Hi Hans,
Thanks for your remarks. Regarding scientific method. There is a wide difference of opinion on that topic. I studied the philosophy of science books and they don't agree, and I studied the history of science books and they don't agree. My conclusion is that there is only a broad agreement on what it is and agreement that there are many different interpretations of it. If you disagree with my view then that is your opinion to do so.
There is a large literature addressing problems of method in science and the application of the so called method. I cited several books that address that in my references. You should read them. There is a specific problem regarding the work of Mr Ivor Catt. He has cited an experiment called the Wakefield experiment that refutes the currently accepted theory of EM. His web site has an extensive documentation of resistance to his views. The bottom line is scientists frequently don't follow the scientific method.
I was able to only briefly discuss my view of the method. My view is that the method only demonstrates sufficiency and can not prove necessity of any tested theory. So it can only say if a theory might be true, and not that it is necessarily true. In the case of Ivor Catt, he cites an experiment that disproves accepted theory, but that is dismissed because of the prejudice that science already knows the truth, so the new theory can never get considered.
Regarding mathematics. I have read many books on the philosophy and methods of mathematics. Aristotle showed that the idea that the nature is mathematics, a Pythagorean idea, was faulty. Modern science has revived that conception and advocated it without fully understanding what is involved. My view is that mathematics is a human invention and is purely a creation of the human mind in its attempt to understand nature. It is not what nature is made of.
The thesis of my essay was that the tools of modern science are insufficient to understand the larger aspects of reality, and I proposed going back to the tools of philosophy and specifically suggested Aristotle as a starting point. That introduces the conception of a Final Cause. I suggested some axioms that ought also to be considered as well. My suggestion was based upon the inability of physical science methods to address the philosophical problems being posed in the essay contest.
As regards the conception of God or deity. It is pretty easy to misinterpret that concept. I am merely suggesting that science take God seriously, or frankly admit that the scientific method excludes it from the discussion. However, doing that severely limits the kinds of knowledge that science can legitimately claim to know. It looks like the current conception of science is to claim it can know or prove everything without limits. That is obviously false, and scientists would be better advised if they would frankly say that they don't deal in truth but only in what might be true about the physical world alone.