Why Do Models Work?

“The Cognitive Art of Feynman Diagrams” by
Edward Tufte - installation at the Fermilab art gallery

Why Analogistic Models Contain Significant Content

Without a doubt the actual content of analogistic models has to be the key to their relevance in scientific explanation. For though they are clearly never fully accurate descriptions, and certainly also are always less than totally accurate explanations of the phenomena they are used to tackle, they are also never totally arbitrary inventions, they must contain something objective about the modelled situation.

Let us attempt to reveal what their contained objectivity can be.

Now, though we can, and do, insist that they are analogues for what we are investigating, they are not, and could never be, 100% accurate – containing a full set of one-to-one mappings, they are intrinsically similar situations, and they, therefore, reflect the common sequences, and kinds of entities and properties found throughout Reality quite naturally.

Perhaps surprisingly though, even artificial analogistic models can also be profitably constructed to aid in the understanding of newly addressed phenomena, as long as the constituents involved are taken from concrete evidence of possible components occurring elsewhere in concrete Reality. The method then is to involve such initially unrelated elements into a model, expressly to deliver the actually noticed properties of the thing that you are attempting to explain. Indeed, even more surprisingly, it is often these kinds of analogistic models that deliver the most profound insights, and can also demolish false assumptions dramatically. I will definitely include the mention of such a model later in this paper.

So, let us start by looking at a series of valuable examples of various kinds of analogistic models. James Clerk Maxwell’s famous model of the Ether (that was then presumed to fill all of the Empty Space in the Universe) was just such an informed and creative construct. He knew about many kinds of phenomena, which he had to explain, and the usual simple (and magical) Ether was just too vague to explain anything adequately for him. So, knowing what he wanted to produce from his model, he brought together (without any evidence) the sorts of constituent that might, if appropriately organised, deliver what hew knew was necessary. He adventurously constructed “vortices” and “electrical particles” into an analogistic model, and from this he managed to deliver his famous equations of electromagnetic radiation.

His model did not by any means reveal the actual form of the Ether, and his constructs didn’t exist as such, but his model delivered a great deal more than any of its predecessors, and even more than he designed it to deliver. His resultant Equations were revolutionary. Now, before we explore why such “fictitious” models worked, let us look at some others. Einstein’s Space-Time continuum was also an analogistic model. Once again, no one could prove such a thing actually existed, but it did deliver what Einstein knew were properties that needed explanation. His famous Theory of Relativity was based upon this model, and many things, in addition to what he consciously put into it, which came out of his constructs have since been confirmed in Reality.

Even Niels Bohr’s original model of the structure of the atom with a central positively charged nucleus, surrounded by orbiting electrons in an entity which was mostly empty space, was taken from the Planet-moon systems observed in our Solar System. It was not a true description of it, but yet another analogistic model.

Once again, it defined far more than the models that it replaced, and that was again because it contained more real features within its conceived-of forms.

Even later, when confronted with a confusing maze of “fundamental particles”, Richard Feynman devised his famous Feynman Diagrams – they were, of course, the most abstract of analogistic models, and delivered what no other models could, namely what was called Quantum Electro Dynamics (QED) – the most accurate and useable way of dealing with this amazing Particle Zoo.

And, there is, perhaps, the most audacious version of an analogistic model produced by Yves Couder in his attempt to find a new way of revealing the secrets of the sub atomic world, by modelling it in the Macro World out of unbelievable components. He revolutionised experimental physics by devising and constructing a model entirely out of silicone liquid and various vibrations, resonances and crucial recursions. He managed to create his famous “Walkers” entirely from the above, which was a kind of self-maintaining entity with properties closely comparable to those within the atom.

Finally, the author of this paper, confronted the anomalies of the famed Double Slit Experiments, decided to devise an undetectable Paving of Empty Space composed of undetectable particles – in fact mutually orbiting pairs, each consisting of one electron and one positron, which, because of their opposite matter types and electrostatic charges, became undetectable in this joint form. Yet, this paving actually fully explained the anomalies of the Double Slit Experiments without any recourse to the flights of fancy delivered by the Copenhagen Interpretation of Quantum Theory, when that is used as the sole dependable source for dealing with all sub atomic phenomena.

All the anomalies fell away! Nothing of idealist philosophy was needed to make sense of what occurred, the new materialistic, analogistic model of Empty Space did it without difficulty. [It was both as analogistic, and as artificial, as Maxwell’s model of the very same thing].

Needless to say, a barrage of criticism followed, either from the mechanical materialists of the old school, or from the idealists of the new school, with, as a banker, the fact that no such Paving had been physically detected! But, of course, that isn’t the point, is it? What is important has to be whether this analogistic model explained a great deal more than anything else could. Now, how can we explain these relative successes clearly based upon non-existing constructs?

Their value is that they are determined by the features in Reality to be explained – and, initially, at least, this can only be achieved by organising what is generally known into a purposely constructed model, aimed by using real features from elsewhere, into an amalgam, which delivered what was required. Such a model would never be the Absolute Truth, but it can be both intelligently and intelligibly constructed to contain more Objective Content – elements, parts or aspects of the Truth, than what it replaces. And in doing so, it makes the actual real phenomenon more understandable: and also by crucially revealing things that were absent previously, makes further developments more likely, if only by establishing a whole new kind of model, which allows us a great deal more to consider with some aspects real, and others intelligent placeholders for what has yet to be revealed. But, why should these analogies even be available? Why should such similar (though possibly also profoundly different) resonances occur in such different contexts? The answers must be contained in what it is that is similar in all phenomena, and hence possible everywhere in one way or another?

We really have to address the question, “What is common throughout all possible phenomena that always guarantees that such analogies will certainly exist?” It must be that they are all – every single one of them, always produced as the result of many different, simultaneous factors, which will always come together into overall situations of Stability (if only temporary). Form the possible results of such complexities, when the factors present are NOT separable, eternal laws, but on the contrary, mutually interacting and modifying arrangements, which will finally settle into a selfmaintaining overall stability.

Clearly, features will become present which are a result of this higher level of stability, and hence about how such mutually modifying factors arrive at such a state. Such properties will be true, at least at the abstract level, of all such systems. Indeed, when you think about it, it is likely that all phenomena are such! The search for fundamental particles and their basic eternal laws is therefore a pluralist myth. No matter which “law” you choose to address, it is certain to be the stability reached by multiple factors at an even lower level! The aims of pluralist Sub Atomic Physics are impossible to achieve, with the assumptions and principles that underlie the entire area of study.

The Principle of Reductionism is clearly based entirely upon Plurality, and hence assumes that Analysis will be always possible, all the way down to its targeted Fundamental Particles. These suggested analogistic commonalities seem to indicate very different relations could be expected to get to such stabilities in very similar ways. Such things as spins and orbits are likely to occur at all levels, as are things like vibrations, resonances and recursions. It is very likely that this is what we are settling upon with our analogistic models. Not ultimately Absolute Truths, but commonly occurring natural resonances, which we term as Common Objective Contents.

This article has been taken from the new special issue of the Shape journal Analogistic Models III