Bringing Mathematics to Theology

Since I am a math teacher rather than a theologian, I bring tools to the table that must be subject to the scrutiny and criticism of the real theologians already there.  So what does a hammer-wielding math teacher see in current popular theological discourse that looks to him like his proverbial mathematical nail?

Let me start with my tool of choice:  Calculus.  In this discipline we make use of the simple algebraic concept of coordinate location, using equations called functions to model or predict where some point should be on a graph as a function of its horizontal location.  So if a function is described by the equation y = square root of x, then we know it will be at a height of 2 when x is 4, or it will be at 3 when x is 9 and so forth, all of which fall on a smooth curve.

Plot of square root of x

Plot of square root of x

Calculus students take an interest not just in where the curve is for a given horizontal location, but also where it is going.  I.e. we would like to know its derivative (math jargon for its slope, or how steep it is) at that point.  Is the curve at that spot nearly level such that advancing just a bit horizontally would yield very little rise or fall?  Or is the curve very steep at that point such that a small horizontal advance would yield a very large vertical change?  And furthermore, how fast is the curve steepness itself changing?  To answer all these questions, one has to look beyond the state of the function (where it is) at the point in question, and examine the points immediately preceding and following in order to evaluate function behavior around that point.  And this brings me to my proposed theological application.

We spend a lot of time studying what various great church fathers wrote about scriptures, creation, humanity, and the Divine direction in the midst of it all.  This is as it should be, since we are a part of history with both location and direction just like a curve or line on a graph.  So if we are to know our place and direction in history we should be well-read on those who have best been able to articulate a coherent, and (with regard to Scriptures) a divinely inspired account for us to study.

Now; it has famously been noted that there are only two kinds of people in the world:  Those who think there are only two kinds of people in the world, and those who don’t.  With that comical self-critique in mind, I will indulge in what I hope to be a useful generalization that there are two categories of approach applied to our reading of ancient authorities.  And we see these categories beginning to clash a bit in some of the insightful critiques following the Aquinas article at the Biologos site.

The first of those two approaches is this:  evaluate where the respected historical authority stood on the issue at hand, by examining their writings for direct references to that issue.  That is, determine a position much as a mathematician might plug a number into a function and evaluate the resulting output.

An example of this ‘positional evaluation’ approach is used when we dispute over issues of how Christians should live, work, interact with government, etc.  We ask, what did the early church and apostles do?  And some may seek to emulate what they find.  If a religious tradition sees great importance on, for example, the mechanics of a baptism ceremony, they might appeal to scriptural precedent.  Did the apostles baptize by sprinkling water on the head?  Or did they find the nearest body of water and fully immerse?  We look for scriptural precedent on many subjects.  Did early Christians take up arms?  Or were they pacifists?  Once the answer to the particular issue is located in Scripture or other writings, then for the ‘positionist’ the argument has been laid to rest with finality.  The faithful need only emulate.

It gets more difficult when the issue is exclusively a modern one about which the ancient writer had no knowledge.  It is impossible to directly see what any of the apostles might have thought about electronic computers since such novelties were not part of that culture.  Or what did Moses think about other galaxies?  There is no direct reference to which to appeal.  It simply was not in their ‘domain’ of consideration.

‘Domain’ is also the mathematician’s word for the numbers that may be plugged into a function.  Note that negative numbers are not in the domain for the square root of x.  The curve abruptly terminates at zero.  It is no good asking where the function is as we go to the left.  It simply isn’t there.  But we can productively ask where it goes as the curve disappears off the right side of the graph.  We call this extrapolation.  Just because writings (or plots) do not show our answers directly, mathematicians and theologians don’t throw up their hands in despair.  We draw out inferences, find the rules in play and use them to find valid answers for new situations.

We find this in play, for example, at Biologos with a posted 2-part essay about St. Thomas Aquinas in which the author speculates about how Aquinas would view current evolutionary thought.  Others write about earlier church fathers like St. Augustine of Hippo, or even apostles and earlier prophets themselves, making variously supported conjectures about how some of them would approach today’s issues.

This second approach I’ll call the “trajectory” method.  ‘Trajectory’ implies motion and change along with the calculus concept of a changing slope of a curve.  We see this approach exemplified when the appeal is to consider the “movement” of the Spirit in some past situation.  For example, is the command, “an eye for an eye” a static command to be followed even today and for all time?  Most Christians will readily acknowledge that such a command was a needed limitation *in its historical context* on the open-ended vengeance in which a whole village might be murdered over the rape of one woman.  But the Spirit was not finished with the people of God as would be seen with Christ’s later commands in which even limited vengeance is taken off the table.  The people of God are being taken somewhere – we see movement.  Even limited vengeance is not to be a final position for the people of God.

Some of the more fundamentalist atheists cannot imagine any notion of ‘movement’ on religious questions and answers that are purported to be from God; they insist that a static God would have plopped one law down for all time delivering all of creation instantly to a final paradise.  This rigidly positionist stand does not allow for consideration that a personal God might do something in any other way; thus they reject God.  But back to the trajectory approach…

A church in our local community has a poster up stating:  “Never place a period where God has placed a comma.”  To which I imagine a conservative reply:   Would these folks ever acknowledge a period if God used one?  Or is God never allowed to use periods?  That poster expression epitomizes a ‘trajectorist’ approach to issues.   Regardless of your own comfort with one end or the other of this, we should acknowledge that both are needed, and our balancing between both, sometimes closer to one than the other is already part of our theological life and was for early Christians too.

See, for example, how they dealt with new issues in Acts 15.  It is the ‘solidly’ (if one may excuse the use of that word here) trajectorist notion in play when Christians today argue for more openness to, for example, alternate sexual orientations; or for dropping strict Sabbath or food laws (with curiously little controversy around the latter example).  While staunch positions can be found denouncing many things as abominations –even in the New Testament for some of these, the trajectorist rightly points out that the early church met to consider some new questions in new ways, and had to discern where the Spirit was leading rather than what historically static position could be found for adherence.

This all remains in play today as well as we consider science issues that were largely non-existent for all the early church fathers.  So we lean on trajectories revealed from their writings including the Bible itself for clues to their attitudes and how they moved in response to similar issues of their day, deriving hints as to how they might respond to our new issues.  I suggest that this is not just a modern addition to theological traditions, but a time-honored (more importantly a Scripture-honored) approach in seeking to apply God’s Word across every aspect of our lives in any age in which we find ourselves, so long as the trajectorist does not use his approach to the exclusion of all positionist claims.

It is a fair question to ask what a Calvin, Aquinas, Augustine, Paul, or yes – especially Jesus, would do given such information input as we seem to have in today’s intellectual climate.  Indeed, the very existence of so many valuable church writings for the last couple thousand years implies the continuing movement of the Spirit even if one does accept the finality of a closed canon.  Acknowledging a firm foundation does not repudiate the existence of valuable layers of structure built upon it.  Indeed the Lord will someday reveal if we build with gold or straw.

So what are the inferences that we can legitimately use, and where do they – where does God – lead us?  Well, that is where the rubber meets the road just as my essay here conveniently comes to a close.  But it is on these interesting points that so many others launch in as can be found here and at various other web outlets.  I simply wanted to provide a hopefully useful tool for readers to identify how issues are being presented as the debate continues.

Merv Bitikofer

About Merv Bitikofer

Merv has been a teacher at Flint Hills Christian School since 1993 and has also been active with his family in Manhattan Mennonite Church. Science and faith issues have long held his interest both personally and professionally, and he is passionate about cultivating a more robust intellect among the wider Christian community in the service of Christ.
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16 Responses to Bringing Mathematics to Theology

  1. Jon Garvey Jon Garvey says:

    Merv, thanks for transferring this discussion from the BioLogos thread, and expanding it with the mathematical detail.

    My first response (as a mathematical retard) would be that it’s important to get the calculus right, so that the trajectory one projects from Scripture or tradition is actually on the graph at all. In that sense it’s maybe more like experimental science than maths – all the theology that’s been done, and developed, over the centuries enables one to extend the curve in a way that doesn’t suddenly go off at a tangent to what’s happened before.

    Hermeneutically, of course, it also means understanding the basis on which doctrine was originally reached either in Scripture, or in the tradition. For example, when Jesus bases his teaching on adultery and marriage on the situation at creation, it’s a lot less negotiable than if he had appealed, say, to what society would deem “decent”.

    • Merv Bitikofer Merv Bitikofer says:

      Thanks, Jon.

      It is interesting too that Jesus seems to go over Moses’ head (even as he appeals to the ‘law of Moses’ which I suppose included Genesis since it is part of the Pentateuch). So even though Moses issues allowances because of hardened hearts, Jesus pulls what we take as a new command out of earlier creation that wasn’t explicitly spelled out there. The question to me then is, whose authority is on display here: the Genesis narrative? or Jesus’ authority? It seems to me that the non-negotiable part of it comes from the fact that Jesus said it.

      For an example of some things uttered with a very different kind of appeal, I recall at least one point where Paul (I Cor. 11:14) actually does seem to pull out the “what seems decent” card. Does not the very nature of things teach that long hair is degrading to a man? He expected his Corinthian audience to find this self-evident. Not that he had any Scriptural injunction against long hair available (at least none that I remember off the top of my head so to speak); but I do find it fascinating that apostles sometimes did concern themselves with cultural mores of the time.

    • Lou Jost says:

      Paul’s notions on long hair, and the need for women to cover it in church, may have been based on an ancient belief about reproductive biology:
      http://experimentaltheology.blogspot.com/2012/09/head-coverings-in-worship-why-female.html
      Bizarre and speculative, but there it is.

      • Merv Bitikofer Merv Bitikofer says:

        I had no idea! I guess it made sense to them. My wife insists that Paul didn’t know much about women anyway.

        • Lou Jost says:

          Maybe the belief had its origin in the observation of capillary action in ropes and fibers? Like watering a plant by wicking?

        • Jon Garvey Jon Garvey says:

          There’s a good case for saying that Paul was a widower – it was pretty much mandatory for a rabbi to be married, and his use of the word “unmarried” isn’t equivalent to “a bachelor” so much as to “ex-married.”

          The long hair bit was the example I was thinking of, which was always of interest to those of us from a certain generation of hippies (I’ll show you a pic of my non-Pauline college hair one day). It’s an example where the reasoning, evidently clear in the 1st century, is opaque to us, and so encourages speculation that may be off the mark. James Hurley (who slept my floor when the Tyndale House accommodation was full) did a study on all these questions with explanations much more related to both Hebrew and Greek sociology than biological theories.

          So it’s a good example of where going by the letter is more legalistic than spiritual, pending some definitive study that reveals the underlying principle Paul had in mind.

          Still, it’s always interested me how the sixties hirsuteness has given way again to the generalisation Paul assumes for the first century.

          • Merv Bitikofer Merv Bitikofer says:

            Jesus also was often called ‘Rabbi’ by his disciples too. And I have heard that used (by modern gnostics / DaVinci Code enthusiasts etc.) to make a case for Jesus having been married too.

            To consider it so, however, makes it rather fantastically necessary that nobody ever asks Jesus about his wife or refers to her when they would have had ample opportunity or curiosity to do so. Most fatally in I Cor. 9:5 where Paul is feeling defensive about his own ministry, he mentions that the apostles and others had believing wives, when surely he would have used the immediate slam dunk case that the Lord himself had a wife, had that actually been the case.

            I’m not questioning your application of Hebrew customs here –you are more knowledgeable than I about that. But we can note at least one case where a rabbi apparently never married.

          • Merv Bitikofer Merv Bitikofer says:

            For some like me, it’s a moot point –or should I say dome?

            Wouldn’t they have noticed that short haired women get pregnant just as easily as long haired women? Or maybe so few women had short hair the few counter-examples were not enough to greatly disturb the prevailing notion.

            It would be interesting to see what new perceptions and/or realities feed our current cultural norms in addition to what we inherit from ancient traditions.

  2. Merv Bitikofer Merv Bitikofer says:

    I didn’t mean to imply that the authority of Genesis is lessened by Jesus’ use of it — it is strengthened as is often pointed out.

    How Jesus uses it is what I find instructive from your example. So is this one of those examples where we are permitted to emulate Jesus’ methods? In some ways we dare not assume we have the same prerogative he enjoyed. And yet if I have a conviction that “we should care for creation because God said it was good” –am I not doing the same thing? Some would interpret the command to Adam to care for the garden to be an implied command to all of us, but it still requires initiative to extend that to all that we stewardship-minded folk pack into it today. We may be leaning on a ‘trajectory’ style thought in doing so.

    • Jon Garvey Jon Garvey says:

      Jesus wasn’t so much applying Scripture to a new situation with his divorce teaching, as correcting a new trend some of the rabbis were taking (David Instone-Brewer is the go-to man on this) – which made a new taste for easy divorce more palatable to them. His exposition of the Mosaic passage on remarriage to the same guy after divorce stands up on its own as a critique of lazy interpretation, and his citation of Genesis 2 just adds weight to it.

      If a preacher said we should care for creation because it’s good I wouldn’t argue, but I would say it’s an inadequate case from the texts. Genesis 1 implies man’s creation as vice-regent over creation – but alone, that has been used by, say, Francis Bacon as an absolute right to exploitation, though most Christians have taken note of many OT passages implying our working of the earth on God’s behalf (eg God’s ownership of the cattle on the hills, his forbidding of defoliation in war “because you are not fighting the trees”).

      Genesis 2 shows stewardship of a specific sacred space on God’s behalf. What ties the lordship of the whole earth with the stewardship of ch 2 is the understanding that Genesis 1, too, is about God’s creation of sacred space – the whole cosmos. It is good becuase it is God’s temple, and so ought to be treated as such by those he appoints to run it “in his image”.

      That idea was inherent in the text from the start, but forgotten in our times – but it mattered less before we were in a position to trash the planet in a number of ways. Maybe it’s providential that the recovery of the ANE concept of the cosmic temple coincides with the need for it. I certainly agree that the “trajectory” of interpretation requires us to broaden our vision to the global ecology simply because we have gained so much new power over it, for good and for ill. Even that is a delayed fulfilment of what was implied in the creation ordinance of Genesis 1.

  3. GD GD says:

    This takes me back many years, but if memory serves, Jesus was addressed as “good teacher” and Rabbi – the latter term was derived from the Jewish order which sought to bring the scriptures to the people, rather than those who were centred on the Temple in Jerusalem. In other words, people recognised that Christ went amongst the people and taught them; I do not think He was ever considered part of that particular Order, and thus it is unlikely that He would have adopted the habits and actions of the Rabbis.

    Paul on the other hand was an exceptional student and he would have adopted the habits and cultures of his particular order, before his conversion.

    On the remarks about women, I read these to mean that Christians should not adopt outlandish and shameful fashions of that day. I would challenge anyone to improve on Paul’s teachings regarding women, as for example in Eph 5:25, which shows the outstanding basis for a sound husband-wife relationship.

    The notion of a trajectory on matters such as these seems misplaced imo.

  4. Merv Bitikofer Merv Bitikofer says:

    It may well be; though I think a lot of churches misuse some of Paul’s teachings to try to silence women today in ways that aren’t (I would argue), truly Spirit-led. Of course that’s more a case of possible positional thinking in which even the position may be evaluated incorrectly.

    If we really took Paul seriously in all his teachings then single people would be the “1st class” citizens of today’s church instead of married people, but ignoring Paul’s advice we turn that on its head, venerating married people and looking with suspicion on older single people (unless they are part of an official holy order of some kind.)

    But we could productively look at the reasons Paul thought as he did (imminent return of Christ…, badly needed church organization…) and see all some of the logic behind his exhortations. Unless we’re willing to go whole-hog with everything he taught (and I don’t think I know any conservative Christians who do), then we are already using trajectories of some sort … it may be worth knowing which, why, and how Scripturally warranted.

    I do appreciate how Paul differentiates between what he considers his own opinion and what he considers less negotiable. Even if we today canonize everything he said as (in theory at least) non-negotiable, he at least was willing to recognize otherwise about his own advice.

    • Jon Garvey Jon Garvey says:

      Merv

      I guess you’re thinking of the passage in 1 Corinthians that says “Not I, but the Lord” and “I, not the Lord.”

      The common tendency to look at that as “authoritative” v “my personal opinion” is misleading, I think – Paul is actually saying more like “The Lord taught directly on this, so I’m quoting him” and “He didn’t teach on this, so I speak with the authority of his apostle.”

      Bearing in mind we accept Pauline doctrine in Romans, and the rest of the corpus, on the latter authority (or else we’d simply refer back to Jesus, were that teaching in the gospels), I don’t think the teaching is mere suggestion, any more than all the prophets and apostles’ teaching. Open to interpretation, of course – but then so is Jesus’s teaching on marriage, once one realises the context in which he taught it was not on e in which his words meant “all divorce is always wrong.”

    • GD GD says:

      I would differentiate between accepting or “going whole-hog” on anything, as this would imply a slavish, unthinking approach to faith, so if this is what you mean (that we consider and reflect on any teaching) by “trajectories” than I would agree with you. However, I suggest that scripture requires more than simply reading it, but a desire to understand the meaning, intent, and especially why it is given to us, and from there seek to apply it to our personal life and actions. This makes all of us one class, be it apostle or ordinary persons like you and me.

  5. Merv Bitikofer Merv Bitikofer says:

    Excellent point, Jon — thank you. It isn’t that I’m looking for excuses to dismiss some of Paul’s teachings; he is indeed an authority within the canon. One just hopes that people can look beyond the letter to see why he wrote what he wrote lest they believe that marriage is always a bad option unless somebody’s passions are out of control. (I know that doesn’t do justice to what Paul is actually teaching here, but to those who wish to draw out a list of rules from every jot and tittle found, they may be in danger of forming legalisms that they should rather be holding loosely.)

  6. Merv Bitikofer Merv Bitikofer says:

    I posted mine as yours went up just now, GD. Thanks for your clarifications and corrections on points I am trying clumsily to make.

    You are absolutely right about the Scripture needing more than just our reading…
    Part of my interaction with Scripture is often to “tug” on it a little too, which might be interpreted by others as disrespect or irreverence. I don’t intend it that way, but that doesn’t mean I shouldn’t be called on it either.

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