From: "Víctor M. Hernández L." vhernan@gauss.mat.uson.mx
Subject: Conjecture
Professor Ernst von Glasersfeld:
From time to time I take again the wires of a conjecture:
1. As you probably know, Mandelbrot´s work introduce us to a new geometric objects called fractals, usually
generated applying recursively a simple procedure (or algotirhm) to its own outputs, by means of wish it may produce
the most complicated sets ever viewed before, including those who have rational dimentions. Consequently, we have
new instruments to see, think and describe the world´s objects surrounding us.
2. From my point of view, the human cognition is in somewhat manner the most intrincated and complex space ever the
human intend to see, think and describe as and intelligible object, in order to develope it conciently from a
didactical point of view
3. This description is a conditio sine qua non the didactical efforts can have some viable concretions lying on it.
4. The conjecture is thinking in the mother language as the prototype action or procedure that a person applying it
recursively on his (or her) daily life as the outputs of the procedure, can develope the enormous complexity we can
name as the human cognition.
¿Could you share with us some theoretical or practical elements to reject this conjecture?
In other case, ¿Could you share with us some papers or references to get closer in develope some didactical
consequences for mathematical education?
Best from Hermosillo, Sonora. Mexico.
In advance, thanks for your time and attention ...
Víctor M. Hernández L.
Dear Mr. Hernandez,
I, too, have great respect for Benoit Mandelbrot and his invention of fractals. I don't
think, however, that this new instrument enables us "to describe the world's objects surrounding us".
Rather, with this instrument we generate patterns that enable us to sistematize areas of experience that
formerly showed no regularities at all. In my view, fractals are a new way of SEEING, and they have no more
independent "existence" that numbers - or a coast line, which is one of Mandelbrot's favorite examples
(where exactly should you draw the coast line when the tides shift it all the time, when waves keep moving up
and down on beeches and there are millions of rocks of which you cannot say whether they belong to the land or the
sea? But it's nevertheless a useful fiction). I agree that "thinking in language" is a powerful tool (and
manifestation) OF cognition; but the source of cognition itself is our mysterious capabilty of REFLECTING and
constructing regularities in our experience.
On the question of mathematics education, here are some references:
L.P.Steffe, E.von Glasersfeld, J.Richards, & P.Cobb (Eds.), Children's counting types: Philosophy, theory,
and application. New York: Praeger, 1983.
L.P.Steffe (Ed.), Epistemological foundations of mathematical experience. New York: Springer, 1991.
von Glasersfeld, E. (Editor). Radical constructivism in mathematics education. Dordrecht: Kluwer 1991
Best wishes,
Ernst von Glasersfeld.
