God and Nature Summer 2024
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By Ken and Cheryl Touryan
Mathematics has been called the Language of God. Einstein called it the “poetry of logical ideas.” It is mysterious in many ways, one being the way it turns up in entirely unexpected connections, where it often permits an accurate description of observed phenomena.
Mathematics is the science of skillful operations with concepts and rules developed just for this purpose. Early on, it was formulated to describe entities in the physical world (like geometric shapes), but advanced math formulates concepts that are not immediately accessible physically. It is amazing that certain regularities can be discovered by mathematics that turn out to be true throughout the universe.
Mathematics has been called the Language of God. Einstein called it the “poetry of logical ideas.” It is mysterious in many ways, one being the way it turns up in entirely unexpected connections, where it often permits an accurate description of observed phenomena.
Mathematics is the science of skillful operations with concepts and rules developed just for this purpose. Early on, it was formulated to describe entities in the physical world (like geometric shapes), but advanced math formulates concepts that are not immediately accessible physically. It is amazing that certain regularities can be discovered by mathematics that turn out to be true throughout the universe.
Indeed, the Laws of Nature are written in the language of mathematics. |
An example of math being used to establish a universal law is found in Newton’s discovery of the Law of Gravity, which explained in mathematical terms the gravitational force that acts on a falling body. The force of gravity (which on earth exerts an acceleration of 9.8 meters/second^2) is proportional to mass, but independent of the size, material, and shape of the falling body. Intuitively, this doesn’t make sense, but it was proven by dropping a rock along with a feather in a vacuum. Both fall at the same rate!
Kepler provides another example (1). When he was trying to explain his observations of planetary orbits, he found the answer among the geometric axioms first established around 200 BC by Greek geometer Apollonius of Perga, who developed the trigonometry of conic sections. His formula describing an ellipse led Kepler to apply it to planetary orbits eighteen centuries later.
There are, of course, examples of more recent mathematicians as well whose work has demonstrated the wonder of the connection between math and the observable universe.
Albert Einstein, in his creative application of physical laws to gravitational fields in the universe, was unable to develop an equation that would allow him to complete his Theory of General Relativity (2). In 1913 he was led to the equations that Bernhard Riemann had developed in the mid-1800s. By 1915, his reformulating of the mathematics of gravitation in terms of Riemannian geometry was complete, and he applied his new theory to the behavior of galaxies as well as other astronomical phenomena. It was revolutionary in terms of understanding the universe and has been demonstrated to be correct through many observations.
Physicist Murray Gell-Mann was fascinated by the various elementary particles and forces that kept showing up in Quantum Mechanics. He introduced the concept of ‘quarks’ to describe the fundamental building blocks of strongly interacting particles. Along with other physicists, he developed the mathematical Standard Model (3) to explain how these forces and particles interact, for which he received the Nobel Prize in 1969. Using this model, Peter Higgs led a team that predicted a particle or boson with zero spin, no electric charge, and no color charge that interacts with mass. This particle is very unstable, decaying almost immediately. It was named the “God Particle” because of its mysterious nature. In 2012, using the Large Hadron Collider in Switzerland, the God Particle was detected and named the Higgs-Boson after Dr. Higgs, who had predicted its existence decades before using the mathematics of the Standard Model.
These examples demonstrate the fact that mathematics, scribbles on a piece of paper that describe abstract concepts in a human mind, can predict and/or explain phenomena observed in nature. Nobel Laureate Eugene Wigner wrote a short paper on this amazing phenomena in 1960, calling the effectiveness of mathematics in explaining the natural world “unreasonable”, saying that “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve” (4).
Indeed, the Laws of Nature are written in the language of mathematics. And these laws are true whether you travel within the macro-world of galaxies or the micro-world of quarks. Humans seem to be located at the mid-point of these worlds, and yet can describe the physical reality of both. It is like being between a microscope and a telescope, and comprehending both. Truly awe-inspiring! As Einstein said, “The eternal mystery of the world is its comprehensibility… The fact that it is comprehensible is a miracle.”
Those who come up with some of the most creative and innovative concepts combine the strict rules of mathematics and logical thinking with an imagination that soars beyond the rational. God has given us two eyes for a reason. With only one eye we lack depth perception. Looking at nature from just one perspective (rational, for example) limits our understanding of the whole. We need both eyes, the rational based on sensory input and the imaginative based on creative vision. This is true in mathematics as well as our personal lives. When we see with our physical and our spiritual eyes, we are led to bow in worship before our Creator God. King David expressed this wonder beautifully in Psalm 8:
When I look at the night sky and see the work of your fingers--
the moon and the stars you set in place—
what are mere mortals that you should think about them,
human beings that you should care for them?
Yet you made them only a little lower than God*
and crowned them with glory and honor.
You gave them charge of everything you made,
putting all things under their authority.
*Elohim, also translated as “angels”
(New Living Translation)
References
1 Max Caspar, . Kepler. Courier Corporation, 2012.
2 Kip S. Thorne and Stephen Hawking Black Holes and Time Warps: Einstein's Outrageous Legacy W. W. Norton & Company, 1995
3 Murray Gell-Mann, Elementary Particle Physics, Springer 1972, p. 733-761
4 Wigner, Eugene P. "The unreasonable effectiveness of mathematics in the natural sciences." Mathematics and science. 1990. 291-306.
Kenell (Ken) Touryan retired from the National Renewable Energy laboratory in 2007 as chief technology analyst. He spent the next eight years as visiting professor at the American University of Armenia (an affiliate of UC Berkeley). He received his PhD in Mechanical and Aeronautical Sciences from Princeton University with a minor in Physics. His first 16 years were spent at Sandia National Laboratories as Manager of R&D projects in various defense and advanced energy systems. He has published some 95 papers in refereed journals, authored three books, and co-owns several patents.
Cheryl Touryan is a scientist by osmosis, having participated with Dr. Ken Touryan in ASA activities for over 50 years. Along with being a wife and mother, Cheryl has been involved with ministry to marginalized women and children in developing countries for forty years, part of that time with World Vision. Cheryl and Ken are passionate about encouraging young people to approach the natural world with wonder, which hopefully will lead to worship of the Creator God. They wrote a book together for young people called Wonders in our World. Currently living in a retirement village, Cheryl continues to follow her passion by writing monthly articles on such topics for the local community.
Kepler provides another example (1). When he was trying to explain his observations of planetary orbits, he found the answer among the geometric axioms first established around 200 BC by Greek geometer Apollonius of Perga, who developed the trigonometry of conic sections. His formula describing an ellipse led Kepler to apply it to planetary orbits eighteen centuries later.
There are, of course, examples of more recent mathematicians as well whose work has demonstrated the wonder of the connection between math and the observable universe.
Albert Einstein, in his creative application of physical laws to gravitational fields in the universe, was unable to develop an equation that would allow him to complete his Theory of General Relativity (2). In 1913 he was led to the equations that Bernhard Riemann had developed in the mid-1800s. By 1915, his reformulating of the mathematics of gravitation in terms of Riemannian geometry was complete, and he applied his new theory to the behavior of galaxies as well as other astronomical phenomena. It was revolutionary in terms of understanding the universe and has been demonstrated to be correct through many observations.
Physicist Murray Gell-Mann was fascinated by the various elementary particles and forces that kept showing up in Quantum Mechanics. He introduced the concept of ‘quarks’ to describe the fundamental building blocks of strongly interacting particles. Along with other physicists, he developed the mathematical Standard Model (3) to explain how these forces and particles interact, for which he received the Nobel Prize in 1969. Using this model, Peter Higgs led a team that predicted a particle or boson with zero spin, no electric charge, and no color charge that interacts with mass. This particle is very unstable, decaying almost immediately. It was named the “God Particle” because of its mysterious nature. In 2012, using the Large Hadron Collider in Switzerland, the God Particle was detected and named the Higgs-Boson after Dr. Higgs, who had predicted its existence decades before using the mathematics of the Standard Model.
These examples demonstrate the fact that mathematics, scribbles on a piece of paper that describe abstract concepts in a human mind, can predict and/or explain phenomena observed in nature. Nobel Laureate Eugene Wigner wrote a short paper on this amazing phenomena in 1960, calling the effectiveness of mathematics in explaining the natural world “unreasonable”, saying that “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve” (4).
Indeed, the Laws of Nature are written in the language of mathematics. And these laws are true whether you travel within the macro-world of galaxies or the micro-world of quarks. Humans seem to be located at the mid-point of these worlds, and yet can describe the physical reality of both. It is like being between a microscope and a telescope, and comprehending both. Truly awe-inspiring! As Einstein said, “The eternal mystery of the world is its comprehensibility… The fact that it is comprehensible is a miracle.”
Those who come up with some of the most creative and innovative concepts combine the strict rules of mathematics and logical thinking with an imagination that soars beyond the rational. God has given us two eyes for a reason. With only one eye we lack depth perception. Looking at nature from just one perspective (rational, for example) limits our understanding of the whole. We need both eyes, the rational based on sensory input and the imaginative based on creative vision. This is true in mathematics as well as our personal lives. When we see with our physical and our spiritual eyes, we are led to bow in worship before our Creator God. King David expressed this wonder beautifully in Psalm 8:
When I look at the night sky and see the work of your fingers--
the moon and the stars you set in place—
what are mere mortals that you should think about them,
human beings that you should care for them?
Yet you made them only a little lower than God*
and crowned them with glory and honor.
You gave them charge of everything you made,
putting all things under their authority.
*Elohim, also translated as “angels”
(New Living Translation)
References
1 Max Caspar, . Kepler. Courier Corporation, 2012.
2 Kip S. Thorne and Stephen Hawking Black Holes and Time Warps: Einstein's Outrageous Legacy W. W. Norton & Company, 1995
3 Murray Gell-Mann, Elementary Particle Physics, Springer 1972, p. 733-761
4 Wigner, Eugene P. "The unreasonable effectiveness of mathematics in the natural sciences." Mathematics and science. 1990. 291-306.
Kenell (Ken) Touryan retired from the National Renewable Energy laboratory in 2007 as chief technology analyst. He spent the next eight years as visiting professor at the American University of Armenia (an affiliate of UC Berkeley). He received his PhD in Mechanical and Aeronautical Sciences from Princeton University with a minor in Physics. His first 16 years were spent at Sandia National Laboratories as Manager of R&D projects in various defense and advanced energy systems. He has published some 95 papers in refereed journals, authored three books, and co-owns several patents.
Cheryl Touryan is a scientist by osmosis, having participated with Dr. Ken Touryan in ASA activities for over 50 years. Along with being a wife and mother, Cheryl has been involved with ministry to marginalized women and children in developing countries for forty years, part of that time with World Vision. Cheryl and Ken are passionate about encouraging young people to approach the natural world with wonder, which hopefully will lead to worship of the Creator God. They wrote a book together for young people called Wonders in our World. Currently living in a retirement village, Cheryl continues to follow her passion by writing monthly articles on such topics for the local community.