Why Does Science Work?

Post Author: Bill Pratt

Very few people ever think about why science works; they just take it for granted.  Some of the great scientists, however, have wondered about this question.  Philosopher John Lennox, in his book God’s Undertaker, quotes Albert Einstein’s ruminations on the question of why the universe is comprehensible:

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 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 being constantly reinforced as our knowledge expands.

Einstein is saying that we should expect a chaotic world, a world which cannot be grasped by the mind.  The fact that the world is able to be understood by human minds is a ‘miracle’ that deserves explanation.  In particular, why does physical reality map to mathematics?  Surely this fact demands an accounting.

Lennox notes that Paul Davies finds this mapping to be truly astounding.  Davies comments that much of the mathematics applied to modern science “was worked out as an abstract exercise by pure mathematicians, long before it was applied to the real world.  The original investigations were entirely unconnected with their eventual application.” (emphasis mine) Why?  Surely this is strange.

Lennox continues, “The relationship between mathematics and physics goes very deep and it is very hard to think of it as some random accident.”  Professor of Mathematics Roger Penrose has this to say: “It is hard for me to believe . . . that such superb theories could have arisen merely by some random natural selection of ideas leaving only the good ones as survivors.  The good ones are simply much too good to be the survivors of ideas that have arisen in a random way.  There must be, instead, some deep underlying reason for the accord between mathematics and physics.”

Not wanting to posit an agent behind this mystery, some skeptics will say that science itself explains the accord between math and physics.  But this cannot be so.  Lennox recounts the following words of John Polkinghorne: “Science does not explain the mathematical intelligibility of the physical world, for it is part of science’s founding faith that this is so.”

So why does science work?  Why do math and physics work together so well?  Lennox offers the Christian answer to this question:

The intelligibility of the universe is grounded in the nature of the ultimate rationality of God: both the real world and mathematics are traceable to the Mind of God who created both the universe and the human mind.  It is, therefore, not surprising when the mathematical theories spun by human minds created in the image of God’s Mind, find ready application in a universe whose architect was that same creative Mind.

The non-theist is left with a real quandary.  Without a Mind behind reality, the fact that abstract mathematics directly applies to reality remains a profound mystery.  The non-theist is left, in essence, with blind faith in science.

  • In my free ebook on comparative mysticism is a quote by Albert Einstein: “…most beautiful and profound emotion we can experience is the sensation of the mystical. It is the sower of all true science. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and most radiant beauty – which our dull faculties can comprehend only in their primitive form – this knowledge, this feeling, is at the center of all religion.”

    E=mc², Einstein’s Special Theory of Relativity, is probably the best known scientific equation. I revised it to help better understand the relationship between divine Essence (Love, Grace, Spirit), matter (mass/energy: visible/dark) and consciousness (f(x) raised to its greatest power). Unlike the speed of light, which is a constant, there are no exact measurements for consciousness. In this hypothetical formula, basic consciousness may be of insects, to the second power of animals and to the third power the rational mind of humans. The fourth power is suprarational consciousness of mystics, when they intuit the divine essence in perceived matter. This was a convenient analogy, but there cannot be a divine formula.

    http://www.peacenext.org/profile/RonKrumpos

  • Boz

    In particular, why does physical reality map to mathematics?

    It is the other way around – mathamatics maps to reality. A version of mathamatics that did not work with reality would be quickly discarded as useless or even dangerous. Using a different version of mathamatics to build a bridge could lead to many deaths when it collapses.

    Other versions of mathematics have been created, by adjusting the axioms used in normal mathamatics. But these other versions are only thought exercises, they cannot be applied. An example: http://www.freewebs.com/value-by-factor/

    In particular, why does physical reality map to mathematics?

    Asking this question is analogous to the famous puddle that marvels at the construction of the hole that it is in – the hole perfectly fits our famous puddle, how miraculous. “it is very hard to think of it as some random accident”. Surely this could not happen by chance alone?

  • Anonymous

    God is infinite and incomprehensible. God is every bit as profound a mystery as the fact that abstract mathematics directly applies to reality. That science works may well be a quandary. Nevertheless, the theist is just kidding himself if he thinks that he has resolved the quandary by labeling it “God.” All he has done is substitute one that is beyond his comprehension for another.

  • Boz,
    You think that the mathematical laws that were discovered centuries before being applied to science just happened to coincide with reality by blind luck and that “alternative” mathematical laws have been tried and discarded? Really?

    I read the website you pointed me to to, and I didn’t see how the “mathematics” on this page were ever tried on science and discarded. In fact, it looked like there were no “alternative mathematics” at all. He was just making up new ways to symbolize the same mathematics we already have. Maybe I misunderstood, but could you please point out to me which new mathematical laws this website has discovered that have been tried by scientists and discarded?

  • Vinny,
    No Christian believes that God is totally beyond comprehension, as this is a position of total agnosticism about God. If we can’t know anything about God, then who are we worshiping? What does the word “God” even mean? Pantheists may talk this way about God but not Christians. We believe that God can be known, just not completely.

    We know that God is a rational person who created man. That hardly fits your assertion that God is beyond comprehension. We see that science works and we know that a rational, personal, creator God exists. Therefore that God is a good explanation for why science works.

  • Andrew Ryan

    “You think that the mathematical laws that were discovered centuries before being applied to science just happened to coincide with reality by blind luck”

    Boz said no such thing. That the maths we formulated maps reality is not ‘blind chance’. Pythagoras didn’t accidentally stumble across his theorum for triangles by blind luck, he worked it out. If it didn’t fit reality, then the theorum wouldn’t have got very far!

    “and that alternative mathematical laws have been tried and discarded? Really?”

    Boz didn’t say that either. He said “A version of mathamatics that did not work with reality WOULD be quickly discarded”. It would be pretty obvious to everyone straight away if Pythagoras’ theorum didn’t correctly allow one to calculate the hypotenuse of a triangle.

    “Maybe I misunderstood”. I’m afraid I think you did, because the question you finish on has nothing to do with Boz’s description of the site.

  • The Chisel

    Wether or not you believe God created the universe, Math (and thereby science) works because it begins with measurment and observation. All other theorem, including physics and Eintsiens theory of relativity begin with basic arthmetic, measurement, and counting.

  • Boz

    you misunderstand me.

    You said that mathematical ideas are: “applied to science” , “tried on science” , “tried by scientists”. This shows a narrow understanding of what science is.

    Science is the gaining of knowledge through experimentation. Science is done every day by every person on earth. Even you and me! Every time we open a door, buy/sell items, drive a car, lift an object. Those things are all tests of the real world, and of the formulas that describe the real world.

    If I lifted an object, and it accellerated up in to the sky, away from the ground, that would disprove the gravitational constant, G.

    Mathamatical laws were implicitly known via science (that is, implicitly known to some humans by everyday experimentation), before they were written down by famous ancient men.

    It was known that a circumference is a bit more than three times the diameter, before the number 3.14159265 was written. It was known that A+B = B+A , and AxB = BxA, long before the phrases “Commutative Law”, and “Associative Law” were written. Arched bridges were built long before the formula for a Catenary was written. Houses were built before the first architect. Thrown stones followed the arc of a parabola. Debts and loans were negative numbers. Some plants and flowers have fractal patterns. Heavier objects carried more force. Friction slowed things down. Pendulums were used.

    In ancient times, mathematical laws described what already existed.

    In this way, the mathematical laws were moulded to fit the world that we live in.

    So the original question that you asked is the wrong way around: (why does physical reality map to mathematics?)

  • Anonymous

    Bill,

    In my experience, different Christians believe lots of different things. Personally, I would be very wary of saying “all Christians believe this” or “no Christians believe that.” By the same token, I tend to be skeptical of apologists who make such statements.

    While I try to avoid absolutes, I would say that most Christians I know are humble enough to acknowledge that they only understand or comprehend God to the extent that God manifests or reveals himself. They would concede that God in his essence or nature is unknowable and unapproachable. While I would not claim that all Christians view God as a profound mystery, I can say that the thoughtful Christians for whom I have respect do so.

  • Since you are speaking for Boz, then what was his point then?

  • Andrew Ryan

    You have a habit of seeing things in posts that are not there! I never claimed to speak for him, I make no claims about his points either. I merely pointed out that he said anything close to what you claimed he did.

  • In order for you to know that I misunderstood his points, you must know what his points are. I am just asking what his points are. I truly thought I knew, but you say that I don’t. If you know that I am wrong about what he said, then I am just asking you to explain what he said. Boil down his comments for me so that I can properly respond.

  • Boz,
    It seems you have broadened the definition of science to mean “sense experience.” We take in information by our senses and draw conclusions from that information. That is clearly not the definition of science that most people understand.

    However, I agree that all of our knowledge derives originally from sense experience, but mathematical laws and formulations abstract from our sense experience. Nobody has ever seen a perfect line, or point, or triangle, or plane, or parabola. Those things do not exist in the real world, but mathematicians were able to abstract these concepts from what they saw in the real world.

    Mathematicians have always continued to abstract further and further away from what their senses experience. In other words, they build on higher and higher levels of abstraction that are more and more disconnected from anything they’ve ever seen in reality. I know because I had to take numerous Calculus classes to get my engineering degree.

    What is fascinating, then, is that after building these massive abstract structures, scientists during the Enlightenment and afterward came along and found that these abstract structures actually applied to physical reality in ways never imagined by the men who built the abstractions. That is what is so amazing.

  • Andrew Ryan

    “In order for you to know that I misunderstood his points, you must know what his points are.”

    Bill, you were telling Boz ‘You think…’ and then saying things that I couldn’t find anywhere in his posts. And I’ve already given quotes where you attribute points to him that he simply didn’t make.

    In a single example, compare:
    Boz: “A version of mathamatics that did not work with reality WOULD be quickly discarded”
    Bill: “alternative mathematical laws HAVE been tried and discarded? Really”

    I don’t know what more I can do to point out your mis-reading.

    At any rate, why ask me to paraphrase Boz again, AFTER he’s already re-explained his points again below, in his post beginning “you misunderstand me”?

  • The Chisel

    can you define what you mean by “mathematical laws and formulations *abstract* from our senses?”

  • Abstraction is the process of considering objects of our senses according to what they have in common while leaving out of consideration all that is not common to them. It is an act of the intellect whereby we move farther and farther away from the world of senses into the world of concepts and ideas. The farther we move away from concrete, particular objects in the real world, the more abstract we get. If you’ve ever taken Calculus courses, you know that the concepts taught in those courses are very far away from the world of concrete objects. It is extremely abstract.

  • Anonymous

    I notice that Lennox conveniently leaves out from Einstein’s letter One could (yes one should) expect the world to be subjected to law only to the extent that we order it through our intelligence. Ordering of this kind would be like the alphabetical ordering of the words of a language. The miracle he’s talking about is order when it doesn’t have to be this way a priori, yet it really is, and external to our intelligence.

    This has consequences you’re not going to like.

    What you utterly fail to note – as does Lennox – is that this means that any designing god was constrained by the laws of nature – specifically gravity. The existence of the universe requires the existence of the laws of nature. In other words, without these laws the universe could not continue to exist. Therefore god in this universe is constrained by them. Yet you believe god – specifically Jesus – can suspend them at will (walk on water, raise from the dead, etc.). As Einstein suggests, this suspension of the laws of nature – specifically physics – would destroy his ‘creation’.

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