Friday, August 13, 2010

Developing Doctrine and Ecclesiastical Evolution

There must surely be peace among Christians, so why doesn’t that harmony exist? Our biggest problem is dissent and heresy, namely what constitutes lawful dissent and what constitutes heresy. In 2000 years of development, why isn’t there a single Church? Well actually there is, if we subscribe to the Creeds – One Holy Catholic and Apostolic et c.Well then which is it? Rome? Constantinople? The inhabitants of one little building in Texas?

How can we tell? Well, time has passed and this means there needs to have been some evolution of the Church to bring us here. If I may move back to my mathematical heritage here, Evolution requires and Object to Evolve and rules by which it evolves. Change the rule and you change the way the Object evolves in time. Mathematically this would take place using a set of initial conditions for the Object and a function of time, recurrence relation, differential equation, as the Rule.

To illustrate these methods, we’re going to Evolve some numbers. Think of them as a population of some animal if you wish.

We could simply define the size of the population at time t as a function of time, for example f(t)= t+1, which means that whatever t is, f(t) is what you get just add one to t. The number f(t) is the size of the population at time t (seconds, years, millennia whatever you like) when we start measure. So initially, when we start measuring, t=0 and the size of the population is f(0)=0+1=1. So the initial population is 1. If we’re measuring time in years, then after 100 years, the population is f(100)=100+1=101, i.e. the size of the population after 100 years is 101. Still with me? The point is that in this situation when the rule (in this case the rule f) is given for all time, right from the start and all sizes of population are obviously determined, in this case very easily.

We could use a recurrence relation. Start with the numbers 0 and 1 and then use the rule “add the two previous numbers to get the new number” In this case we get the sequence

0, 1, 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8

generating 0,1,1,2,3,5,8,... – the famous Fibonacci sequence.

It’s more difficult for us to work out what the 100th number will be but we can still see how the thing is eveolving.

Mathematically, the evolution of physical systems is described by differential equations. This is a bit difficult to describe to non-mathematical readers, and if you’ve borne with me so far, thank you and well done. A differential equation only tells you how fast to travel and in which direction. For example, if I tell someone keep turning left at 3 feet a second, then he’s going to spend his time walking in circles. Yet this is how many physical systems act: we will know their velocity at any position and time, and have to work out where they will go. This makes for very complicated mathematics and leads to chaos theory. For examples of this we can look at the Lorentz equations which produce some remarkably complex behaviour.

The differential equation style evolution requires only knowledge of the speed and direction in which we are moving at any point. If we’re actually in the system that’s evolving, then this is the best that we can do. If we’re in the system, then we do not have knowledge of the whole system, but rather only local information. Slight changes to a differential equation make big changes in the long term, so constant readjustment needs to be made in order for the system to compare well with reality. If the differential equations are particularly complicated, mathematicians have to resort to numerical methods to analyse the solutions which aren’t always well behaved.

All this mathematical jargon brings me to the main question. In 2000 years since the Lord walked with us before His Ascension, what rule of Evolution did He leave us? St Paul gives us a rule in that what we receive from one generation we pass on to the next. Of course, how we pass it on becomes important especially with the change in time. How the rule adapts to the change in time needs careful thought. It’s clear that what must not change is the Word of God, the message of Salvation and Love of God, of the promise of Eternal Life and a Relationship with the Divine Author.

What we now have after 2000 years is a fragmented Christianity where people refuse to recognise the results of others’ evolution. Cardinal Newman in his Essay on the Development of Christian Doctrine says that the Development of Doctrine should not be a mathematical process, or at least does not have a mathematical sense of continuity. A properly mathematical sense of continuity really means that small changes have small effects in the short term. If I change the function f(t)= t+1 to f(t)= t+1.5, then the change is small in the long term. However, if I change the function, f(t)= 10 x t to f(t)= 11 x t, then in the short term we have a tiny difference 10 versus 11, 20 versus 22. By the time we’ve got to 2,000, we have 20,000 versus 22,000 – a big difference.

Of course, the best thing to do is to check out that point in time where the change was made in Christian doctrine. Again, if we’re in the system, we’ve got a problem in that we cannot travel backwards in time and see precisely what that change is, we have to rely on the interpretation of historical documents which is no easy thing when there are so many factors here.

Now this is the mess that Christianity faces: fragmented by all kinds of different rules of evolution. Do all people who claim to be Christian share a common teaching? Is there truly a prescribed method of Doctrinal Evolution? Cardinal Newman’s has been both a method for conservative and liberal Roman Catholics – how can that be? So what do we do to unite Christianity?

Of course, it is an expression of Faith that we hold to the system that we do, and we should hold to that Faith strongly. However, how should we be treating those whose system need only be slightly different in order to produce very different effects? Dare we leave them or try to live with them?

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