The Way-Back Machine

Take a ride with me back to this blog on October 4, 2019, when the donkeys were braying about the weather and lamenting the lack of a weather tax.

Fear not, the donkeys are planning on sacrificing conservatives for the sake of their weather god. Jo and Ho have pledged to do it no matter the cost to the rest of us.

In his 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 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 brought this into 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.”

11 known dimensions of space-time.

 

In Germany

65 COMMENTS

  1. In regards to Math, dude, you’re thinking too hard. Math is. It exists whether we wish to acknowledge it or not. Just like God. And trying to fudge the math to fit one’s needs is like Pelosi saying she’s a good Catholic, in other words, it doesn’t work.

    As to the Ottomans, mayhaps if all the Eastern and Western nations hadn’t been squabbling like a pack of Democrats over a pile of cash, then they could have put paid to the Ottomans a long time ago.

    And Communism is a religion, actually more of a cult. At least a lot of the Bible has been proven to actually have happened. Nothing of the positive side of Communism has come true. Of course, they assure me that nobody’s really done Communism and Socialism correctly, so we should try ‘one more time.’

    Gack.

    Rather do math. Where, using high math, the limit of 2 x 2 gets close to, but never reaches 4… Simple stuff, really.

    • No, it’s because you do Algebra intuitively, in your every day life. Same with most math. Like vectors… Vectors are serious applied math which makes sense when explained simply, but most math programs make vectors out to be some weird conjuring stuff. It took a simple explanation in a sci-fi role-playing game for vector analysis to make sense to me.

      If only teachers taught math like game designers do…

        • Instead of indoctrinating…

          Sigh.

          I was in school when it became obvious when teaching transitioned to indoctrination. About 1978. Out went the old text books, in came the new text books and, lo and behold, things were sometimes radically different or just outright missing.

          • About the same time Pop-Psyche took off and got integrated into schools and Personnel…excuuuse me, HR…departments. My era as well, saw it happening. Couldn’t put my finger on it at the time. Looking back it is clear as day.

  2. Einstein also said, “Things should be made as simple as possible, but no simpler.”

    Which is my reaction to advanced mathematics, theoretical physics, and cosmology.

    • Mathematics is just another language. Like music, or Russian or Swahili. As Kle wrote below, we use it all the time even if we think that we’re not.

      The difference is that mathematics can be clearly understood whether you’re speaking Russian or Greek or English. And it does help to explain an order to the universe.

    • I seriously doubt it.
      Also, define “math skills”. Most people think of calculations when they say “math skill”. That’s not mathematics, that’s arithmetic. Some actual mathematics genius (I forget who) was able to multiply two 4-digit numbers in his head as a little boy (e.g. 3429 x 1546). This impressed the hell out of everyone, but in his adulthood as a proper mathematician, he dismissed this as a trivial ability. “Mathematically speaking, the most important thing is, as a child I said “If you take away a hundred from fifty, then you have 50 below zero.” (I made up the numbers, but the quote is genuine.) In other words, as a very little boy, this mathematician had conceptualized *integers* as a class, whereas most people live in the realm of pure natural numbers.

      • Yes, mathematics transcends the visible world – and what we define as the “real world”, which may or may not be real. However whenever I hit my thumb with a hammer, it’s real enough.

    • Saying that is so racist. You’re never going to find a place in the new world order when you’re quoting God or mathematics….or Einstein, who was white.

      War is peace, freedom is slavery, ignorance is strength. Keep to the basics, WWW, and you’ll learn to worship old Great great granddad and Camel-A (was Big Brother).

      • Ignorance is bliss, not strength, L-L, and I have that on the very learned authority of my wife, who only recently told me that if ignorance was bliss, I must be the happiest man on the planet. And since God knows she’s never wrong about anything, it must be true.

        You’re probably right about the rest of it, though, except for that worshiping those two grifters part. Not for all the bribes in China. Same as you, I expect…..

  3. Knew a highly intelligent scientist engineer type without an ego, older man at that time. He emphatically stated to deny God is to deny life itself, and anyone willing to give it some thought would see His hand in everything. Math and God’s Creation go hand in hand, math complexity helps with the unveiling of wondrous detail He created while showing us how little we know. When peeling back the onion.

    The “syllogism” seems like circular logic to me, often used by those who deny God when stating “the universe was created because it needed to be created, that is, something out of nothing.

    The Dems have over-played their hand by over-winding their toys…mass exodus from SF, Chicago, NYC happening…cant leave fast enough. Their agenda will collapse on itself like a political black hole, and nature abhors a vacuum.

    Really thought provoking post this morning…your brilliance is showing. h/t

  4. Unfortunately, the math argument is circular and backwards.

    Mathematics is not an “invention”, nor a standalone mental construct. Mathematics is a system to describe reality, it is a language that allows us to discuss what is. OF COURSE we find it in nature all the time, if we didn’t, that would mean we were using it to describe nature incorrectly.

    As for algebra, I use it every day, and I bet everyone else does, too. Example: figuring out what range my car has on a tank of gas, and how much it’s going to cost me to get where I need to be. All those word problems everyone always hated were actually algebra.

    -Kle.

    • Mathematics is discovering an order to the universe. It’s the language we use to explain that order. The question, maybe better put, is one of whether there is “another”, yet undiscovered language that does it better. Maybe the unified field law? Because calculus breaks down at the quantum level where things get really weird (and to me, more interesting).

      The question may be whether “God” is that order to the universe, though I don’t think that the path to God is through mathematics (to answer WSF’s question, above). But mathematics is clearly a way to appreciate the universe.

      Mathematics is a language that we can (hopefully) agree on where “feelings” are difficult to quantify – but they’re valid. Just difficult to meter and measure.

      • It’s the reason that most great mathematicians were clergy. Think about it. The supposedly science-denying Catholic Church was and still is a hub of science. Either clergy, lay-members or funded by.

        And Galileo didn’t get excommunicated because he said something against the Church. He got excommunicated because he was an asshole who, when someone else said the Sun was the center of the solar system, basically put a verbal beatdown so hard on the guy that his works were dismissed forever. Until they were dug up after Galileo said the same damned thing.

        • Good point. I always liked math, got decent at it, then became a pastor later in life (bi-vocational). Direct cOrrelation? Could be, and might fit into a syllogism.

          • You’re like Schrödinger’s cat, both fire-and-brimstone pastor and Camperfixer at the same time. (Stand by for a discussion of the cat on the next Sunday Sermonette.

          • We all have our strengths and God-given talents, one never knows when they will be employed for His need or put to the test when strife surfaces. I did pound the podium once while making a point, surprised myself. But as an engineer type I also knew it could handle it. Direct correlation often produces good results.

  5. 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.

    Perhaps the conclusion could be that the universe is a product of mind? Just not our minds.

    When the Bible says that we’ve been created in God’s image, people tend to think of that image as being our overall physical selves. When we meet God, he will look like another human. Maybe it means God is the Creator and being in his image means we are creative. The biggest difference between man and other animals is our creativity.

      • If we allow it? I see no mass demonstrations about being locked out of churches during the ‘pandemic’ that also allowed pot shops and liquor stores to stay open.

        One thing that was always available in the Soviet Union. Alcohol.

        Think about it. Ban religion but alcohol is still allowed even for the little people…

  6. One of the many things I like about this website is its engagement with realism and the “epistemological quest.” But, good as this powerful sermon is on Truth or the accordance of mind to thing, I’m a bit confused.

    LL, you didn’t mention IM (Identity Mapping) once. We all know it’s an important factor in mathematics. Perhaps it was implicit in the homily?

    • Yes indeed I have brought that up here on this very blog in conjunction with mathematics.

      However the Sermonettes can’t be overly long or we all get bound up in the mud (not sandy Arizona mud, but nasty red Georgia clay style mud). There are a number of ways to look at the same problem.

      And we’re back to the argument of clothes. It’s good to take on an idea, try it on like a suit of clothes and run around with it, before you take it off and try on a new suit. Sometimes if we wear the same suit too long, we forget what’s underneath. Many people go through life imagining that they are their clothes.

      Imagine if I was just hacking out text on the blog – the weekly polemic. The learning process for all of us comes with the interaction in comments. I’m at best, an illegally parked car in the cul-de-sac of life with a few answers (like Pelosi is obviously is a witch and the scriptures offer suggestions in that regard) and more questions.

  7. I’m late to the game here, but a question to all those theologically minded.
    Is the universe *complete*? Meaning, was all reality created and fixed by a certain timepoint, by the Divine? Or is there the possibility that we are in some sense a “choose your own adventure” wherein broad macro parameters are fixed, but micro details of reality are not?

    My theology (in any tradition) is weak, but my belief is that we, as individuals, have a great deal of influence on our personal life trajectory and fate. Is it possible to extend this perspective so that we (the collective we) are helping to work out the minute details of reality?

    A number of cultures (e.g. Australian aborginal) use the metaphor (or actual literal belief, I dunno) that Reality was spoken or *sung* into existence. (I suppose this is not all that different from In the Beginning was the Word.) There is a grand score, which among everything else, created us. But as creations, can we not add to that score? Perhaps mathematics is the means by which we can do that.

    Or I’m blaspheming.

    • Some who visit this blog may consider it blasphemy. Others may not. Therein lies the journey.

      I choose to view this life as school, where we come to better understand cause and effect. And we learn it or we don’t. I also admit that I could be wrong.

      The idea of wearing angel wings and praising until the heat death of the universe has very little appeal. I would hope that in the next life they’d find me something better/more interesting to do.

      But please, please, put me somewhere different than where they put Adam Schiff, Nancy Pelosi, Swalwell and Jerry Nadler because there, in that place, I don’t know that strangling them would impart the same satisfaction that it would here.

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