Yes, let’s take an example of why space-time is incommensurate.

In Newtonian theory (what Notalle calls classical mechanics), events take place in absolute Space, and that Space is Euclidean in three dimensions. Three lengths of spatial coordinates can identify any event per this system theory -

S=x^3

Whereas the set T of temporal moments of an event, ie, the location of the event in Time, is only the one-dimensional timeline (t1), such that the structure A of Space and Time is simply the Cartesian or cross product of Space and one-dimensional Time -

So for a given classical system, we have …

A = ST = x^3 *t^1

Flattened continua (space-time) take recourse to Minkowsky space-time, which differs from Newtonian Space AND Time in that is not defined by the Cartesian product S x T = x3 * t1, but by a pseudo-Euclidean, flattened Space in four dimensions -

Therefore, in Relativity (and hence Notalle) we have …

S=x^4

In Special Relativity, one encounters a continuum defined as four-dimensional, additive space-time in the function for the square power of the latter that permits its expression in terms of the c2 constant we find in the Einstein field famous E=mc^2 -

So, for Relativity and anything else building upon it …

dS2 = dx1^2 + dx2^2 +dx3^2 - c^2 (dt^2)

Since we must follow the Einstein prescription for “c” as a unity function and write the timeline strictly as the length, t=x4, which corresponds to our Minkowski-Einstein postulate, we have -

dS^2 = dx1^2 + dx2^2 +dx3^2 - dx4^2

Pay cautious attention to what just happened in the final term as it becomes evident how timeline (dx4^2) is now a negative term in four-dimensional Space.

More importantly, it is apparent that such a ‘projected’ continuum could never describe an energy continuum or the superimposition of manifolds that form distinct energy multiplicities. The objection raised here and expounded upon by many physic dissidents, most notably for me, Harold Aspden, and du Gabriel (see Fermat’s Last Theorem and Einstein’s Four Light Postulates for details, is the use of ADDITION to couple the dimensions. As you point out, this is a critical step and the central issue in coupling continuum elements, field or otherwise.

We object not simply to the abuse of the sign of addition to a couple of dimensions—primarily when volume itself defines Euclidean.

Space is l3, and it makes explicit the powers of multiplication implicit in the exponent. The totality of the mathematical operations undergirds the reduction of a continuum S to x^4 that must be apprehended and rejected as fiction. If you go through the vid chats released shortly after Dr. Farrell published “The Demon in the Eukr,” I presented a brief commentary on the paper Levi-Civita published addressing the use of tensors in mapping these flat geometries.

It is not energy that is a function of Space and Time, but the latter two manifolds, which are a function of energy, from which they also derive their intrinsic commensurability - an insight completely unknown to present-day physics. That is, neither space and time nor space-time are vessels in which energy is held. Energy, as such, is the progenitor of both Space and Time and all commensurate activities known as multiplicities, waveforms, and their superimpositions, resulting in particulate matter.

Flattened continuum geometries are merely content with representing the multiplicity of Time as if it were just a special (and single) dimension of the multiplicity Space as shown above. This is the case for both classical mechanics, Relativity, and Quantum car mechanics.

But consider the classical dimensional function for energy - it is written as a function of three distinct dimensionalities (mass m, length l, time t), deemed to be irreducible, and in a product relationship -

E = m l^2 t^-2

Precisely because such an abstract form of energy affects ponderability (as it carries the property we denote as mass), one may properly speak here of mechanical energy and its effects. But what to say of massfree energy, imponderable energy - what is the natural form of its function?

E = l^3 t^-2

E=(not mc^2) but E=ST=l^3t^2

The versor equilavlent:

E=ST

Energy is a function of space and time, not space-time; energy is not within the vessel of space-time; space and time are energetic features.

In this way, we find it apparent how energy is a function of a given volume of Space, and its cross-product superpositions with Time become resonant synchronicities. This provides for both Space and Time to be defined energetically.