On the nature of Celtic knots...

When I gave my talk at the ISSS meeting, at Asilomar last summer, I used the example of Celtic knots to illustrate several of my father's points regarding reductionism and the limits of reductionistic approaches/techniques in certain types of analysis. The main issue is that a reductionist approach assess material "things" but never the relational aspects as important "things" in and of themselves. When the system being analyzed is one that is generated mainly by the relations between things (such that the same relations using a different material would generate the same system pattern), reductionistic techniques are less than helpful. I thought it might be useful to post these analogies for the list.

Celtic knots have always fascinated me because they embody certain qualities that are reminiscent of many of the "truths" we intuit about life and time, in general. As such, they cover some of the same territory that Robert Rosen's scientific work also covered. So it's a natural progression to begin using these as visual illustrations of certain concepts.

All physical Celtic knots (as opposed to pictures of them) are made of the same three ingredients: a piece of long, thin material, "empty" space, and the relations which create the pattern. There are many distinctive patterns that can be created using these three ingredients, one of which is represented in the photo. Clearly, we could recreate the exact same pattern using a shoelace, a piece of ribbon, a leather strap, a willow branch... anything that has a few basic properties such as sufficient length, width, and flexibility. The material used doesn't really matter beyond those basic requirements. What matters are the relations, which are unique to each pattern. Interestingly, these relations can also be analyzed and categorized (for example: relations of the physical material to "empty" space, relations of physical material to itself, etc.). But the whole point (of these particular relations and these ingredients) is the end result-- to generate this particular design; this specific Celtic knot. Everything else is entirely driven by that imperative.

Any change in the relations will not create this particular Celtic knot design, whereas any change in the material may not have any effect on the design at all. In other words, there is a set of material changes we could make that would maintain the base conditions required of the material by the design, such that any change of material from within that set will not affect our ability to generate the design.

It's important to point out that the base conditions required of the physical material are all mandated by the requirements of the finished design, as well. So these specific properties of the material are entirely relational to the nature of the end result.

If we are presented with a new system, never before encountered, and it happens to be a physical version of the Celtic knot represented in the photo, above, how would science go about analyzing the system? What would our current techniques and approaches require as steps of that analysis? If we had absolutely no prior knowledge of such a system, the first step is to disassemble it. We would take it apart and start quantifying. In doing so, we would be sacrificing the organization of the system, which is where the relations are, and reducing it to what the system is made of. However, we don't regard "empty space" as a component. So we are left analyzing the material itself-- and how can we possibly learn the information that specifies the nature of the material? That information is in the (intact) organization as well.

Yet... Celtic knots are simple systems! So, if reductionism is inadequate, used alone, to analyze this kind of relational aspect of a simple system, how much more inadequate is it to analyze complex systems? The usefulness of the above exercise, I think, is in answering the question; what could be done differently in order to learn the essential information that reductionist techniques can't get at?

I think science is already doing some of those things, but doesn't recognize what it means. Therefore, since the reasoning behind the requirement is missing, the requirement is not understood or even listed as an essential aspect of scientific analysis. The missing link in science, from my point of view, is the acknowledgement of the relational aspect in causality.

I'd be interested in hearing whether this particular analogy is helpful to the list, and/or what other dimensions suggest themselves from it.

Cheers,

Judith

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