“Although the seal is hidden, the wax stamped by the seal (hidden though it is) yields clear knowledge of it”

“Although the seal is hidden, the wax stamped by the seal (hidden though it is) yields clear knowledge of it” July 18, 2023


The Observable Universe!
A simulated view of the entire observable universe, approximately 93 billion light years (or 28.5 billion parsecs) in diameter. The scale is such that the fine grains represent collections of large numbers of superclusters. The Virgo Supercluster—home of our own Milky Way galaxy—is marked at the center, but is too small to be seen in the image.  Which ought to give you some sense of the vastness of the thing!  (Wikimedia Commons public domain image by Andrew Z. Colvin.)


I posted here a few days ago about Dante and the salvation of the unevangelized. (see “Catholic theology made no such provision”), based upon a reading of Prue Shaw’s Reading Dante: From Here to Eternity.. Here is another passage from Dr. Shaw’s superb book that is relevant to the topic:

When Dante makes his confession of faith to Saint Peter in the Paradiso, he offers a grammatical gloss on the mathematical conundrum of three-yet-one: e credo in tre persone etterne, e queste credo una essenza, sì una e sì trina, che soffera congiunto “sono” ed “este.” (Par. xxiv 139–41) (and I believe in three eternal persons, and I believe them to be one essence, an essence so one and so threefold that it takes “are” and “is” simultaneously.) That is to say, the verb to be is used of it correctly in the plural (are) and in the singular (is) at the same time. . . .

Had such knowledge been accessible to unaided human reason, the great philosophers of the ancient world, who had intuited the oneness of the divinity, would have understood it. As it is, they are forever excluded from the beatific vision because revelation was unavailable to them.

And here is a passage that is redolent of signs of intelligent design, as viewed by an exceptionally brilliant medieval Christian thinker:

Dante draws a distinction between the two terms: “in His image” can only properly be said of human beings, whereas “after His likeness” can be said of the whole of the created world. That created world bears the mark of its maker: totum universum nihil aliud [est] quam vestigium quoddam divine bonitatis. “The whole universe simply is an imprint of divine goodness” (Mon. I viii 2). Vestigium is literally a “footprint.” Twenty-first-century physicists at CERN in Switzerland using the Large Hadron Collider have used this same image of the footprint to describe what they were looking for and indeed have now found—evidence from which they infer the existence of the Higgs boson, which is believed to give mass to all the other subatomic particles.

Dante uses another image, with a venerable tradition going back to Plato, when he talks of God’s creative act in fashioning the universe in terms of wax and seal. Just as wax bears and reveals the image of a seal that has been imprinted on it, and the imprinted image remains visible even when the seal itself cannot be seen, so the cosmos displays in itself evidence of its divine origin: occulto exisente sigillo, cera impressa de illo quamvis occulto tradit notitiam manifestam. “Although the seal is hidden, the wax stamped by the seal (hidden though it is) yields clear knowledge of it” (Mon. II ii 8).

Specifically, it is the order apparent in creation that mirrors the divinity: Le cose tutte quante hanno ordine tra loro, e questo è forma che l’universo a Dio fa simigliante. (Par. i 103–5) (All things have an order which relates them one to another, and this is the form which makes the universe resemble God.) We have it on biblical authority that this order in creation can best be understood by means of mathematics or numbers: omnia mensura et numero et pondere disposuisti. “You have arranged all things by measure and number and weight” (Wisdom of Solomon 11, 21). The search for mathematical principles in how the universe is structured is endorsed by the Bible.

Dante is not so much interested in trying to prove the existence of God through the ingenious workmanship displayed in the created world as he is in understanding how that world works.

The search for mathematical principles at work in the structure and functioning of the universe is not just a medieval preoccupation. That same search continues to drive the endeavours of modern physicists and astronomers. When Nobel Prize–winning theoretical physicist Richard Feynman (a Jewish nonbeliever) talked of his awe in the “mathematical beauty of nature,” he was expressing an emotion that Dante and his contemporaries would have understood perfectly.

And this, as well:

Researchers working at CERN in Geneva using the Large Hadron Collider speak of the simplicity and beauty of the mathematical principles that underlie the variety of existence. Fractal geometry is another underlying structural principle that unifies natural phenomena from the very small to the very large. The excitement modern scientists feel at these discoveries is the excitement Dante’s poem communicates about numbers and their significance.

My own appended reflection:  Dante’s fellow Italian (of a later generation) Galileo Galilei has sometimes been called the father of observational astronomy, the father of modern physics, and even the father of science.  And maybe so.  Perhaps his greatest contribution, though, was what might be called the “mathematization” of science.  (Perhaps that’s what is actually intended when he’s said to be the father of physics and the father of science.)  Galileo famously declarex that the Book of Nature, as he termed it, is “written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these, one is wandering in a dark labyrinth.”

The Hungarian-American theoretical physicist Eugene Wigner (1902-1995), wrote a famous essay in 1960 entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”  In it, he observed that the fact that the mathematical structure of theories in physics and some of the other natural sciences often points the way forward not only to further theoretical advances but to empirical predictions — and he remarked that such congruence between our mathematical notions and the world outside our heads is, or at any rate ought to be, surprising to us.  Why is the world like this?  Is there any requirement that universe should be rational, and accessible to our reason?


Posted from Seattle, Washington

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