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George Spencer Brown’s Laws of Form are routinely cited in the context of theories dealing with self-referential processes, autopoiesis and second-order-cybernetics. Niklas Luhmann, in particular, refers to Spencer Brown all the time and makes extensive use of his terminology: law of calling, law of crossing, re-entry, etc. I never understood what the buzz was all about, maybe because I grew up with computers so that “paradoxical” statements such as n = n + 1 never seemed quite that paradoxical to me. Self-referential expressions of that nature, obviously, are part of a loop. In other words, for my generation, using time, iterations, or operationalization as a means to resolve the paradoxa that Luhmann and his followers were so enamored with came naturally and simply wasn’t such a big deal. Similarly, the quasi-mystical tone in which many of Spencer Brown’s followers discuss the creation of “something from the void” by way of an initial distinction was lost on me. Of course, you need a “difference that makes a difference,” because a white circle on a white plane blends into the background. It appears to me that the “law of calling,” the “law of crossing,” “condensation,” and “cancellation” can very easily be understood in terms of a simple robot (or a turtle in logo) tooling about on a white plane. The turtle scans the color of the plane directly underneath it. Once it detects a change (e.g., because a line is drawn across the plane), its internal state is inverted. If the turtle’s internal state started with 0 the crossing of a line changes it to 1, if it started with 1 the crossing changes it to 0. Now imagine a circle, drawn onto the plane.

The turtle crosses from the outside (the “unmarked state”) to the inside (the “marked state”) (0 → 1) and then, after a while, from the inside to the outside (1 → 0).

The fundamental response of the turtle to entering and exiting a form (0 → 1 → 0; or 1 → 0 → 1) doesn’t change, no matter how many non-overlapping circles there are on the plane. Hence the “form of condensation,” whereby {}{} = {}.

But what if there’s a circle within a circle? The first crossing inverts the turtle’s state and so does the second crossing.

Consequently, the turtle’s state inside the second circle is identical to the turtle’s state outside the first circle, which results in the “form of cancellation” {{}} = _.

The story gets somewhat more interesting, once we move from arithmetic to algebra, where A is a variable that can take the values {} and _ (mark and no mark). Then, you get expressions like:

(1) A = {{A}}.

For A = {}, the expression reads {} = {{{}}}, which, applying the form of condensation, resolves to {}={}. For A = _, the expression reads _ = {{}}, which resolves to _ = _. So far so good, but what about this:

(2) A = {A}.

For A = {}, the expression reads {} = {{}}, which, applying the form of cancellation, resolves to {} = _. And for A = _, the expression reads _ = {}. In other words, if A is a mark, then the value of the function is not a mark, and if A is not a mark, then the value of the function is a mark. It turns out that A = {A} describes an oscillator.

For Spencer Brown’s followers this is nothing short of the creation of time from form, which may be right but (at least to me) sounds somewhat more grandiose than the operation really is. For anyone who wants to get a glimpse into Spencer Brown’s Laws of Form without having to read the original (and I can’t blame you), check out Robertson, Some-thing from No-thing: G. Spencer-Brown’s Laws of Form, Cybernetics & Human Knowing, Vol.6, no.4, 1999, pp. 43–55.

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