Why Does Math Work? Why are Fundamental Equations Beautiful?
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* Mathematics is One of the Languages of God: Real Science Radio speaks with James Nickel, author of Mathematics: Is God Silent? Nickel talks with Bob Enyart about Albert Einstein and how the personal creator God is the answer to the question that Einstein wrestled to answer. Bob and James also talk about Isaac Newton, Johann Kepler, and why science was stillborn in ancient Greece. Bob wrote the following article about Einstein and math as he was inspired by James Nickel's evening presentation at the Rocky Mountain Creation Fellowship.
* How Einstein and Others Can Use Their Minds To Make Discoveries: As pointed out by author James Nickel, mathematicians turn away from the physical universe and yet make astounding discoveries that help to explain the world of matter and energy. Using their minds, rather than microscopes or telescopes, these discoveries come decades and even centuries before their real-world counterparts make the discovery by observational science, or before technological advance enables confirmation. RSR suggests as an example mathematician and astronomer Joseph-Louis Lagrange who discovered the gravitationally stable Lagrange Points where today we position our most important exploratory satellites. Lagrange was born in Turin, Italy in 1736 and discovered these points with his mind. Time Magazine's Albert Einstein: The Enduring Legacy says that today's "high precision instruments such as atomic clocks and lasers... have shown that he was absolutely on target with the equations he worked out with nothing more than a pencil." And describing an Einstein visit in 1931 to California's Mount Wilson Observatory where Edwin Hubble had been making astronomy history with a 100-inch reflecting telescope, Richard Lacayo writes for Time that, "When the astronomers there boasted that their telescope could probe the structure of the universe, Elsa quipped: 'My husband does that on the back of an old envelope.'"
* Einstein's Lab Where He Discovered Special Relativity: Materialists often claim though, along with many similar atheist cliches, that you can only know that which your five senses tell you. (But which of their five senses told them that?) For today's atheists are becoming increasingly uncomfortable with the reality of logic, with the existence of truth, and even with information itself.
* 2012 Update: Einstein Confuses Lawrence Krauss: As an extraordinary example of today's atheists trying to distance themselves from the realm of ideas, theoretical physicist Lawrence Krauss (emphasis on the theoretical), in his book A Universe from Nothing, attempts to refute the phenomenon described by Nickel, that mathematicians often use their minds, rather than scientific equipment, to make astounding discoveries of the physical universe. In support of his denial, he presents an anecdote about Albert Einstein which, even in Krauss' own telling, EXACTLY contradicts Krauss' own reason for telling the story. Einstein used telescopes, yes, to make an astronomical observation, yes, but NOT to form his theory, for his theory had already been written on paper. Discover magazine's Richard Panek explains:
In the late 17th century, Isaac Newton helped inaugurate a scientific revolution by taking Galileo's observations of the heavens' motions and expressing them mathematically. Then in the early 20th century, Albert Einstein helped inaugurate a second scientific revolution by reversing that process, taking his own calculations and looking for their physical expression in the heavens.
[Update: Atheists are rather touchy on this subject. For example, when this RSR article was first posted, we provided Cherenkov radiation as an example of a pre-discovery as already described for years on Wikipedia. Yet shortly after we made that point (and the link), the Wikipedia article was edited (as happens, including for example when we posted about mammoths) to downplay the extraordinary significance of the prediction of this radiation made in the 1880s by Oliver Heaviside! But to take this further, this self-taught physicist also illustrated the main point of this article when he realized that complex numbers which include the imaginary square root of -1 were useful in describing electrical circuits! In the Krauss' example above, Einstein used his eyes to make an observation to confirm the theory he already established with his mind. For Einstein is not renowned for his eyesight but for his intellect.]
* Comprehending What Einstein Said Was Incomprehensible: Einstein wrote that it was "incomprehensible" that the non-physical realm of "ideas" could even exist in a physical world. It was "incomprehensible to him that non-physical mathematics, which itself is not composed of matter or energy, could describe so beautifully the physical universe. The explanation for this phenomenon is one that Einstein (and Krauss) reject a priori. Mankind can understand the correspondence between pure ideas and physical phenomenon only by the realization that the universe was designed in the mind of God. So its workings can be discovered by the mind of men who are made in God's image. However, Einstein denied the existence of a personal God. Yet in more accurate science, as Kepler is paraphrased, we are thinking God's thoughts after Him.
* Astounding and Unexpectedly Beautiful Equations: E = mc2. Exploring unexpected and even startling symmetry and patterns from the microscopic to the galactic scale, mathematicians often describe their work as an aesthetic pursuit of beauty, as Lacayo quotes Einstein that relativity was his "most beautiful discovery." Similarly, scientists enjoy the inverse square law, the beauty of Maxwell's equations, and of Boltzmann's formula for entropy, which is even engraved on his tombstone. And as math becomes increasingly purely theoretical, it seems to do an even better job at describing reality, as with the use of the square root of negative one, not only as in describing electrical circuits in the 1800s, but also today for describing quantum mechanics. Ludwig von Mises similarly writes in Human Action, that contemporary philosophers "are entirely wrong in their endeavors to reject any kind of a priori knowledge and to characterize logic, mathematics and [economics] as empirical and experimental disciplines. ... Moreover, it is not experience but thinking alone which teaches us that, and in what instances, it is necessary to investigate unrealizable hypothetical conditions in order to conceive what is going on in the real world" pp. 32, 65.) So ignoring their five senses, the mathematicians who turn away from the physical world to the non-material world of ideas, seeking pleasure from pure intellectual elegance, often end up being the ones who come closest to describing the physical nature of the cosmos. Atheists struggle with this phenomena because it suggests that the universe originated with the desire for beauty in the mind of a personal Creator.
* Mathematics Useless for Moral Truth: Conversely, while math helps man to understand physical reality, it is no use whatsoever regarding moral truth. Moral understanding never involves numbers. As American Right To Life put it in their Albert Einstein: In His Own Words article:
In 1936 Einstein famously wrote, 'the most incomprehensible thing about the world is that it is comprehensible,' and in 1944, remarking about Bertrand Russell, he described the ability to get from matter to ideas as a 'gulf-logically unbridgeable,' which some scientists and linguists refer to as Einstein's Gulf, and in 1950, Einstein wrote that 'science can only ascertain what is, but not what should be,' necessarily excluding from its domain 'value judgments of all kinds.'
Neither math nor science are helpful in establishing moral truth. American Right To Life uses this vital concept in developing their strategy to re-criminalize child killing. The secular humanist utilitarian philosopher John Stuart Mills is frequently paraphrased as calling for the greatest good for the greatest number. Sadly and ironically, the Southern Baptist Convention's chief ethicist Richard Land uses such situational ethics to defend support for funding the killing of some unborn children (for example), in an attempt to save other unborn children. Such utilitarian moral relativism contrasts with the simple biblical command to "obey God" (Acts 5:29), which never requires solving multiple simultaneous equations to determine right from wrong. God does not ask us to calculate arithmetically the number of possible future positive or negative results from our actions. Those actually following Christ would never submit to the criminal who says, "shoot this one in the head and we'll spare those," nor would they support funding the killing of some children to defund the killing of others. Instead of requiring advanced math skills, God refers to entire nations as "children," and gives men commands that even a child could understand. "Do not steal." "Do not bear false witness." "Do not kill the innocent." And don't "do evil that good may come of it." See more at AmericanRTL.org/exceptions#numbers.
* Did Richard Feynman See God? When accepting his Nobel prize in physics, Feynman said, "The fact that electrodynamics can be written in so many ways... was something I knew, but I have never understood. It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms... An example of that is the Schrödinger equation and the Heisenberg formulation of quantum mechanics. I don't know why this is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature. A thing like the inverse square law is just right to be represented by the solution of Poisson's equation, which, therefore, is a very different way to say the same thing that doesn't look at all like the way you said it before. I don't know what it means..." Feynman might have been observing yet another manifestation of the one to many solution, that is, the plurality in the Godhead. Perhaps multiple persons of the triune God, each being transcendent, impressed themselves on physical reality. Thus, the biblical truth applies, pun intended, even in physics, that "a matter is established by two or three witnesses." In his book QED (which we quote at rsr.org/three), Feynman asks how many fundamental actions are there to account for nearly all phenomena in the universe regarding light and electricity to which he answered: "There are Three!" This reminds us of later in his Nobel lecture where said, "This then is another, a third way, of describing quantum mechanics, which looks quite different than that of Schrödinger or Heisenberg, but which is equivalent to them." And a final observation from Feynman's Nobel prize lecture that reinforces the point of this RSR program, "Dirac obtained his equation for the description of the electron by an almost purely mathematical proposition."
* James Nickel Speaks Tonight in Denver: The Rocky Mountain Creation Fellowship welcomes Nickel who has traveled from his home in Washington to present to us Why Mathematics Works. Nickel has:
- taught math for nearly 30 years
- teaches at the Potter’s School which partners with homeschool families
- has been a computer systems analyst
- was a mathematical analyst in the 1970s for the United States Navy at Pt. Mugu Naval Air Station in California
- is a Senior Fellow of Mathematics at the Center for Cultural Leadership, and
- is an Adjunct Professor of the History and Philosophy of Mathematics at Rivendell Sanctuary, a worldview college in Minneapolis, Minnesota (which has on faculty one of Bob's favorite authors, Nancy Pearcey).
Stephen Hawking Flashbacks: Go to the Moon to Avoid Global Warming: First, end-of-the-world doomsday prophet atheist astrophysicist Stephen Hawking wants mankind to respond to the problems of global warming by colonizing the Moon or Mars evidently forgetting that the Moon's daytime temperature is over 200 degrees (107 C) and that neither location has liquid water or oxygen. The Sun is Earth's source of global warming, and because Mars is 50 million miles further from our Sun, its temperature ranges from 1 degree F down to 178 below! So mankind should flee from a temporary one degree fluctuation in the Earth's temperature into about 200 degrees, above and below zero, and say good-bye to liquid water and oxygen. And if global warming is so threatening to mankind, why does Hawking overlook the more logical safe havens of Antarctica, Greenland and Siberia?
* Hawkings: The Aliens Will Be Mean: Now, Stephen Hawking is urging mankind: "Don't talk to the aliens!" Why not? They may be mean! (Like on Star Trek, no?)
* Hawking's Circular Reasoning Exposed on Origins: Hawking says that the matter of the universe came from energy borrowed from the gravitational energy of the universe, to which Real Science Radio asks, "What universe?" If you're explaining the origin of the universe, you cannot appeal to the universe itself. And Hawking claims that the laws of physics produced the universe even though 1) Big Bang cosmology claims that those laws did not exist prior to the Big Bang and 2) laws can't do anything. For example, the law of the conservation of angular momentum doesn't make anything and doesn't start anything moving. Newton's laws of motion don't make billiard balls move on a table but rather, they explain movements that occur.
Today’s Resource: Get the Spike Psarris DVD What You Aren't Being Told About Astronomy! Have you browsed through our Science Department in the KGOV Store? Check out especially Walt Brown’s In the Beginning and Bob’s interviews with this great scientist in Walt Brown Week! You’ll also love Dr. Guillermo Gonzalez’ Privileged Planet (clip), and Illustra Media’s Unlocking the Mystery of Life (clip)! You can consider our BEL Science Pack; Bob Enyart’s Age of the Earth Debate; Bob's debate about Junk DNA with famous evolutionist Dr. Eugenie Scott; and the superb kids' radio programming, Jonathan Park: The Adventure Begins! And Bob strongly recommends that you subscribe to CMI’s tremendous Creation magazine!
Online Math Tutorials for Kids (and adults :): To better understand some simple, and more complex, concepts in math, check out BetterExplained.com!
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