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Thank you so much for your outstanding essay-post, dearest sister in Christ, and the excellent example!

In a situation like that, it seems to me mathematics is your friend — for it points beyond what can be ordinarily perceived and directly experienced.

I'm looking forward to seeing how Professor Jim Hill and Dr. Barry Cox manage to integrate a faster-than-light particle into Einstein's theory (assuming they're able to do that, of course).

Indeed. And I agree of course!

Here's another example to think about, namely knot theory and the unreasonable effectiveness of mathematics in the natural sciences.

There are actually two facets to the "unreasonable effectiveness," one that I will call active and another that I dub passive. The active facet refers to the fact that when scientists attempt to light their way through the labyrinth of natural phenomena, they use mathematics as their torch. In other words, at least some of the laws of nature are formulated in directly applicable mathematical terms. The mathematical entities, relations, and equations used in those laws were developed for a specific application.... The passive effectiveness, on the other hand, refers to cases in which abstract mathematical theories had been developed with absolutely no applications in mind, only to turn out decades, or sometimes centuries later, to be powerfully predictive physical models.

The above quoted from your link! I just loved the idea of mathematics as the "torch" that scientists use to light their way forward, the "active effectiveness" aspect.

An example of "passive effectiveness" might be Reimannian geometry — a species of non-Euclidean geometry developed by Hermann Reimann in the nineteenth century without any particular practical application in view. But then later on, Einstein picked it up "off the shelf," as it were, and employed it in the development of his theories of relativity.

Also at your link is a link to another interesting article on the Fibonnaci series — a numerical series that appears to be firmly embedded in the natural world; e.g., the branching points on stems, the "packing" plan of seeds on a sunflower seed head, et al.

Truly the "unreasonable effectiveness of mathematics" is amazing!

Thank you so very much dearest sister in Christ for the link, for your deep interest in this subject, and for your kind words of support!