*This is the second in a series of blog posts about a work done by Dr. David Lee Cale, professor at West Virginia University. Cale, a polymath, is chiefly a philosopher, trained in physics, political science, mathematics, economics, and numerous other disciplines, holds a Ph.D. in philosophy, an M.B.A., a B.A. in political science, and is ABD in economics, and is a notable ethicist. The work of his being examined is “The Simplest Possible Universe,” a monograph that synthesizes ancient Greek and Scholastic styles of thinking with modern physical insight. The work is striking, in that its brand of creativity is not common in modern intellectual enterprises. Retaining the good sense and substance of modern physics, Cale employs modes of thinking that are on loan from times nearly forgotten. The objective of this blog series is to deconstruct the monograph, examine its components, and assess the merits of each, redoubting where possible. At the end, if efficacious, an attempt at resynthesis of the project, consequent upon the conceptual retooling, will be made. *

Section 1.4 through the remainder of chapter one of *The Simplest Possible Universe *(SPU) is loaded with dense, interesting thought. I have had numerous discussions with Dr. Cale regarding this next idea: the idea of scaling infinity.[1] The discussions have been contentious and enjoyable, as we navigated the possible avenues regarding this topic —and it is an extremely complex one. The idea is to construct a boundless infinite space. If I understand correctly, while each ‘e’ is intended to represent an infinite extension, as ‘each e can be approximated by an infinitely extended line’ (pg. 5), each ‘e’ can be conceptualized as a finite unbounded extension, too.[2] My reason for understanding ‘e’ to represent this is equation 7, i.e., the fact that the summation of the collection of every ‘e’ equals ‘E’. Furthermore, I take it that the idea behind unbounded finite extensions is to avoid an infinite unscaled extension as having end points. One minor issue, which continues the theme of trying to understand the difference between physics and mathematics, is what to make out of these unbounded extensions. If ‘e’ is unbounded, then one might take it to be analogous to an open set in set theory. If that is the case, then what is the difference, physically speaking, between a bounded and unbounded version of ‘e’? This is splitting philosophical hairs, but it is most certainly valid, and it is this sort of question that may bring more clarity to particular features of the model. Another question left out there is whether each ‘e’ is similarly constructed as ‘E’ is, by summation. It’s not addressed, and though seeking to avoid the Cantor-Gödel debate, this seems to be an ontologically significant question, in the sense that it adds a fractal-like aspect to the construction of SPU, which, one would think, makes it more complex than it was.

One point stands to garner praise, most definitely. Cale saw very clearly the issue of having points arise in SPU, if he hadn’t predicated some fundamental width to an ‘e’. Over coffee, I have given quite a bit of criticism to Hellman and Shapiro’s “The Classical Continua without Points,” which seeks to build a continuum without points.[3] All sorts of problems fall out of this kind of attempt, the reason being that no fundamental length is predicated to some aspect of extension. This is an issue when any n-dimensional extension is intersected with a second in an n+1-dimensional space. Building such spaces, ground up, so far as I have seen, do not work out for this reason. In the example just given, of crossing n-dimensional extensions, a point is always the product. That is not a problem for SPU, which, given the same scenario, admits a fundamental n+1 geometric entity, which is not a point. At the time of writing this, I am very much on the side of writers pushing for fundamental discretized lengths in physics, even beyond reasons given in relation to gravity.[4]^{,} [5]^{,} [6]^{,} [7] The strength of this aspect of SPU, not relying on points, nor on extensions only, lends tremendous value to the model. Cale says, ‘For the purposes of this model this minimal diameter is called *the quantum of *SPU *extension*’ (pg. 5).

In all of this, one point that needs a much more thorough drawing out is how, what I called in the last blog post, the double layer ontology achieves a zero quantity. Certainly, based on the description given on pg. 6, Cale has something a little bit different in mind than what I described. SPU’s ‘*intrinsic law of space*’ could probably do with some sort of illustration. For the reader, I’ll explain what I understand to be going on: It appears that each region of space has either a positive or negative impression, and that space, in its natural empty state, requires both of these impressions simultaneously. Without the impressions, there is no capacity to contain, and either “impressed” state expresses a possibility; the combination of states together admits the capacity for the region of space to contain. It’s for this reason that Cale maintains each ‘e’ must express an “equal opposite,” which is quite the abstract concept, if not provided the additional context that I have attempted to develop. Now, it’s the nature of these “impressions” that becomes problematic. Let’s break this down and develop a ground-up view of the issue.

As far as can be seen, rather than roll the ontological notion of containment in with “impression,” in the way that I would, it uses directionality to represent each state. This is, at once, very good and very much a problem. It’s great because each ‘d’, positive and negative, admits a degree of freedom to the space. Think about what that’s so important: most spatial models, being so downright mathematical, not respecting ontological simplicity (let alone natural metaphysical structural aspects that result from ground-up construction), take for granted the coupling of dimensions with degrees of freedom. Once again, Cale makes an absolutely crucial and fascinating point. That an object contained in a space in motion in one direction would, out of some logical necessity, be able to go in reverse, is a *non sequitur*; time may be structured in such a way, for example, not allowing a second symmetrical degree of freedom.[8] The problem is the conflation of degrees of freedom with the ontological capacity to contain. Maybe they can be reduced to one concept, but it is not immediately clear that degrees of freedom and the ontological capacity to contain are the same, because the former is a dynamical capacity, the latter a non-dynamical capacity.

Speaking of dynamics, the major issue that arises with chapter one is the lack of introduction of kinematics and dynamical concepts. For example, the speed of light is introduced before the nature of time is explicated. Moreover, the concepts, such as the ‘will to nothingness,’ is given no extensive explanation, and it is, consequently, difficult to know what to do with them.

In the following two blogs of this series, one will finish the first chapter (e.g., reflections) and begin into the second; the other will bring out a concern regarding SPU and modern cosmology.

[1] Pierre Duhem, in his *Aim and Structure of Physical Theory*, and Enrico Fermi, in his 1936 lecture series on *Thermodynamics*, noted the ins and outs of scaling a quality, introducing quantification, and how such would be done to infinity is currently beyond me; any scaling requires, I believe, an arbitrary non-included reference point, and I am not sure how to broach this problem when dealing with infinities.

[2] Cale says that equation 7 describes a ‘non-Euclidean, non-Cartesian geometry,’ but it should be noted that, here, it is almost certain that he doesn’t mean ‘non-Euclidean’ in the sense of Gauss, Riemann, Lobachevski, and Bolyai, but, rather, simply ‘not Euclidean.’

[3] Hellman, Geoffrey, and Stewart Shapiro. “The Classical Continuum without Points.” *Phil-Sci Archive*. http://philsci-archive.pitt.edu/9409/1/The_Classical_Continuum_without_Points-_9-12_13th_draft.pdf.

[4] Hagar, Amit. “Minimal Length in Quantum Gravity and The Fate of Lorentz Invariance.” *Studies in the History and Philosophy of Modern Physics* 40, no. 3 (2009): 259-67.

[5] Hagar, Amit. “Length Matters: The Einstein–Swann Correspondence on the Constructive Approach to Special Relativity.”*Studies in the History and Philosophy of Modern Physics* 39, no. 3 (2008): 532-56.

[6] Hagar, Amit. Length Matters – The History and The Philosophy of the Notion of Fundamental

Length in Modern Physics (*forthcoming*)

[7] Hagar, Amit. Squaring the Circle: Gleb Wataghin and the Prehistory of Quantum

Gravity (*forthcoming*)

[8] For more discussion on this, see Feliz Alba-Juez’s *Records of the Future – Classical Entropy, Memory, and the ‘Arrow of Time’ *(Quantum Physics free of Folklore #1).