Louis Kauffman’s Paper Proposal

The Virtual Continuum and Second Order Cybernetics

Beginning with a void, we explore outward to infinity in the manner
of Laws of Form and the classical theory of sets and ordinals. Beginning with no-thing we embrace nothing (with braces!) and find the enclosure of emptiness { } that mathematicians call the empty set, and that G. Spencer-Brown might call the First Distinction. Embracing embracing, we find the next simplest form {{ }}, and this is the form of second order cybernetics, where one can apply any concept to itself: thinking thinking, designing designing, distinguishing distinguishing, observing observing. Thus we find second order cybernetics right at the beginning in the emergence from a void. The rest of the paper will examine the consequences of this point of view for cybernetics and mathematics. In particular, we shall see how infinity and virtual infinity arises and how these notions are related to the cybernetics of self-reference and to the inevitable limitations of language that lead us to imagine problems about the existence of worlds, where in fact, there is no problem and no world to be problematic in the context of creating creating.
Remarks. In mathematics there is a unique empty set { }. How does this come about? It comes about via the definition that two sets are equal if and only if they have exactly the same members. Any two empty sets have the same number of members, namely NONE! So any two empty sets are equal. When we speak of emptiness or a void, it is a different matter. There are as many voids as there are observers.
A void is a clearing made by some observer. A void is a relative emptiness. A void is a creative place to start making whatever might be made. Thus I have started this abstract with the phrase “beginning with a void”. I do not begin with anything absolute. I begin with a quiet space cleared by the author for the sake of creation. It is in such a space that reflection and self-reference can occur. It is in such a space that cybernetics might unfold. It is in such a space that we might contemplate embracing embracing and arrive at a second order. There is one further matter to remark upon. How did mathematics get away with this uniqueness of the empty set, if the empty set is just a sort of void? Ah yes. That happened by the definition of equals. Equal does not mean identical. Equal means sharing some property such as having the same members. So there could be many empty sets — all different containers with nothing in them. An empty bag. An empty vase. An empty mind. An empty bracket. But the definition in the mathematics says that they are all “equal” since they are all empty. This is the power and the tragedy of mathematics, that it can span infinities by ignoring particularities and embracing properties. Cybernetics provides a context of understanding for the embracing of embracing.

Cybernetic traditions:

  • 3) Experimental epistemology; constructivism; philosophy of science
  • 7) Art; design; music; literature

1 thought on “Louis Kauffman’s Paper Proposal

  1. Faisal

    Lou,
    You said:
    There are as many voids as there are observers.

    Interesting. So if you want to model a void you are really modeling an observer. Does this mean there is third order cybernetics or do we stop at second?

    Reply

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