Going slightly loopy

File:Progressive infinite iterations of the 'Nautilus' section of the Mandelbrot Set.ogg

On 3rd June, the funeral of an old friend brought together a few friends who had known him and me since our university days, horrifyingly 40 years ago now, for an occasion which was partly sad, partly joyful (as he was possessed of a powerful sense of humour which ignored the bounds of taste and propriety, and a lot of stories about him were exchanged) and partly stimulating. In discussion afterwards, although I don’t remember any of shoes, sealing wax or cabbages being mentioned, pretty much any other topic you might think about was – and one was founded on Rob’s very wide set of interests, which had brought together people from many different spheres of life, some for the first time.

This was also a feature of our university life, as the group I traveled there with included people who had been part of the Physics, English and Geography departments, and probably the largest group there was musicians – Rob had been an enthusiastic and eclectic lover and performer of music. In conversation with Rob’s son Ruaridh, it seemed that these days, students tend to stick with people from the same department and frequently the same course. In our day, there were a lot of interlocking friendship groups which linked through Rob, through myself and through others of our group, or rather set of groups, due to our extensive ranges of interests (in which Rob and myself coincided in a fair few areas). I think it’s a pity that university doesn’t seem to produce that kind of varied friendship network these days. Mind you, this might well be because we seem to be pushing children to look to a future career in their choice of subjects earlier, and thinking of university degrees as vocational rather than as discursively educative.

Circles of friendship led to thoughts of loops, and recalled a post I wrote a while back about (inter alia) Douglas Hofstadter’s idea of “Strange Loops” ; Hofstadter was talking of feedback loops within our consciousnesses, and posited that these could well amount to working models (albeit simplified ones) of people we knew well – and I think few of us will not recognise the sensation of “someone else’s voice” (generally a loved one) telling us something. Rob was certainly very much alive in memory on Friday, and will be for many years to come. I may, indeed, have been channeling Rob when we came out of the chapel; someone asked “which way is the Links Hotel?” and I answered “left”. “How do you know?” they asked. “Because if it was to the right it would be the Rechts Hotel”…

And, having found myself talking theory of language and the Sapir-Whorf hypothesis on the way home, it was natural to keep thinking “loopy” thoughts. I don’t like the strong version of Sapir-Whorf, which seems to me to be self-evidently wrong; if you can’t formulate a thought without language, I can see no way in which you can start the process of developing a language. However, iteration would allow the use of rather vague words, and repeated use and development (in a kind of feedback loop) would make them more specific. I find that use of words is hugely facilitated by keeping them at least a little fuzzy in the definition anyhow!

Iterative procedures might well apply equally to concepts. Consider for a moment Niels Bohr’s model of the atom, which is actually still taught (because it’s clear and not excessively wrong), which was closer than the previous, but not as complete as the quantum mechanical model which followed soon afterwards. To quote the article “So why has the Bohr atom stayed around? “It gives us a good place to start the conversation about the composition of the atom,” says high school chemistry teacher Dr. Jason Dyke.” The replacement theory, which surrounds the nucleus of the atom with probability density clouds looking rather like inflatable cushions, still incorporates the basic concept that the nucleus is central and the electrons are dispersed around it.

Is this “the truth” of the situation? Well, if an iteration is involved, you start with a guess, feed it into an equation which you develop for the purpose and from  that generate a better guess. I can remember being overwhelmed by the beauty and simplicity of this process back in my teens, when I was introduced to the standard first example, finding a square root. You divide the number you’re trying to find the root of by the guess, average that result with your guess, and that produces your second guess. It converges fairly quickly on the value you want, to any desired accuracy – but it never quite gets to an absolute answer (you can test this by applying the process to a number you already know has a whole number square root, such as 4…).

If, as I suspect, this kind of process applies to all our thinking (and Hofstadter is right that our consciousnesses are the result of a set of feedback loops), it is never going to be possible for us to say that any model we have of a physical process is “the truth”, though we might well suspect that we are extremely close to it. I couldn’t therefore ever quite be a philosophical realist, at least not a scientific realist.

One product of this is the strong tendency in science for progress to take place largely by “fine tuning” some aspect of a Theory which has already proved itself by explaining most of the available data and by successfully predicting data which we didn’t have when the theory was formulated. As an example, every advance in the broad biological scheme which is the Theory of Evolution since Darwin has been a tweak, even such major changes as punctuated equilibrium and the “inheritance of acquired characteristics” through epigenetics.

But, of course, this all depends on the iterative procedure being convergent, i.e. the feedback loop damps rather than amplifies slight variations. A positive feedback loop is divergent, and is responsible for the scream as a microphone is brought too close to a speaker, thus amplifying any extremely slight sound round and round until the pained humans responsible turn it off or move the microphone away. There are also iterative functions which produce chaotic results, one of which is the Mandelbrot set. Are we looking at convergent iterations at any point? Only the results can show – if they start becoming more and more extreme,

How do we therefore know that the process we are using to refine our concepts is convergent, rather than divergent or chaotic?

With reference to the question of God, Richard Beck recently posted something apropos. Can we use a positive feedback model to characterise our developing concepts of God, and is God therefore a feature of our universe which can be, if not completely accurately, at least approximately described in full? Obviously, Beck reacts against this, as would probably anyone who feels strongly that God is beyond our comprehension in more than the technical way I describe above, that he is a mystery and must remain that way. The emotional part of me certainly feels that way, and the rational part might be inclined to go along with that; certainly that-which-is-God as experienced in peak mystical moments is something well beyond the ability of my reason to understand in full.

But my reason is not happy about anything being in principle immune to examination and clarification. What is more, hosts of present and past theologians have spent much time and ink in trying to establish what God is like, and therefore what God might do.

And, unless you are a Deist, who consigns God to something very akin to another force of nature, albeit one whose operation is more removed from our experience than science can examine (such as the “blind watchmaker” version of the uncaused cause of all), there must be some aspect of God which is capable of being examined, analysed and at least to some extent predicted. If none of these are possible, God cannot have any effect whatsoever in the universe as we now experience it; any effect is accessible to reason (even if reason cannot make complete sense of it…).

If this is the case (and I think it must be) then an iterative procedure should be capable of moving steadily closer to the reality of that-which-is-God, even if it can never capture that exactly, or capture the fullness of God (though I am minded of Col. 2:9, which says “For in Christ all the fullness of the Deity lives in bodily form… “). One might reasonably hope that the more recent the theology or philosophy, the closer to something reliable it may come. That is, unless the procedure is divergent, in which case the later models may diverge more and more from the original (which would perhaps be the position of the Biblical fundamentalist).

I suggest, however, that we do not really see either of these features when we press ahead with newer and more sophisticted theologies and philosophies; what we see is, in theology, an oscillation between the poles of immanence and transcendence (and theologies which privilege either at the expense of the other are hugely incompatible), and in philosophy an oscillation between singular (and incompatible) ontologies (such as materialism or panpsychism) with occasional forays into dualism (such as Cartesian dualism) .

This argues to me that we might be looking at a third type of iterative procedure, the oscillating iteration. In this kind of iteration, values converge not on one point but on two, and nothing will persuade them to “split the difference”; a point halfway between the two poles is more wrong than either of the poles is. I will grant that in mathematics the type of limit you get, convergent, divergent, wandering or oscillating, is very dependent on the way in which you set up the system, which might mean that we merely need to rethink our entire basis of thinking itself and we will have a singular end point. However, it may also mean (and for the time being, I think, does mean) that we are stuck with a dual reality, transcendent and immanent, matter and mind.

And we have to live with there being at least two equally “right” answers to everything…

(OK, the title gives it away – this may be just a loopy idea!).

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