format specification in this post). Basically, formal specifications are a way to write a software program (his specifications) in a formal mathematic syntax. Now, my question is: if I got these brains damage cited up there, will I always be able to read and understand a specification wrote in Z (a formal specification language)? Personally I have doubts because I think that there are more things involved then just mathematical syntax understanding.

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