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:
“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,”
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