The Argument from Maths in Seven Quick Points

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1) As Galileo put it, the laws of physics are written in the language of mathematics . Many have discussed just how remarkable this is. Theoretical physicist Paul Davies writes, ‘Yet the fact that “mathematics works” when applied to the physical world – and works so astonishingly well – demands explanation, for it is not clear we have any absolute right to expect that the world should be well described by mathematics.’ (Davies, 1992, p.150)

Eugene Wigner famously wondered at the unreasonable effectiveness of mathematics. Now, some might argue that Davies and Wigner ought not to have worried about such questions. After all, what other sort of universe could exist? Surely every universe could be described by mathematics? However, as Alvin Plantinga points out, this misses the depth of Wigner’s insight:

 “…what is unreasonable, in Wigner’s terms, is that the sort of mathematics effective in science is extremely challenging mathematics, though still such that we humans can grasp and use it (if only after considerable effort).” (Plantinga, 2012, p.284)

There are numerous other ways that our universe could have been. It could have been a maelstrom of random activity. But this would exhibit no regularity or law; it would have no discernible pattern that could be described by simple formula. Indeed, because there are many more ways to be disordered than there are to be ordered, we would expect a universe that existed by impersonal chance to be anarchic and unruly. A universe ordered by laws that can be described in the language of mathematics seems much likelier if theism is true.

2) In fact, the patterns that physics reveals are quite stunning in their elegance. Our universe is not only ordered; it seems to have been so ordered by a mathematician of the highest order using deep, advanced mathematics! This is the hall-mark of design.

3) Perhaps conscious agents can only exist in universes in which “mathematics works”. In the absence of conscious agents, no one would be around marvel at all the complex order in the universe. So, given conscious observers exist it was inevitable that they would observe a universe in which mathematics works.

However, we must not confuse A: if conscious agents exist they will observe an ordered universe with B: it is inevitable that human observers exist. (A) is a rational belief, but (B) seems very implausible. Given all the ways our universe could have turned out, an exquisitely ordered universe was extremely improbable. Therefore, given atheism, our existence was extremely improbable. Furthermore, our universe might have been inhabited by conscious agents who lacked our capacity for deep mathematics! The comprehensibility of the universe remains mysterious on atheism.

4) The success of science in describing many aspects of the universe from the large scale structure of the cosmos down to the subatomic level is astonishing. When you stop to think about, however, it is far from obvious why any of this has been possible. Why is it that scientists here on Earth are able to unlock the mysteries of the universe? There does not seem to be any good reason to think that the universe had to be like that at all.

5) Even if evolution by natural selection had occurred on a few million planets the emergence of human intelligence was still incredibly improbable. And why unguided natural selection should produce beings with a capacity for, and an interest in, deep mathematics is anyone’s guess. A grasp of second order differential equations was hardly essential for our ancestor’s survival on the grassy plains of Africa.

True, it would be advantageous to know that five wolves are more dangerous than two. But any behaviour that made our ancestors move away from the larger group of predators could have been selected for. Doesn’t it seem a little fortuitous that we survived because our brains are capable of abstract thought? And that much, much later in the history of our species those brains would have enough capacity to turn to matrices and imaginary numbers?

6) Nobel prize-winning physicist Paul Dirac said that ‘it is more important to have beauty in one’s equations than to have them fit experiment’ (quoted in Davies, 1992, p.176). Why should such a strategy of focusing on beauty prove to be so successful? Is there any reason to think that the universe must conform to our notions of beauty? Sir John Polkinghorne, a former professor of mathematical physics at Cambridge University and now an Anglican priest, comments on this state of affairs as follows:

There is no a priori reason why beautiful equations should prove to be the clue to understanding nature; why fundamental physics should be possible; why our minds should have such ready access to the deep structures of the universe. It is a contingent fact that this is true of us and our world, but it does not seem sufficient simply to regard it as a happy accident. Surely it is a significant insight into the nature of reality. (Polkinghorne, 1998, p.4)

7) Furthermore, the human passion for mathematics goes beyond the desire to predict events and to control our environment. We seek to understand the universe, to see how it all fits together. We seem hard-wired to seek deep, profound patterns that connect the wild variety of things in our world. Again, isn’t it a little too convenient that we have an appetite for wonder a yearning for understanding and a brain that is capable of achieving both?

Bibliography and Further Reading

Paul Davies, (1992), The Mind of God, (London: Simon & Schuster) , 

Alvin Plantinga, (2012), Where the conflict really lies (Oxford University Press)

John Polkinghorne, (1998), Belief in God in an Age of Science, (New Haven, Conn.: Yale University Press)


William Lane Craig gives a brief summary of the argument from maths here:

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