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!
Penrose also cites the Mandelbrot set as an example of something mathematicians did not create. Or to put it another way, the Mandelbrot set exists - like Reimannian geometry or pi - and the mathematician came along and discovered it.
Boogieman mentioned higher dimensions and the discussion has moved into string theory. But one of the more elegant solutions only requires five dimensions (P.S. Wesson)
That said, all of you might find Wesson's work on time rather interesting: Time as an Illusion