Why Science Does Not Disprove God by Amir Aczel

Author:Amir Aczel
Language: eng
Format: epub, mobi
ISBN: 9780062230614
Publisher: HarperCollins
Published: 2014-04-01T16:00:00+00:00

Roger Penrose’s three worlds, which mutually overlap: mathematics, the physical world, and the human mind.

Some of the purely mathematical world of ideas as defined by Plato reflects information about the physical world, although there are elements of the pure math world that have nothing to do with the real world; some of the physical world affects and is represented in our minds, and parts of it are inaccessible to human consciousness and understanding; and part of what goes on in our minds is accessible to representation in the world of pure mathematics, while other mental processes are perhaps non-mathematical.

Parts of mathematical truth are inaccessible to mental reasoning: the diagram “permits the existence of true mathematical assertions whose truth is in principle inaccessible to reason and insight”; there is a “possibility of physical action beyond the scope of mathematical control”; and there is allowance for “the belief that there might be mentality that is not rooted in physical structures.”

Penrose is influenced in his thinking about mathematics by the work of the Austrian logician Kurt Gödel, who showed that in any system of mathematics there will always be propositions whose truth is inaccessible to us—we are unable to determine whether they are true or false (I will discuss Gödel’s work later in the book). Penrose’s conclusions are very profound and speak to the topic of this book and tell us that science has limitations. The limitations arise from the fact that perhaps not everything in nature is given to mathematical analysis, not all the content of mathematics is accessible to our mind, and the human mind itself may not be wholly reliant on and derived from purely physical or material notions.

The Nobel Prize–winning quantum physicist Eugene Wigner of Princeton wrote a landmark paper in 1960 that addressed the mysterious nature of the relationship between mathematics and physics and related sciences. Wigner had contributed much to physics using very advanced mathematics; in particular, he was one of the pioneers (with Hermann Weyl) of using abstract mathematical groups to model physical phenomena. Group theory is the mathematical branch dealing with symmetry, and as Wigner and Weyl have shown, symmetries can reveal deep secrets about physical reality.

Such symmetries, for example, allowed Steven Weinberg, another American Nobel laureate, to predict the existence of a particle and the actual masses of two particles: the so-called Z and W bosons, which act inside nuclei of matter to produce radioactive decay. The fact that the pure mathematics of group theory can produce such accurate physical predictions is remarkable. The connection between mathematical groups and physics was established by the German-Jewish mathematician Emmy Noether. Noether, who came to America just before the Second World War to escape Nazism, proved two major theorems that established the relationship between the symmetries of group theory and the all-important conservation laws in physics (such as the conservation of energy, which says that energy can neither be created nor destroyed).

In his 1960 paper, in which he marvels at the amazing relationship between mathematics and science,

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