Two quotes:
First on the "House that Jack built" method of explanation from Eddington, Beyond the veil of Physics:
[.."I am going to expound [Einstein's Law] in a way so complete that there is not much likelihood that anyone will understand it. Einstein's law, in its analytical form, is a statement that in empty space certain quantities called potentials obey certain lengthy differential equations. (memo [remember to] explain potential)
We might conceive a world in which the potentials at every moment and every place had quite arbitrary values. The actual world is not so unlimited, the potentials being restricted to those values which conform to Einstein's equations. What are potentials? They can be defined as quantities derived by quite simple mathematical calculations from certain fundamental quantities called intervals. (mem. explain interval)
If we know the values of the various intervals throughout the world , definite rules can be given for deriving the values of the potentials. What are the intervals? They are relations between pairs of events which can be measured with a scale or a clock or both (mem. explain scale and clock)
Instructions can be given for the correct use of scale and clock so that the interval is is given by a prescribed combination of their readings. What are scales and clocks? A scale is a graduated strip of matter which ....(mem. explain matter)
...matter may be defined as the embodiment of three related physical quantities , mass, (or energy), momentum, and stress. What are. mass, momentum and stress?.....They are rather formidable expressions containing the potentials and their first and second derivatives with respect to the co-ordinates.
What are the potentials?......"]
the second from Jeans, A Universe of Pure Thought:
["The making of models or pictures to explain mathematical formulae and the phenomena they describe is not a step towards, but a step away from reality; it is like making graven images of a spirit." ]
What then is the purpose, indeed the use of a worded explanation beyond a cycle of definitions that never quite touch the shadows as only the mathematical formula themselves perhaps do?
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+Tri Sat Nava agreed that a mathematical symbol may embody an edifice of definitions. I like your image of an image-less state behind their (token?) images. That is ok, we will regress to the basics of set logic when tracing down awards from any one definition.
The question of circularity though comes down to equalities of expressions it seems. For General Relativity the metric potential is a measure of the stress of nearby energy-momentum which itself bypasses a definition as such in being defined as the source of connection curvature through the metric.
Think of an explanation of electric charge that is not content less if not circular: that additional attribute of matter beyond its inertial mass which renders the imbued body susceptible to the Coulomb/Lorenz force if placed in a certain field called an Electric field, that is produced by bodies that have the additional attribute of inertia. F=ma appears to conveys a one way cause-effect: you put mass, m in a gravitational field g (here acceleration field g is a noun not a verb as acceleration, a suggests) it will feel a force, a verb, F=mg. (But equating two nouns to a verb seems strange after all?)7w
+Lee McCullochJames Indeed, "token" images. This is an interesting angle to look at this from and it does seem strange. Would a proper way of framing the question, just so that I understand, be: How it is that natural forces could incite, in a mind, the crafting and use of two nouns to describe a verb when transcribed from the mathematical formulae that are devised to represent them?7w- +Tri Sat Nava "Natural forces" would seem too pre-supposing, what is a force after all: that which influences those things that generate it.
We could dilineate stuffness things in the above : matter-stuff of the measuring instruments themselves from conceptual things like the metric-potential that facilitate the measuring. Doesn't help me but can't dwell as hurts.
Maybe the shift that Penrose et al push for in physics from an emphasis of universe of "things" to a universe of "events" is more illuminating? A Reduction program where the elemental "object" is the conformal null cone that dilineates those events that can be influenced by prior ones. A Reduction program based on verbs rather than as was traditional the nouns of quarks, leptons, strings and knots. Interactions would be the elemental event-objects of the universe that effect the cause and effect relationship.
The object-subject conundrum only arises after all when an object is the subject of observation; that entails at some level the reflection/emission of a photon or the excitation of a particle that is detected by some photomultiplier/ eye etc. That is an "event". Quantum determinism dances its merry dance until that event that is the "collapse" of the wave function.7w - +Tri Sat Nava to likely be no clearer: F=ma can be read as an "inertial" equation where the effect of a (verb) force on a test body is to (verb) accelerate it in proportion to the inertial rest mass, m of the "test" body.
Einsteins Equivalence principle though equates inertial acceleration, a to gravitational acceleration, g. The man in the elevator falling through a field g experiences the same F/m as a man purely inertially accelerating at a=g m/s/s. I think of g in the first instance as a definitive Faraday (force) "field" , although as Eddington tells us above it is strictly only a (mathematical) vector "potential" field.
But acceleration,a, the act of free-fall is also a vector field, a "thing" (of mathematics that is) in the sense that it could be described as a bundle of tangent vectors of the tangent space to "actual" space. Traditionally we use a double-headed sharp arrow to represent it on our free body diagrams.
If we agree to call the vector calculus of differential equations as the kinematics (the set of descriptive objects used to describe the mechanisms) of Mechanics. Observational measurements are framed in terms of the kinematical objects of tensor -vector fields. As such we appear to "objectify" these kinematical objects because they can be represented a directed line segment: "Acceleration" is no more the verb that describes the rate of change of the rate of change of displacement of an object, rather it just is a vector field object. But again is is not a tautology: acceleration is an object because it can be represented by an arrow, that is a directed line segment which in itself has no substance: their is no instantiation of vector as thing in actuality.
No more that is, than the act of measuring the distance (via the metric) to determine the rate of change over some clock-read interval, a verb? But it seems here I am conflating the acts of measuring with the measure itself, is this tangle the root of the subject-object conundrum?7w - +Lee McCullochJames Probably not the root but is certainly a part of it and I am not entirely sure if it would be a conflation. If I understand what is implied by what you have expounded on, is it that you find these "mathematical objects" [bundles of tangent vectors] to be confounding in that, by not being actual entities, they can yet serve as a mechanism that can point to things that are and that by accepting them to be the kinematical objects of mechanics we thus should deploy the use of verbs to describe the phenomenon instead of nouns because of the rate of change in which things occur and are measured?
There is a book I will quote where an aspect of this, I think, is mentioned:
"[regarding Hegel's]....long-standing objections to the compatibility of force and human consciousness i.e., how is it possible to think about force, which altogether is exterior to thought? For Hegel, there is an insurmountable gap between the mediations of consciousness and the immediacy of force." - Pg. 147, Kantian Imperatives and Phenomenology's Original Forces: Kant's Imperatives and the Directives of Contemporary Phenomenology by Randolph C. Wheeler7w - +Tri Sat Nava Interesting to note the "representation" theory used by Cohl Furey to realise the generations of fundamental particles. The "stuff" of the world "becomes" as a "realisation" or a "representation" of an Algebra: here the Standard Model SU(3) × SU(2)xU(1) of fermionic stuff is built from a Clifford Algebra, CL(6) ~ℂ⊗𝕆 while bosonic stuff becomes from Clifford Algebra, CL(2)~C⊗H
Complex "Octonians" have three sets of representations: two triplets akin to 3 pairs of the generations of quarks (u,d);(c,s); (t,b); one singlet akin to 3 pairs of generations of (e, mu tau; and neutrino partners).
Her short lecture series makes it all seem straightforward if not obviously accessible!
ℂ⊗𝕆 realises SU(3)_C × U(1)_em /Z3
C⊗H delivers the left and right-hand Weyl spinors6w
