From William Lane Craig’s *Reasonable Faith.* With special apologies, of course, to the war on math people:

Think about it… Mathematical entities like numbers, sets, and equations are non-physical and abstract. They can’t cause anything. Yet, for some reason, the physical universe operates…mathematically.

As Galileo put it, “The book of nature is written in the language of mathematics.”

“Scientists do not use mathematics merely as a convenient way of organising the data. They believe that mathematical relationships reflect real aspects of the physical world. Science relies on the assumption that we live in an ordered Universe that is subject to precise mathematical laws. Thus, the laws of physics, … are all expressed as mathematical equations.” – Paul Davies

So, how do we explain the astonishing applicability of math to the physical world?

Those who think math doesn’t apply have probably bought into the oppressive idea that 2 + 2 = 4 And all social ills can be traced to that awful myth. 😉

*Hat tip:* Philip Cunningham

I encourage everyone interested in this subject to read this great (and short) paper on it:

On the Logic of Being and Wigner’s Astonishment Regarding the Applicability of Mathematics

Think about it a different way. The Universe works in certain ways and we have invented a very flexible and powerful language which we can use to model how it works. Like a map, it abstracts key elements of what we observe and uses them to create a model of what is there and just as the map is not the territory so is a model not the same as what is being modeled.

Gödel’s incompleteness theorems should be considered as well. The result is that we choose the math that seems to be the most applicable. Then, we amaze ourselves at how precisely it models the physics of a clockwork universe. And finally, we find unsettling and irreconcilable anomalies that force us to choose different math so we first enter a science fantasy phase. Rinse and repeat.

Just saying.

-Q

Seversky @ 2

The universe works a certain way, since it was designed to work in a certain way. Without design, nothing would work. There would be no order, since order cannot arise out of chaos.

@ Seversky @ 2

You haven’t a clue what you are talking about, Seversky.

Mathematics was not “invented” – it was discovered and aspects are still being discovered.

And it is nothing at all like a map – a mathematical model contains relationships (that what the equals, =, sign shows) and it contains variables., neither of which are present in the common understanding of a map.

In general I agree with

Seversky; the question about whether mathematics is discovered or invented is almost purely philosophical and you can easily ‘do’ or apply mathematics without worrying about its origins at all.I believe the notation, the order we discover theorems, the problems that guide what work is done are historical and cultural. But I believe the underlying mathematics is constant, always. I think it has to be. But, that is just my opinion.

I think the map analogy is pretty good: a map contains arbitrary and abstract symbols which are placeholders for other quantities and objects. Not all of them physical by the way: a one-way traffic indicator is separate from the line indicating a street or road and represents an aspect of the road that is not inherent in the road itself.

Variables in mathematical equations represent unknowns which are usually fairly well constrained to a particular value or function or operator; they you try and figure out which values or functions or whatever satisfy the equation.

So, the analogy is not perfect but a map and an equation are both arbitrary, abstract representations of other things.

BobRyan: There would be no order, since order cannot arise out of chaos.Who said the universe started out as chaos? I don’t think anyone says such a thing.

You don’t know what you are talking about either, JVL.

Mathematical relationships existed long before they were discovered. Pythagoras described the relationship between the sides of a right angled triangle on a flat plain – he didn’t invent it.

By stretching commonsense to breaking point someone might possibly argue that discovering the PROOF that proves the validity of a theorem is actually an “invention,” but if you said that Andrew Wiles “invented” his proof of Fermat’s Last Theorem you would be laughed at for years and rightly so.

The comparison given with a map is is simplistic to the point of craziness – produce an equation that describes, say, a street scene, make up your own variables.

A crucial belief that allowed the rise of modern science in medieval Christian Europe, was not only the Christian’s belief that the universe itself is contingent upon the Mind of God for its existence,,,

,,, was not only the Christian’s belief that the universe itself is contingent upon the Mind of God for its existence, but was also the Christian’s belief that any mathematics that might describe this universe was also contingent upon the mind of God for its existence.

As Edward Fesser notes in the following article, for Christian scholastic philosophers of the medieval period “Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts,” whereas for ancient Greek philosophers, “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.” As Dr. Feser noted, in Platonic thought, ‘the mathematical realm is a rival to God rather than a path to him.’

As Peter S Williams noted, “the Greeks held that this order is necessary and that one can therefore deduce its structure from first principles. Only biblical thought held that God created both form and matter, meaning that the world did not have to be as it is and that the details of its order can be discovered only by observation.”

And as Paul Davies noted, ” What we now call the laws of physics they (the Christian founders of modern science) 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.”

As an example of how the Christian founders of modern science viewed any mathematics that might describe this universe as being contingent upon the Mind of God, the following quote is perhaps the most direct. Shortly after discovering the mathematical laws of planetary motion, Kepler stated, ““O, Almighty God, I am thinking Thy thoughts after Thee!”

Likewise in 1687, Sir Isaac Newton, after discovering the mathematical law of universal gravitation, (which has been referred to as the first major unification in physics), 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;”

As well, 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.,,, For them, the coherence of nature resulted from its origin in the mind of its Creator.”

As well in quantum mechanics and relativity, we find that both Eugene Wigner and Einstein are on record as to regarding it as a ‘miracle’ that mathematics is applicable to the universe. In fact, Einstein went so far as to disparage ‘professional atheists’ when he called it a miracle:

Godel’s incompleteness theorem adds considerable weight to the Christian’s belief that mathematics, especially any mathematics that might describe this universe, must be contingent upon the Mind of God for its existence. As Stephen Hawking himself honestly confessed, “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”.”

And as Stanley Jaki noted,

Bottom line, due to Godel’s incompleteness theorem(s), even if a single overarching mathematical theory happened to be found that described the universe (instead of the two that we currently have, (i.e. General Relativity and Quantum Mechanics), we still would find it necessary to postulate God for why that particular equation, out of an infinity of other possible mathematical descriptions, happened to describe the universe:

Yet we do not have just one mathematical ‘theory of everything’ that describes the universe. We have two theories, General Relativity and Quantum Mechanics, that simply refuse to unified into a single overarching ‘theory of everything’.

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.,,,”

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.”

Moreover, when theorists try to combine the two theories, 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.

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 to be our most successful theories ever in the history of science),

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),,” 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 the ‘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,,,’

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:

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:

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 of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”

Verse:

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’, 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 regressed back into ancient Greek rationalism in which math served as a rival to God rather than a path to Him.

In short, modern day theoretical physicists have apparently, for the most part, forgotten the philosophical presuppositions that enabled the Christian founders of modern science to make their breakthrough into modern science in. the first place.

Seversky & JVL, you would profit from reading the paper JB links at 1. Mathematics has a substance embedded in reality expressed in possible worlds including this actual one. There is a study that in key parts explores and discovers patterns, features, entities and structures, antecedent to axiomatisations. Axiomatisations on key points, are accountable to the body of facts [eg || + ||| –> ||||| ] and insofar as they reflect the structure well, allow us to further explore. Where, mathematics as study can then be seen as the study of the logic of structure and quantity. Axiom systems, which perhaps capture a too central part of modern conceptions are logic world constructs. Insofar as they reflect necessary being aspects of structure and quantity they apply to any possible world. In other aspects, there is more flexibility and they may or may not reflect our world. Here we blend over into scientific laws, theories and models . . . including those useful as they are good enough for practical work. KF

Belfast: Mathematical relationships existed long before they were discovered. Pythagoras described the relationship between the sides of a right angled triangle on a flat plain – he didn’t invent it.Umm, I agreed with that. Did you actually read what I wrote?

The comparison given with a map is is simplistic to the point of craziness – produce an equation that describes, say, a street scene, make up your own variables.I admitted the analogy wasn’t perfect but a map and an equation have some similar characteristics.

In some sense vector graphics are groups of equations describing an image. So, if you took a photo of a street scene, converted it to vector graphics you would get a series of equations.

What JVL is saying is like saying whether or not Stonehenge was invented or discovered is philosophical. And we know that is total nonsense. Mathematics work only because the universe was Intelligently Designed using mathematics.

ET: What JVL is saying is like saying whether or not Stonehenge was invented or discovered is philosophical.I was talking about mathematics not inanimate physical objects.

And we know that is total nonsense. Mathematics work only because the universe was Intelligently Designed using mathematics.We don’t know that. Just asserting it’s true proves nothing. And don’t get snippy about the word prove, in mathematics you can prove things.

Seversky: “the map is not the territory so is a model not the same as what is being modeled.”

Exactly. That is why mathematics is not causative. That is why saying, as Hawking did, that gravitation is a result of the M-theory is nonsensical. That is why attributing the causative power to the the laws of nature is nonsensical.

The laws of nature are nothing but a description of natural regularities. The laws of nature cannot cause anything to happen. As Lennox aptly said, the laws of economics did not put a single penny into my bank account.

Nature had a beginning (which actually seems to be a scientific consensus today). However, its beginning is

necessarilysuper-natural, otherwise there is a contradiction. Science can cope with providing descriptions of how the already existing matter/energy behave over time but, necessarily, being applied to the question of how it all came to be, science is on fool’s errand and reduces to sci-fi.ES, though logic of structure and quantity is not actively causal, logical impossibility of being due to contradictory core characteristics — square circles — and necessity of being tracing to say that a distinct possible world is just that, distinct and possible, will constrain what is or can be. Thus we come to structures and quantities inherent in distinct possible worlds, thus necessary structured frameworks that define the core of mathematics. See the paper linked at 1. KF

JVL:

It still applies.

Nice quote-mine. Are you 3 years old?

Neither mathematics nor living organisms would exist if the universe wasn’t intelligently designed using mathematics. Mathematics is directly linked to the laws that govern the universe.

JVL@15

“We don’t know that. Just asserting it’s true proves nothing. And don’t get snippy about the word prove, in mathematics you can prove things”

What other suggestions do you have, considering that nothing comes from absolutely nothing?

Bornagain77 @9 and 10,

Great answer! The Logos forms, ties together, and maintains two currently incompatible mathematical descriptions of reality. KF @12 articulates this concept excellently in mathematical terms!

Regarding KF @14, Let me agree that the mathematics identifies a relationship between components similar to a state diagram. In two senses, it’s not causal. In other words, in one sense the relationships could not have caused themselves, and in the other sense, a state diagram is static without a push. But . . .

The problem with JVL’s assertion is that “inanimate physical objects” ARE fundamentally mathematical probabilities according to quantum mechanics!

But to have probabilities, including quantum fluctuations, one needs Time. No Time equals no probabilities or fluctuations. According to Einstein, Space and Time are part of a single, unified manifold. Once you have space-time, you can now have mathematical probabilities that manifest themselves as “quantum foam” or mass-energy.

Information and logic govern these. Reminds me of Genesis 1:1-5 and John 1:1-3.

-Q

ET: It still applies.Why? On what grounds?

Nice quote-mine. Are you 3 years old?I offer my opinion and you accuse me of quote mining?

Neither mathematics nor living organisms would exist if the universe wasn’t intelligently designed using mathematics. Mathematics is directly linked to the laws that govern the universe.Again, this is pure assertion with no hard evidence to back it up. I appreciate that this is your opinion but it is not fact. We don’t know.

Kushanto: What other suggestions do you have, considering that nothing comes from absolutely nothing?I don’t have any other suggestions; I am merely pointing out that we don’t know. AND who ever said that nothing came from nothing?

Querius: The Logos forms, ties together, and maintains two currently incompatible mathematical descriptions of reality.What two descriptions are those?

The problem with JVL’s assertion is that “inanimate physical objects” ARE fundamentally mathematical probabilities according to quantum mechanics!Show me the work behind this assertion.

But to have probabilities, including quantum fluctuations, one needs Time. No Time equals no probabilities or fluctuations. According to Einstein, Space and Time are part of a single, unified manifold. Once you have space-time, you can now have mathematical probabilities that manifest themselves as “quantum foam” or mass-energy.For example?

JVL

Asinus asinum fricat.Seversky

Under evo-materialism,

we have invented nothing.Certain brain structures/ neurons have been “selected” because MAGICALLY (materialism’s key word) they “produced mathematics”.Or even worse, they are “spandrels” (not even f***ng selected, just “free-riders”) that MAGICALLY (materialism’s key word) “create maths”.

How the hell can a brain “create mathematics”? What neurochemicals are “math-creators”? Does the brain “secrete” 2+2? Does an accountant

(homunculi)live inside our heads? And more important: does he/she get paid a fair wage?Materialism= magical non-sense.

JVL,

You might want to read some books on quantum mechanics and general relativity. I’m not going to write one for you in a reply. LOL

-Q

The reductive materialism that Darwinian evolution is based upon is simply a non-starter for ever explaining, number 1, the existence of the mathematical laws of the universe,,

,,, and the reductive materialism that Darwinian evolution is based upon is also a non-starter for ever explaining, number 2, why man, as a supposedly purely material being, has the capacity within himself to comprehend this immaterial realm of mathematics (and logic).

The fact that man himself can comprehend this transcendent, beyond space and time, ‘Platonic world’ of mathematics, offers fairly compelling evidence, in and of itself, that man must also possess an immaterial mind and soul.

As Charles Darwin’s contemporary, Alfred Russel Wallace himself stated, “Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation.”

And as Michael Egnor stated, “Human rationality is different because it is immaterial. Contemplation of universals cannot have material instantiation, because universals themselves are not material and cannot be instantiated in matter.,, We are more different from apes than apes are from viruses. Our difference is a metaphysical chasm,,,”

Verse:

Moreover, it is not only that Darwinian materialists lack an explanation for why the universe is described by mathematics, or for why we have the capacity within ourselves to comprehend this immaterial world of mathematics, it is that the materialism that undergirds Darwinian thought actually denies the existence of anything beyond the material realm. i.e. Darwinian materialism actually denies the existence of immaterial mathematics!

And seeing that mathematics undergirds all of science, engineering, and technology, and seeing that the reductive materialism that Darwinian evolution rests upon actually denies the very existence of immaterial mathematics, then, of course, Darwinian materialism immediately disqualifies itself from ever being considered a truly ‘scientific’ worldview in the first place.

Moreover, Darwinian atheists may not like it one bit, but our use of immaterial mathematics to describe the laws of the universe is VERY harmonious to a Theistic view of reality. As Paul Davies explained,

And as David Berlinski stated, “There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time….”

Verse and quotes: