Joined: Oct. 2005
December 30, 2020 at 7:04 am
As to this question:
Even if you don’t believe in God, can you at least believe that 2+2=4?
Well, it turns out that, via Godel’s incompleteness theorem, that although atheists may believe 2+2+4, atheists simply have no way of proving that 2+2=4.
Godel’s incompleteness theorem was born out of the fact that mathematicians could not mathematically ‘prove’ that 1+1=2. You can pick up some of the details about that fact at 10:00 minute mark of the following video
BBC-Dangerous Knowledge – Part 3 of 5
So the answer to the question, “Even if you don’t believe in God, can you at least believe that 2+2=4?”, turns out to be, “No. not really. Without God, you simply have no way of ‘knowing’ that 2+2 really does equal 4.”
As Vern Poythress, (Doctorate in Theology, PhD in Mathematics, Harvard), described the mathematical dilemma that Godel put Atheists in, “Because of the above difficulties, anti-theistic philosophy of mathematics is condemned to oscillate, much as we have done in our argument, between the poles of a priori knowledge and a posteriori knowledge. Why? It will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties. In sections 22-23 we shall see how the Biblical view furnishes us with a real solution to the problem of “knowing” that 2 + 2 = 4 and knowing that S is true.”
A BIBLICAL VIEW OF MATHEMATICS
Vern Poythress – Doctorate in theology, PhD in Mathematics (Harvard)
15. Implications of Gödel’s proof
B. Metaphysical problems of anti-theistic mathematics: unity and plurality
Excerpt: Because of the above difficulties, anti-theistic philosophy of mathematics is condemned to oscillate, much as we have done in our argument, between the poles of a priori knowledge and a posteriori knowledge. Why? It will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties. In sections 22-23 we shall see how the Biblical view furnishes us with a real solution to the problem of “knowing” that 2 + 2 = 4 and knowing that S is true.
As to, “(anti-theistic philosophy of mathematics) will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties.”,,,,
You don’t have to take Vern Poythress’s word that atheists will forever be stymied In their efforts to provide an explanation as to why we have a intuitive capacity to understand mathematics, nor why the external world might be describable by mathematics, Both Wigner and Einstein are on record as to regarding such a situation to be a ‘miracle’,
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
In fact, Einstein went so far as to chastise ‘professional atheists’ in 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.”
Interestingly, a essential belief in the rise of modern science in Medieval Christian Europe 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.”
“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.”
– Paul Davies
The following quote succinctly captures how the Christian founders of modern science viewed any mathematics that might describe this universe as being the product of the Mind of God.
In 1619, Johannes Kepler, shortly after discovering the mathematical laws of planetary motion, stated,
“O, Almighty God, I am thinking Thy thoughts after Thee!”
– Johannes Kepler, 1619, The Harmonies of the World.
Moreover, besides viewing any mathematics that might describe this universe as being the product of the Mind of God, and that view of mathematics being essential to the rise of modern science in Medieval Christian Europe,,, besides all that, when we rightly allow the Mind of God ‘back’ into science, then a successful resolution to the most enigmatic problem facing theoretical physicists today readily pops out for us.
Namely, the most enigmatic problem facing theoretical physicists today is that we do not have just one mathematical theory describing the universe, but we have two mathematical theories that describe this universe, i.e. Quantum Mechanics and General Relativity, and these two theories simply refuse to be mathematically reconciled with each other.
In fact, there is an infinite mathematical divide that separates the two theories.
As Sera Cremonini states, ” the quantum version of Einstein’s general relativity is “nonrenormalizable.”,,, “The problem with a quantum version of general relativity is that the calculations that would describe interactions of very energetic gravitons — the quantized units of gravity — would have infinitely many infinite terms. You would need to add infinitely many counterterms in a never-ending process. Renormalization would fail.,,,”
Why Gravity Is Not Like the Other Forces
We asked four physicists why gravity stands out among the forces of nature. We got four different answers.
Excerpt: the quantum version of Einstein’s general relativity is “nonrenormalizable.”,,,
In quantum theories, infinite terms appear when you try to calculate how very energetic particles scatter off each other and interact. In theories that are renormalizable — which include the theories describing all the forces of nature other than gravity — we can remove these infinities in a rigorous way by appropriately adding other quantities that effectively cancel them, so-called counterterms. This renormalization process leads to physically sensible answers that agree with experiments to a very high degree of accuracy.
The problem with a quantum version of general relativity is that the calculations that would describe interactions of very energetic gravitons — the quantized units of gravity — would have infinitely many infinite terms. You would need to add infinitely many counterterms in a never-ending process. Renormalization would fail.,,,
Sera Cremonini – theoretical physicist – Lehigh University
Likewise, Professor Jeremy Bernstein states the situation as such, “there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite.”
Quantum Leaps – Jeremy Bernstein – October 19, 2018
Excerpt: Divergent series notwithstanding, quantum electrodynamics yielded results of remarkable accuracy. Consider the magnetic moment of the electron. This calculation, which has been calculated up to the fifth order in ?, agrees with experiment to ten parts in a billion. If one continued the calculation to higher and higher orders, at some point the series would begin to break down. There is no sign of that as yet. Why not carry out a similar program for gravitation? One can readily write down the Feynman graphs that represent the terms in the expansion. Yet there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite.
The theory is not renormalizable.
Jeremy Bernstein is professor emeritus of physics at the Stevens Institute of Technology.
December 30, 2020 at 7:06 am
Moreover, when theorists try to combine the two theories, i.e. Quantum Mechanics and General Relativity, then the resulting theory predicts that spacetime, atoms, and even the universe itself should all be literally blown apart. Here are a few references that get this point across.
“There are serious problems with the traditional view that the world is a space-time continuum. Quantum field theory and general relativity contradict each other. The notion of space-time breaks down at very small distances, because extremely massive quantum fluctuations (virtual particle/antiparticle pairs) should provoke black holes and space-time should be torn apart, which doesn’t actually happen.”
– Gregory J. Chaitin , Francisco A. Doria, and Newton C. a. Da Costa – Goedel’s Way: Exploits into an Undecidable World
“In order for quantum mechanics and relativity theory to be internally self-consistent [Seeking consistency between quantum mechanics and relativity theory is the major task theoretical physicists have been grappling with since quantum mechanics emerged], the physical vacuum has to contain 10^94 grams equivalent of energy per cubic centimeter. What that means is, if you take just a single hydrogen atom, which is one proton and one electron and all the rest of the atom is ‘empty space,’ if you take just that volume of empty space, … you find that you end up with a trillion times as much vacuum energy as all the electromagnetic energy in all the planets, all the stars, and all the cosmic dust in a sphere of radius 15 billion light-years.”
To summarize, the subtle energy in the vacuum space of a single hydrogen atom is as great as all the electromagnetic energy found in everything within 15 billion light-years of our space-time cosmos.” ,,,
Dr. William Tiller – Human Intention
Cosmic coincidence spotted – Philip Ball – 2008
Excerpt: One interpretation of dark energy is that it results from the energy of empty space, called vacuum energy. The laws of quantum physics imply that empty space is not empty at all, but filled with particles popping in and out of existence. This particle ‘fizz’ should push objects apart, just as dark energy seems to require. But the theoretical value of this energy is immense — so huge that it should blow atoms apart, rather than just causing the Universe to accelerate.
Physicists think that some unknown force nearly perfectly cancels out the vacuum energy, leaving only the amount seen as dark energy to push things apart. This cancellation is imperfect to an absurdly fine margin: the unknown ‘energy’ differs from the vacuum energy by just one part in 10^122. It seems incredible that any physical mechanism could be so finely poised as to reduce the vacuum energy to within a whisker of zero, but it seems to be so.
– per nature
The 2 most dangerous numbers in the universe are threatening the end of physics – Jessica Orwig – Jan. 14, 2016
Excerpt: Dangerous No. 2: The strength of dark energy
,,, you should be able to sum up all the energy of empty space to get a value representing the strength of dark energy. And although theoretical physicists have done so, there’s one gigantic problem with their answer:
“Dark energy should be 10^120 times stronger than the value we observe from astronomy,” Cliff said. “This is a number so mind-boggling huge that it’s impossible to get your head around … this number is bigger than any number in astronomy — it’s a thousand-trillion-trillion-trillion times bigger than the number of atoms in the universe. That’s a pretty bad prediction.”
On the bright side, we’re lucky that dark energy is smaller than theorists predict. If it followed our theoretical models, then the repulsive force of dark energy would be so huge that it would literally rip our universe apart. The fundamental forces that bind atoms together would be powerless against it and nothing could ever form — galaxies, stars, planets, and life as we know it would not exist.
And yet, despite both theories contradicting each other to the point of literally blowing the universe apart, the fact remains that quantum mechanics and general relativity are both tested to extreme levels of precision, (in fact, both general relativity and quantum mechanics are consider, by a wide margin, to be our most successful theories ever in the history of science),
The Most Precisely Tested Theory in the History of Science – May 5, 2011
Excerpt: So, which of the two (general relativity or QED) is The Most Precisely Tested Theory in the History of Science?
It’s a little tough to quantify a title like that, but I think relativity can claim to have tested the smallest effects. Things like the aluminum ion clock experiments showing shifts in the rate of a clock set moving at a few m/s, or raised by a foot, measure relativistic shifts of a few parts in 10^16. That is, if one clock ticks 10,000,000,000,000,000 times, the other ticks 9,999,999,999,999,999 times. That’s an impressively tiny effect, but the measured value is in good agreement with the predictions of relativity.
In the end, though, I have to give the nod to QED, because while the absolute effects in relativity may be smaller, the precision of the measurements in QED is more impressive. Experimental tests of relativity measure tiny shifts, but to only a few decimal places. Experimental tests of QED measure small shifts, but to an absurd number of decimal places. The most impressive of these is the “anomalous magnetic moment of the electron,” expressed is terms of a number g whose best measured value is:
g/2 = 1.001 159 652 180 73 (28)
Depending on how you want to count it, that’s either 11 or 14 digits of precision (the value you would expect without QED is exactly 1, so in some sense, the shift really starts with the first non-zero decimal place), which is just incredible. And QED correctly predicts all those decimal places (at least to within the measurement uncertainty, given by the two digits in parentheses at the end of that).
And since quantum mechanics and general relativity are both tested to such an extreme level of precision, (and we can thus have a very high level of confidence that both theories are, in fact, true mathematical descriptions of reality), and since Godel’s incompleteness theorem itself requires something to be ‘outside the circle’ of mathematics (Hawking),,”,,,
“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”. Thus, based on the position that an equation cannot prove itself, the constructs are based on assumptions some of which will be unprovable.”
Stephen Hawking & Leonard Miodinow, The Grand Design (2010)
,,,, since all that is true, then it is fairly safe to assume that there must be something very powerful that must be holding the universe together in order to keep it from blowing itself apart. ,,,
For the Christian, this theoretical finding from our very best theories in science, (i.e. that something very powerful must be ‘outside the universe’ that is holding this universe together), should not be all that surprising to find out. Christianity, a couple of millennium before this ‘infinite’ conflict between the General Relativity and Quantum Mechanics was even known about, predicted that Christ is before all things, and ‘in him all things hold together,,,’
He is before all things, and in him all things hold together.
Dr. William Dembski in this following comment, although he was not directly addressing the ‘infinite’ conflict between General Relativity and Quantum Mechanics, offers this insight into what the ‘unification’ of infinite God with finite man might look like mathematically:
The End Of Christianity – Finding a Good God in an Evil World – Pg.31
William Dembski PhDs. Mathematics and Theology
Excerpt: “In mathematics there are two ways to go to infinity. One is to grow large without measure. The other is to form a fraction in which the denominator goes to zero. The Cross is a path of humility in which the infinite God becomes finite and then contracts to zero, only to resurrect and thereby unite a finite humanity within a newfound infinity.”
And being found in appearance as a man, He humbled Himself and became obedient to the point of death, even the death of the cross. Therefore God also has highly exalted Him and given Him the name which is above every name,
Moreover, if we rightly allow 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), if we rightly allow the Agent causality of God ‘back’ into physics, then that 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:
November 2019 – despite the fact that virtually everyone, including the vast majority of Christians, hold that the Copernican Principle is unquestionably true, the fact of the matter is that the Copernican Principle is now empirically shown, (via quantum mechanics and general relativity, etc..), to be a false assumption.
(February 19, 2019) To support Isabel Piczek’s claim that the Shroud of Turin does indeed reveal a true ‘event horizon’, the following study states that ‘The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image.’,,,
Moreover, besides gravity being dealt with, the shroud also gives us evidence that Quantum Mechanics was dealt with. In the following paper, it was found that it was not possible to describe the image formation on the Shroud in classical terms but they found it necessary to describe the formation of the image on the Shroud in discrete quantum terms.
The evidence for the Shroud’s authenticity keeps growing. (Timeline of facts) – November 08, 2019
What Is the Shroud of Turin? Facts & History Everyone Should Know – Myra Adams and Russ Breault
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 (Trillion) Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”
Astonishing discovery at Christ’s tomb supports Turin Shroud – NOV 26TH 2016
Excerpt: The first attempts made to reproduce the face on the Shroud by radiation, used a CO2 laser which produced an image on a linen fabric that is similar at a macroscopic level. However, microscopic analysis showed a coloring that is too deep and many charred linen threads, features that are incompatible with the Shroud image. Instead, the results of ENEA “show that a short and intense burst of VUV directional radiation can color a linen cloth so as to reproduce many of the peculiar characteristics of the body image on the Shroud of Turin, including shades of color, the surface color of the fibrils of the outer linen fabric, and the absence of fluorescence”.
‘However, Enea scientists warn, “it should be noted that the total power of VUV radiations required to instantly color the surface of linen that corresponds to a human of average height, body surface area equal to = 2000 MW/cm2 17000 cm2 = 34 thousand billion watts makes it impractical today to reproduce the entire Shroud image using a single laser excimer, since this power cannot be produced by any VUV light source built to date (of note: the most powerful available on the market today only capable of several billion watts)”.
The ENEA study of the Holy Shroud of Turin concluded that it would take 34 Thousand Billion Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.
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.
Thus in conclusion, and although much more could be said about this topic, the main impasse for modern day physicists today in finding the ‘theory of everything’, i.e. a unification between General Relativity and Quantum Mechanics, apparently, seems to be that modern day physicists have, basically, completely forgotten the philosophical, i.e. Christian, roots that gave rise to modern science in the first place, (i.e. That the universe, and math itself, are both the result of the ‘thoughts of God’), and have instead regressed back into ancient Greek rationalism in which math served as a rival to God rather than a path to Him.
KEEP IT SIMPLE – by Edward Feser – April 2020
Excerpt: 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.
There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind, including the divine mind.
In short, modern day theoretical physicists have apparently, for the most part, completely forgotten the philosophical presuppositions that enabled the Christian founders of modern science in medieval Christian Europe to make their breakthrough into modern science the first place. Namely, that any mathematics that might describe this universe must be the product of the Mind of God,,,
“O, Almighty God, I am thinking Thy thoughts after Thee!”
Johannes Kepler – 1619 – stated shortly after he discovered the laws of planetary motion.
He seems sane