Faraday, Maxwell and the Design of Nature

At first blush, people think scientists experiment and measure and observe and analyze and then experiment some more....working with eyes, ears, and hands. Then they summarize it all with one of those compact scientific laws like f=ma or E=mc².

It doesn't work that way. Instead, from a very few measurements or observations, scientists work with mathematics, deriving equation after equation, confident that such equations will find application in physical reality. And it turns out to be that way. Thus Galileo obtained his laws of motion, Kepler his laws of planetary movement, and Newton his laws of gravitation. The close correlation of math with the physical world greatly impressedthese scientists, as we should be impressed by it today, but largely aren't. Does it not show the design in nature? Galileo summed it up with "God wrote the universe in the language of mathematics."

It's convenient for mathematics to work that way since there is only so much experimenting one can do with objects millions of miles away. Not to mention things very tiny....things we can't even see, let along poke our fat fingers into. One hundred years after Galileo, Kepler & Newton figured out the big things, others focused on the small. Magnetism and the flow of electrons [electricity], for example. At first the two were thought to be unrelated phenomena, buy later they were linked. In 1785, Charles Coulomb published the law of force between two electrically charged bodies, q1 and q2:

F =- k(q1·q2/r²)   where k is a constant and r is the distance between the two bodies.

What even the dumbest person in class must note is the law's identical form to that of gravity, a wholly different phenomena. The gravitational attraction between two masses (m1 and m2) is

F = k(m1·m2/r²)

The only difference is that electrical force can attract or repulse, depending on whether the two bodies have equal or opposite charges; gravity always attracts.

Along came Michael Faraday, who discovered electromagnetic induction. He found that if you rotate a rectangular frame of wire through a magnetic field, you generate electricity in that wire, it's intensity rising and falling as the frame rotates, mathematically described by the sine function.

Furthermore, when Faraday passed current through a coil of wire, a magnetic field was produced which would induce current in a separate coil of wire. But how far apart could the coils be? What if he tried a longer coil or a tighter coil? How would that change things?

Since you can't see any of this, it was left to a mathematical physicist, Robert Maxwell, to figure the results. He worked out through math that current flowing through a coil of wire produced an electrical field in the surrounding space. And that electrical field gave rise to a magnetic field. Which gave rise to an electrical field, which gave rise to a magnetic field, and so on. When "pushed" by current flowing though the originating wire, these electromagnetic waves traveled great distances, and did so, he calculated, at 186,000 mi/sec.

But wait! Light had already been measured as traveling at just that speed. You don't suppose....Yes! Light was part of this electromagnetic spectrum, only at a much different frequency. And how is it generated? By passing electricity through tightly wound tungsten filaments, same as Faraday generated lower frequency waves from coils of different materials and dimensions.

In time, other "slots" of the spectrum were filled in: radio waves, infrared rays, x-rays, gamma rays. We now make endless and routine use of the spectrum, yet nobody knows just "what it is" that travels through space. It is described mathematically. As Alfred North Whitehead put it: "The originality of mathematics consists in the fact that in the mathematical sciences connections between things are exhibited which, apart from the agency of human reason, are extremely unobvious."

Physicist Heinrich Hertz observed: "One cannot escape the feeling that these equations have an existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them." [italics mine]

Yes, we do get a lot out of them. So much so that we've become completely oblivious to what was "put into them" in the first place and who did the "putting." "One cannot escape the feeling," Hertz stated. Yet today's materialistic society has managed to do just that.

For since the creation of the world God's invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that men are without excuse [for ignoring him].   Rom 1:20    NIV

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Many of the particulars here are found in the book Mathematics and the Search for Knowledge, by Morris Kline.


Kepler, Newton, Galileo, and God

"God wrote the universe in the language of mathematics"....Galileo

That about sums up [HA! pun intended] how early scientists felt about mathematics. They cherished it, they advanced it, they found in it an essential tool in revealing just how God worked. And that was their motive: to uncover the design of God and thereby give him praise. We've all seen those math formulas in which gravity, force, acceleration and everything else can be expressed with just a few variables. Why should that be? Why should things not be a hopeless mishmash, like our sock drawer? The answer is what Galileo said...God wrote the universe, and he used mathematics as a language.

Scientists commonly thought that way back then, much to the exasperation of today's atheists. When Kepler worked out the laws governing planetary motions [they move in ellipses, not circles] and published the results, he suddenly let loose with a paean to God, smack dab in the middle of his treatise. If you didn't know better, you'd think it was one of the Bible psalms. Would any scientist be caught dead doing such a thing today?

"The wisdom of the Lord is infinite; so also are His glory and His power. Ye heavens, sing His praises! Sun, moon, and planets glorify Him in your ineffable language! Celestial harmonies, all ye who comprehend His marvelous works, praise Him. And thou, my soul, praise thy Creator! It is by Him and in Him that all exists. that which we know best is comprised in Him, as well as in our vain science. To Him be praise, honor, and glory throughout eternity."

It's not bad. I'd put it with the Psalms, if it were my call. But nobody asked me.

Does it not dovetail with this one, which is in the Bible?

"You are worthy, Jehovah, even our God, to receive the glory and the honor and the power, because you created all things, and because of your will they existed and were created."   Rev 4:11

Contrary to popular belief, those early scientists really didn't experiment much. Instead, they worked out the math, since they were convinced that was how God designed things. When they made experiments it was mostly to confirm results, or as Newton once said, to convince the "vulgar," [He also told how he made up the story of the falling apple to dispose of "stupid" people who asked him how he discovered laws of gravitation.] And Galileo, when describing an experiment of dropping two different masses from the top of a ship's mast, has his fictional creation, a fellow named Simplicio, [!] ask whether he actually made such an experiment. "No, and I do not need it, as without any experience I can confirm that it is so because it cannot be otherwise," was his reply. He worked mostly with mathematics.

Accordingly, Isaac Newton played with the notion of firing a giant cannonball from a mountaintop with just enough velocity, not too much and not too little, that it's ordinary straight line path would be continually offset by the earth's pull so that it would orbit the planet indefinitely. Of course, he didn't actually perform such an experiment, it was all in his head. Working from a few known quantities (radius of the earth, distance a body falls in the first second) he deduced laws of universal gravitation, and, like Kepler, gave God all the glory:

"This most beautiful system of sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being...This Being governs all things, not as the soul of world, but Lord over all."   Mathematical Principles, 2nd edition

Oddly, though mathematics has proven so astoundingly successful at describing the universe we live in, it's success lies in giving up on a greater goal. Long before Galileo, Aristotle and his contemporaries wanted to know what things were. They didn't bother much with description, since that seemed of secondary importance. Only when scientists reversed priorities did they discover mathematics served as an amazing tool of description, though not explanation. This lack of explanation was a sore point for some of Newton's contemporaries, steeped in the tradition of Aristotle. Leibniz, who independently of Newton, discovered calculus, groused that Newton's gravitational laws were merely rules of computation, not worthy of being called a law of nature. Huygens labeled the idea of gravitation "absurd" for the same reason: it described effects but did not explain how gravity worked.

Newton agreed. In a letter to a Richard Bentley he wrote: "That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed form one to another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."

Describing how things work through mathematics has led to scientific triumphs that knock the socks off all of us, and contemporary scientists have gone far beyond Newton. Yet impressive as they are, are they anything more than cheap card tricks when compared to the goal of explaining why things work? Is the latter reserved for the mind of God?

O the depth of God’s riches and wisdom and knowledge! How unsearchable his judgments [are] and past tracing out his ways [are]! For “who has come to know Jehovah’s mind, or who has become his counselor?” Or, “Who has first given to him, so that it must be repaid to him?” Because from him and by him and for him are all things. To him be the glory forever. Amen        Rom 11:33-36

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Many of the particulars here are found in the book Mathematics and the Search for Knowledge, by Morris Kline.

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Tom Irregardless and Me     No Fake News but Plenty of Hogwash


Einstein, Euclid, and Parallel Lines

Parallel lines eventually meet. All you have to do to prove it is to look down the railroad tracks toward the horizon. You can see clearly that the rails touch.

A contributor informed me, without much tact, that my scientific method was lacking in rigor. "Sheepandgoats, you moron! It’s perspective! Walk down to where they seem to meet and you will see they are as far apart as ever."

So I walked down to where they seemed to meet and, sure enough, they were just as far apart as ever. Okay, so apparently they remain separated by an unchanging distance. Parallel lines never meet.

Or do they?

With mathematical lines you can accomplish exactly what perspective suggests.

Imagine a straight horizontal line. Mathematical lines, you will remember, are endless. They extend forever. Now picture a line perpendicular, a vertical line. Of course, the two lines will intersect. Call that point of intersection point I. Now travel two feet up that perpendicular line, two feet above I, and choose another point. Call it point P. We call it P for pivot. Pretend that you can pivot the entire line around that point, as if that vertical line was a compass needle pivoting around the center.

As you pivot the vertical line, what happens to point I? It moves farther and farther down the horizontal line, doesn’t it? As you continue to pivot your vertical line, so that it is more and more starting to resemble a horizontal line, 2 feet above your original line, point I really zooms out there. And it seems like, when you finally get your “vertical” line parallel (from the pivot point P of view) point I must “jump the track.” It must leave that horizontal line. It must disappear. Otherwise, your two lines can never really become parallel.

But where is that point of jumping the tracks? Can you identify it? Pick a point at random. Call it point J. That is the last point the two lines have in common. After that the two lines are separate. They never touch, as we’re told parallel lines never do.

But, geometry also teaches us that between any two points, it is always possible to draw a straight line connecting them. So take a point one foot further than J on the original line. Call it point F. And you can draw a straight line from point P to point F! So point J is not the last common point after all! You can quickly see that there never will be a last common point.

So parallel lines do indeed intersect, at infinity!

Obviously, then, mathematics does not really describe reality. Or does it?

Well….if you build on your new parallel lines derivation, you come up with a different, oddball, non-Euclidian geometry. And it turns out, that geometry does have application in reality, because reality is decidedly oddball, as we know from trying to wrap our heads around relativity. And, what’s even worse: quantum mechanics.

When science is experimenting in the lab, it is easy to explore and deduct. You just mix chemicals, take cover, and see what happens. You taste or feel or weigh the results. But you can’t do that on the cosmic scale….it’s too far away. And you can’t do it on the subatomic scale….it’s too tiny to insert your fat fingers. Therefore scientists use mathematics to go where their instruments cannot, utilizing the fact that math correlates highly with the way things are.

A total eclipse of 1919 furnished proof of Albert Einstein’s theory of special relativity, first published in 1905. If Einstein was right, an object of huge mass (the sun) would bend light (from the stars behind it) and the angle of the bend could be recorded by scientists. If Einstein was not right, there would be no bending of light, and that too, could be verified by scientists. Einstein was right.

But the frizzy haired physicist wasn’t on pins and needles the night before the big test. He wasn’t sweating it. He knew his theory would hold.

The math worked.
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If you try the parallel lines trick on your pals, (amaze your friends!!) some, depending on who your friends are, will grasp it right away. Others will argue with you forever. And some will get mad. I suspect the third group feels threatened. Indeed, we may need to live forever to figure this out.

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“God wrote the universe and the language that he used was mathematics.”      Galileo


Weapons of Math Instruction

Whereas religious experts are a dime a dozen at the Whitepebble Religious Institute, there really is only one science and math authority: Tom Tombaugh. And even his credentials are modest: he claims to be a distant cousin of Clyde Tombaugh, discoverer of disgraced wannabe planet Pluto. Nevertheless, he’s all we have, so if he doesn’t show, it really creates a void. Truth be known, Whitepebble keeps Tombaugh around to counterbalance Tom Sheepandgoats, Tom Weedandwheat, Tom Wheatandweeds, and Tom Fishandchips - religious nuts who otherwise drive him up a tree.

The Institute had a recent staff meeting and Tombaugh didn’t show. Of course, Whitepebble made a thorough search, only to find that he had been stopped at the border on his return trip from Krukordistan! A concurrent news headline told it all:

NEW YORK - A noted researcher for the prestigious Whitepebble Religious Institute was arrested today at John F. Kennedy International Airport as he attempted to board a flight while in possession of a ruler, a protractor, a set square, a slide rule and a calculator.
At a morning press conference, Attorney General Alberto Gonzales said he believes the man is a member of the notorious Al-gebra movement.
He did not identify the man, who has been charged by the FBI with carrying weapons of math instruction. "Al-gebra is a problem for us," Gonzales said.
"They desire solutions by means and extremes, and sometimes go off on tangents in a search of absolute values. They use secret code names like 'x' and 'y' and refer to themselves as ' unknowns', but we have determined they belong to a common denominator of the axis of medieval with coordinates in every country.

Ah, well. So much for our science division

[the news report is not my writing. I wish it were. My best efforts to trace it led here, but in stripped form, it has been around even longer.]

 

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Tom Irregardless and Me                    No Fake News but Plenty of Hogwash