Saturday, November 17, 2007

Self Evident Dimensional Perspective

Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition. Alain Connes

John Merryman in comment section:
Can they propose these dimensions as anything more then the copyrighted product of their own imagination and not loose control over the idea?

Okay I have a problem with the term "static."

I'll just give you an example of what I am thinking in relation to how we may perceive dimension and then of course, there is a mathematical interpretation of topological spaces that others are better qualified to speak on. How could there be such a geometrical interpretation at such quantum levels.

Is there such thing as "a breakdown of time" within the context of measure? It is my ignorance that separates me from the more educated here, yet it is not without wanting to understand, that I am pushing this point further.

Think about the following concept for a moment.

Savas Dimopoulos:

Here’s an analogy to understand this: imagine that our universe is a two-dimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.

Here we are given a new look into another dimension? A shift from what is euclidean, to what is now non-euclidean. It is really quite simple to understand "what Einstein did" when we now talk about gravity.

Juan Maldacena:

Strings existing in the five-dimensional space-time can even look point-like when they are close to the boundary. Polchinski and Strassler1 show that when an energetic four-dimensional particle (such as an electron) is scattered from these strings (describing protons), the main contribution comes from a string that is close to the boundary and it is therefore seen as a point-like object. So a string-like interpretation of a proton is not at odds with the observation that there are point-like objects inside it.

While it is abstract, the move to thinking in the new way is important while we are looking at the whole picture.

Albert Einstein

The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighboring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." I am sure the reader will appreciate with sufficient clearness what I mean here by "neighbouring" and by "jumps" (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum.Albert Einstein p. 83 of his Relativity: The Special and the General Theory

There are deeper philosophical questions here about being a realist and an anti-realist.?

René Thom

See:René Thom:René Thom (September 2, 1923 – October 25, 2002) was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became celebrated for one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Christopher Zeeman). He received the Fields Medal in 1958.

Photograph by Paul Halmos

Much emphasis has been placed during the past fifty years on the reconstruction of the geometric continuum from the natural integers, using the theory of Dedekind cuts or the completion of the field of rational numbers. Under the influence of axiomatic and bookish traditions, man perceived in discontinuity the first mathematical Being: "God created the integers and the rest is the work of man." This maxim spoken by the algebraist Kronecker reveals more about his past as a banker who grew rich through monetary speculation than about his philosophical insight. There is hardly any doubt that, from a psychological and, for the writer, ontological point of view, the geometric continuum is the primordial entity. If one has any consciousness at all, it is consciousness of time and space; geometric continuity is in some way inseparably bound to conscious thought.

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