Models

Thursday, November 11, 2010

By Steven H. VanderLeest

Why didn’t Jesus do bigger miracles?  He fed the 5,000, and that was pretty big, but it was only one meal.  Why didn’t he feed more people yet, and for more meals? Why didn’t he turn more water into wine, rather than only the last few jars at a single wedding?  Why were only a few lepers healed, when there were so many in need in the surrounding colonies.  Why calm the storm just that once – why stop there?  I think the answer may have to do with models.

When contemplating big or complex concepts we often start by creating a model.  It is not the real thing, but it helps us understand the reality.  It is often smaller or simpler.  The model is a representation, a symbol, a sign.  As school children we all have built models of one type or other:  clay models of a building, diorama shoebox scenes for social studies, solar system models out of Styrofoam spheres, or model volcano for science class.  Hobbyist young and old often work with models:  model rockets, model airplanes or cars built from tiny plastic parts glued together and painted, historical replicas, dollhouse scale models, model railroads.  Sometimes we bring together a group of people that work together to form the representation, such as a Civil War battle historical re-enactment, or perhaps a model United Nations meeting that mimics the real UN.

Scientists and engineers often use mathematical models that attempt to explain reality, characterize a system, or to extrapolate reality (either to unknown situations or to predict the future).  Business professional use financial models to analyze cash flow and evaluate business strategies.  Investment professionals use models to guide investment decisions and predict market movement.  Political gurus use statistical models to predict voter turn-out and voter issues, while election reporters use statistical models and exit poll data to predict winners well before actual counts are complete.  Meteorologists use computer weather models to forecast rain or sunshine.  The military uses computer simulations to play out various battle scenarios (though somehow in the movies, those computer systems never fail to get out of hand and start a real Armageddon, with the hero pulling the plug at the last possible moment).

Engineering models are used to guide the design of technological products.  The models are used to provide insight into optimum size, shape, and material for a desired end.  The model can help the designer determine clearances and interactions, tolerances and offsets.  Models can help the customer evaluate proposed solutions.  Electrical engineers use SPICE electronic circuit models to mathematically mimic the behavior of transistors.  Mechanical engineers use Finite Element Analysis (FEA) models that approximate solutions to partial differential equations, which themselves model physical material characteristics such as elasticity or strength of a material. Engineering models are used to predict the future behavior of an envisioned design, virtually acting out various scenarios with the model to detect failure conditions, anticipate wear or fatigue, confirm safety and reliability, and so forth. 

Though models can certainly be helpful in these many ways, they can also be dangerous.  In class, my students sometimes get the model and reality mixed up.  They simulate a circuit on the computer and then build it in the lab and measure the real behavior.  When they graph the simulated and lab results, the points don’t always line up perfectly.  But interestingly, often they conclude something is wrong with the lab results rather than suggesting that the model is not a perfect mirror of reality.  Why would we think reality should be so clean and pure as a simple mathematical model?  Is f=ma true?  Does force really equal mass multiplied by acceleration?  Precisely?  Or is that simply a model that we use that allows us to get our minds around the problem more easily?  On the whole, we thought Newton had the perfect mathematical model for how matter and forces interact over time—until Einstein showed that Newton’s models were just an approximation, that time was a relative concept.  E. F. Schumacher’s 1973 book Small is Beautiful: Economics as if People Mattered includes a chapter titled “A Machine to Foretell the Future” (pp. 223-240).  He points to computers as a promising new technology to forecast and predict—an amazing possibility!  “Are not such machines just what we have been waiting for?  All men at all times have been wanting to know the future.” (p. 223).  He goes on to consider the likelihood that our carefully constructed mathematical models will yield good forecasts: “What is the meaning of a ‘good mathematical fit?’  Simply that a sequence of quantitative changes in the past has been elegantly described in precise mathematical language.  But the fact that I – or the machine – have been able to describe this sequence so exactly by no means establishes a presumption that the pattern will continue.  It could continue only if (a) there were no human freedom and (b) there was no possibility of any change in the causes that have given rise to the observed pattern.”  I think Schumacher is on to something here.  Modern society is not satisfied with living merely in the moment but constantly is predicting what will come next – on the stock market, in the weather, in fashion, in politics, and more.  Our technological forecasting tools are dangerous because they give us a false illusion of precision, a false security about results that are far from certain, and a false impression that the future is deterministic.  This façade of certainty discounts human free will.  It discourages or even eliminates the use of human judgment concerning the likelihood and impact of future events. 

Now to return to the opening question:  incredible as they were, why didn’t Jesus do bigger miracles?  As God, he certainly could have provided more spectacular displays of his power.  Perhaps it is because the miracles of Christ are models.  They point to a bigger truth.  We need a scale model because the real thing is too big to see, too vast for comfort.  We need a simplified model because the real thing is too complex to understand, too wonderfully intricate to comprehend.  C.S. Lewis suggests this view of miracles in a article published in God in the Dock , as pointers to the greater miracle of ongoing providence: 

There is an activity of God displayed throughout creation, a wholesale activity let us say which men refuse to recognize.  The miracles done by God incarnate, living as a man in Palestine, perform the very same things as this wholesale activity, but at a different speed and on a smaller scale.  One of their chief purposes is that men, having seen a thing done by personal power on the small scale, may recognize, when they see the same thing done on the large scale, that the power behind it is also personal – is indeed the very same person who lived among us two thousand years ago.  The miracles in fact are a retelling in small letters of the very same story which is written across the whole world in letters too large for some of us to see…God creates the vine and teaches it to draw up water by its roots and, with the aid of the sun, to turn that water into a juice which will ferment and take on certain qualities. Thus every year, from Noah’s time till ours, God turns water into wine.  That, men fail to see…  But when Christ at Cana makes water into wine, the mask is off.  The miracle has only half its effect if it only convinces us that Christ is God:  it will have its full effect if whenever we see a vineyard or drink a glass of wine we remember that here works He who sat at the wedding party in Cana.  (p. 29) 

I am grateful to Lewis for such an insight.  Our world, including our technology, does not behave as it does through happenstance.  It is because our God providentially upholds his creation, caring for it and lovingly sustaining it.  Christ’s miracles are reminders of that intimate, personal touch of the Creator.

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(c) 2012, Steven H. VanderLeest