Mathematics and Everything: From Hannah Fry to Stephen Fry. Part 3

For continuity, start with Part 1.

Now—what about Hannah Fry’s TV presentation—“Magic Numbers?” Are they really magic? Or are they like when my gushing business typing teacher from high school days said, “Today we are going to learn how to use the magic margins!” and I said to myself, “This guy really thinks they are magic.”

Remember, Harley—you don’t want to be a donkey here. Remember how you were with Meg, working on her dissertation involving the Heisenberg Uncertainty principle, and the only one who could grade it was her U of R professor because he was the only one who knew what she was talking about? Don’t make the same faux pas with Fry that you made with her—saying something to show that you’re not exactly ignorant about her subject, and in so doing conveying that you are. Don’t be like Ed Norton, trying to impress the financier, casually letting it slip that he is in the “sewer game” himself.

Okay, now. Turn on the TV. What do you notice about math? Yikes! The first thing I notice has nothing to do with math. It is about Fry. She is one attactive woman!

Harley, you gauche slob! That’s even worse! Go back to saying something stupid about math! Nobody cares about physical appearance! It is only the mind we care about! If you didn’t have such a perfect face for radio, you wouldn’t come all unglued when you see one for television!

It made a mixed initial impression on me, and not all of it good. “We cannot be certain of this and we cannot agree on that,” she more or less said, and I added, “but can we all agree that my flowing and flaming red hair is beautiful?” I mean, don’t go telling me that her producer doesn’t know the power of outward appearance. He showcases her as though a model on Vogue Magazine.

And in fact, once I adjusted to it, all was well. It was my bad. Most things are. I had expected some drab and dry old hen chalking formulas on the board. It’s not her. My bad. You use whatever you have to best present your topic. Lord knows I do. Go for it. When they strap Hannah Fry into a zip line harness to show she speeds up just like Galileo said she would, instead of her dull professor of yesteryear dropping a marble and bowling ball simultaneously—well, why not? He wanted to ride a zip line, too, but it wasn’t allowed back then. Now it is.

It may be that the scientists and mathematicians have never been dull, and only now is the stereotype breaking that says they are. It may all be a carryover from my school days, when they would roll into the classroom a towering TV for some “educational television” and the only thing you knew for sure was that it would be BORING.

It’s not that way now. The two Great Courses archeologists I follow present almost as Indiana Jones. One of them was even inspired by Indiana Jones, for he relates how his mom dropped him off as a boy at the multiplex, the movie subtitle said. “Somewhere in South America,” and he said to himself: “There’s a South America?” Who says they have to be dull? It’s a good gig—why not behave as though it is? Paul Halpern may have the largest cache of physicist photos on the planet—all the time he is posting them, showing the good ‘ol (usually) boys of brilliance having a ball. And just yesterday he posted a cartoon with the quantum computer diagnosis: “broken in every way possible, simultaneously.” I added: “And the relativity computer looks broken when they pass it one way, but okay when they pass it the other way.”

So Hannah Fry begins to narrate her program. “Look hard enough to at anything, mathematics is lying beneath,” she says at the show’s outset. Is math all in our heads, invented? she poses the question. Or is it an eternal physical reality, something existing out there, waiting to be discovered?

Then she dives into the same chronology that they all dive into, but it is such a rich chronology that every presentation is different. Farmelo wrote in his book how he was struck in high school that the formula for gravity took the exact same form as the formula for magnetism, different only in that you can reverse the latter. Why should that be? I was struck by it, too. He also said he didn’t recall any of his teachers ever commenting on that peculiarity. Neither do I.

“How could something we invented in our brain have the power to reveal the workings of the universe?” she says, and then inserts clips of a few mathematicians who say confirming things, like how it’s “shocking that mathematics makes predictions about the world around us.”

“It seemed inconceivable that math could be anything other than something we discover,” Fry says, but then she ventures that in the 19th century, people began to wonder if everyone was really as it seemed. “The problem for humans is overriding our instincts, trusting in our intuition,” another guest math-whiz says. Aristotle, clever though he was, got a lot of things wrong. It’s intuitive that heavy lands before light [is it?], so Aristotle stated that it did. Galileo figured it didn’t, wrote the formula to govern falling things, and said the feather falls slower only due to friction with the air. Whereupon, Hannah splices in Apollo moon footage in which they attempted just that experiment—take out the air— and sure enough, they do both land at the same time! She could have done it in some drab school experiment where they pump the air out of some container, but she did it on the moon! Don’t tell me she doesn’t know how to use the modern medium.

Breaking free of Euclid makes it more complicated—now Fry will try to serve up some sympathy with the ‘inventors of math’ view. (But it won’t work with me—I’m on to her—and it’s not clear where she stands herself.) Cantor pours fuel on the fire with his infinites, some of which are greater than others! You would think that an infinity is an infinity is an infinity, but it turns out that some “are more equal than others.” And don’t get me going about that “proof” (Hannah didn’t cite this one—I just threw it in myself) that the sum of all natural numbers is -1/12.

Then there is Descartes, who invented imaginary numbers. They correspond to nothing real in themselves, but they have been used to build bridges from one real place to another, places that otherwise seem to be “you can’t get there from here,” places. The only thing I know for sure about imaginary numbers (always based upon the square root of -1) is that Hobbes, Calvin’s stuffed tiger, helping the boy with his homework, declared that an especially hard arithmetic problem would require their use—the kid’s hair stood on end and his eyes bugged out at the thought.

Okay, so maybe we don’t have to run the “inventors” completely off the planet, but to suggest that anything can be accounted for by what some smart-alek math whiz will concoct is just too much.

Why can’t it just be acknowledged what Job acknowledged? “Look! These are the fringes of his ways, And what a whisper of a matter has been heard of him!” Why should humans assume that they will figure it all out, then come all unglued when they can’t, and somehow work that into a scenario that God doesn’t exist, whereas it should do just the opposite? It reminds me of a old buddy who would overturn the gameboard whenever he saw he was not going to win.

As to Fry being attractive—sorry—maybe I should not have said anything about that. It’s not the thing to focus on. On the other hand, there was a smiling young women, always posing with her motorbike, chalking up hundreds of likes from social media users in Japan. But some sharp-eyed users smelled something amiss. Mirror reflections didn’t look so pretty. Sometimes her arms were hairy! They pushed an investigation and, sure enough, it was a 50-year old guy playing with photoshop! The fellow wasn’t overly repentant. “Who’s going to click on tweets of a 50-year-old guy?” he said.

Exactly. I’ll bet Hannah is a 60-something, pot-bellied, balding slob like me!

 

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Mathematics and Everything: From Hannah Fry to Stephen Fry—Part 2

See Part 1 here.

You can always trust Albert Einstein to come up with good questions. You can trust him to dive into the scientific but not abandon the spiritual. You can’t trust everyone to do that but you can trust him. For example, he says:

“Here arise a puzzle that has disturbed scientists of all periods. How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality? Can human reason without experience discover by pre thinking properties of real things?”

Morris Kline answers. He is not dumb, but forgive me if I suggest that his huge oversimplification is: “What we have achieved by way of mathematical description and prediction amounts to the good luck of the man who finds a hundred-dollar bill while casually taking a walk.”

Replace the hundred dollar bill with a hundred trillion dollar bill and then maybe we can talk. My opening remark will be, “When was the last time you found a hundred trillion dollar bill?”

It’s like Douglas Adams (the Hitchhiker’s Guide to the Galaxy), who also isn’t dumb. In fact, he’s smart, just like Kline is. But, like Kline, he hugely oversimplifies it. Try oversimplifying a paragraph of his book, and he’d howl like a rhesus.

Adams addresses people who believe that God must exist because the world so fits our needs. He compares them to an intelligent puddle of water that fills a hole in the ground. The puddle is certain that the hole must have been designed specifically for it because it fits so well. The puddle exists under the sun until it has entirely evaporated.

Whoa! What a great illustration! All you need do for it to be perfect is find an intelligent puddle of water. It is as though these pillars of thought leadership just dissolve into mush when they try to explain away what any 5-year-old knows can’t be explained away.

Take this tweet from Richard Dawkins—no one sneers at God more than he: He quotes Einstein again, just like I did in opening this post: “The most incomprehensible thing about the world is that it is at all comprehensible,” the great one says. Dawkins adds: “But what is the alternative to comprehensible? What kind of a world would it be if it were incomprehensible? What would it look like?” He even invites his audience to “discuss” his moronic question.

My contribution was that it would look like this:

249317F3-D2C3-405A-BFEE-FE5B46CE065C

Careful, Tommy, careful. Remember, Dawkins (and Kline, and Adams) is a Great Man, and you are not. You really going to call him moronic? You really going to go the route of the one who doesn’t suffer fools gladly—and a fool is anyone who disagrees? Really?

Sigh...of course I am not. I am chastened. Dawkins has more Twitter followers than I do—and THAT probably is not only what the world would look like if it were incomprehensible, but the greatest proof that it is! Even so, sometimes a child with fewer followers than he must say: “The emperor has no clothes!”

 

Now, if I say that Hannah Fry’s doing a math show to make me mad, it must be conceded that math can make a person mad. It is not so directly transferable to reality as may at first glance appear—and in accounting for this, the renegades are emboldened to take shots at God.

Everyone knows that parallel lines never meet. They know that by looking down the railroad tracks. The rails may seem to converge, but it is just an illusion. So do you think that simple math (geometry) will come down on the side of illusion or sense? It comes down on the side of illusion! In real life, if you walk down a few hundred yards, you see they are still apart—they don’t touch. In geometry, they do!

Do a thought experiment Start in your head with two perpendicular lines; one is horizontal, and one is vertical. They cross. Call the point where they cross ‘P’. Grab hold of the vertical line just above the horizontal line and start to pivot it. What happens to ‘P’—that point of intersection? Doesn’t it move farther and farther down the horizontal line. At what point does it “jump off” to make the two lines parallel?

When I played this trick on guys in the workplace, some saw right away that the lines would never separate—designate a place of separation, and why can you not draw a straight line from the pivot point to a point just a bit further down from your separation point? Some guys walked away scratching their heads. Some got mad, as though I was messing with reality.

It’s like that other scenario of how in a race someone gaining can never pass the one in the lead, since he would first have to close half the distance, and he couldn’t do that until he had closed half that distance. And he couldn’t do that until he had closed half that distance, and so forth. It doesn’t end. The runner catching up can never pass. But go to the races and you will see that he does all the time.. So math can mess with your mind. It does screwy things.

So can you seize upon such things to throw out God? “Mathematics is the alphabet with which God has written the universe,” says Galileo, but since there are some strange letters in that alphabet, that means he didn’t write it. Can you go there? Why not do a Job instead?  “Look! These are the fringes of his ways, And what a whisper of a matter has been heard of him! But of his mighty thunder who can show an understanding?”  (Job 26:14)

The woman following Jesus thought it enough to touch his outer garment, and it did wonders for her when she did. She didn’t have to try the garment on herself. Why doesn’t that satisfy the scientists? Why can’t they just acquiesce to “My ways are higher than your ways?” (Isa 55:8-9)

Return to Einstein, and even my observation of him that he will delve into the scientific without junking the spiritual, ofthe developing field on quantum mechanics, he observed:

“Quantum mechanics is very worthy of respect. But an inner voice tells me that it is not the genuine article after all. The theory delivers much, but does not really bring us any closer to the secret of the Old One. I . . . am convinced that He does not play dice,”

Alas, Einstein caught Him playing dice!—the weirdness of quantum mechanics has proven true. But it didn’t stumble him. He didn’t say, “Well, I guess there isn’t any Old One.” He said (not literally) “Well, I guess Old One is older than I thought, and a cagier too.” I mean, who says he has to spell it all out for humans to understand readily. He’s God. He can do what he wants. “If I were hungry,” he says at Psalm 50:12, “I would not tell it to you.”

Exactly. Are humans going to help him out?

See Part 3.

 

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Mathematics and Everything—From Hannah Fry to Stephen Fry—Part 1

I see one of those mathematics shows trying to make me mad is coming up on PBS. Subject: Is math discovered? Or is it invented? The show is hosted by Hannah Fry. It is entitled: Magic Numbers. “Look hard enough at anything, mathematics is lying beneath,” she says. “Is math all in our heads, invented? Or is it an eternal physical reality, something existing out there, waiting to be discovered.”

Now, can a guy be forgiven for thinking that a dumb question? E=mc2, for example. Why should it be that way? Why should it be writable in such a simple way? Why shouldn’t it be a hopeless hodgepodge? I mean, just try writing the formula for this:

C3030D38-E63E-429D-8375-52D7965D3621

Mathematics is the alphabet with which God has written the universe,” said Galileo. Duh. It all reduces to usually very compact math.

But along come others to say that mathematics is not discovered at all. It is invented. The learned one fuss and fret, tossing away one measure that doesn’t work after another, till they finally find something that does work to describe something. You mean that there were a few thousand wanna-be Galileos describing gravity in all sorts of harebrained ways, until the master himself came along and found a way to reduce it all to a few letters and numbers?

Something about this “dissident” (which is now the mainstream) view reminds me of Larry King telling how it was with 7-Up. The soft drink was wildly successful—but only after the inventor flopped with 1-Up, 2-Up, 3-Up, 4-Up, 5-Up, and 6-Up..

So I’m in the mood to be surly. All I can say is that Paul Halpern had better stay on the right side of this. He may. He is a scientist, which is fine. He doesn’t extend it (so far as I know) to scientist-philosopher-cheerleader-atheist, which is not so fine. I am embarrassed to say I have not yet read his Synchronicity (which title implies he is not in the latter category), but I mean to. It’s on the list.

I did start to review his 2019 book, The Universe Speaks in Numbers, only it turned out to be not his book. It was from Graham Farmelo! Paul let me tweet on for quite some time before he said, “Um, you know, you’ve got the wrong guy. Graham’s a good writer, but he’s not me.” I was following them both on Twitter and I got them mixed up!

I had also almost reviewed Morris Kline’s 1985 book Mathematics and the Search for Knowledge. Alas, both reviews are still on the drawing board, and may never get off it (unless they do so right now. Alas, I can no longer find my Farmelo notes—it drives me nuts!) Kline offers gems like: “The work of the sixteenth, seventeenth, and most eighteenth-century mathematicians was...a religious quest. The search for the mathematical laws of nature was an act of devolution that would reveal the glory and grandeur of His handiwork.”

It works for me. But it wasn’t until the second, or maybe even third, reading, that I realized Kline himself doesn’t buy that view. He sides with the inventors, not the discoverers! Is that what is called “confirmation bias” that I had not noticed it before?

“Each discovery of a law of nature was hailed as evidence of God’s brilliance rather that that of the investigator,” he writes, and I should have noticed in the phrasing that Kline seems to think it wrong that it should be that way. Newton, Galileo, Kepler, and others took for granted that it was right to credit God’s brilliance rather than their own. Is it a mark of moderns that they want the credit?

Regarding a contribution of Faraday, Kline writes, “It may be too much to expect that . . . the function sine x should serve. Yet nature never ceases to accommodate itself to man’s mathematics.” Is it only me who draws the parallel of the would-be tourist who envisions paradisiac scenes of Tahiti, then goes and finds such a place, and says, “nature never ceases to accommodate itself to man’s daydreaming!” I mean, what is wrong with people? He saw Tahiti on the brochures—then he went and discovered it.

Kline elaborates: “If math is discovered, not invented, then it must exist somewhere. Where? Would not the plain answer be in the mind of God a la Galileo—god wrote the universe in the language of mathematics. But what if one does not believe in God?”

Well, I would say in that event that nature has provided a fine reason to reconsider, but if you don’t want to believe in God, you don’t want to believe in God. Kline is not so easily dissuaded.

Kline says: “Whereas until around 1850, mathematical order and harmony were believed to be inherent in the design of the universe and mathematicians strove to uncover that design, the newer view, forced on mathematicians by their own creations, is that they are the legislators who decide what the laws of the universe should be. They impose whatever plan or order succeeds in describing restricted classes of phenomena that for inexplicable reasons continue to obey the laws.”

Nah, I don’t buy it. But you might buy it if you think the “inexplicable reasons” is just “one of those things” and it doesn’t otherwise get under your skin.

“Does this last fact mean that there is an ultimate law and order that mathematicians approximate more and more successfully? There is no answer to this, but at the very least, faith in mathematical design had to be replaced by doubt,” Kline says. Is it, “There is no answer to that?” Or is it, “There is no answer that I accept to that?”

Ultimately, is it not other factors, not mathematical at all, that determine whether that “doubt” becomes “conviction?”

“Yet what of the calamities of nature-earthquakes, meteorites striking the Earth, volcanoes, plagues-the unanswered questions of cosmogony, and our ignorance of what lies beyond our ken in our own galaxy, to say nothing of other problems facing humanity, do these not deny any likelihood of ultimate order?” Note that having or not having an answer to the problem of suffering and evil influences one’s assessment of the power of mathematics. The “other problems facing humanity”—problems that he has no answer for—bother Kline. And the only reason earthquakes, meteorites striking earth, and volcanoes registers on his scale is that they cause additional “problems facing humanity.” So it all boils down to: Why is there suffering and evil?

Hannah’s Fry’s kin, fellow Brit Stephen Fry, comedian, is also obsessed with this question. Only they are not kin, but upon doing an online search, I found I was not the only person to speculate they were. Nah, there’s no relation, the fact-check site told me—they don’t even follow each other on social media. But they both in a roundabout way (Fry, through her fellow mathematician Kline) settle into the same question: Why would a supposed God of love permit evil and suffering?

Stephen Fry does more than “settle into” it. He rams it headlong, like one of those horned animals ramming his fellow on Nature just to prove ‘Who’s the man?’ He rams it so forcefully that he triggers violation of the since-repealed Irish Blasphemy law. He figures (not unreasonably) that if an answer exists to evil and suffering, the self-proclaimed experts of the clergy will have it. Since they merely issue such pablum as “God works in mysterious ways,” he erupts into fury.

“Why should I respect a mean-spirited, capricious, stupid God who creates a world that is so full of injustice and pain?....Bone cancer in children, what’s that about? How dare you create a world in which there is such misery that is not our fault. It’s not right. It’s utterly, utterly evil. . . . Because the god who created this universe, if it was created by God, is quite clearly a maniac, an utter maniac, totally selfish.”

I develop this topic at some length in the “Fake News” chapter of I Don’t Know Why We Persecute Jehovah’s Witnesses —Searching for the Why. After all, “Why so Much Suffering?” is a chapter title of their basic Bible teaching book, and has been dealt with in more or less identical words throughout the Witnesses’ history. But the Witnesses stand for the “wisdom that cries out in the street” of Proverbs 1:20. “Hogwash!” the world thinkers are inclined to say. “It cries out from the quadrangles. Only ignoramuses are to be found in the street,”

See Part 2

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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

>>>>>>>>>>>>>>>>>>>>>>>>>>>

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

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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

Defending Jehovah’s Witnesses with style from attacks... in Russia, with the ebook ‘I Don’t Know Why We Persecute Jehovah’s Witnesses—Searching for the Why’ (free).... and in the West, with the ebook ‘TrueTom vs the Apostates!’ (free)

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

Defending Jehovah’s Witnesses with style from attacks... in Russia, with the ebook ‘I Don’t Know Why We Persecute Jehovah’s Witnesses—Searching for the Why’ (free).... and in the West, with the ebook ‘TrueTom vs the Apostates!’ (free)

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

Defending Jehovah’s Witnesses with style from attacks... in Russia, with the ebook ‘I Don’t Know Why We Persecute Jehovah’s Witnesses—Searching for the Why’ (free).... and in the West, with the ebook ‘TrueTom vs the Apostates!’ (free)