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Karl Giberson, Ph.D

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Mathematics and the Religious Impulse

Posted: 08/08/10 12:38 PM ET

The most trivial part of the relationship between science and religion, and yet one that generates lots of debate, is the simple question of compatibility: Can they co-exist? I have written a bit about this, but I have to confess that this question is boring. Establishing that two things can exist at the same time is not an engaging enterprise, because it leaves unanswered the question of whether either of those things should exist at all. Pornography, as we know, is compatible with unbridled free enterprise (yawn). But should either, or both, of those things exist? Now that is a real question.

When it comes to science and religion, I think the onus is on the religious believer to justify the existence of religion. Science, while not without its warts, has done so much good for the human race that it gets a pass on this one. Nobody wants to go back to the good old days when human life expectancy was 30 years and infant mortality was 50 percent. Religion, on the other hand, is ambiguous. Intelligent people like Sam Harris can argue, as he did in The End of Faith, that we would all be better off if religion went away. And the arguments are reasonable and provocative. But there are no books by intelligent people (at least that I am aware of) arguing that we would all be better off if science went away.

So why religion?

I want to offer, by way of a short parable, a partial explanation for the religious impulse and why so many of us are driven to embrace realities that go beyond what science can establish with clarity.

Imagine that a friend is taking you on a stroll down a long, seemingly endless, incredibly noisy hallway. As you enter the hallway the noise is deafening, a combination of explosions, crumpling metal, loud music from incompatible genres, babies crying, talk show hosts yelling, and so on. As you wander down the hallway, your friend explains that his company can make filters that eliminate any kind of noise, as long as they know exactly how those noises are produced.

He demonstrates the technology for you. As you cross a line marked "10" he turns on a filter that eliminates the sound of explosions. At 9 the crumpling metal disappears. By 5 there is just loud talking, babies crying, and discordant music. At 1 there is nothing but beautiful music and a talk radio host yelling something about his taxes being too high. At 0 the talk radio noise is gone. You have come to the end of the hallway and are standing on a balcony on the opposite side of the building looking out into a dark abyss. The beautiful music seems to be coming out of the darkness.

"Impressed?" says your guide, to which you answer, "Of course." But you can't help but wonder about the beautiful music. Where is it coming from? How is it being produced? Can the high-tech filters shut it out?

"We don't know anything about this music," says your friend. "And our filters won't work on any sounds unless we know exactly how they are produced. Our technology is based on understanding the production of the sounds, not the sound itself." He turns to leave. "But aren't you puzzled by this music?" you ask. "Surely you must have some explanation for it."

"Nope," he says. "I used to wonder about the music but, as you can see," he gestures into the abyss, "there is nothing there. I am a scientist, not a mystic. I will agree that there is indeed music there, but that is as far as I am willing to go. If you want to believe in some 'invisible orchestra in the abyss,' go ahead."

I use this example because we can all identify with music, and few of us would be satisfied with the parsimonious worldview of our friend. Our impulse would be to go further, to find some way to understand, even if the evidence seemed entirely inadequate.

Now, replace "noise and sounds" in this parable with "nature," and replace the beautiful music coming from the abyss with mathematics. Nature on the surface is, to be sure, noisy and full of countless interesting things, from planets to people to protons. And we can note the varied flora and fauna of our existence and explain some it to our satisfaction. But as we apply our scientific knowledge to the world and drill down to the bedrock of our understanding, eliminating the noise and complexity of nature, we find something quite wondrous. At the end of the great hallway that takes us from the social sciences to the natural sciences, through biology and chemistry and ultimately to physics, we find ourselves at last in the presence of a most beautiful and unexplained symphony of mathematics. There is a grandeur that comes gradually into view as we get closer and closer to the foundations of our world. Across the dark abyss, this mathematics comes clearly into view, out of nowhere, explaining the world around us while remaining unexplained itself.

Contemplating the mystery that is mathematics led the Nobel Laureate Eugene Wigner to pen a provocative and widely reprinted essay about the "Unreasonable Effectiveness of Mathematics." It has led Sir Roger Penrose -- one of our greatest living mathematicians -- to postulate the existence of a non-physical "Platonic realm" beyond the physical to make sense of the world. Einstein once commented, in reference to the power of mathematics, "The eternal mystery of the world is its comprehensibility."

The quest for the deepest understanding of the world does not compel all of us to ponder the origin of mathematics. Many of us don't like math, have no idea what it means to say that "equations rule the world," and are thus not awed by math. And the quest does not lead all of us who are awed by such mysteries into religion. But those that understand the eternal mystery best impulsively lean over the railing into the abyss because they know in their bones that there is something out there. Whether they encounter something depends on factors that elude many of their less imaginative peers. This is a deeply religious impulse: one that goes beyond science, but not one without motivation.

 
 
 

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The most trivial part of the relationship between science and religion, and yet one that generates lots of debate, is the simple question of compatibility: Can they co-exist? I have written a bit abo...
The most trivial part of the relationship between science and religion, and yet one that generates lots of debate, is the simple question of compatibility: Can they co-exist? I have written a bit abo...
 
 
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02:22 PM on 08/24/2010
Please, do not mistake an equation for the truth or evidence for proof.

Mathematics is a language. Proof is a logical construct that does not exist outside of one's head.

Just because one has a word for it does not mean much. Even if one can muster a preponderance of evidence to support one's belief, the admission of evidence will always be subject to the discretion of a human mind (even if it's only one's own).

Only action gives meaning to a belief.

Are you willing to expend resources to test a theory? Then you must believe it is true.

Are you willing to fight for your country? Then you must believe it is right.

Are you willing to love your enemy as God loves you? Then you must believe in the Christian God.

Even if one says "Yes" to all of the above and acts accordingly, one would have proved nothing.

But one's actions gives one's life meaning and life to one's words.

It's just not healthy to live in one's head.
05:42 PM on 08/18/2010
I suppose that what Dr Giberson is trying to say is something like this: the urge or impulse that drives someone to fully explore evolution, or cosmology or quantum mechanics or relativity is the same urge or impulse that drives someone to experience the transcendental, the world of the spirit. Not that the experience is the same; but the impulse the driving force is the same. I think he honestly wants to avoid the useless science vs religion blather. My own personal experience (n=1) comes from having done all of the above. I have explored at some depth all four of those sciences and the math that goes with it (man that relativity stuff is tough!!) and i have experienced the transcendental, world of the spirit. It takes a lot of years!! I have to say that the impulse is not the same and neither is the experience. When I go to my observatory on a crisp clear winter's night and look at orion, or the double-double, I do marvel at the beauty of the universe. When I consider evolution I can't but help being awed by how everything ties together and is explained; it is so beautiful . Opening up to transcendence brings the experience of calm peace, joy, oneness, love. The thing is that you don't need a divinity and certainly not religion to experience transcendence.
05:42 PM on 08/18/2010
It is worth recalling the root meaning of religion: tie or bind. It is more of a western tradition, since the word conveys different things in the east. Through religion we tie or bind ourselves to something or the perception of someone. I think of Thomas Merton, Teilhard de Chardin, Theresa of Avila who saw beyond religion to something else, essentially to untie and release the bindings.
The BioLogos purpose is to bring religion and science together. The site is worth a visital though much is the regular blather, there is an exceptionally bad piece on theodicy and evolution.
02:57 PM on 08/16/2010
Mathematics rises from a recognition of pattern, it is not a music rising from the void.
Religion rises from the lack of understanding of what happens, past, present, and future. We create myth to explain what we do not understand and myth becomes religion.
Mathematics, at this time, as an absolute answer fails when we get to the very micro and we are forced to deal with probabilities, almost like creating a myth to explain what is happening. Unlike religion mathematics will continue to refine and correct, not to simply fall back on the "it is so" model the vast majority of religion fall back on when our eyes see other than what religion says we should. Religion claims to have the truth to show us the way. Mathematics simply shows the patterns we have found, not as a force of its own
11:54 AM on 08/15/2010
Science of course has also lead to guns, bombs and soon the destruction of the planet through pollution. It is naive to blame religion, science, or jerry springer for the actions of people.
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dubbleplusgood
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12:54 AM on 08/15/2010
god and math. I fail to see what one has to do with the other. Is it because you believe math is not a physical object so it's outside the natural and of the supernatural? Maybe it is physical. Math already exists as patterns in nature - we simply observe, study and use those existing patterns.
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Shawn de Montaigne
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03:19 PM on 08/14/2010
I would suggest the writer check out Derrick Jensen as an intelligent sort who opposes science in its present form. I disagree with Jensen 90 percent of the time, but his intelligence is indisputable.

This article is a bit too wishy-washy; it fails to deliver the goods in the end, offering us only the typical materialist/nihilist/fatalist bromides, and not very well at that.
12:53 PM on 08/14/2010
If the writer is serious about wanting to get a handle on the mystery of mathematics then I suggest that rather than just pontificating about his less imaginative colleagues he get down to some serious study of the philosophy of mathematics which addresses precisely the kind of questions he seems to find interesting.

Try this for starters.
http://en.wikipedia.org/wiki/Philosophy_of_mathematics

There have long been many different schools of thought that attempt to better understand and explain mathematics. So rather than just wittering on perhaps he would be better off dong some research and writing a serious piece on the subject.
12:45 PM on 08/14/2010
"...the quest does not lead all of us who are awed by such mysteries into religion. But those that understand the eternal mystery best impulsively lean over the railing into the abyss because they know in their bones that there is something out there. Whether they encounter something depends on factors that elude many of their less imaginative peers. This is a deeply religious impulse: one that goes beyond science, but not one without motivation."

So people like the writer are more imaginative than his peers who are not subject to the religious impulse he experiences. Of course, the religious impulse does not lead him one whit closer to understanding the unreasonable effectiveness of math, or indeed any other interesting insights. So this piece is just a statement that when he experiences wonder he interprets it as a religious experience. Nothing more.
09:39 AM on 08/14/2010
Good article. I'm reminded of that old Northern Exposure episode where Chris falls for a female mathematician who is researching pai, thinking that if she can just keep taking the sequence out far enough she will be able to understand the secret of God.

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02:49 PM on 08/12/2010
** No “God-the-Geometer **

“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” -- Einstein

Like language, mathematics can manipulate abstract conceptions of the world through symbols. Neither language nor mathematics uses symbols or expressions found "in the world," since there are no concepts in the world to find.

No god taught an Adamic language. No god excogitated the universe through mathematics. Science make empirical models of the world using math. The "fit" between model and world is never perfect.

Mathematics provides testable models which “are not certain". Models are not unassailable descriptions of nature. Nor do models provide ontologically irreplaceable explanations of nature. Mathematical theorems supply so-called irrefutable truths which “are certain" only since they follow from distinct, coherent, and finite axiom sets.

Euclid and Riemann differ over the famous “parallel postulate.” There is no quasi-religious dogma at issue concerning the axiom sets.

Axioms, unlike dogmas, give rise to sane outcomes. As internally consistent alternative geometries, Euclid and Riemann live and let live. But they cannot both be "true" of space-time. They present incompatible models of the world. No “necessary truth” comes along for the ride from math to lab.

"God the Geometer" arises before Plato in Pythagorean geometric number mysticism and proto-philosophy. Religion like philosophy has always sought a marketing halo effect from alleged sources of certainty.

Certainty is a chimera.
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EminemsRevenge
06:06 AM on 08/11/2010
Scroll DOWN when you go here:

http://blogs.myspace.com/index.cfm?fuseaction=blog.view&friendId=18105618&blogId=431724192

Isaac Asimov had the most plausible explanation of Genesis that should be a preface in EVERY bible...
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DrBlizzardo
12:36 AM on 08/11/2010
As a scientist, I not only "hear the music" and appreciate it, I want to know what it is, who is making it and how it is being made...I am completely unwilling to simply "gesture into the abyss and say 'there is obviously nothing there'."

This whole argument is a false analogy and a straw man argument. Can't we do a little better here?

Besides, Andy Schaffly, via Conservapedia, has amply proven that Einstein's Theory of Relativity is both false AND a liberal plot (oh, no, I'm not absolutely not making this up...check out: http://tpmmuckraker.talkingpointsmemo.com/2010/08/conservapedia_founder_takes_on_the_notorious_liber.php) so I'm afraid mathematics as a tool is out for all of you bible thumpers out there.

I'm sure you are relieved.
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ohmercy
12:28 AM on 08/11/2010
Great article.

It is only in the last several years that I (don't?) understand what I am missing in not having been exposed to mathematics when I was younger.
Because of my interest in quantum physics (what little I can "get" from what I read) I find myself disgusted that I have no mathematical skills.
When I went to grammar school math was nothing like what kids learn today. Same with High School (graduated in 1967) I think I only had one year of Algebra and a bookkeeping and record keeping courses. sure, calculus, geometry and trig were taught in the "college prep" track but I wasn't college bound back then. If I remember correctly there were only 2 tracks= college prep and not college prep!
A few years ago I took a beginning logic course as I needed one math course to finish a degree program and nothing else was open.
It was HELL! I couldn't get it- it may as well have been klingon! I'd get a whisper of something and then it was gone again. It was such a disappointment to me. If I were younger and had a younger more agile mind I think I would start at the beginning and try to learn math from the basics of algebra- (because who can remember? not me!) on up till I couldn't do anymore.
It really is so fascinating and mysterious.
10:54 PM on 08/10/2010
There is a basic error here that is often made (by both sides it seems) in these debates. It is true that there are limits to what science can tell us. And it is also true that there is good reason for people to want to try to understand the things that cannot be settled by science. It would be unnatural to stop there. But what that most naturally justifies is philosophy, not religion. One cannot legitimately get from a desire to understand to the leap to faith in some theory of the unknown.

It is a mistake to think that science constitutes the limits of what we can usefully contemplate. But it is equally a mistake to think that this justifies a leap to religion. And thinking that the existence of a platonic realm of numbers does anything to justify mathematics is just bad philosophy.