Here is one example of math, as descriptive tool, being used to paper over a theoretical fail;
When cosmic redshift was first observed, the conclusion became that distant galaxies are moving away, in space. Though as it became evident this redshift increases proportional to distance in all directions, making it seem as if we are at the center of the universe, it was changed from an expansion in space, to an expansion of space, because spacetime!
Which would seem to totally ignore the essential axiom of Special Relativity, that the speed of light is constant to all frames. If intergalactic light is being redshifted, it isn't constant to intergalactic space. More lightyears.
If it was, it would have to speed up, as space expands, but that would negate the cause of redshift.
The presumption is that space actually exists as this dimensional fabric and as it's stretched, the waves/photons are stretched as well. It is as if light is a wavy line and as it gets pulled apart, the line gets less wavy.
Which totally ignores the actual process generating the wave, the energy traveling. For example, waves in water are due to the energy traveling through the water. Now with light, it is assumed the Mickelson Morley experiment invalidated the aether, but this overlooks the fact that we only know it has wavelike properties as it is being absorbed into the detecting medium.
Basically two metrics of space are being derived from the same light. One based on the speed and one based on the spectrum. Given the theory is "expanding space," rather than "tired light," the speed is being used as the denominator and any actual reference to distance is measured in lightyears. As Einstein said, "Space is what you meaure with a ruler" and the only ruler used is the speed of light. The assumption is that somehow the speed and spectrum of the same light are defining different categories of space.
So this three dimensional coordinate system is being treated as though it is more fundamental than the space and activities in space it is mapping. Are longitude, latitude and altitude fundamental to the biosphere of this plant? It's the map versus territory problem and the map is treated as some platonic totem. If all properties are removed from space, it has the qualities of infinity and equilibrium. Which is implicit in SR, as the frame with the fastest clock and logest ruler would be closest to the equilibrium of the vacuum.
We are at the center of our point of view, so an optical effect would be worth considering. It has been observed that while single spectrum light only redshifts due to recession, multispectrum light 'packets" will redshift over distance, as the higher frequencies dissipate faster, but that means we are sampling a wave front, not observing individual photons, which opens a large can of worms, as to whether the quantization of light is fundamental, or a function of absorption and measurement.
I could go on, but I think this is a good example of what is really lousy, flawed math being used to paper over a flawed theory, rather than going back and tearing apart the assumptions built into it.
If an accountant tried this, the IRS would be calling.
