From time to time I get email alerts from Quora, a website where users post questions and others answer them. Occasionally the answers are of excellent quality. Here’s an example of a good one.
The question, which vexed me all my adult life (though less so lately), was this:
Does mathematics actually exist in the universe or is it simply a human construct?
Here, in full, is the answer given by one Josh Anderson, who lives in Penang, Malaysia. (Bold text and italics are reproduced as they appeared in the original. I’ve also added a link to Wigner’s famous essay.)
In his famous essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences, the Nobel Prize winning physicist Eugene Wigner wrote that the correspondence between pure mathematics and the natural world was “something bordering on the mysterious.” “There is,” he said “no rational explanation for it.”
It makes sense to say that basic mathematics was developed to describe things in the everyday world. We can understand the origin of things like counting and addition and how to calculate area. However, as Wigner goes on to argue, this simple explanation fails to account for so much of what we see.
The work of professional mathematicians often involves incredible ingenuity and extraordinary feats of logic. Some theorems and proofs take years to work out. And yet, astonishingly, many of the most brilliant and insanely abstract concepts turn out to model real world phenomena perfectly. They fit like lock and key.
Consider for a moment just how extraordinary this is. We have this set of things our minds seem to have produced in an abstract, non-physical realm of ideas. And we have another category or set of things we’ll call “things the universe does.”
Then, as history unfolds, we discover that there is exact correspondence between various mathematical concepts and the “things the universe does.” There’s a kind of remarkable overlap between what’s going on in our minds and what’s going on out there. And very often the math was worked out long before we went looking out in the world for a fit.
To quote Wigner, “It’s difficult to avoid the impression that a miracle confronts us here.”
This is remarkable. The things the universe appears to be doing at the level of physics is mirrored in the mathematical realm. The universe, it seems, is behaving in accordance with the products of mind.
Is mathematics something humans invented?
If you answer yes, how did something that is purely an artifact of mind get out there in the wild? How does it make it into the very fabric of the external world?
Around every corner in physics we find concepts no one thought would ever show up in the familiar world. But they do. Crazy, non-intuitive principles and things no one ever dreamed would leave the pages of mathematics journals turn out to be exactly what is needed to describe what the world is doing.
You could almost put this into a syllogism:
Premise one: Mathematical entities are the products of mind.
Premise two: The universe behaves according to mathematical entities.
Conclusion: Therefore, the universe behaves according to the products of mind.
But maybe we’ve got this all wrong. Maybe mathematical entities are not actually produced by our minds . Yet, if we change our story and accept that mathematics is somehow really out there, really existing in a humanity-independent way, we still have not managed to escape from this conclusion. In fact, if it’s discovered and not invented, the mystery is even more profound.
Now we have this realm of abstract ideas and relationships, an infinite logical landscape which we have direct access to through our minds. And yet, while non-physical, somehow this realm guides the behavior of things in the physical world.
It seems inescapable. Something mind-like is running the world, providing the framework, the tracks for physical reality to run on.
Einstein himself struggled to explain how this could be: “How is it that mathematics, being after all a product of human thought, is so admirably appropriate to the objects of reality? Is human reason then, without experience, merely by taking thought, able to fathom the properties of real things?”
If anyone in history had a right to comment on this issue it was Einstein. He, relying more or less entirely on thought-experiments, was able to unlock some of the best kept secrets of the universe. He himself found this astonishing, saying famously “The most incomprehensible thing about the world is that it is comprehensible.” Why should what’s really out there have corresponded meaningfully to what was going on in his mind?
Einstein spoke reverently, even religiously, of the experiences he had in beholding the “radiant beauty” that shone forth when he sought to peer into the mysteries of the universe. He was satisfied, he said, with a sense of the “marvelous structure of existence” and his “humble attempt to understand even a tiny portion of the Reason that manifests itself in nature.”
Speaking of mathematics in particular, he wrote:
“Pure mathematics is, in its way, the poetry of logical ideas. …In this effort toward logical beauty, spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.”
The more you think about it, the more remarkable it becomes. How is it that, with little more than some deep reflection, a man sitting alone in a Swiss patent office was able to grasp the profoundest secrets of space and time? What does it say about the universe that pure thought is able to disclose many of its deepest enigmas?
The philosopher David Wood brings this into sharp focus:
“Before you knew that the universe is governed by elegant mathematical equations, would you have had reason to await that? Would you expect the universe to be like that? Of course not. Mathematics is a language. The universe is operating according to language. This should not be at all surprising for those who believe in God. It should be horrifying to atheists, because that is the last thing you should expect.”
For a look at the role mind plays in life see the following: Josh Anderson’s answer to Is it possible to prove beyond a reasonable doubt that intelligence was required to create life?
Pretty good, no?
40 Comments
Except that the universe predates the existence of the human mind by billions of years. That’s assuming this isn’t yet another thing the eggheads have lied to us about, of course. There has been some debate as to whether Einstein was a fraud. His theory of general relativity, assuming he didn’t steal it, seems to be falling out of favour these days. Roger Schlafly, son of the late Phyllis Schlafly, says as much in his book How Einstein Ruined Physics (2011).
It’s just sad at this point. AS. Let’s call it a day, OK?
I don’t really care too much about Einstein either way. But the disparity between the age of humanity and the age of the universe does present an insurmountable problem for anyone who claims it was all made for us.
AS – you are inserting an artificial dichotomy between Man and Nature. But I’m just checking in here and Malcolm’s comment suggests you’re just a contrarian.
Thanks for posting this Malcolm. After a lifetime of religious practice, which I was never able to do very well, I’ve arrived at the conclusion that the Universe is God and Life is the Universe dreaming about itself. It’s hard for me to put into words, but I’m not talking about materialism; I’m actually as convinced of the reality of the Divine as I’ve ever been.
You should watch ex-Catholic Mike Flanagan’s series Midnight Mass, all the way to the end. Nuanced and philosophical in, of all things, a pop-Gothic horror series.
In follow up, I’m also convinced of Bruce Charlton’s triad of literal Eldritch Evil (which implies a Divine Good) though we start parting ways somewhat quickly after that.?
How is it artificial? It’s simply a fact. Modern humans aren’t even a million years old, and the universe is billions of years old. That’s a pretty big discrepancy. You can’t just ignore it.
First, you’re straw-manning. Nobody’s arguing the “universe was made for us.” Second, you seem to be implying mathematics as a post hoc human construct when it’s actually a priori, just like organic chemistry is a priori to flora and fauna. Again, this is an artificial dichotomy between man and the universe.
If you believe in anthropocentric things like God and an afterlife, then yes, you believe the universe was made for us. And I never said mathematics is a human construct. It’s our interpretation of phenomena that is clearly very real. If it wasn’t, we wouldn’t reap the benefits that we do. It wouldn’t have any utility.
“But the disparity between the age of humanity and the age of the universe does present an insurmountable problem for anyone who claims it was all made for us.”
What is time to God?
Whether time is an inconvenience to him is irrelevant. The fact remains that countless species have enjoyed chronological primacy over man. Why would God do that? Why would he create dinosaurs and prehistoric beasts? Why would he give them dominion over the earth? Why would he arrange for metacognitive lifeforms to evolve in such a painstaking and undignified fashion from lesser beings? No intermediary stages would be necessary for an omnipotent designer.
You’re making human, temporal value judgments.
Maybe there’s more to all of this than we understand, or are capable of understanding.
After all, it isn’t as if all questions are answered, or everything satsfactorily explained, by nihilistic materialism. (Not even close.)
So we are free to choose.
Appealing to the incomprehensibility of God’s motives might just be the lamest cop-out of all time. The fact is that there would be no need for an omnipotent being to create anything, whether it’s this appalling world or a paradise. Nihilistic materialism doesn’t tie itself in knots trying to excuse the inexcusable. It concedes the obvious.
No, nihilistic materialism fails spectacularly at explaining the deepest questions, and throws up its hands with promissory notes of what science will explain one of these days, all while complimenting itself on not falling for the “cop-out” that creation just might have a Creator.
Doesn’t tie itself in knots? No, no, it just, for example, posits infinities of unobservable “multiverses” to explain the incredible fine-tuning of the physical constants of nature. (Because the idea that they are that way on purpose would be, you know, a cop-out.)
Consciousness? The “unreasonable effectiveness of mathematics in the natural sciences”? Nothing to see here, folks.
At the very least, sir, do yourself a favor and admit that it’s an open question. Open your mind, and your heart. You have — quite literally — nothing to lose.
But these are just God-of-the-gaps arguments. You can’t explain it, so you plug it up with God. The Problem of Non-God Objects is the basis for my atheism. Theists are at a loss to explain why an omnipotent, omnibenevolent creator would make a universe with the abysmal properties that we see. A planet with less than 1% potable water isn’t very hospitable. The world is full of these absurdities. Theists cannot offer an explanation, precisely because no God would behave in this way. I wouldn’t dream of doing it, so why would a higher power? The only kind of God that’s even remotely tenable is the demiurge.
Ah, but the gaps are awfully stubborn, and they are in all the most important places: ultimate origins, the existence of mathematical order, the astonishing complexity of life, and if course the impenetrable mystery of that which is the primary feature of our very existence, namely our conscious experience itself.
Meanwhile, for fear of the horrifying prospect of a creative Intelligence, atheism offers us “multiverses of the gaps”, “neuroscience of the gaps”, etc., and assures us that if we just “trust the science”, all will be well — except, that is, for the bleak and empty purposelessness of the vast, accidental wasteland it describes.
As I said, you’re free to choose. But don’t kid yourself that the choice you’re so stuck on is so obviously the better one, intellectually or otherwise.
Life is needlessly complex. There are far too many variables, and gratuitous suffering abounds. Like I said before, a Rube Goldberg contraption that achieves nothing. The simplest way to determine the value of something is to ask ourselves whether we would freely choose it if we were under no duress. For the overwhelming majority of things in life, my answer is a resounding no.
As for the questions that materialism has not yet been able to answer, the theists dig themselves into a hole by asserting that God is the answer, because it introduces agency into all this. This inevitably invites the question they dread above all others: who in his right mind would deliberately create a world that falls so short of the ideal? There are questions we atheists cannot answer, at least not yet, but this isn’t one of them.
All of those bizzarities you mention are the product of Einstein’s theories. Let’s take a gander at the description for Schlafly’s book:
“Einstein is considered the world’s greatest genius for creating the theory of relativity, but his role is extremely misunderstood. How Einstein Ruined Physics explains relativity, how it was discovered, and how it fits into a long history of trying to understand motion and symmetry. Modern physicists describe a fantasy world that has less and less to do with reality. They tell of alternate universes, cosmic singularities, and extra dimensions. They have not turned up any conclusive evidence, but still they insist on following Einstein’s example, searching for the next revolution.
Einstein’s is famous for uniting space and time in the theory of general relativity, and for revolutionizing science with pure thought. But his famous relativity paper merely postulated what had previously been proved, and he did not even understand why space and time were being united. The crucial ideas behind relativity are motion and symmetry, and these are the most basic ideas in all of science. Relativity was the culmination of an ancient quest to understand the motion of the Earth. The story takes us from Ancient Greeks like Aristotle, through medieval debates over Copernicus and Galileo, up to the modern search for dark matter.
It has become fashionable in physics to aim for abstract Einsteinian revolutions instead of explaining observable realities. Schlafly dispels the myths about physics progressing by pure thought and shows us why following Einstein’s dream is very bad idea.”
You should know that a proposition is no less tenable just because you find the implications unbearable.
If I may jump in here, I do think Christianity answers the literally abysmal dichotomy you worry about Autisticus Spasticus. Pascal certainly thought so. (“The eternal silence of this infinite space frightens me” and all that.) Jacques Barzun describes this matter eloquently in his From Dawn to Decadence.
Autis?
You got in your family tree a relative name of Musey?
Just curious.
“All of those bizzarities you mention are the product of Einstein’s theories.”
And yet, somehow, Einstein’s edifice — built entirely on “the unreasonable effectiveness of mathematics” — stands, a century on, wholly unshaken and unrefuted, and is confirmed by observation at every turn.
The “bizzarities” you refer to have nothing to do with Einstein’s approach; they are simply there. The fine-tuning of the constants, for example, are why materialists posit unobservable multiverses. And as for consciousness, well, physical science doesn’t even have an idea of what an explanation would look like. It’s like trying to explain love, or justice, by building something out of rocks, or trying to communicate the engineering specifications of a hydroelectric generating station by playing the trombone.
As for “needless complexity”, it seems to me that you are so embedded in the astonishing complexity itself that you blithely take it all for granted, when it is the very miracle of its existence in the first place you should be marveling at in awe. Who are you to say what is needful, and what is needless? A mouse might look at the inside of a computer and “what’s the point of all this?” But that doesn’t mean that it has no point, or ought to have been done differently; it only means that the observer is a mouse.
My atheism overlaps quite a bit with my anti-natalism. I joined Substack in October and I have produced two essays thus far. An Indictment of Life is the second, and I think reading it will be immensely beneficial to you. My objection to your God’s creation has much in common with my ethical objection to procreation. Here is the link to my page.
AS,
My strongest case against anti-natalism is simple, and personally, more than sufficient: my two children and (so far) three grandchildren are happy and love life, and they give us great joy.
You don’t have to live in such darkness. The choice is yours; the door is open.
And if you knew anything about ethical anti-natalism, you would know that the point you just raised is irrelevant. I advise you to read it. It took me three years to write it. You will learn a great deal.
Oh, I’m well familiar with philosophical anti-natalism. (Among many others, Bill Vallicella has written about it often.)
I just don’t find it compelling at all. I consider it a bleak and grotesque philosophy of despair, based on a rejection of all transcendent meaning, purpose, or goodness.
And while you may find my point irrelevant, it isn’t irrelevant to me. (And in a world entirely without purpose, in which everything is just a meaningless accident, why should I care about anything else?)
P.S. One thing about anti-natalist movements: they tend to get out of the way in a generation or so. (Sometimes they leave behind nice wooden furniture.)
Like I said, just because we find something unpalatable, doesn’t mean it can’t be the truth. And just because humanity craves some transcendent meaning, doesn’t mean there is one.
Your children and grandchildren exist and have an interest in continuing that existence. On the other hand, potential persons have no interest in coming into existence.
Anti-natalism is memetic, not genetic. We all descend from a long line if individuals who were reproductively successful, so a predisposition towards anti-natalism cannot be hereditary.
AS,
I never suggested that anti-natalism was genetic. (That’s obviously absurd, although of course a lot of memes are passed from parents to children.) My point was that anti-natalist movements tend to extinguish themselves, as one would imagine.
If you think life is a blessing, then of course you’ll want to pass it on. If you think it’s a curse, then you won’t. (But if that’s really the way you feel, why are you even hanging around?)
I really haven’t anything more to say. All I can do is to remind you that you are very young, that there is a very great deal that you do not know or understand, that people’s views can change over time; and to implore you to consider that you may be mistaken.
The choice is yours.
To say that anti-natalists extinguish themselves implies that the philosophy is passed down genetically. This is evidently false, since no anti-natalist has parents who were also anti-natalists. People adopt this philosophy because they are persuaded by it.
If you are well versed in the philosophy, as you dubiously claim, then you already know the answer to that question. The answer is provided in my essay. I won’t tell you here, because that would rob you of what little motivation you have to read it.
I am supremely confident that there is no creator and no afterlife. If it turns out that I am wrong, it will not be due to any logical flaw on my part, but to the creator’s malevolence and irrationality. I would say I look forward to crossing swords with him, but that would imply I had any faith that he exists.
Again: if a philosophical movement chops off the mist important means of propagation — namely having lots of kids and raising them to believe in its memeplex — then it will fizzle out over time. (We have a perfect example in the Shakers.)
You yourself said that Islam’s high birthrate was its primary engine of growth!
We’re done, I think.
Again: if a philosophical movement chops off the mist important means of propagation — namely having lots of kids and raising them to believe in its memeplex — then it will fizzle out over time. (We have a perfect example in the Shakers.)
You yourself said that Islam’s high birthrate was its primary engine of growth!
We’re done, I think.
Islam spreads memetically via indoctrination. Its devotees grow up in an intellectually restricted environment, never encountering any other explanation for the world’s origins than the doctrine they absorb and regurgitate like mindless automatons. Like all religions, Islam thrives among primitive, insular people who are not exposed to contradictory information during their formative years.
In stark contrast, anti-natalism is a position which mature adults from many different walks of life have embraced. There is no brainwashing, coercion or threats involved. Ideas will exist as long as people exist, and if people no longer exist, anti-natalism will have achieved its goal.
Fine, so don’t have kids then. (With a sourpuss like you for a parent, I’m sure they’ll thank you for it.)
Meanwhile, the rest of us will be getting on with life.
See ya. Good luck.
Don’t be mad at me, Malcolm. I’m just trying to teach you. Please think about reading my essay. I addressed every objection I could think of, but I would like you to read it, so you can tell me if I missed any. I had written it with a specific audience, my old ethno-nationalist friends, in mind. Many of them have the same vitalist outlook you do. I remain sympathetic to their struggle, if for no other reason than my strong sense of justice, but I’m not so fussed about winning the game anymore. I don’t really think there’s anything to be won.
No, you have nothing to “teach” me here. I’m more than twice your age, and have been thinking hard about all of this since long before you were born. I know precisely where you are “coming from”, because I’ve been there myself, and out the other side. Intellectually, as I have argued at length in these pages, belief in God and purpose is a free choice.
I consider anti-natalism morally repugnant; it is a philosophy of pride and despair. Why “pride”? Because it takes a dangerous degree of self-inflation to flatter ourselves that we can see so clearly through all of the sublime mystery of Creation as to be able to pass judgment on it as empty of all intrinsic value and meaning. And this is why Pride is the deadliest sin: because it blocks the door to God. (I know this personally because I myself have moved from atheism to hopeful agnosticism only with the greatest reluctance and difficulty.)
We should cultivate humility, awe, and gratitude for the astonishing blessing of existence, not this shabby disdain you want to “teach” me. I believe it is not only a tragic error; it is also a horrifying manifestation of evil.
Good day, sir. I pray, for your sake, that you live long enough to find real love — above all, for yourself, and for your intrinsic worth — and someday to reject this appalling doctrine of darkness and death.
P.S. I’m not mad at you. I’m sorry for you. And you should remember that at 32, you may still have room to grow in wisdom, even if it might not seem that way to you now.
If it is prideful for us to object to our mistreatment and attempt to defend ourselves, then yes, we are very prideful, and unashamedly so.
Much as I would like to continue this discussion, your increasing irritability dissuades me. And I have to say, your obstinate refusal to read the essay I spent a great deal of time and effort writing is trying my patience.
Oh, I’m “trying your patience”, am I? My God, sir, listen to yourself. Who do you think you are? Nobody asked you to come in here and lecture us.
So: please feel free NOT to continue this discussion. My own patience was tried long ago by your presumptuous arrogance, unreflective overestimation of your modest intellect, inability to distinguish premises and conclusions, and your sophomoric, uncomprehending dismissal of anything that lies outside your dismal, poisonous, Procrustean worldview.
As I said before: if existence isn’t worth the effort, then why hang around?
At the very least, kindly don’t hang around here. I have tried to be as nice as I can to you, to sympathize with your pain, and to offer you what hope I can, but I’ve had enough. You have all the charm of a walking cadaver, and I am asking you now to leave, and not come back.
You didn’t try that hard, or else you would have read it. Is it really that much to ask? Come along, now. Are you an American or an American’t?
Actually, I do plan to die alongside my mother, but the residual Christian ethics within the legal system and wider culture has made it excruciatingly difficult to obtain the means to a peaceful exit. The God Squad do so love to make their faith our problem.
I have been here before. You don’t seem to remember. I might come back again, unless you shore up the door. I’ll be the Q to your Captain Janeway. Ciao.
Oh, I remember you very well from before — well enough that I groaned inwardly to see that you’d come back. (It’s my own fault for being so generous to commenters that I almost always make some effort to engage.)
Why would I bother to read your essay? How arrogant do you have to be to think that you can simply show up and demand that people take time out of their day to read your scribblings?
And even if you could persuade me of the utter meaninglessness of human existence (which you couldn’t, because I have already confronted this question, as argued by better minds than yours, since before you were born) — why on earth would I want to to be persuaded of that? Did I not make clear that I consider your counsel of despair to be a monstrous evil?
Imagine you offered me a pill that would lead immediately to bleak existential despair, and drive me to suicide. Do you actually think I, or any sane person, would take it?
As for your whining about finding “the means to a peaceful exit”: go to Oregon if you want to extinguish yourself. Or try Canada, or Switzerland. Or buy a gun, or a rope, or find a cliff. This isn’t rocket science.
Just don’t come back here. I mean it. I sincerely tried to offer you hope and sympathy and good will, and you sneered at all of it. So go away.