causality, linearity, recursion

Innocence is the child, and forgetfulness, a new beginning, a game, a self-rolling wheel, a first movement, a holy Yea.
– Nietzsche, Thus Spake Zarathustra, “On the Three Metamorphoses”

Causal fallacies have always intrigued me:  confusing correlation with cause, causal oversimplification, ignoring reciprocal causality, etc.  But the “deep geometry”[1] of most of the causal fallacies in our textbooks is linear.  In everyday discourse, when someone asks you a “why?” question, it tends to evoke a linear cause-effect reference-frame.  Most science and medicine is built on discovering “causes” (even if they be multiple).  To this day, we utilize the same linear “cause-effect” logic as Aquinas when he used Aristotelean physics to argue for the existence of a Prime Mover (today’s physicists argue for a “Big Bang,” for similar fear of infinite regress).  Circular reasoning is to be assiduously avoided.

To be sure, there is a certain elegance to the use of linear causal reasoning.  But are there any other kinds of causal logic?  This question brings me to my recent interest in feedback loops.[2]  Sufferers of panic attacks know the feeling of fear itself becoming the cause of fear.  Addicts of many ilks know how hard it is to “break the cycle.”  Believers of all sorts can’t seem to reason their way out of their preferred ideological system.[3]  All of these are resilient, everyday examples of feedback spirals.

So what do feedback spirals, inertia, idea-systems, addictions, anxiety, fugues, and fractals have in common?  Neither linear logic nor circular logic, but rather, what I might call “spiral” or “recursive” logic.  Recursive logic is a logic in which some recursive function helps format successive iterations.[4]  Recursive logic is, for example, one component of Deleuze and Guattari’s “Rhizome.”  Following their lead, perhaps what should be most fascinating to modern logicians the task of working out a rhizomatic logic.

Rhizomatic logic has been approximated since Newton as momentum, inertia, eddy currents, slippery slopes or the like.  For centuries “Nature” has abhorred as “vacuous” anything nonlinear, (which, strangely enough, has been defined as the exclusive domain of the “circular”).  “Lines and circles only!” they pronounced, pounding their ivory gavels.  But we’re all rhizomes.  We’re on a roll.  Shakespeare says it well in his Sonnet 73:

In me thou see’st the glowing of such fire
That on the ashes of his youth doth lie,
As the deathbed whereon it must expire,
Consumed with that which it was nourished by.

This thou perceiv’st, which makes thy love more strong,
To love that well which thou must leave ere long.

Today’s dinner feeds tomorrows hunger.  Today’s sex begets tomorrow’s…sex.  Fear is contagious.  We speciate.  All self-replication–especially with transformation–shares in this recursive function.  Why should recursive causal logic be anathema to logicians?  Is it an event horizon, a rabbit hole, a labyrinth?  Are we afraid to be caught up?  Or is the deep geometry just too difficult?


[1] Deep geometry, like Chomsky’s “deep structure,” is a nod to the notion that human sapience tends to be governed by very primitive algorithms.  Adapting Lakoff-Johnson (1980), human cognition is metaphor all the way down.
[2] Actually, I prefer the term “feedback spirals”–whereas “loop” captures the recursive aspect of their algorithms, “spiral” describes both their recursive aspect and their variance with iteration.
[3] On the aesthetic side, recursive logic also functions prominently in fugues and fractals.  For more examples, see Doug Hofstadter’s excellent work Godel, Escher, Bach.
[4] cf. Mandelbrot’s famous equation, z=z2+c.


One thought on “causality, linearity, recursion

  1. Linear logic proves a product of linear time. In downward spirals the linear time element is represented up-to-down; in upward spirals, the opposite. [Down is bad; up is good.] Feedback works within this model. The logic of complex systems–toward which Deleuze & Guatarri tend–introduces a giving pause. States emerge from a dizzying confluence of interconnected and largely invisible causes. The past of X is as wide open as the future of X. Hierarchy of organizational/conceptual/phenomenal levels further complicates the equations.

    Per Godel, all reasoning is circular, self-referencing, self-perpetuating, self-rolling. The trick is to stretch the coil as far as possible–travel the greatest distance. [Forward is good] Represented in two dimensions this oscillation appears as a wave-function. Resonate with Godel. Feel the vibe. Surf the string. As the book says, “We may be through with the past but the past ain’t through with us….”

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