Arch. Myriam B. Mahiques Curriculum Vitae

Sunday, April 29, 2012

Is the set of Mandelbrot discovered or invented?

Set of Mandelbrot

As you can see in my CV, my line of research is Fractal Urban Morphology. That´s why I´m so interested in fractals. I´m still reading Pi in the Sky, by John D. Barrow and I´ve already ordered The Artful Universe, same author, it seems promising to me.
Well, in Chapter ¨Footsteps through Plato´s footnotes¨ Barrow says that Pythagoreans began to see things solely as numbers, that are immanent property of things; that is numbers are ¨in¨ things and cannot be separated or distinguished from them in any way. As  a contrary point of view, I read that Plato maintained that we discover the truths and theorems of mathematics: we do not simply invent them; for him, mathematics is an  (wonderful) example of a particular form of knowledge that owed nothing to the process of human recognition.
Then, in chapter ¨The Platonic world of mathematics¨ (p. 261), Barrow says that the most famous exponent of Platonism was undoubtedly Kurt Gödel. And, what ´s more important for me ¨Most recently, the belief in ¨Pi in the sky¨ Platonism in mathematics has  been forcefully restated by Roger Penrose who uses the example of the intricacy of structure displayed by fractals like the Mandelbrot set, which he claims ¨is not an invention of the human mind: it was a discovery. Like Mount Everest,... it is just there¨, to argue that this bottomless structure is not invented by the mind, rather,
though defined in an entirely abstract mathematical way, nevertheless (it has) a reality about it that seems to go beyond any particular mathematician´s conceptions and beyond the technology of any particular computer... it seems clearly to be ¨there¨, somewhere, quite independently of us or our machines.¨ (P.262)

Above, the set of Mandelbrot and three variations. All fractals generated by arq. Myriam Mahiques

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