(mathemtical) language as a barrier to (mathematical) maturity

I can understand why immigrants refuse to learn a new language. It is difficult, but that’s not the important part. It not only takes time, but also mental tolerance at the expense of ordinary cognitive development, that is to say, the mainstream of thought entertained by the ambient society. We often appreciate polyglottal quality for its implication of social adaptability, but it obliviates the fact that often people place a higher weight on the actual cultural performance, rather than the potential to do so. And that’s perfectly reasonable since the end result of education is to outperform the teachers and output more intelligent actions. It is a constant toss-over between preparation and  physical engagement. A new language is admittedly a huge amount of preparation for the simple task of associating with a certain percentage of the population in the world. It’s arguably unnatural in the sense that the linguistic legacy should be considered part of the evolutionary heritage of the people, genetically entrenched and therefore resistant to external identification. Of course one of the focal points in the generic evolution vs creationism combat is how to justify this radical diversity and at the same time mutual immitability in the light of either theory (the latter might better be called interpretive art, for lack of more sanctimonious phrases).
   Even in the domain of mathematics, phenomena like cultural anorexic syndrome are common also. An analyst often finds category theory a bit too convoluted to stomach even though at heart they sneered at all the "obvious" constructions that a seasoned logician or algebraist could spend hours trying to recreate on a blackboard. In general it’s not just a lack of interest, but a lack of common language that prevents a fruitful communication between the two. The initial survival stage of learning one’s first language, whether in real world or the mathematical domain, has the purest motivation and hence result in maximal efficiency. That is why choosing one’s initial field of interest is as important as having a good direction for the work henceforth. The secondary motivations consists chiefly of confidence building and searching for connections, which upon closer scrutiny reveals dispensibility and lack of devotion. Mathematics, in contrast with human lingua, however, is more about idea extraction, rather than the nitty gritty details (such as irregular verbs in human lingua), which are completely profaned in the arbitrariness of notations these days due to a shortage of alphabet and overflow of new concepts. I would say on the one hand there is less to get used to than ordinary languages, but is also much more demanding than the acquisition of a well-established human language since the beast to put under control is not just an ancient carcass, rather an ever-expanding soul who expects contribution from its very subscribers. In this sense we are abstracting and generalizing the notion of a language to perhaps an animate media, through which one interfaces between the human world and the world of growing body of mathematical knowledge. Whereas one could view this corpus of knowledge as some high ideal of truth, analogous to the notion of God in monotheistic religions, the exclusive ability to appreciate and reveal through various perspectives (such as the different kinds of interpretations in geometry which facilitate the proofs of many theorems) the content of this ideal makes the field a sociological and anthropological innovation over the old school of religious piety.
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About aquazorcarson

math PhD at Stanford, studying probability
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2 Responses to (mathemtical) language as a barrier to (mathematical) maturity

  1. Jinyun says:

    wow… profound thinking…

  2. yimiao says:

    天 那 ,  晕 倒

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