Dear Brian,
In response to Tom you said: "Why a world should have such unseen and unusable dimensions is unclear", then you claimed a virtual world needs only one extra dimension; presumably on the basis of 'usefulness'. And your remark about complex number theory's "imaginary" dimension is misleading---complex numbers are simply 2D representations, as of course you know.
I don't think I agree with you (or my hero, Feynman) that "a real field is a mathematical function we use to avoid the idea of action at a distance". Real fields appear to distribute energy over space. I don't believe that mathematics (the 'map') can accomplish this, only reality (the 'territory') can do this.
Then you say you like fields, but they cannot be perceived directly. Forgive me for quoting my earlier fqxi essay, but I can't discuss direct perception any better than I did: (http://www.fqxi.org/community/forum/topic/561)
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"Upon what must a fundamental theory of physics be based? ...it should be formulated in terms of human reality, not abstract formulations. Either it is based on directly and immediately sensed reality or it is based on some abstraction that is claimed to represent reality. Current theories are based on physics abstractions such as:
Gravity, String theories, Electromagnetics, Quantum field theories, Strong and weak forces, Dark matter and energy, Extra dimensions, Extra universes, Consciousness
Of these, only two, gravity and consciousness, are immediately sensible and directly experienced by humans. I am directly aware of gravity and I am directly aware that I am conscious. I have no direct, immediate, awareness of any other physics on the list (with the exception of a small range of electromagnetic radiation). All other entities, if they exist, are sensed through the medium of some measurement apparatus (as complex as the Large Hadron Collider or as simple as iron filings in a magnetic field)-yet none is directly sensed. Even muscular detection of a magnetic field is possible only through the medium of a held magnet. Gravity and consciousness are directly sensible, requiring no external apparatus, and hence are deemed suitable for the basis of a physical theory that does not depend upon belief in either equipment or logical argument. We *know* these two entities exist. All else should depend on these."
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Brian, you claim the VR model is a testable theory because "what processing creates it can be derived by reverse engineering." I'm older than you and my first logic design class (text: "The Logical Design of Digital Computers" by Montgomery Phister, 1958) argued that economics dictated a certain problem be solved by mechanical relay logic. I've designed with vacuum tubes, transistors, TTL-MSI, PALs, microprocessors, minicomputers and FPGA hardware, and written in Fortran, BASIC, PL-1, VisiCalc, JAVA, 8080, 8051, and 80386 assembly code, and many others, and I've designed multi-tasking incrementally compiling operating systems, ISDN connections to the internet, and much more, and I very sincerely doubt that reverse engineering the "processing output" to a meaningful, that is, architectural, level, is possible. My not so humble, but very knowledgeable, opinion. And if you can't reach the architectual level, then the VR model is more or less indistinguishable from God.
Edwin Eugene Klingman