Pierre Curie (1894): “Asymmetry is what creates a phenomenon.”
Against symmetry, is what constitutes time as a measure. So there is this argument in there too.:)
My aim in this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole. This is in contradiction with the Platonic view of mathematics held by many physicists and mathematicians according to which, mathematical truths are facts about mathematical objects which exist in a separate, timeless realm of reality, which exists apart from and in addition to physical reality. –A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics
The point I think I am making, is that in issuance of any position, any idea has to emerge from an a prior state in order for the “unitary whole” to be fully understood? Timeless, becomes an illogical position, since any idea in itself becomes an “asymmetrical view” as a product of the phenomenal world. Symmetry then implies, a need for, and a better description of the unitary whole.
There is a constant theme that I observed with Lee Smolin regarding the effectiveness of the idea about what the Platonic world means in face of being a realist of the natural world. So in one stroke, if we could but eliminate the question about the Platonic world of forms, would we see that Platonism is a duelist of nature, and not a realist of the kind that exists as a product of the natural world. But more then this, the idea somehow that the platonic world is a timeless truth about our existence.
The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.
[3 M. Polanyi, in his Personal Knowledge (Chicago: University of Chicago
Press, 1958), says: “All these difficulties are but consequences of our
refusal to see that mathematics cannot be defined without acknowledging
its most obvious feature: namely, that it is interesting” (p 188).]
So you can see that I attain one end of the argument, against being a naturalist, given I hold to views about the Platonic world? Against FXQi, and its awarding program regarding the selection of the subject as an awardee, if I counter Lee’s perspective?
There are many other classes of things that are evoked. There are forms of poetry and music that have rigid rules which define vast or countably infinite sets of possible realizations. They were invented, it is absurd to think that haiku or the blues existed before particular people made the first one. Once defined there are many discoveries to be made exploring the landscape of possible realizations of the rules. A master may experience the senses of discovery, beauty and wonder, but these are not arguments for the prior or timeless existence of the art form independent of human creativity. See: A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physicsBy Lee Smolin
I have my own views about what constitutes what a naturalist is in face of what Lee Smolin grants it to be in face of the argument regarding what is an false as an argument about what is invented or discovered. So of course, full and foremost, what is a naturalist?
But again, let us be reminded of the poet or the artist,
Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. –BERTRAND RUSSELL, Study of Mathematics
You see, Lee Smolin’s argument regarding naturalism falls apart when we consider the context of the nature of the quasi-crystal given, we understand the nature of the quasi-crystal signature? It is necessary to understand this history.