Tag Archives: Physics

William Lane Craig on the unexpected applicability of mathematics to nature

You might remember that Dr. Craig used a new argument in his debate with Lawrence Krauss in Melbourne, Australia.

My notes on the debate record it thus:

The unreasonable effectiveness of mathematics:

  • The underlying structure of nature is mathematical – mathematics is applicable to nature
  • Mathematical objects can either be abstract objects or useful fiction
  • Either way, there is no reason to expect that nature should be linked to abstract objects or fictions
  • But a divine mind that wants humans to understand nature is a better explanation for what we see

And now Dr. Craig has expanded on it in the Q&A section of his Reasonable Faith web site.

The question:

Dear Dr Craig

Firstly can I thank you for all your work. My faith in Christ has been enormously strengthened through studying your work in apologetics in particular and I have grown in confidence in my Christian witness.

My question relates to numbers and mathematics as a whole. On the Defenders podcast you state that as God is the only self-existent, necessary being, numbers and mathematical objects, whilst being useful, don’t actually exist as these too would exist necessarily and independently of God. If this is the case, how can it be that mathematics is so easily applied to the natural world? Surely if mathematics only existed in our minds, we would expect to see no correlation between it and how the physical world actually is?

Michael

United Kingdom

Excerpt from the answer:

As philosopher of mathematics Mary Leng points out, for the non-theistic realist, the fact that physical reality behaves in line with the dictates of acausal mathematical entities existing beyond space and time is “a happy coincidence” (Mathematics and Reality [Oxford: Oxford University Press, 2010], p. 239). Think about it: If, per impossibile, all the abstract objects in the mathematical realm were to disappear overnight, there would be no effect on the physical world. This is simply to reiterate that abstract objects are causally inert. The idea that realism somehow accounts for the applicability of mathematics “is actually very counterintuitive,” muses Mark Balaguer, a philosopher of mathematics. “The idea here is that in order to believe that the physical world has the nature that empirical science assigns to it, I have to believe that there are causally inert mathematical objects, existing outside of spacetime,” an idea which is inherently implausible (Platonism and Anti-Platonism in Mathematics [New York: Oxford University Press, 1998], p. 136).

By contrast, the theistic realist can argue that God has fashioned the world on the structure of the mathematical objects. This is essentially what Plato believed. The world has mathematical structure as a result.

This argument was also made by mechanical engineering professor Walter Bradley in a lecture he gave on scientific evidence for an intelligent designer. You can read an essay that covers some of the material in that lecture at Leadership University.

Excerpt:

The physical universe is surprising in the simple mathematical form it assumes. All the basic laws of physics and fundamental relationships can be described on one side of one sheet of paper because they are so few in number and so simple in form (see table 1.1).

[…]It has been widely recognized for some time that nature assumes a form that is elegantly described by a relatively small number of simple, mathematical relationships, as previously noted in table 1.1. None of the various proposals presented later in this chapter to explain the complexity of the universe address this issue. Albert Einstein in a letter to a friend expressed his amazement that the universe takes such a form (Einstein 1956), saying:

You find it strange that I consider the comprehensibility of the world to the degree that we may speak of such comprehensibility as a miracle or an eternal mystery. Well, a priori one should expect a chaotic world which cannot be in any way grasped through thought. . . . The kind of order created, for example, by Newton’s theory of gravity is of quite a different kind. Even if the axioms of the theory are posited by a human being, the success of such an enterprise presupposes an order in the objective world of a high degree which one has no a priori right to expect. That is the “miracle” which grows increasingly persuasive with the increasing development of knowledge.

Alexander Polykov (1986), one of the top physicists in Russia, commenting on the mathematical character of the universe, said: “We know that nature is described by the best of all possible mathematics because God created it.” Paul Davies, an astrophysicist from England, says, “The equations of physics have in them incredible simplicity, elegance and beauty. That in itself is sufficient to prove to me that there must be a God who is responsible for these laws and responsible for the universe” (Davies 1984). Successful development of a unified field theory in the future would only add to this remarkable situation, further reducing the number of equations required to describe nature, indicating even further unity and integration in the natural phenomena than have been observed to date.

The whole paper that started this off is called “The Unreasonable Effectiveness of Mathematics”, and it is a must read for advanced Christian apologists. You can read the whole thing here.

Positive arguments for Christian theism

Why does God allow so much natural evil from earthquakes?

My friend Eric Chabot of Ratio Christi shared this video with me, which features chemist Fazale Rana.

The video runs under 4 minutes:

Basically, there was an atheist who challenged the idea that nature is designed because there are things in nature which cause suffering, like earthquakes and volcanoes.

Now the first thing to note is that atheists commonly think that God’s job is to make humans happy. If he doesn’t make humans feel happy – regardless of their knowledge of him and relationship with him – then he is a big failure. Many atheists think that, it is one of the most common reasons why people become atheists. But of course anyone who reads the Bible and reads the story of Jesus knows that the purpose of life on God’s view is for humans to know him and to be disciples of a suffering Messiah who sacrifices himself in order to obey God the Father.  So that’s the first thing to say – purpose of life not happiness, but knowledge of God and being a disciple of Jesus. This may involve all kinds of suffering, and that’s to be expected.

Second, there is a response to the problem of evil based on the necessity of natural laws. The argument goes that you can’t have genuine morality without a predictable, knowable system of natural laws.

But I want to talk about something different in this post. In the video, Dr. Rana thinks that many of the things that cause suffering in the natural world are actually necessary for life to exist at all. He provides the example of plate tectonics in his video above, and I want to take that one and add to it the example of heavy element production and the stellar lifecycle. These are both from a book called “Rare Earth”, which is written by two non-Christians – Peter Ward and Donald Brownlee, but I’ll link to web sites to make the case.

Plate tectonics.

Here’s an article from Reasons to Believe by Dr. David Rogstad, who has a PhD in physics from Caltech – the top school for experimental science. The article not only goes over the basic plate tectonics to carbonate-silicate cycle connection, but it adds a newer discovery to boot.

Excerpt:

Earthquakes are a byproduct of plate tectonics, a theory in geology developed in recent years for explaining motions near the surface of the Earth. One of the benefits from plate tectonics is that Earth maintains the right levels of carbon dioxide (CO2) in the atmosphere to compensate for the Sun’s increasing luminosity. This is accomplished by what is called the carbonate-silicate cycle. CO2 is removed from the atmosphere through weathering. The weathered products are eventually drawn into the Earth’s interior via plate tectonics. Processes inside the Earth’s interior release the CO2 back into the atmosphere via volcanoes. While all aspects of this mechanism are not yet fully understood, it has been instrumental in providing a stable environment for life on the Earth for billions of years.

New research provides yet another component that appears fine-tuned for life. In a letter in the September 27, 2007 issue of Nature together with a corresponding news release from the University of Bonn, Arno Rohrbach and his colleagues have discussed another mechanism similar to the carbonate-silicate cycle. It also depends on plate tectonics but, in this case, the mechanism controls the amount of oxygen on the surface of the Earth.

Oxygen becomes bound up in various oxides which are then drawn into the Earth’s interior, where various processes result in its being incorporated into an exotic mineral called majorite. The results reported in this letter established that majorite functions as a kind of “reservoir” for oxygen, and when the majorite ascends nearer to the surface of the Earth it breaks down and releases its oxygen. Some of this oxygen also binds with hydrogen released from the interior of the Earth to form water. The authors have referred to the whole process as an “oxygen elevator.”

They go on to say that “without the ‘oxygen elevator’ in its mantle the Earth would probably be a barren planet hostile to life. According to our findings, planets below a certain size hardly have any chance of forming a stable atmosphere with a high water content.”

This research confirms the existence of one more finely tuned mechanism that depends on plate tectonics and contributes to an environment that can support life. It also gives humans one more reason to be appreciative rather than dismayed when we experience an earthquake that breaks some precious possessions beyond repair.

Astronomer Dr. Hugh Ross who has a PhD in Astronomy from the University of Toronto and did a 5-year post-doctoral work at Caltech, adds to this with another discovery.

Excerpt:

In the December 2007 issue of Astrobiology Stanford University geophysicists Norman H. Sleep and Mark D. Zoback note that the higher tectonic activity during Earth’s early history could have played a key role in cycling critically important nutrients and energy sources for life. The production of numerous small faults in the brittle primordial crust released trapped nutrients. Such faults could also release pockets of methane gas and molecular hydrogen. The methane and hydrogen could then provide crucial energy sources for nonphotosynthetic life. Finally, the production of faults could bring water to otherwise arid habitats, such as rocks far below Earth’s surface.

Faulting, generated by active and widespread tectonics, allowed a youthful Earth to support diverse and abundant life. This enhanced diversity and abundance of life quickly transformed Earth’s surface into an environment safe for advanced life. Also, the buildup of biodeposits for the support of human civilization occurred more rapidly due to active tectonics.

The more rapid preparation of Earth for humanity is critical. Without such rapid preparation, humans could not come upon the terrestrial scene before the Sun’s increasing luminosity would make their presence impossible (due to excessive heat).

So that’s the science behind earthquakes. So that’s a brief look at why we need plate tectonics for life, and we just have to buck up and take the earthquakes with it. It’s not God’s job to give us happiness and health. That’s not his plan. People who complain about earthquakes have to show how God could get the life-permitting effects of earthquakes without wrecking his ability to succeed in his plan to make people know him and follow him. But how can an atheist do that? They can’t. I think that people just need to realize that humans are not in charge here and we have to live with that. We have to accept that we didn’t make the universe, and we don’t get to decide what purpose it has. God decides.

On to star formation.

Star formation

Atheists often complain that the universe is too big or too old (which is actually the same thing, since the more time passes, the more it expands). The fact of the matter is that life appeared the earliest it could appear – we needed the universe to be a certain age before it could support life.

Dr. Hugh Ross explains in this article.

Excerpt:

The second parameter of the universe to be measured was its age. For many decades astronomers and others have wondered why, given God exists, He would wait so many billions of years to make life. Why did He not do it right away? The answer is that, given the laws and constants of physics God chose to create, it takes about ten to twelve billion years just to fuse enough heavy elements in the nuclear furnaces of several generations of giant stars to make life chemistry possible.

Life could not happen any earlier in the universe than it did on Earth. Nor could it happen much later. As the universe ages, stars like the sun located in the right part of the galaxy for life (see chapter 15) and in a stable nuclear burning phase become increasingly rare. If the universe were just a few billion years older, such stars would no longer exist.

The Rare Earth book explains the details on p. 40-4:

The trick for getting from helium to the generation of planets, and ultimately to life, was the formation of carbon, the key element for the success of life and for the production of heavy elements in stars. Carbon could not form in the early moments following the Big Bang, because the density of the expanding mass was too low for the necessary collisions to occur. Carbon formation had to await the creation of giant red stars, whose dense interiors are massive enough to allow such collisions. Because stars become red giants only in the last 10% of their lifetimes (when they have used up much of the hydrogen in their cores), there was no carbon in the Universe for hundreds of millions to several billion years after the Big Bang—and hence no life as we know it for that interval of time.

[…]The sequence of element production in the Big Bang and in stars provided not only the elements necessary for the formation of Earth and the other terrestrial planets but also all of the elements critical for life—those actually needed to form living organisms and their habitats.

[…]The processes that occurred during the billions of years of Earth’s “prehistory” when its elements were produced are generally well understood. Elements are produced within stars; some are released back into space and are recycled into and out of generations of new stars. When the sun and its planets formed, they were just a random sampling of this generated and reprocessed material. Nevertheless, it is believed that the “cosmic abundance” mix of the chemical elements—the elemental composition of the sun—is representative of the building material of most stars and planets, with the major variation being the ratio of hydrogen to heavy elements.

[…]Many stars are similar in composition, but there is variation, mainly in the abundance of the heavier Earth-forming elements relative to hydrogen and helium. The sun is in fact somewhat peculiar in that it contains about 25% more heavy elements than typical nearby stars of similar mass. In extremely old stars, the abundance of heavy elements, may be as low as a thousandth of that in the sun. Abundance of heavy elements is roughly correlated with age. As time passed, the heavy-element content of the Universe as a whole increased, so newly formed stars are on the average more “enriched” in heavy elements than older ones.

[…]The matter produced in the Big Bang was enriched in heavier elements by cycling in and out of stars. Like biological entities, stars form, evolve, and die. In the process of their death, stars ultimately become compact objects such as white dwarfs, neutron stars, or even black holes. On their evolutionary paths to these ends, they eject matter back into space, where it is recycled and further enriched in heavy elements. New stars rise from the ashes of the old. This is why we say that each of the individual atoms in Earth and in all of its creatures—including us—has occupied the interior of at least a few different stars.

What he’s saying is that heavy elements are created gradually because of the star formation lifecycle. The first generation of stars are metal-poor. The next generation of stars is better. And so on until we get to stars that can support life by providing a steady, stable amount of energy – as well as other benefits like planets with an atmosphere.  Our planet is 4.5 billion years old, and the universe is about 14 billion years old. Simple life appears about 4 billion years ago on Earth. That means we got life practically immediately, given that we had to develop the heavy elements needed to make a life-supporting star, a life-supporting planet and our physical bodies

Physicist Victor Stenger debates William Lane Craig: Does God Exist?

This debate took place on March 1, 2010 at Oregon State University.

In this debate, Victor Stenger does affirm his belief that the universe could be eternal in his second rebuttal (1:02:30), thus denying the standard Big Bang cosmology. He also denies the law of conservation of energy and asserts that something can come from nothing in his concluding speech (1:33:50). He also caused the audience to start laughing when he said that Jesus was not moral and supported slavery. There is almost no snark in this summary. Instead, I quoted Dr. Stenger verbatim in many places. I still think that it is very entertaining even without the snarky paraphrasing.

The debate includes 30 minutes of Q&A with the students.

Here is the MP3 file for the audio.

Here’s the video of the debate:

Dr. Craig’s opening speech:

  • The ontological argument
  • The contingency argument
  • The cosmological argument
  • The moral argument
  • The resurrection of Jesus (3-fact version)
  • Religious experience

Dr. Stenger’s opening speech:

  • There is no scientific evidence for God’s existence in the textbooks
  • There is no scientific evidence for God acting in the universe
  • God doesn’t talk to people and tell them things they couldn’t possibly know
  • The Bible says that the Earth is flat, etc.
  • There is no scientific evidence that God answers prayers
  • God doesn’t exist because people who believe in him are ignorant
  • Human life is not optimally designed and appears to be the result of a blind, ad hoc evolutionary process
  • The beginning of the universe is not ordered (low entropy) but random and chaotic
  • It’s theoretically possible that quantum tunneling explains the origin of the universe
  • The laws of physics are not objectively real, they are “our inventions”
  • Regarding the beginning of the universe, the explanation is that something came from nothing*
  • Nothing* isn’t really nothing, it is “the total chaos that we project existed just before the big bang”
  • If something has no structure, then “it is as much nothing as nothing can be”
  • Consciousness is explainable solely on the basis of material processes
  • There are well-informed, rational non-believers in the world and God would not allow that

Dr. Craig’s first rebuttal:

Stenger’s argument that there is no objective evidence for God’s existence:

  • First, it is not required that God rely only on objective evidence in order to draw people to himself (Alvin Plantinga)
  • Second, God is not required to provide evidence to everyone, only to the people who he knows would respond to him
  • Third, Craig gave lots of objective evidence, from science, history and philosophy
  • Stenger asks for certain evidence (answered prayers, prophecy, etc.), but Craig presented the evidence we have

Stenger’s argument that the balance of energy is zero so “nothing” exists:

  • if you have the same amount of assets and liabilities, it doesn’t mean that nothing exists – your assets and liabilities exist
  • Christopher Isham says that there needs to be a cause to create the positive and negative energy even if they balance
  • the quantum gravity model contradicts observations
  • the vacuum is not the same as nothing, it contains energy and matter
  • the BVG theorem proves that any universe that is expanding must have a beginning

Stenger’s argument that mental operations can be reduced to physical operations:

  • mental properties are not reducible to physical properties
  • epiphenomenalism: is incompatible with self-identity over time
  • epiphenomenalism: is incompatible with thoughts about other things
  • epiphenomenalism: is incompatible with free will
  • substance dualism (mind/body dualism) is a better explanation for our mental experience
  • God is a soul without a body
Dr. Stenger’s first rebuttal:

Craig’s cosmological argument:

  • Craig’s premise is “everything has a cause”, but quantum mechanics has causeless events
  • There are speculative theories about how something could have come into being uncaused out of nothing
  • “I don’t know of a single working cosmologist today who believes there was a singularity prior to the Big Bang”
  • “If there wasn’t a singularity then there’s no basis for arguing that time began at that point”
  • “There’s no reason from cosmology that we know of that the universe can’t be eternal”
  • “When I talk about an eternal universe, I mean a universe that has no beginning or end”
  • The Hartle-Hawking model doesn’t have a beginning
  • “There was no violation of energy conservation by having a universe coming from nothing”
  • “The universe could have come from a previous universe for example or even just from a region of chaos”
  • The paper by Vilenkin is counteracted by other papers (he doesn’t specify which ones)

Craig’s moral argument:

  • Dr. Craig is arguing from ignorance
  • But morality can be decided by humanity just like governments pass laws, and that’s objective
  • Dr. Craig has too little respect for the human intellect
  • I don’t need to tell me that slavery is wrong
  • The Bible supports slavery
  • Atheists can behave as good as theists
  • Morality just evolved naturally as an aid to survival

Craig’s resurrection argument:

  • No Roman historians wrote about the execution of Jesus but none of them did
  • The empty tomb is doubtful because it is only mentioned in the gospels, not by Paul
  • John Dominic Crossan says there was no empty tomb
  • Christianity only survived because the Roman empire thought that they were useful

Dr. Craig’s second rebuttal:

Craig’s cosmological argument:

  • There is no reason to prefer an indeterministic interpretation of quantum mechanics
  • Dr. Stenger himself wrote that deterministic interpretations of quantum mechanics are possible
  • The vacuum in quantum mechanics is not nothing
  • The quantum vacuum he proposes cannot be eternal
  • The cosmological argument does not require a singularity
  • The Hartle-Hawking model is from 1983
  • Hawking says that there is a beginning of space and time after that model
  • The Hartle-Hawking model does still have a beginning of time – the model is not eternal
  • The BVG theorem that requires a beginning for expanding universes is widely accepted among cosmologists

Craig’s moral argument:

  • Stenger redefined objective to mean that most people agree with it – but that’s not what objective means
  • Objective means right and wrong whether anyone accepts it or not
  • Richard Dawkins himself says that on atheism there is “no evil and no good” – why is he wrong?
  • Even Dr. Stenger says that morality is the same as passing laws – it’s arbitrary and varies by time and place
  • But on his view, right and wrong are the same as deciding which side of the road to drive on
  • But somethings really are right and some things are really wrong

Craig’s resurrection argument:

  • Josephus is a Roman historian and he wrote about Jesus, for example
  • There were four biographies of Jesus are the best sources for his life
  • The scholars that Stenger mentioned are on the radical fringe

Dr. Stenger’s second rebuttal:

Knowledge and the burden of proof:

  • Dr. Craig has to bear the burden of proof, not me – because his claim is more “extravagant”
  • “I don’t have to prove that a God was not necessary to create the universe”
  • “I don’t have to prove that a God did not design the universe and life”
  • “I don’t have to prove that the universe did not have a beginning”
  • “I don’t have to prove that God did not provide us with our moral sense”
  • There are a lot of books written about how morality evolved naturally
  • “I don’t have to prove that the events surrounding the supposed resurrection of Jesus did not take place”
  • Bart Ehrman says that the gospels are generally unreliable (Note: Ehrman accepts all 3 of Craig’s minimal facts)
  • Just because people are willing to die for a cause, does not make their leader God, e.g. – the Emperor of Japan

Aesthetic concerns about the universe:

  • I don’t like dark matter and I wouldn’t have made the universe with dark matter
  • I don’t like the doctrine of penal substitution
  • I don’t like the doctrine of original sin
  • I don’t like the heat death of the universe

Dr. Craig’s conclusion:

The case for atheism:

  • Dr. Stenger had two arguments and he has to support his premises
  • Dr. Craig addressed his two arguments and each premise and Dr. Stenger never came back on it

The contingency argument:

  • Dr. Stenger has dropped the refutation of this argument

The cosmological argument:

  • The theoretical vacuum he proposes cannot be eternal

The moral argument:

  • He asserts that things are wrong, but there is no grounding for that to be objective on atheism

The resurrection of Jesus:

  • There are surveys of scholars on the empty tomb and 75% of them agree with it
  • Bart Ehrman agrees with all 3 of the minimal facts that Dr. Craig presented
  • Ehrman’s objection to the resurrection is not historical: he’s an atheist – he thinks miracles are impossible

Religious experience:

  • No response from Dr. Stenger

Dr. Stenger’s conclusion

The cosmological argument:

  • “I argued that we have very good physical reasons to understand how something can come from nothing”
  • “There is a natural tendency in the universe… to go from.. simpler thing to the more complicated thing”
  • The transition from a vapor to a liquid to ice shows how something could come from nothing
  • “It cannot be proven that the universe had a beginning”

The moral argument:

  • Objective morality, which is independent of what people think, could be developed based on what people think
  • “Jesus himself was not a tremendously moral person… he had no particular regard for the poor… he certainly supported slavery… he was for the subjugation of women” (audience laughter)

The resurrection argument:

  • Bart Ehrman says that the majority of the gospels are unreliable

Religious experience:

  • I don’t see any evidence that there is anything more to religious experience than just stuff in their heads

God’s purpose of the world should be to make people feel happy:

  • God could have made people feel happier
  • God could have made people not die
  • God could could have made the universe smaller: it’s too big
  • God could have made it possible for humans to live anywhere “even in space”