Can Dimension and Probability Define Reality?

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Discussion Overview

The discussion revolves around the concepts of dimension and probability in the context of physics, particularly how they relate to defining positions and the nature of reality. Participants explore the implications of these concepts in theoretical frameworks and their potential meanings in physics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant, Ted Erikson, proposes that a position or location can be identified without dimension and with zero probability of measurement, suggesting this implies a point.
  • Erikson discusses the varying meanings of "dimension" and "probability," noting that dimension can be a hyperbolic synonym with many interpretations, while probability can be objective or subjective.
  • Erikson relates his ideas to an FQXi physics essay contest, arguing that three non-collinear points can define a 2-D equilateral triangle, leading to a probability versus dimension plot that suggests a third dimension emerges at 100% probability.
  • He further claims that four points are necessary to define the space occupied by matter, implying a connection to space-time and higher dimensions.
  • Another participant questions the need for definitive definitions of "dimension" and "probability" in physics.
  • Some participants suggest looking up definitions on Wikipedia, indicating a desire for clarity on the terms used in the discussion.
  • Erikson revises his initial post, acknowledging errors and refining his arguments about dimensions and probabilities, including claims about infinite dimensions for certain probabilities.

Areas of Agreement / Disagreement

The discussion features multiple competing views regarding the definitions and implications of dimension and probability. There is no consensus on the meanings or their applications in physics, and participants express differing opinions on the clarity of these concepts.

Contextual Notes

Participants express uncertainty about the agreed meanings of "dimension" and "probability," and there are unresolved mathematical implications in Erikson's extrapolations. The discussion reflects a range of interpretations and assumptions that are not fully clarified.

SdogV
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Anyone care to critique this talk abstract for the CSAAPT Meeting, 3/16/2013?

DIMENSIONAL PROBABILITIES
by
Ted Erikson
R/E Unltd, Chicago

What identifies a position or location but has no "dimension" and zero "probability" of measurement? Certainly this implies a point. But what are totally agreed upon meanings of the quoted words? Summing up an extensive web search, dimension is a hyperbolic synonym with many meanings while probability can be either objective (result of experimental outcomes) or subjective (e.g. Bayesian).

Dimension and probability appeared significant in an FQXi physics essay* contest that I entered last summer to define panpsychism. Three non-collinear points can define a 2-D equilateral triangle, i.e. area. With one point as an origin for place probabilities of the other two and extrapolating a probability versus dimension plot, a third dimension, i.e. volume, emerges at 100% probability!

Four such points are required to define the space occupied by matter, i.e. protons, electrons, and neutrons. Again, referred to one point as an origin in a regular tetrahedron, extrapolations imply 4-D, i.e. space-time and a minus1-D. Pyramid extrapolates to~7 dimensions and a minus 1/2 dimension.

Are space-time dimensions and probability really understood?
_________________________________________________________
* http://fqxi.org/community/forum/topic/1409
 
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SdogV said:
Anyone care to critique this talk abstract for the CSAAPT Meeting, 3/16/2013?
The horror... the horror...
 
So, what is a definitive definition of "dimension" and "probability" to use in Physics?
 
Please just look up those words in Wikipedia.
 
mitchell porter said:
Please just look up those words in Wikipedia.

See first entry for what was found there and elsewhere!
 
Revised: Errors revealed in re-reading first draft post above. Sorry, too impulsive.

DIMENSION AND PROBABILITY
by
Ted Erikson
R/E Unltd, Chicago

What identifies a position or location but has no "dimension" and zero "probability" of measurement? Certainly this implies a point. But what are totally agreed upon meanings of the quoted words? Summing up an intensive web search, dimension is a hyperbolic synonym with many meanings while probability can be either objective (result of experimental outcomes) or subjective (e.g. Bayesian).

Dimension and probability appears as significant in an FQXi physics essay* contest that I entered last summer to define panpsychism. In a 2-D equilateral triangle, with one point as an origin for other two, a probability versus dimension plot shows extrapolated evidence of 0-D and 3-D as expected. For vertices of a 3-D regular tetrahedron as 4 points, treated in the same fashion as 16 trees, implies evidence that extrapolate to minus 1-D and ~4-D. For a 4-D pyramid, (minus ~1/2)-D and ~7-D appears.

Four such points are required to define the space occupied by matter, (i.e. protons, electrons, and neutrons). For spherical spaces, I conclude an infinite-D for a 100% probability and well below 50% for anything less considered.

Are space-time dimensions and probability really understood?
_________________________________________________________
* http://fqxi.org/community/forum/topic/1409
 

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