Learning category theory (which I did after I wrote a dissertation and several papers in finite fields) certainly changed and improved the way I did mathematics. The change indeed deserves to be called a transformation. In a similar way, my ability to program in Basic improved remarkably when I learned the basic ideas of structured programming and did a little programming in Pascal. But I am reasonably sure that these transformations in my thinking occurred because I learned important new concepts such as limit, adjoint, while-loop, etc. Learning new concepts transforms one's thinking. I am not a linguist, but I know something of Whorf's ideas; I don't understand how one can disentangle the effect of knowing the different concepts that different cultures have from the effect of knowing their language. This brings up the question: Can concepts be differentiated from language? I say via introspection that the answer is "certainly", because when I concentrate on a mathematical problem (or how to reassemble a machine or write a complicated program) the "talking" in my head goes away and is replaced by pictorial concepts located in mental space. Some people claim that this never happens to them. If that is true, it would appear that people come in two different varieties, from Mars and from Venus maybe. But I suspect that the people who claim it never happens are simply wrong: they lack sufficient introspective ability. --Charles Wells
Does the debate -elements and their belongingness vs. functions and their composition- support Sapir-Whorf hypothesis that the way we think is a function of the language we use. In other words, language can transform thinking. According to this doctrine of linguistic relativity, =93users of markedly different grammars are pointed by their grammars toward different types of observations=85and hence are not equivalent as observers, but must arrive at somewhat different views of the world=94 (Whorf 1956, p. 221).
Whorf, B. L. (1956) Language, Thought, and Reality: Selected Writings of Benjamin Lee Whorf (ed. J. B. Carroll) MIT Press, Cambridge, MA.
Thanking you, Sincerely, Posina Venkata Rayudu
=3D=3D=3D=3D=3D Posina Venkata Rayudu C/o: Sri. S. S. Chalam Advocate & Notary Public H.No: 39-4-10, Innespeta Rajahmundry =96 533102 Andhra Pradesh, India Phone: 91 (0883) 444232
Charles Wells, Emeritus Professor of Mathematics, Case Western Reserve University Affiliate Scholar, Oberlin College Send all mail to: 105 South Cedar St., Oberlin, Ohio 44074, USA. email: charles@freude.com. home phone: 440 774 1926. professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html genealogical website: http://familytreemaker.genealogy.com/users/w/e/l/Charles-Wells/ NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm