Mathematics, rightly viewed, possesses not only truth, but supreme beautya 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
In a Question below, is it worth it, to look at the context of what groups who gather might spark to the rest of society(click on it)? Look at what it has done for myself, and the reasons why such inductive/deductive features seem to be a part of the origins of cognitive functions that mathematically display itself?
Is there a theme in this regard through my blog that I had questioned earlier and links brought forth to raise awareness of what might have been implied in that true "consciousness sense" about the very nature of our involvement in the nature of reality?
But then too, awareness, about the death of such sensations. This is most troubling to me, if such model consumptions had made this impression then what had happened to the views as they exploded into the other realms? Other Realms? Why would I introduce Thales as a culminative vision about what could emerge and the father of geometry? Models make our view culmnative and increase the vision capabilites. Is there no one here that see differently after they had crossed a page to find that in our new tomorrows we see reality a little different now?
You have been touched at a most deep level, that goes beyond the death of such sensations as Toposense, or momentums of curvatures. A microscopic eye now, to the quantum nature, right next to your reading from this screen. It's in the air all around you, this potential? :)
Mathematics(logic?) and experiment?
I respond in that thread, and although it would seems disjointed from the rest of the commentaries, I thought I was talking directly to Sean's opening post. So I have linked the post on the very title as I have done with previous entires, as they have been setting the pace for my thinking about what views they share and what safety net is placed out there for us lay readers.
Would this impede my question as to the relation of philosphy in Sean's opening statement, to find that it had found a trail that leads to reasons why funding and perspective on it, should be thought about most carefully. Held in the esteem, with which one's adventures in physics and mathematics might have benefited society?
I understand this need for determination, and as well, the need to reaffirm what philosophy might hold in regards to truly active memebers of the science community and the projects they are engaged in. Would they have a distain for the philosophy of mathematics?
I left a question mark out there, and this question although never answered did see some slight comment in relation to the philosophy that where such logic might have gained in relation, being mentioned. I'll have to explain this some more so you understand that I am working hard to make sense of what is out there and viewed, whether in the tabloids, or what ever generalizations made by mathematicians, or the physicist who looks that little bit further.
Shall I quickly respond to the thread commetary or should I continue? I thnk it important that I respond to the comments rasied but I'll do this after by highlighting the area that spoke to me in relation to this train of thought.
I linked a quote from Plato on the idea of philosophy in my comment. I wil be moving from that position.
Philosophy of Mathematics
Foundations Study Guide: Philosophy of Mathematics by David S. Ross, Ph.D.
The philosophy of mathematics is the philosophical study of the concepts and methods of mathematics. It is concerned with the nature of numbers, geometric objects, and other mathematical concepts; it is concerned with their cognitive origins and with their application to reality. It addresses the validation of methods of mathematical inference. In particular, it deals with the logical problems associated with mathematical infinitude.
Among the sciences, mathematics has a unique relation to philosophy. Since antiquity, philosophers have envied it as the model of logical perfection, because of the clarity of its concepts and the certainty of its conclusions, and have therefore devoted much effort to explaining the nature of mathematics.
You have to understand that although I am deficient in the math skills many have, it is not without effort that I am enaging myself in what appears to be beautiful and simplistic design when completed as a model. When we look at what the Wunderkammern had to offer in a revitalizing and dusting off of, models that were concretized for us. Did they lanquish until they were refurbished to the museums of time, so that we may again look at what mathematics has accomplished for us. In ways, that are very abstract and beautiful? What then exist as you gazed into the magnetic field, the dynamcis of brane held issues and the exemplification of design in those branes? It had to follow consistent and progressive developement in the physics of.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner
The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his 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).]
Social constructivism or social realism
Now here is the part, that while I saw the devloping nature of the tread of thinking and comments how would I answer and stay in tune? I previously spoke of John Nash and the inherent nature of mathematics as it could pierce the bargaining process, that to have this moved t a dynamcial social and constructive pallette developed in the ongoing relations of nations, why would such a scoial construct not be recognized as to the direction and strength of what mathematics might mean from a cognitive and developing brain that we have.
This theory sees mathematics primarily as a social construct, as a product of culture, subject to correction and change. Like the other sciences, mathematics is viewed as an empirical endeavor whose results are constantly compared to 'reality' and may be discarded if they don't agree with observation or prove pointless. The direction of mathematical research is dictated by the fashions of the social group performing it or by the needs of the society financing it. However, although such external forces may change the direction of some mathematical research, there are strong internal constraints (the mathematical traditions, methods, problems, meanings and values into which mathematicians are enculturated) that work to conserve the historically defined discipline.
This runs counter to the traditional beliefs of working mathematicians, that mathematics is somehow pure or objective. But social constructivists argue that mathematics is in fact grounded by much uncertainty: as mathematical practice evolves, the status of previous mathematics is cast into doubt, and is corrected to the degree it is required or desired by the current Mathematical Community. This can be seen in the development of analysis from reexamination of the calculus of Leibniz and Newton. They argue further that finished mathematics is often accorded too much status, and folk mathematics not enough, due to an over-belief in axiomatic proof and peer review as practices.
This gets very comlicated for me. Yet I recognize the inhernet pattern at the basis of these negotiatons and the games involved. More to follow, and short on time.