Freeman Dyson (1923–2020) explains:
I find it a miracle. I mean, I don’t pretend to understand it and I think it is absolutely marvellous that nature somehow thinks like a mathematician, that was what James Jeans said that… that God appears to be a mathematician. And it is astonishing that somehow all these weird mathematical ideas which we have invented for purely aesthetic reasons, essentially just as works of art, as intellectual constructions, turn up then unexpectedly to be used in nature. There’re so many examples of this, of course. Of course the classic case was differential geometry which was invented by Gauss for very practical purposes, just for projecting maps from the spherical earth onto a plane, onto a piece of paper, so he invented this differential geometry as a way of representing curved surfaces on a flat plane. And then 50 years later Riemann applied that to a description of space and conjectured that space itself might actually be curved, but it was still sort of purely an intellectual hypothesis without any kind of physical basis. And then another 50 years later it turned out to be the essential tool for Einstein to understand gravitation. It is in fact what Einstein used for general relativity. So it’s built… it’s built deep into the structure of space-time.
No wonder New Atheism petered out. Ultimately, maybe they couldn’t argue with the math.
The only disagreement I have is we don’t invent math, anymore than we invent the laws of physics. All formulas already exist and waiting for the right mind to discover what was created by an intelligent designer called God.
Logic of structure and quantity.
Interestingly, a essential belief in the rise of modern science was the Christian belief that mathematics, especially any mathematics that might describe this universe, was, and is, the product of the Mind of God.
And as Paul Davies observed, “All the early scientists, like Newton, were religious in one way or another. They saw their science as a means of uncovering traces of God’s handiwork in the universe. What we now call the laws of physics they regarded as God’s abstract creation: thoughts, so to speak, in the mind of God. So in doing science, they supposed, one might be able to glimpse the mind of God – an exhilarating and audacious claim.”
And as Ian H. Hutchinson noted in the following article on Faraday and Maxwell, “Lawfulness was not, in their thinking, inert, abstract, logical necessity, or complete reducibility to Cartesian mechanism; rather, it was an expectation they attributed to the existence of a divine lawgiver.”
In 1619, Johannes Kepler, shortly after discovering the laws of planetary motion, stated,
Likewise in 1687, Sir Isaac Newton, after discovering the law of universal gravitation, (which has been referred to as the first major unification in physics),
Likewise in 1687, Sir Isaac Newton, after discovering the law of universal gravitation, stated that, “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.,,,This Being governs all things, not as the soul of the world, but as Lord over all;”
It is also interesting to note that physicists today have regressed back to the “pre-scientific” belief that mathematics has an existence that is independent of the Mind of God.
As Paul Davies further explained, “Christians envisage God as upholding the natural order from beyond the universe, while physicists (today) think of their laws as inhabiting an abstract transcendent realm of perfect mathematical relationships.”
That physicists today “think of their laws as inhabiting an abstract transcendent realm of perfect mathematical relationships” and that mathematics is not ‘contingent’ upon the Mind of God for its existence, is, philosophically speaking, a major step backwards for today’s physicist compared to the Christian founders of modern science.
Physicists today, especially with the proof of Godel’s incompleteness theorems sitting right before them, simply have no basis for their belief that mathematics, all by its lonesome, can somehow function as a God substitute,
As the following article states, “Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous.”
Stephen Hawking himself, an atheist, honestly admitted that “Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”
As well, Steven Weinberg, also an atheist, also honestly admitted that, ” “I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that.”
In fact, there are an infinite number of mathematical theorems that could have described the universe but don’t, As Gregory Chaitin pointed out, “what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. ”
Mathematics, contrary to what the vast majority of theoretical physicists believe today, simply never will have the capacity within itself to function as a God substitute.
As Dr. Brice Gordon explains, “The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,,
Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”
As to “a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them” it is also interesting to note that ‘free will’, i.e. “a mind that can choose”, plays a fundamental role in Quantum Mechanics itself,
As Steven Weinberg explains, “In the instrumentalist approach (in quantum mechanics) humans are brought into the laws of nature at the most fundamental level.,,, the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.,,, In quantum mechanics these probabilities do not exist until people choose what to measure,,, Unlike the case of classical physics, a choice must be made,,,”
In fact Weinberg, again an atheist, rejected the instrumentalist approach precisely because “humans are brought into the laws of nature at the most fundamental level” and because it undermined the Darwinian worldview from within. Yet, regardless of how he and other atheists may prefer the world to behave, quantum mechanics itself could care less how atheists prefer the world to behave.
For instance, and as leading experimentalist Anton Zeilinger states in the following video, “what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”
The Kochen-Specker theorem undermines the determinism of atheistic materialists in the most fundamental way possible in that “it would not even be possible to place the information into the universe’s past in an ad hoc way.”
As well, with contextuality we find that, “In the quantum world, the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation”
Moreover, this recent 2019 experimental confirmation of the “Wigner’s Friend” thought experiment established that “measurement results,, must be understood relative to the observer who performed the measurement”.
On top of all that, although there have been several major loopholes in quantum mechanics over the past several decades that atheists have tried to appeal to in order to try to avoid the ‘spooky’ Theistic implications of quantum mechanics, over the past several years each of those major loopholes have each been closed one by one. The last major loophole that was left to be closed was the “setting independence” and/or the ‘free-will’ loophole:
And now Anton Zeilinger and company have recently, as of 2018, pushed the ‘free will loophole’ back to 7.8 billion years ago, thereby firmly establishing the ‘common sense’ fact that the free will choices of the experimenter in the quantum experiments are truly free and are not determined by any possible causal influences from the past for at least the last 7.8 billion years, and that the experimenters themselves are therefore shown to be truly free to choose whatever measurement settings in the experiments that he or she may so desire to choose so as to ‘logically’ probe whatever aspect of reality that he or she may be interested in probing.
Thus regardless of how Steven Weinberg and other atheists may prefer the universe to behave, with the closing of the last remaining free will loophole in quantum mechanics, “humans are (indeed) brought into the laws of nature at the most fundamental level”, and thus these recent findings from quantum mechanics directly undermine, as Weinberg himself stated, the “vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.”
Moreover allowing free will and/or Agent causality into the laws of physics at their most fundamental level has some fairly profound implications for us personally.
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:
To give us a small glimpse of the power that was involved in Christ’s resurrection from the dead, the following recent article found that, ”it would take 34 Thousand Billion Watts (34 trillion Watts) of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”
Verse:
So mathematics is good if it leads towards God but bad if it leads towards a multiverse?
Sev, there is no sound empirical warrant for a multiverse. By contrast, the ordering of the observed cosmos is akin to the working of a mind. KF
Sev claims that,
The multiverse, where it is mathematically held that an infinite number of Severskys exist, (as should be needless to say), commits epistemological and mathematical suicide:
Also of note:
The multiverse is just moar evidence for God. Materialism can’t account for a UNIverse and that means there isn’t any way it can account for a multiverse.
Roger Penrose describes his metaphysical world view as a tripartite one consisting of the physical world, the mental world and separate and distinct mathematical world. He goes on to explain that… ’there is the relationship between these three worlds which I regard, all three of them, as somewhat mysterious or very mysterious. I sometimes refer to this as “three worlds and three mysteries.” Mystery number one is how is it that the physical world does in fact accord with mathematics, and not just any mathematics but very sophisticated, subtle mathematics to such a fantastic degree of precision. That’s mystery number one.’
However, since Penrose is a non-theist (according to Wikipedia, which quotes a BBC interview) I don’t see that he has any other choice but to postulate the existence of a separate transcendent Platonic realm. But this is probably too high of a cost for other naturalists to pay (of course, it’s unthinkable for a died-in-the-wool materialist.) That’s no doubt why, as we have typically seen here before, a stubborn resistance to the idea that mathematics is discovered by several of our interlocutors. But if we reject the idea of a transcendent mathematical realm where does our mathematical knowledge and know-how come from? From our minds– which is an epiphenomena of our brains… which is the product of a long mindless evolutionary process. If you begin with those assumptions that’s where the logic leads you, therefore, mathematics must be a human invention. The problem is that you first need to prove that your metaphysical presuppositions are true or that they are more probably true than not.
On the other hand, here are several good reasons as to why I believe that mathematical truth is discovered not invented.
*1. Numbers have properties that do not appear to have been invented. For example, there some unsolved conjectures about prime numbers that are hard to explain if we are the inventors. Namely if we are the inventors why has no one been able to prove (or disprove) that the set of twin primes is infinite? Or why do the Goldbach conjecture and Riemann Hypothesis continue to be unsolved? Wouldn’t the putative inventors of mathematics be able to resolve these problems?
*2. The applicability of mathematics to the real world. For example, sometime ago, in an earlier thread I pointed out that “One of the most significant discoveries in science was the discovery of the inverse square law (credited to Kepler for light) which is derived directly from the geometry of a sphere. The ISL applies to both electromagnetism and gravity, though the force constants for each vary.”
https://www.thehighersidechatsplus.com/forums/media/inverse-square-law-and-wave-function.105/full?d=1503980290
Where would physics be without this discovery? And that’s only one example.
*3. It appears that the human mind and brain are preadapted to do mathematics. What immediate survival advantage would doing higher mathematics and doing it accurately have for a highly evolved species of hunter-gatherer apes?
*4. The universality of mathematics. SETI enthusiasts have suggested that we could use mathematics to communicate with ETI’s. For example, “In the 1985 science fiction novel Contact, Carl Sagan explored in some depth how a message might be constructed to allow communication with an alien civilization, using prime numbers as a starting point, followed by various universal principles and facts of mathematics and science.”
https://en.wikipedia.org/wiki/Communication_with_extraterrestrial_intelligence
How could mathematics be universal if it was invented by us?
*5. Historically mathematics set the stage for the scientific revolution. Kepler and Galileo and Newton were all mathematicians who believed that at its root the universe was mathematical. In other words, they began with the assumption that the universe could be described mathematically.
*6. Mathematics is grounded in rational deductive logic which is used in not only in the natural sciences but in criminal investigations and legal justice systems around the world.
*7. Mathematics is objectively true. For example, it doesn’t matter what your opinion is or what you believe about the following numbers: 32319, 32321, 32323, only one or two of them could be a prime numbers or none of them could be. However, your subjective opinion is irrelevant and there nothing you can do or believe to change the facts.
Freeman Dyson always has interesting and insightful things to say. I’m glad I had the chance to meet him and chat briefly with him a few years ago. Truly a genius.
Some time ago on another thread I wrote:
Or in terms of the principle of sufficient reason: If the universe is contingent (it had a beginning in space and time) then it lacks a sufficient reason for its own existence. Invoking the so-called multiverse does not solve this problem because a collection of contingent things, even a very large or infinite collection of contingent things is not sufficient to explain its own existence. That was Leibniz’s point in his argument refuting an infinite regress.
Also notice that for the atheist to argue that only contingent things exist he must smuggle in, or coopt, some theological concepts: infinite being, eternality and transcendence. For example, invoking the multiverse is an attempt to bring in an outside “transcendent” cause. Furthermore, it’s a purely metaphysical argument that is neither self-evidently true nor scientifically provable. Even if we are someday in the far distant future we are able to create artificial wormholes, as Kip Thorne suggest in his book, Black Holes & Time Warps, which he argues could theoretically tunnel through into another universe, how would we know that we are really in another universe? How could we ever know that there are an infinite number of other universes? In other words, are we supposed to accept (believe) the idea of the multiverse on faith? So then it appears that the claim that atheistic naturalism/materialism is more reasonable than theism is just so much pretension and posturing.
Furthermore, none of this explains why we as a species are “hardwired” to ask these kind of questions? Why do we feel so compelled to explain our own existence? Why, for example, does the atheist-materialist feel so compelled to explain away all possible explanation but his own? Or an incorrigible agnostic to claim absurdly that because he doesn’t know, therefore, nobody knows?
Has anyone ever witnessed the existence of a multiverse? Just like macro-evolution, it has never been witnessed. Without someone actually witnessing something, it cannot be a scientific theory. In order to be a valid theory, a hypothesis must be something that is witnessed and the results replicated.
Stephen Hawking in one of his later books claimed that the universe could “create itself from nothing.”
Ironically one of Hawking’s early collaborators, Roger Penrose, “who worked closely alongside Hawking in developing gravitational singularity theorems,” was highly critical of Hawking’s later work.
https://www.indcatholicnews.com/news.php?viewStory=16815
On the other hand, at least Hawking was honest enough try to start his argument with the succinct premise. The problem is that his premise that “the universe can create itself from nothing” is totally absurd. Any theory (metaphysical or scientific) which begins there is DOA. And obviously that doesn’t prove God is unnecessary as Hawking boasted. However, it does prove that there some highly educated intelligent people who believe some very foolish things.
john_a_designer @ 14
Hawking was a Darwinist. The universe creating itself is no more foolish than the belief that macro-evolution exists.
There are three big problems with the multiverse “theory:”
First, as some others have already pointed out, there is absolutely no evidence that a multiverse exists.
Second, it’s not a scientific theory but a metaphysical speculation which can only be accepted on the basis of faith.
Third, nobody has any idea how one universe could create another. Or, if there is some other mechanism for creating other universes, what is that mechanism?
Hawking was a believer in Darwinism. The concept that the cosmos is generating itself is no more ridiculous than the conviction that macro-evolution is taking place.
And then there’s the supra-multiverse(tm) that generates multiverses. It’s multiverses all the way up . . .
-Q