The Smallness of the Large

Just the tiniest little thing: Jesus Christ, lying in the manger. Those who have ever held in their arms a newborn baby, will know how delicate they are. Without a word, this fragile creature tells us to be careful with him. His neck is weak, and his head must be supported. Your attention rivets on the miniature eyelids, mouth, and nose.

One of the reasons I believe in God – the proper, Triune, Catholic God – is His way with paradox. This strikes me as true to my own experience of the universe we currently occupy, which is full to busting with scale reversals.

Were Christ, indeed, the Author of this universe, I would expect Him to show the same “sense of humor” – by which of course I don’t mean, “telling jokes.” Or perhaps, there are jokes far beyond laughter.

This begins with the magnitude of the heavens: the normal human perception of distance to the stars, and to the stars beyond the stars beyond them. (It is a myth that any of our ancestors thought they were close. Regardless of their cosmological schemes, all men have known that the stars are very far away, and that they speak of immensity.)

But at the other end is a sub-atomic scale. It seems to parody the large, in smallness. There are distinct specks within specks, and specks within those, down to “force carriers” and “flavors.” We find the Singularity where, if physics has any coherency at all, we have reached the interface with “nothing.”

That is to say, there cannot be smaller, in any material scheme for small, for the same reason that the universe cannot be larger. At least, not as we have found it to be. We could run the abstract numbers up and up, or down and down – but in either case we come to that hard, material Singularity. Go any farther in either direction, and we’re not in this universe any more.

So where are we on this scale?

Man, standing around one fathom tall, is right in the middle, midway between the “nothing” and the “everything.” In the numbers we’ve been able to compile, our position is rather spookily at the intersection of all roads.

As we’ve come to learn, mostly in the quite recent past, the strangeness is insupportably great, for the universe itself is “tuned” to many dozen – perhaps many hundred, perhaps many more – precise settings of physical “law” or constants. Adjust the dial ever so slightly – adjust so slightly any one of those dials – and the very possibility of Man is obviated.

Of course, the observation is tautological, but even in that we see God’s hand: that He left us with the freedom to see, or refuse to see, what is dead obvious.

In a limited, merely scientific way, since 1931 at the latest, the existence of “God” has been irrefutable. That was the year in which the finitude of the universe was established beyond reasonable doubt: that it had an origin, at a calculable “first moment” in time; that it has from that a calculable size; and what has a beginning must have an end. (See: Georges Lemaître.)

Msgr. Lemaître with Albert Einstein, c. 1932
Msgr. Lemaître with Albert Einstein, c. 1932

And towards the end of that last century, in the later 1990s, the chief hint was provided to calculate that end. For not only can we now know the universe is expanding, but also that it expands at a constantly accelerating rate. We must reach a point where the universe itself comes up against the good old speed of light: and once again, a Singularity. (See: Accelerating universe.)

A small thing, perhaps, as that ingenious Belgian physicist, Monsignor Lemaître, once had to explain to his pope, who was on the verge of announcing that the Catholic cosmology had been scientifically proved. For as the good priest said, it is just science, which rattles about from day to day. The part that takes us from two plus two, to four, will always have to be supplied by Faith.

Science only shows what’s there, not the meaning of it. Yet the nature of the universe remains plain to see, whether on the grand cosmic scale, or in little biological facts, provided to our senses directly. The acorn and the oak are one, from never before, to never after. Whether through telescope, or microscope, we see the same in a glass, darkly.

Modern man can look at the large, and he can look at the small. There is nothing wrong with God-given eyes, should we wish to use them; nor in the blind, with the mind’s eye. Nothing has ever been concealed from a man, that the man needed to know. But oh, he is willful.

What modern man has trouble seeing, is the large in the small, and the small in the large. Our ignorance – which can be stupefying, compared with ignorance in ages past – fastens upon one thing at a time, with ever-diminishing attention spans. In effect, we have lost the ability to see and think at the same time.

And to this modern mind, as to others past in the habit of missing the point, the whole idea of God presented in this swaddled bundle of human flesh, is nonsense. God, should He turn out to “exist,” must be infinitely large; this baby is way too small.

A real God would take anything He wanted; this baby missed out on the inn.

A real God would be all-seeing; this baby sleeps in Mary’s arms.

A real God would arrive with angelic armies; this baby lacks even a security guard. . . .

We could construct a litany like this, of ways in which Jesus Christ was not very plausible. Even to many ancients, as we know, the whole idea of Him came as something of a little joke. Surely the Christians could not be serious.

Imagine their surprise when, paradoxically, that little baby conquered their world.

David Warren

David Warren

David Warren is a former editor of the Idler magazine and columnist with the Ottawa Citizen. He has extensive experience in the Near and Far East. His blog, Essays in Idleness, is now to be found at: davidwarrenonline.com.

  • Silent - Friday, July 7, 2017
  • Tom Williams

    thank you David, you never disappoint with your wit and clarity. “There are none so blind as those who cannot see” We stumble in the darkness while the light shines all around us.

  • Rusty

    Having taught evening classes at the college level some years ago (as a way of giving back, for it by no means was a way of making money), the thing I most wanted to open to my students was the need to “connect the dots”, to see how one thing affects and is affected by another, and is part of a much larger whole.

    These patterns may be discerned to provide a context within which what is immediate and factual may be given meaning. Mr. Speaker, it is perhaps the main reason I enjoy reading your blog and contributions to publications such as this. It is not enough to repeat what has been said elsewhere; it adds grist to the mill only when the insight into what is said elsewhere helps illuminate what we know in our bones, but have not previously articulated.

    Keep writing sir.

  • Rich in MN

    One thing I find fascinating is how the very physics of the macrocosm and the microcosm are currently irreconcilable by any workable models yet hypothesized. I am certainly not up on the latest versions of “string theory,” but the whole notion of the “Uncertainty Principle” seems so counter-intuitive to our rather Newtonian way of viewing the world.

  • Anthony

    Very Catholic article.Thanks!

  • Robert A Rowland

    The wonders and splendors of the universe clearly demand an omniscient creator. Using the stars to navigate clearly manifested the mathematical precision of the universe to me.The Way, Truth, and Life is the emancipator for faith, and free will is a blessing for those who do God’s will or a curse to those that reject it. .Why are we surprised that God chose a baby to confound the wiles of the world?

  • Alley Upta

    The trouble with pure self-indulgence is that it cannot, on principle, admit bounds, and so must seek to exile all else to dwell exclusively in its own, progressively smaller, cosmos.

    Often when I read Mr Warren I am reminded that, while God made us for beatitude, we are mean enough to look for sense.

  • Paul

    Thanks for the article. I admire the main idea. God does marry incongruous things in the Incarnation. He sends the rich away empty, and fills the starving…

    As a practicing quantum physicist, though, the science analogy made me wonder. The small is actually quite different from the large. That was the whole surprise at the beginning of the 20th C. Small stuff obeys different rules than we expected based on the rules obeyed by the universe above our heads. We call those rules quantum physics – the science of small stuff. There’s a whole field on how one set of laws gives way smoothly but quickly to non-quantum, e.g. Newtonian-like laws at the scale of very roughly about 100 atoms – the quantum-classical transition.

    A few other points about science that may interest you:
    One commonly unknown fact about the size of the universe is that just because there is a beginning in time about 14 billion years ago does not mean the the universe must have a finite size – it could have been infinite spatially from the beginning and expanded, always remaining infinite. Think of an infinite tiled floor – at the centre of each tile a galaxy. Just as you expand a photo on the computer by dragging its corner, and each pixel moves apart from every other pixel, so could the infinite tiled floor expand with no one tile being singled out as the special “centre of expansion”. Think of sitting on a pixel on the nose of a photo of a person’s face, and drag the window’s corner to expand it. Every pixel around it moves away, and it may seem like the nose is the centre of the expansion. But sit on a pixel on the chin, and you’d see all the surrounding pixels moving away from it too. Now imagine the picture being infinite – infinitely many people perhaps – and yet you can expand it by grabbing anywhere with the mouse and dragging, or pinch and zooming. So we could have an initially spatially infinite universe, which expands continually.

    You’ll see in popular science books terms like the “size of the universe”: these are mostly loose ways of talking about the bit we can see in our telescopes, the “visible universe”. The universe could actually stretch much beyond this (including infinitely far) but the light from these stars hasn’t had time to reach us yet.

    And just because the universe has a beginning in time, it needn’t have an end in time, if e.g. it keeps expanding… though the night sky would get dimmer.

    Distant galaxies do separate from each other with a speed greater than that of light, yes, but that’s nothing to do with a singularity. Such superluminal speeds are common in an expanding universe: Earth is probably expanding with a speed greater than light compared to really distant galaxies, and we feel ok :). The dictum that one can’t go faster than light only applies locally, to e.g. a light beam that you emit from your location: good luck outracing it. Distant objects have no such constraints.
    Generally I find talk of a singularity on the web and in some popular science books very loose and very speculative, unless you’re meaning the technical idea of singularities in General Relativity I’d stay away from books that make much of it. It’s usually a bad sign for me.

    Isn’t there is a role for natural reason in Catholicism – do we really need the Faith to tell us 2+2 = 4? What did you mean here?
    Some things like e.g. the Trinity are forever beyond natural reason. But other things (including, interestingly, some revealed things according to St Thomas Aq) are reachable by natural reason.

    You’re quite right that one can miss the wood for the trees in science – great personal knowledge of the ways the bits of the universe move and interact, but no philosophical stance on why it exists, and moves in an ordered way. We’re mostly trained just as scientists – that takes all our energy — and lose our competence very quickly when we try to act as philosophers. As one has to beware of when reading popular science books by scientists too busy to have a prayer life or read the Bible.

    Fr Barron makes the point on the first episode of Catholicism that Jesus DID arrive with armies – the heavenly host=stratias=army. His power is not an earthly army, but real power none-the-less. In the Passion (Mt 26:53) Jesus says “Do you think that I cannot appeal to my Father, and he will at once send me more than twelve legions of angels?” Sounds like he has some serious force at His disposal. He doesn’t use it then because that’s not the Father’s plan for his life at that point. But later in the Book of Revelation, angels are very forceful, dishing out plagues.

    Credentials: Physics PhD from Berkeley, then 15 years research and lecturing in universities and over 20 papers published on quantum physics.

    • JoyInTheLord

      Thank you for your post, Paul. I read your follow-up post to David before this one. Your questions are valid, and I am interested to know your answers to those. Could you refer me to some links, or will those links that you provided to David suffice?

      My Catholic faith got a strengthening dose while doing graduate work in teaching mathematics at a Jesuit university. I was overwhelmed by the fact that every leaf of a tree, or any blade of grass, is unique. I came to this realization while doing polar graphs for the first time. I am a small mind trying to understand things with reason, but yes, I have accepted them first before in faith.

      Two questions: what is ‘singularity’, and what is ‘critical density’ in physics? Please explain in layman’s terms.

      • Paul

        Hi JoyInTheLord,

        the links in my second post are sufficient evidence for the 3 scientific errors listed there.

        I’m not sure which of my other questions you’re asking about. I’ll answer some, and if you meant others let me know and I’ll do those.

        About 2+2=4, I think it’s fairly clear Plato, Aristotle and Euclid knew this as clearly as we do, centuries before the Faith. There is a role for natural reason in Catholicism, both for natural things and ideas like mathematics, and even for some of the truth about God. E.g. the Catechism no. 50 says “By natural reason man can know God with certainty, on the basis of his works. But there is another order of knowledge, which man cannot possibly arrive at by his own powers: the order of divine Revelation.”

        That nature of the Trinity is one of the latter: those teachings that are forever beyond unaided natural reason.

        Another point : 2+2=4 is a truth of mathematics, not physics. Physics is a science, and all our laws are approximate. You can see this because they get replaced! Newton’s laws got replaced by Einstein’s General Relativity in one direction, and by Quantum Mechanics in another, and we expect both GR and QM to be replaced by a theory we haven’t found yet, which may in turn be replaced by another if its deficiencies become measurable.
        Whereas 2+2=4 is a statement about mathematical ideas. These exist in our minds and not in the real world (point out to me on what planet the ideal infinite straight line lives, infinitely long and infinitely thin). It’s important to distinguish these different worlds: the tangible universe we live in, and the world of precise ideas. Mathematics lives in the latter and is eternal: that’s why 2+2=4 isn’t ever going to change.

        Mathematicians assume axioms and deduce from them, just like we postulate the rules of chess and then play the game. Are the rules of chess right or wrong? Neither really, but perhaps most other rules would give rise to less interesting games.
        Similarly mathematicians care more if their axioms are fruitful mathematically, giving an interesting theory with perhaps useful connections with other parts of mathematics.

        2+2=4 is simply a logical consequence of the axioms one assumes in mathematics: one proves this usually in say the first year of undergraduate mathematics degree after getting to know the axioms. Mathematics isn’t really a science, in the modern sense of the term. It has no experiments that could falsify its axioms or conclusions. That’s one reason why it tends to be a separate university department.

        Physics is different : it’s a claim that real tangible things obey certain mathematical patterns. This claim can be falsified.

        About the stratias of the heavenly host, I think we have to take seriously Matthew’s 12 legions.

        Singularity? First, it’s a mathematical term. Plot f(x) = 1/x versus x, and you’ll see something special happens about x=0. The curve blows up to +infinity and -infinity. That’s what a mathematical singularity is – some function becoming infinite about some point.
        To be more precise, as one must with the infinite, there is no such number +infinity or -infinity in the usual (un-extended) real numbers. So one can’t set f(0) = +infinity, for example. One can use the recipe f(x) = 1/x to define f(x) everywhere away from x=zero, but not at it because 1/0 doesn’t have a meaning for real numbers. Usually a book will either leave f undefined at x=0 (so f is a function defined on the real line R less the set {0} ) or you could by hand set f(0) to be any number you want, say f(0)=0.
        And when I say the curve blows up to +infinity, that’s mathematical shorthand for f(x) gets as large as you please. The longer statement of this is that, given any number like, say, a billion, one can find a real number delta>0 such that for any real x between 0 and delta exclusive, f(x) is greater than a billion. (In our example here, pick delta = 1 / a billion, and it’ll work). So mathematics never says f(x) becomes infinite, just that it becomes on some region sufficiently near 0, as large as you please.

        Now the physics. When we find our mathematical equations of the world predicting that some measurable quantity becomes larger and larger without any limit, that’s a singularity. That’s one odd prediction: usually our predictions say e.g. the temperature on Tuesday will be between 70 and 100 degrees. You’ve never heard a valid weather forecast which said the temperature on Tuesday will become higher and higher without limit, as the day goes on.

        The most famous early singularity that I know of is the singularity in the tidal forces as we approach the centre of a black hole. Singularities are a bit of a buzz word outside working science, and to distinguish the good writers about popular science from the bad it’s good to ask my Q2: which quantity (here tidal forces) are becoming infinite, and has someone measured that they get larger and larger without any limit, and when?
        That’s why I asked Mr Warren to do so: if he gets in that virtuous habit it’ll prevent him believing every claim of singularities he comes across, and give him the knowledge to vet them.

        Our physical laws about tangible stuff are always approximate.
        Their mathematics is interiorly true by definition, because mathematicians just postulate assumptions w/o feeling a need to prove them, but as physics the theories of Newton, Einstein or QM have never applied without some errors to our tangible world because the world hasn’t exactly obeyed their assumptions to begin with.
        Thus when we find larger and larger quantities being predicted by our laws we have reason to guess that they’ve reached the edge of their competence. Einstein’s laws aren’t expected to work 100% at a singularity: we’ve arrived at these laws based on how gravity works usually in the universe where it’s weaker, and to expect them to work 100% in such abnormal circumstances is like expecting your body to respond as it usually does, but a bit more so, when you put it under much greater stress – instead it’s more reasonable to expect something new and painful to happen.

        Critical density? It’s a density of something (X) at which something else critical (Y) happens :). It’s used in many places in physics, with X and Y varying appropriately. For example, for electrons, when their density is reduced enough, they suddenly form something called a Wigner crystal.

        Did you have a specific example of a critical density in mind, say in astrophysics? There the density rho of matter, radiation and vacuum energy combined determines if the universe is spatially finite (like the surface of a sphere, e.g. the Earth’s surface where if you go far enough in one direction you’ll return to where you started from the other side), spatially infinite and flat like an infinite plane, or spatially infinite and curved like the surface of an infinite saddle – bending different ways in different directions. As one lowers the density (rho) one passes through these three states in that order, the infinite plane case occurring at just one value of rho called the critical density and separating the two other types of behaviour. Hence this density is special = critical.

        • JoyInTheLord

          Thank you for the reply, Paul. And that was some post. You did explain well singularity from the point of view of math, but I doubt my understanding when you talked about singularity in physics. I remember hearing that word in a graduate math course but totally forgot about it, until I read this article. Critical density is an entirely new concept to me —well, it’s physics and never dabbled really seriously in that one. I like your epsilon-delta limit explanation. Sounds real calculus to me.

  • E Waugh-Ok

    Thanks.

  • David Warren

    You’d think a guy with all these credentials would also give his name. You’d also think he’d understand the concept of infinity: that it cannot be expanded. Or that Lemaitre’s theory positively excludes any initial spatial infinity: for time and space themselves extend from that initial “cosmic egg.”

    I also failed to appreciate the attempt to undermine my point that the small “parodies” the large. This is hardly a denial of the distinction between quantum and non-quantum forces, to which I was actually alluding.

    For the rest, I find the comment of “Paul” a twirl of obfuscations.

    • “Do you not know? Have you not heard? Has it not been declared to you from the beginning? Have you not understood from the foundations of the earth? It is He who sits above the circle of the earth, And its inhabitants are like grasshoppers, Who stretches out the heavens like a curtain and spreads them out like a tent to dwell in. He it is who reduces rulers to nothing, Who makes the judges of the earth meaningless.…” (Isaiah 40:21-23) Notice that the Name of God starts with the smallest letter in the Hebrew alphabet.

    • Mark Millward

      Don’t be so darn prickly and proud David. Paul is simply counselling not to sell the timeless truths of the Catholic Faith short by hitching them to scientific theories whose “truth” is highly contingent on future discoveries as well as being purely material in outlook.

  • John_QPublic

    Interesting article.. I like this line: “…we see God’s hand: that He left us with the freedom to see, or refuse to see, what is dead obvious.”

    The new documentary “The Principle”, takes a different line, and questions the Copernican principle itself based on modern observations. Some of Lemaitre’s ideas are still possible, but most importantly, the earth likely finds itself in a special or preferred location in the universe. Lawrence Krauss, Michio Kaku, George Ellis, Julian Barbaour, and others explore this idea in a very interesting and controversial film. “The Principle” opened in Chicago, and is showing starting January 23rd in Burbank and Orange California, and Spokane, Washington (all AMC). “The Principle” is sure to take the faith and science discussion to the next level.

  • JoyInTheLord

    Your post is very poetic. It is a poem in prose. It is a lyrical lyric, an odiful ode. Thank you.

  • kathleen riney

    Our God is “I AM WHO AM”……Ever Present with His WORD, & The HOLY SPIRIT……All Who could not be Contained, were Present in the Womb of the Virgin….The Creature Carried what Cannot be Contained, her Creator, her Son, HIS Word, & The Holy Spirit……for 10 Lunar Months…..A glimpse into the Mystery of The Ark of The Covenant…Mary was The Completed Ark……Think too of Joseph! The Humility, Trust & Love he showed…Joseph taught The Creator of All that is, was & ever will be, Carpentry! “And He returned home & was Subject to them….” after they found Him in the Temple….I LOVE our poor, scraggly, (on the outside) Bride of Christ…..



RECENT COLUMNS

Archives