Pages

Monday, February 04, 2008

Mind Maps: Mathematical Structures?


Plato's doctrine of recollection, however, addresses such criticism by saying that souls are born with the concepts of the forms, and just have to be reminded of those concepts from back before birth, when the souls were in close contact with the forms in the Platonic heaven. Plato is thus known as one of the very first rationalists, believing as he did that humans are born with a fund of a priori knowledge, to which they have access through a process of reason or intellection — a process that critics find to be rather mysterious


What are Mind Maps?


A mind map is a diagram used to represent words, ideas, tasks or other items linked to and arranged radially around a central key word or idea. It is used to generate, visualize, structure and classify ideas, and as an aid in study, organization, problem solving, decision making, and writing.

It is an image-centered diagram that represents semantic or other connections between portions of information. By presenting these connections in a radial, non-linear graphical manner, it encourages a brainstorming approach to any given organizational task, eliminating the hurdle of initially establishing an intrinsically appropriate or relevant conceptual framework to work within.

A mind map is similar to a semantic network or cognitive map but there are no formal restrictions on the kinds of links used.

The elements are arranged intuitively according to the importance of the concepts and they are organized into groupings, branches, or areas. The uniform graphic formulation of the semantic structure of information on the method of gathering knowledge, may aid recall of existing memories.


Well straight to the point then I guess.

Bee:
The important thing about the basis of our societies is not actually its fixed structure but the way to readjust it. A bit of scientific method would be good there.


As I mentioned previously on Backreaction site and in giving subsequent information about this process. It has been a journey of my own discovery, that I would say that at the basis of reality is such a mathematical structure.

I know when this process started for me and it would not serve any purpose at this point to speak to it directly. People have their reasons for and against such a proposal as their being such a mathematical structure, so what currently leads me to say that their are these two opposing views?


Wigner’s Gift Horse By JULIE REHMEYER • Feb 1, 2008 See here for article.

Stephen Wolfram argues that the way to unlock the rest of science is to give up on mathematics and look for explanations analogous to computer code. Very simple computer programs can produce remarkably complex behavior that mimics phenomena science has had difficulty modeling, like the motion of fluids, for example. So studying the behavior of these programs may provide scientists with new insights about these phenomena. Indeed, Wolfram thinks the universe itself may be generated by a computer program simple enough to be expressed in a few lines of code. “If the laws are simple enough, if we look in the right way we’ll find them,” he says. “If they’re not, it will be tougher. The history of physics makes one pessimistic that we could ever end physics. I don’t share that pessimism.”


Tegmark believes in an extreme form of Platonism, the idea that mathematical objects exist in a sort of universe of their own. Imagine that, Tegmark says, “there’s this museum in this Platonic math space that has these mathematical objects that exists outside of space and time,” Tegmark says. “What I’m saying is that their existence is exactly the same as a physical existence, and our universe is one of these guys in the museum.”


Also worth reading is the sum of any position that would infer the stance of Plato versus anti-Plato, to help distinguish whether or not one might have something of value in terms of the question of whether Mathematics is invented or discovered.

Mathematical Platonism and its Opposites by Barry Mazur January 11, 2008. See here.

For the Platonists. One crucial consequence of the Platonic position is that it views mathematics as a project akin to physics, Platonic mathematicians being—as physicists certainly are—describers or possibly predictors—not, of course, of the physical world, but of some other more noetic entity. Mathematics—from the Platonic perspective—aims, among other things, to come up with the most faithful description of that entity.


For the Anti-Platonists. Here there are many pitfalls. A common claim, which is meant to undermine Platonic leanings, is to introduce into the discussion the theme of mathematics as a human, and culturally dependent pursuit and to think that one is actually conversing about the topic at hand.


Mapping the interaction from a scientific point of view?

As I read through the article I had previous insights while reading through Sir Roger Penrose's lecture on the Extended Physical WorldView. While I myself had picked the title, it would have been nicer to show the very image on the start of that lecture.



This is a important statement I am making below because it distinguishes between where we think we might be going in terms of computer technologies versus what will always remain within the human domain.


So on the one hand one might think about technologies in the 21st Century and wonder if computer technology can ever reach the status of Consciousness with which the "synaptic event" could include images, all the while it would include all the history to that point?


While it is never clear to me about the origins of the universe, it had some relation in my mind to what first allowed any soul's expression. While I had shown the relation to the synaptic event, there had to be a place created for such an expression, to be fortunate and validated.

Do I know what plan for every individual is, of course not, but that you choose such an expression is self evident. There is much to the word, "self evident" that remains to be explored within context of this site, and of value, in the iconic image of Raphael's expression with Plato and Aristotle at it's centre.

Now, neuronic networking is supposedly the platform computer technologies can take in their designs, but what true aspect of the emergent process could ever define the human being and one's potential? The information that could enter such an synaptic event within your own thinking mind?

So the process is one of self discovery. About processes within your own self that allow one to possibly develop the new mathematics that speak directly to the very unfolding of the universe?

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).]


What can arise from any person, to have defined that it reaches back into the forms. That it chooses to manifest "as the person" you have become? What lies dormant, that you awake to it in such a way that it will manifest in all that you do, and become part of the "history of recollection" that you unfold in this life, and have learnt these things before? You dream?

I, Robot:

....signs of new life emerge as images photonically flicker in the new logic forming apparatus....

I had a dream....


We might like to think that computers are capable, while the very idea of the "image" holds such vasts amount of information. This is not a new idea from an historical perspective if one ever thought to consider the alchemists of our early science.

How would you contain all the probability and outcomes, with ever looking beyond space and time, to realize that the "heavens" in some way, meet the earth. Manifest within you? Can find re-birthing through you? Inner/outer become one.

No comments:

Post a Comment