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The Mathematics behind the Theology of John
Polkinghorne, and Its Use in Christian Worship

by Thomas L. Scofield, Ph.D.,
Assistant Professor of Mathematics,
Department of Mathematics and Statistics,
Calvin College

I am a mathematician which, in my view and that of many of my peers, makes me an artist. I came to this project hoping to be able to say something concrete about how my art can contribute to the practice of Christian worship. Such an undertaking was a new one for me and, indeed, there seemed little work of this type anywhere. This is understandably so, as the kind of art produced by a typical mathematician is pretty austere, difficult to recommend for worship services.

The layperson (and, indeed, some practitioners) might wonder how a discipline such as mathematics could contribute to any discussion of Christianity, let alone Christian worship. Can a circle, or any geometric figure, be morally good? Many technological innovations made possible through mathematics have been used for dubious, even evil, ends, but does this mean mathematics as a discipline must deal with ethics? Most of us, myself included, would answer "No" to both of these questions. One might think, then, that any attempt to squeeze something theological from the discipline of mathematics is like wringing water from a stone.

I have written an article which I hope may convince you otherwise. The article has yet to be submitted to a journal but, when it is, information will be posted here as to how to find it. In the few paragraphs below, I will describe the layout of the article which, I hope, you will find sufficiently intriguing to obtain a copy of it.

Layout of the Article

The article is divided into four sections. After a brief description of my project in the first section, I give a summary of pertinent elements in the particular point of view from which I approach the subject of God's providence. In essence, this point of view is that of John Polkinghorne, as he expresses it in the book Quarks, Chaos & Christianity: Questions to Science and Religion (New York: The Crossroad Publishing Company, 1996).

In the third section, I discuss some mathematical examples from dynamical systems which, in my view, help to illustrate Polkinghorne's view. I have tried to select ones that

  • are accessible to those with little to no college instruction in mathematics, and
  • have broad intellectual appeal.

While I know that my success on the first of these concerns varies a good deal from one example to the next, I hope even the more difficult ones meet the second criterion. My examples include the Fibonacci numbers, population models, the Butterfly effect, cellular automata and fractals.

A wealth of material, enough to fill numerous books, exists on these items. Naturally, to approach the kind of detail that such volumes contain would result in a very long piece. A different approach would be to assume each example was familiar to the reader, simply commenting on those aspects I find theologically illuminating, but to follow this path would be to impose strict limits on the size of potential readership. The only reasonable alternative seems to be the path I have attempted, that of describing the bare minimum of detail so as to make the article self-contained.

Nevertheless, it is likely that certain examples will feel more accessible than others to the average reader (and which examples are the most remote may vary from one reader to the next). This is where the internet proves most helpful. Most of the mathematical content is sufficiently intriguing that a simple internet search on one of the key words (like, say, 'Fibonacci') yields numerous hits. Hence, the webpage you are now viewing serves the dual purposes of

  • advertising the article to a community of readers who might otherwise not notice it, and
  • providing a portal to links I have found on the internet which do, in my estimation, an above-average job of explaining further the mathematics. The sites have been chosen mostly on the basis of how well they cater to the uninitiated. Many employ a hands-on approach involving diagrams, java applets, and perhaps other means which is impossible to duplicate on paper, or the duplication of which would extend the length of the article unjustifiably.

In the final section, I discuss how the examples of the prior section illustrate Polkinghorne's views that God has used both chance and necessity to bring about the great dance that is the history of our world and universe, and that he continues to interact with his creation, most often in ways which are indistinguishable, except through eyes of faith, from the workings of chance.  I make the suggestion that various elements of creation are so inextricably linked that no single event is isolated, but has profound effects upon many (perhaps all(?)) aspects of creation.  I mention briefly how this realization may affect our prayer lives, and our worship as well, though I elaborate much more on this aspect below.

Links and Applets:

Some Comments not in the Article:

While interspersed among the mathematics of the third section are to be found comments about their features that relate to the theological discussion, the last section is the one focused upon how the mathematics illuminates the theology of Polkinghorne. I do not there claim that these examples prove his views. Rather, they are consistent both with his views and with what is observed in God's creation. And if Polkinghorne's ideas of the providence of God are accepted, these examples suggest (in ways uniquely mathematical) to the Christian a life of other-centeredness, of seeing oneself inside community on the grandest of scale. My own reaction to them is echoed in these words of Orual, sister to Psyche in C. S. Lewis' retelling of the ancient myth of Cupid and Psyche entitled Till We Have Faces (Harcourt, Orlando, FL, 1984), who comes to these sentiments after years of bitterness over the loss of her beloved sibling: "I was no one. But that's little to say; rather, Psyche herself was, in a manner, no one. I loved her as I would once have thought it impossible to love, would have died any death for her. And yet, it was not, not now, she that really counted. Or if she counted (and oh, gloriously she did) it was for another's sake. The earth and stars and sun, all that was or will be, existed for his sake."

So goes the outline of an article I wrote for a general Christian audience. Submitting it to a refereed journal whose primary readership is academic lends to it (assuming it is printed) a certain authority that it otherwise would not have. Were this not a consideration, the article itself (rather than an advertisement for it) would appear at this website, largely without omission from its final published form. There are, however, comments I would like to make which do not appear in the piece. These are words that, I hope, make it clearer that I am writing in service to a seminar on "The Arts, Aesthetic Theory, and the Practice of Christian Worship".

Many of us are looking for meaningful ways to incorporate the Arts into worship, but find it difficult at the local level (i.e., within one's own church body) to find common ground for a basis of selecting works to be used. The congregation that is united in its view of pieces fitting for worship is more the exception than the rule.

Coupled with this reality is another "reality" or, if not conclusively that, at least a commonly held premise. Putting aside statements like "the 'good old' days never were", conventional wisdom is that the typical church paritioner nowadays takes a more consumer-like, self-centered attitude about the opportunities afforded through membership in a church than was true in our grandparents' day.

Let us return to the issue of selecting pieces of art for worship. Some say (see, for instance, Frank Burch Brown, Good Taste, Bad Taste, and Christian Taste, Oxford University Press, New York, 2000) that a congregation divided in its tastes and reactions to various forms of Christian expression has little option but to try to please all sides. Compromise, open-mindedness (expressed on the part of each faction), adaptability - these are the watchwords. While there is no escaping the need for these at times, it strikes me that people who feel they are always making compromises often wear thin, over time, on that principle, eventually seeing church break-up or transfer of membership (which may amount to the same thing) as a better option. Few have ever become energized to the rallying cry of "compromise". While compromise most certainly lies beneath the surface in the most communally harmonious of church bodies, these must consist of people who, despite diverse opinions on style and other issues, have become united in a conviction to certain points of focus alongside which all other issues pale.

In a church where the aforementioned consumer-in-the-pew trend is viewed as neither good nor bad, but simply a fact of life to be embraced and used in the strategic planning of a church - from the kind of architecture incorporated in the building to the type of worship service to the savvy use of public relations techniques to market an image - are united by a singular focus upon numbers. (Surely I betray here that I am not in this camp, and my characterization of its view has all of the disadvantages and benefits of my seeing it from the outside.) Results-based strategic planning is the way business is conducted in the 21st century. If a certain strategy demonstrably leads to larger numbers, greater fervor in the service, etc., there is call for more of the same; if not, it is jettisoned. In such a church, compromise is irrelevant. Those who unite behind this growth-oriented objective have seemingly little difficulty laying aside their personal preferences. (The stories of those members in such churches who prioritize differently are not usually heard.)

There are many of us who, to one degree or another, are uncomfortable with what seems to us a grow-at-any-cost emphasis, and are wary of seeing our own congregations emulate the above-described church bodies. There are any number of reasons we may feel this way, many in my view justified, and others, perhaps, which do not hold water. Whatever the reason, in the absence of being unified behind an emphasis on church growth, one might ask what larger themes are there to unite us despite our differences? Of course, an answer like, "our devotion to Christ" seems appropriate here, but we are all on the road of development in that area, and perhaps only when we reach heaven will it suffice on its own. Despite much preaching to arouse greater devotion, the difficulty in choosing remains (though, almost certainly, it is less than if no calls to devotion were made). Besides, telling a long-term member, disgruntled over the loss of his favorite aspects of worship during a recent change in format, that his devotion to recounting the message of Christ should help him ignore his feelings about the matter, provides no real argument as to why he should not transfer his membership to another congregation where members are equally devoted, and services are more to his taste.

I believe our discussion of chaos and dynamical systems suggests an additional (possible) theme behind which we may unite. What these dynamical systems suggest is that all aspects of God's creation are inextricably linked. If you were braced for an earth-shattering idea, I am sorry to disappoint. I am stating the age-old idea that, in another time, was expressed as "No man is an island". Signs of this are all around us, in the joint efforts of numerous bees to construct a hive, in the taxes collected from many to provide civilian services, in concerns about planning our use of natural resources so that they are sustained along with us, etc. Still, perhaps the mathematics reveals in more stark reality just how interconnected we all are. If such a small disturbance as a single butterfly's flappings (an example from the article) has strong implications for global weather, is there any event however small which might not have unrecognized and significant consequences?

Allow me the opportunity to anticipate and respond to several issues that this raises. The first implication is that it is not just our poor decisions which may yield unwanted consequences, but our good ones as well. Depending on where your Christian walk has brought you thus far, you may nod, say "I knew this without the help of mathematical examples and have come to grips with it", and lightly jump to the next paragraph. For my part, I have found some comfort in C. S. Lewis' exposition, found in Mere Christianity (Macmillan Publishing, New York, 1943), of the view that God will judge us based upon a standard that only he can know, a standard that takes into account both the intent of our actions, and the extent to which we must overcome an opposite predisposition in order to 'do rightly'. Though the result of our actions is therein deemphasized, the truest comfort comes again from words like these of Lewis in Till We Have Faces, where Orual's mentor tells her just before she is to be judged by the gods, "Be sure that, whatever else you get, you will not get justice."

Another implication is that, in some sense, all of creation may be viewed as an organic unit. If each individual - indeed, all of humanity - is but a small component in the grand design of history, with a fate that cannot be divorced from the fates of all other components (as the mathematical examples suggest, and as modern science now says), then where does the concept of "self" come in? Is the only right view one in which self is destroyed? Is it an artificial concept we are to shed? These are deep questions, and I have colleagues in psychology who really should be answering instead of me. Let me answer using metaphors. There are many organizations one may consider within a river. There is the river itself (the extreme global view), and there are all of the subatomic particles inside it (the extreme local view). In between there are many other levels at which to view things. The molecules (H20 and otherwise) provide one level of organization; zooming out further there are eddies located at various places throughout. Similarly, any college, city or corporation is a whole unit which has many levels of substructures. For our part we were created in the image of the only true Self, and we know Christ came to seek and to save the lost. Perhaps Christ's death and resurrection have broader implications than we know, but we know that he cares about us as individuals. Self remains an important construct, one level of organization, not to be overemphasized, not to be lost.

At this point in history, some of us may feel the place self occupies in our vision of reality has grown out of proportion with its true place in that reality. Our reaction to this is not a call for asceticism. Nor do we feel comfortable as Christians affirming, subtly or otherwise, its current size and place in society's collective imagination. We wish to emphasize our place in larger community - a community that includes not just other humans we know, not just the ones we don't know or the ones living today, not just animal and plant life, but all of God's creation.

To many individuals this particular theme may be a hard sell. Even so, I hope the idea of worship themes is not. For them to achieve their desired end of uniting a congregation, they must be ones upon which a congregation decides as a whole, and ones which may be repeated in a number of services. We can hardly expect that themes chosen by a small committee will be caught, much less espoused, by a congregation operationally. Unless the whole assembly has been able to contemplate the importance of a particular focus or theme, would it seriously consider funding a painting, sculpture, theatrical or dance performance that reinforces it at the expense of other, more obvious needs?

If the particular theme I advocate, perhaps on the strength of the mathematical examples given in the article, along with examples from biology, physics and chemistry, captures the imagination of a particular congregation, then there should be a wealth of possibilities for the inclusion of art. While perhaps not everyone would accept Madeleine L'Engle's definition of art ("Christian art", "good art"; these labels are all the same in her view) as "cosmos from chaos" (Walking on Water: Reflections on Faith & Art, Harold Shaw Publishers, Wheaton, IL, 1980), there is a substantial amount of visual art, music and poetry which fits this description. A work which places new light upon otherwise mundane, senseless, even ugly elements - this, to a person who agrees upon my theme as an appropriate focus in worship - would be uplifting even if it goes against that person's stylistic preferences.

I do not wish to list possible works that fit my theme. I am not enough of an expert in any of the liturgical arts to provide such a list and, it seems to me, this should be a project at the local level. The individual church should call upon its own members to put forth candidates for use in the service. I know of one church in Grand Rapids which, having a number of talented people as members, calls for pieces made by these members to be submitted and evaluated by the worship committee for their use. Whether or not this model could be implemented in your local church, what seems best about it (and transferrable) is that the pieces which are used have meaning in one's own congregation.

I pray that the view expressed here proves helpful to some churches. May God bless our efforts as we seek him.

Sources and Recommended Reading

  1. Brown, Frank Burch, Good Taste, Bad Taste, and Christian Taste, Oxford University Press, New York, 2000.
  2. Burger, Edward B., and Starbird, Michael, The Heart of Mathematics: An invitation to effective thinking, Key College Publishing, Emeryville, CA, 2000.
  3. L'Engle, Madeleine, Walking on Water: Reflections on Faith & Art, Harold Shaw Publishers, Wheaton, IL, 1980.
  4. Lewis, C. S., Mere Christianity, Macmillan Publishing Company, New York, 1943.
  5. Lewis, C. S., Till We Have Faces, Harcourt Brace, Orlando, FL, 1984.
  6. Polkinghorne, John, Quarks, Chaos, & Christianity: Questions to Science and Religion, The Crossroad Publishing Company, New York, 1994.
  7. Weil, Simone, "The Love of God and Affliction", Waiting for God, G. P. Putnam's Sons, New York, 1951.

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