5 Replies to “Infinite patterns, beautifully expressed

  1. 1
    daveS says:

    Stunning.

  2. 2
    kairosfocus says:

    A tour de force of the mathematical symmetries expressed in natural and man made architecture. The principles and core patterns of aesthetics are on powerful display. KF

  3. 3
    bornagain77 says:

    I think that Paul Dirac, Richard Feynman, Murray Gell-Mann, and even Albert Einstein himself, would have been very pleased to see these videos since they visually represent the beauty that is inherent in mathematics that describe physical reality. Albert Einstein went so far as to say, ‘the only physical theories that we are willing to accept are the beautiful ones’

    ‘the only physical theories that we are willing to accept are the beautiful ones’
    Albert Einstein – Quoted in Graham Farmelo, It Must be Beautiful: Great Equations of Modern Science (Granta Books, 2002), p. xii. Farmelo provides an extensive discussion of this topic and gives numerous examples from the history of science.

    Likewise Paul Dirac stated that “It is more important to have beauty in one’s equations than to have them fit experiment.”

    A thing of beauty – A. Miller – 2006
    Excerpt: Even when the evidence was going against them, Nobel prize-winners Murray Gell-Mann and Richard Feynman clung on to cherished theories just because they thought they were “beautiful”.
    ,,, back in the 1960s, Paul Dirac famously asserted that: “It is more important to have beauty in one’s equations than to have them fit experiment.” Richard Feynman, too, insisted on believing in one of his theories even when it seemed to contradict experimental data. “There was a moment when I knew how nature worked,” he wrote in 1957. “[The theory] had elegance and beauty. The goddamn thing was gleaming.”,,,,
    In 1957, experimental evidence weighed heavily against Murray Gell-Mann and Richard Feynman’s theory of weak interactions. As we saw, Feynman had declared that the theory “had elegance and beauty. The goddamn thing was gleaming”. In other words, it had an inner perfection that suggested it could be generalised further, it hinted at how to unify the weak and electromagnetic interactions, and its mathematical representation was the simplest that could be constructed. Despite the high reputation of the physicists responsible for the actual experiments, Feynman and Gell-Mann’s response was that there was something wrong with the experiments. They were right. Thus
    although experiments are essential for scientific theories, certain theories are just too important – too beautiful, one could say – to be discarded when the experiments don’t go your way. Perhaps in the future beauty will provide an important criterion for selecting one theory over another, now that theories are emerging which cannot be verified by experimentation as we know it today.
    https://www.arthurimiller.com/AThingofBeautyPERSPECTIVES.pdf

    In fact, one of the reasons that we know string theory cannot possibly be the correct ‘theory of everything’ is because, mathematically, it has morphed into an ugly mathematical monstrosity,

    The part of the book (‘The Trouble With Physics’) I found most interesting was the part which tells how the string theorists were scammed by Nature (or Mathematics). Of course, Smolin doesn’t put it exactly like this, but imagine the following conversation.———
    String theorists: We’ve got the Standard Model, and it works great, but it doesn’t include gravity, and it doesn’t explain lots of other stuff, like why all the elementary particles have the masses they do. We need a new, broader theory.
    Nature: Here’s a great new theory I can sell you. It combines quantum field theory and gravity, and there’s only one adjustable parameter in it, so all you have to do is find the right value of that parameter, and the Standard Model will pop right out.
    String theorists: We’ll take it.
    String theorists (some time later): Wait a minute, Nature, our new theory won’t fit into our driveway. String theory has ten dimensions, and our driveway only has four.
    Nature: I can sell you a Calabi-Yau manifold. These are really neat gadgets, and they’ll fold up string theory into four dimensions, no problem.
    String theorists: We’ll take one of those as well, please.
    Nature: Happy to help.
    String theorists (some time later): Wait a minute, Nature, there’s too many different ways to fold our Calabi-Yao manifold up. And it keeps trying to come unfolded. And string theory is only compatible with a negative cosmological constant, and we own a positive one.
    Nature: No problem. Just let me tie this Calabi-Yao manifold up with some strings and branes, and maybe a little duct tape, and you’ll be all set.
    String theorists: But our beautiful new theory is so ugly now!
    Nature: Ah! But the Anthropic Principle says that all the best theories are ugly.
    String theorists: It does?
    Nature: It does. And once you make it the fashion to be ugly, you’ll ensure that other theories will never beat you in beauty contests.
    String theorists: Hooray! Hooray! Look at our beautiful new theory.
    ———- Okay, I’ve taken a few liberties here. But according to Smolin’s book, string theory did start out looking like a very promising theory. And, like a scam, as it looks less and less promising, it’s hard to resist the temptation to throw good money (or research) after bad in the hope of getting something back for your effort.
    – per amazon review

    The thing that is interesting about this deep connection between beauty and the mathematics that accurately describe physical reality is that both beauty and mathematics are powerful arguments for the existence of God.

    April 2020 – if atheistic materialism were actually true, then beauty must necessarily be illusory.,,,
    ,,, thus, the argument for God from beauty can be stated like this,
    1. If God does not exist then beauty does not objectively exist but it is merely illusory.
    2. Beauty does objectively exist.
    3. Therefore God exists.
    https://uncommondescent.com/intelligent-design/the-problem-of-beauty/#comment-699416

    Beauty and the Imagination – Aaron Ames – July 16th, 2017
    Excerpt: Beauty… can be appreciated only by the mind. This would be impossible, if this ‘idea’ of beauty were not found in the Mind in a more perfect form…. This consideration has readily persuaded men of ability and learning… that the original “idea” is not to be found in this sphere
    (Augustine, City of God).
    https://theimaginativeconservative.org/2017/07/beauty-imagination-aaron-ames.html

    The Reason Why God Is the Beauty We All Seek – Sept. 4, 2019
    Excerpt: God loves beauty. As Thomas Aquinas asserts, God “is beauty itself”[1] St. Anselm argues that “God must be the supreme beauty for the same reasons that He must be justice and other such qualities.”[2] As the contemporary theologian Michael Horton so aptly states in his book The Christian Faith, “God would not be God if he did not possess all his attributes in the simplicity and perfection of his essence.”[3] The reason why we gravitate toward beauty is because God created us in his image.,,,
    In a chapel sermon titled, “Can Beauty Save the World,” Albert Mohler explains,
    “The Christian worldview posits that anything pure and good finds its ultimate source in the self-existent, omnipotent God who is infinite in all his perfections. Thus the Christian worldview reminds us that the “transcendentals”—the good, the true, and the beautiful—are inseparable. Thus when Psalm 27 speaks of the beauty of the Lord, the Psalmist is also making a claim about the goodness of the Lord and the truthfulness of the Lord. While we distinguish God’s attributes from one another in order to understand them better, we must also recognize that these attributes are inseparable from one another.[19]”
    Mohler goes on to state, “Our job as Christians is to remember the difference between the beautiful and the pretty,” because pure beauty is found in goodness and truth.[20] When we gaze upon ascetically pleasing objects or witness kind deeds in this world, we are at best seeing imperfect versions of the pure beauty that can only be found in God.
    https://www.beautifulchristianlife.com/blog/reason-why-god-is-the-beauty-we-all-seek

    KEEP IT SIMPLE by Edward Feser – April 2020
    Excerpt: Mathematics appears to describe a realm of entities with quasi-­divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our ­experience lack. Mathematical objects seem ­immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order.
    How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect.
    https://www.firstthings.com/article/2020/04/keep-it-simple
    Of note: This view the mathematics exists “because they are God’s thoughts” and the Christian view that God created the universe and that the universe has not always existed, (as Aristotle had held), were presuppositions that were necessary in order for modern science to take root in the Medieval Christian cultures of Europe.
    https://uncommondescent.com/philosophy/edward-feser-on-mathematics-and-the-sense-of-the-divine/#comment-695391

    In fact, both Einstein and Wigner are on record as to regarding it as a miracle that we are able to accurately describe the physical universe with mathematics, Einstein even went so far to chastise ‘professional atheists’ in the process of calling it a miracle.

    On the Rational Order of the World: a Letter to Maurice Solovine – Albert Einstein – March 30, 1952
    Excerpt: “You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton’s theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the ‘miracle’ which is constantly reinforced as our knowledge expands.
    There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles.”
    -Albert Einstein – Letter to Solovine

    The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960
    Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.,,,
    It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.,,,
    The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
    http://www.dartmouth.edu/~matc.....igner.html

    As to Einstein’s claim that ‘the only physical theories that we are willing to accept are the beautiful ones’, I would like to point out that a ‘very beautiful’ solution for the much sought after ‘theory of everything’ pops out for us when we rightly allow the Agent Causality of God (back) into physics,

    Specifically,

    First and foremost, allowing the Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim:
    January 2020
    https://uncommondescent.com/intelligent-design/welcome-to-the-brave-new-world-of-science/#c

    Verse:

    Colossians 1:15-20
    The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.

    John 15:13
    Greater love has no one than this, that someone lay down his life for his friends.

  4. 4
    bornagain77 says:

    Hmmm, here is an interesting quote from C.S. Lewis

    “We do not want merely to see beauty, though, God knows, even that is bounty enough. We want something else that can hardly be put into words—to be united with the beauty we see, to pass into it, to receive it into ourselves, to bathe in it, to become part of it.”
    C.S. Lewis, – The Weight of Glory

    Here is another quote from C.S. Lewis that goes along with that line of thought:

    “If I find in myself desires which nothing in this world can satisfy, the only logical explanation is that I was made for another world.”
    – C.S. Lewis, Mere Christianity

    And here is a song that reflects on that rather noble sentiment

    Brooke Fraser – CS Lewis Song
    https://www.youtube.com/watch?v=PycBrNP8dXg

  5. 5
    jawa says:

    Beautiful indeed.

Leave a Reply