I, too, was very pleased with Williams’ general approach to the elucidation of irreducible complexity (“IC”) in autopoeitic (i.e., living) systems (“AP”). [Thank you so much, GGG!]
You point to an interesting problem, that IC can be understood as either “backward-looking” or “forward-looking.” The “linear arrow of time” is the context, which provides a “past” and a “future,” relative to the observer’s “present.” In a sense, it seems that the “backward-looking view” states that irreducible complexity is somehow the product of a build-up of past biological events being “selected for” by Nature.
And yet a model like that would have no way to deal with the idea of information (or intelligence), nor could it explain purposeful, goal-directed behavior — something that is universally observed in animal life.
So I think the “backward-looking” approach will not do. So what does the “forward-looking” approach look like?
To boil it down, in a certain sense it would mean being “pulled” from the future. [But we won’t go into eschatological considerations here.] I gather this is what Williams was trying to get at with his term “inverse causality,” which pops up at level (v) of the AP hierarchy. But if you lay out “inverse-causality” on the “arrow of time,” past–present–future, it doesn’t make any intuitive sense.
Actually, I think Williams gets the problem right if we understand that it’s the “top” of the hierarchy — level (v) — that “pulls” the rest. In the “top-down” direction, none of the five levels is “reducible” to the next level “down,” not singly, nor in any combination of lower levels. Which suggests that each of the five levels possesses information not completely derivable from any or all of the lower levels.
In short, the AP model is "irreducibly complex" in two ways: (1) in terms of the totality of the hierarchical, five-leveled model itself; and (2) in terms of the recognition that no "explanation" of any given level of the hierarchy can be given by any lower level, singly or in any combination (in the range (v) "high" and (i) "low").
To draw an analogy from mathematics, given the origin point 0 (i.e., the "observer"), the “backward looking” view of IC is such that the “arrow of time” represents the “real” line of the complex plane, the x-axis, which deals with the distribution of real numbers. With respect to 0, “past” would be defined on the real line in terms of negative numbers….
So along the real axis, 0 defines the point in time where “future” (i.e, expressed as positive reals) and past (i.e., expressed as negative reals) each “begins”; i.e., are “split apart” into two distinct temporal entities. In order for a future cause to be found, 0 must translate (i.e., "move") along the real line in the positive direction. But the paradox seems to be that, when 0 “finds it,” it must be expressed as a negative real.
The “forward-looking” view, on the other hand, seems to go along the “imaginary” line of the complex plane, the y-axis, which deals with complex numbers. And they really are complex, because a complex number consists of a “real” and an “imaginary part.” There’s a “boost” to complexity over the real numbers right there. Not only that, but the two parts are separable; and each has its own proper form of arithmetic operation: the real part is multiplicative; the imaginary part, additive. So, here we have yet another instance of the complexity boost of complex numbers as compared to the reals. Plus almost unimaginable “flexibility” of the ways in which these concepts can function in “real” contexts.
All of which is simply to indicate that, on my view, the “forward-looking” view would appear to be the more “informed” view, which is what we’re looking for at level (v) of the IC/AP hierarchy: For level (v) “pulls from the top” — and may itself be “pulled” from a source lying outside conventional spacetime….
And this leads me back to “the Platonic world of mathematical forms,” as Penrose puts it. Which still manages to "pull" me forward, in space and time....
Then again, maybe I just have too much time on my hands these days, to be investing it and energy in such problems (which I happen to find delightful)....
Thank you so very much for writing, dearest sister in Christ — and for your very kind words of support. I’ve missed you lately. I hope you’re feeling better!
Truly, Williams' "inverse causality" breaks with the convention of looking backwards in time and changes the dynamics of the debate.
If the investigator only sees the "x axis" - and he is required to do no more to rebut the "irreducible complexity" argument - then he may be inclined to attribute whatever complexity he observes to be a serendipitous emergent property (self-organizing complexity or cellular automata.) The Aristotlean paradigm is serendipitous per se.
For instance, the Aristotlean mathematical paradigm played out in physical cosmology gives us the anthropic principle, i.e. "look no further, we are here so it happened, don't ask why or whether it was even remotely probable." The Platonist mathematical paradigm does not accept hand wringing and asks why this and not something else.
Or to put it another way, when the level of complexity clearly anticipates that which has not yet occurred then it is not serendipitous at all but forward looking. Enter the Platonist paradigm, universals and the "beyond" of space and time.