"In a supertautological theory of reality, it is unnecessary to assume the uniformity of nature with respect to certain kinds of generalization. Instead, such generalizations can be mathematically deduced…e.g. nomological covariance, the invariance of the rate of global self-processing (c-invariance), and the internally-apparent accelerating expansion of the system. (See MAP, M=R, MU)"
http://www.teleologic.org/
"JB: Have you ever considered that the world is an invention, and there's not an a priori existence before discoveries of people like yourself?
BARBOUR: I believe in the world; I'm a realist, but it remains a conjecture.
JB: Isn't this a kind of naive materialism? Wallace Stevens addressed the idea that the words of the world are the life of the world. Norman O. Brown noted that nature isn't created ... it is said. But I don't know of any notable physicists today who are seriously concerned with the role that language plays in the creation of reality.
BARBOUR: The words are meaning something. What impresses me is that, despite what you say, the rules of the game of science have stayed amazingly constant, despite the fantastic changes in how we see the world. Basically, the assumption has always been that that there are material things that move around subject to the constraints of geometry. There is change subject to order. Science---or at least physics---has been about establishing how those changes take place and describing them mathematically. Every now and then they lead to a dramatic new way in looking at the world, but the rules of the game have always been the same really, going right back to geometry and ancient astronomy.
I personally believe the world is still probably very much richer than we imagine, and that we still may well be only just scratching the surface of it. If you climb a mountain range you get different views as you go up. When you've got to the top you can understand what you could see lower down, but you couldn't understand it properly when you were lower down. I see the progress of science being like that, that suddenly completely new vistas are opened up, and you find new ways to think about it. I do think we are discovering the world, not inventing it. But John Wheeler sometimes seems to suggest that we create the universe. He thinks that by insisting on finding a consistent description of it we conjure it up by a kind of conspiracy. He illustrates the idea by a variation of the game of twenty questions in which there is no object at the start of the questioning. Instead, each answer that is given must be consistent with all those already given. Eventually, there emerges some object that matches the answers.
JB: The physicist and poet William Empson wrote the following in "Doctrinal Point" in his Collected Poems:
All physics one tautology;
If you describe things with the right tensors
All law becomes the fact that they can be described with them;
This is the Assumption of the description.
BARBOUR: As it happens, this is about an issue very closely related to quantum cosmology. What is the meaning of general covariance? Empson is arguing that it is a tautology. I think he is right in that but not in the claim that all law becomes the assumption of the description. Tensors relate different things and bring them into lawful connection.
Let's consider a great experience I just had. I witnessed the total eclipse of the sun in France on August 11th. I remember vividly reading as a boy that there would be this eclipse in 1999, the first one visible in England in a long time---actually I went over to France to see it. Now there isn't any doubt about an eclipse; either you see an eclipse or you don't. The astronomers predicted that it would be seen as total in the medieval town of Senlis just north of Paris, and sure enough we did see it total. That's pretty impressive. I don't think there's anything to do with inventing there---the impression of actually seeing the sun totally eclipsed is quite unambiguous. My memories of reading about the eclipse as a boy and my memory of the actual eclipse are not tensors but they are real different things that match up. That's why I believe there's something real out there in the world and that we are getting our hands on it."
http://www.thezensite.com/ZenTeachings/TheEndofTime.htm
Meaning of 'Background Independence'
...
• The existence of non-dynamical fields in gauge theories is a tautology. They should
be exempt from the equation non-dynamical = absolute.
• In our previous examples (Einstein-Fokker, Heat equation) more than the expected
four functions could be set to fixed values. There were ten components of n_(μγ) and
four components of n^(μ). This was the remarkable feature that showed their nondynamical character.
• I propose to maintain the equality background = absolute structures but to refine
the notion of absolute structure, so as to not apply to fields whose non-dynamical
character is merely due to gauge freedoms.
• Mathematically this may turn out to be difficult, as it presupposes a solution to the problem of local (and, eventually, also global) gauge fixation. Degrees of freedom are faithfully labelled by points in a quotient space of the space of Φ’s, whose representation as subspace is highly non-unique.
http://www.itp.uni-hannover.de/~giulini/papers/Covariance_english.pdf
"Our civilization is characterized by the word “progress”. Progress is its form rather than making progress one of its features. Typically it constructs. It is occupied with building an ever more complicated structure. And even clarity is only sought as a means to this end, not as an end in itself. For me on the contrary clarity, perspicuity are valuable in themselves. I am not interested in constructing a building, so much as in having a perspicuous view of the foundations of typical
buildings." -Ludwig Wittgenstein
...
Einstein’s principle of general covariance:
Laws of physics must be definable in any coordinate system and are preserved under arbitrary coordinate transformations
Originally intended to express the general relativity of motion, it actually says that general relativity uses differential geometry
Principle of general tovariance:
Any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos and must be preserved under canonical (“geometric”) morphisms between topoi
Like general covariance, general tovariance has no physical content; it identifies the mathematical language of physics and allows the formulation of an equivalence principle
...
‘A startling aspect of topos theory is that it unifies two seemingly wholly distinct mathematical subjects: on the one hand, topology and algebraic geometry and on the
other hand, logic and set theory.’
S. Mac Lane & I. Moerdijk, Sheaves in geometry and logic: A first
introduction to topos theory. Springer, 1994.
...
Topoi carry the hope of deriving the probabilisitic structure of quantum mechanics from its logical structure (von Neumann)
http://www.math.uni-hamburg.de/home/schreiber/tovariance.pdf
"Quotient space theory (QST), a new granule computing tool dealing with imprecise, incomplete and uncertain knowledge, uses a triplet, including the universe, its structure and attributes, to describe a problem space or simply a space. As one of important theories of granular computing (GrC), QST is very helpful to the study of cognitive informatics (CI). This article summarizes the quotient space’s model and its main principle. Then some basic operations on quotient space are introduced, and the significant properties of the fuzzy quotient space family are elaborated. Finally the main applications of quotient space theory are discussed."
http://www.igi-global.com/bookstore/article.aspx?titleid=3891