I see that your application of metaphor and allegory falls on a different level of order than my own thinking. In that sense, yes Chaos theory is metaphorical, not allegorical. I was thinking more of specific examples of models that exhibit chaos like behavior.. so I did misspeak.

For ex: A model that exhibits chaos like properties is what I would consider to be allegorical, because initial conditions lead the divergence to “circulate” within a set range. I would map the initial conditions as a difference in metaphor, one that never “breaks” the allegory of that particular model.

This reminds me of Paul Ricoeur’s work where he notes that all language/language games are metaphoric in nature; that the breakthrough of the “blank metaphor” copula *is* is the elimination of the latent content of metaphor. And in that sense, what can be said with *is* is limited; we can only say new things metaphorically before they become “nullified” and therefore acceptable as a literal is. In this way, we can consider things like ontology and set theory to be traceable developments in thought as a shared (social) practice evolving alongside human-group processing… which is interesting to think about but I’m not sure what its fuller implications are yet.

Thanks for the links, btw. They are intriguing. I think one difference is that I would see that monads and monoids are equitable, just from different points. It’s almost a truism that attainable truths are describable functors. Gregory Chaitin’s work searching for innumerable “holes” in the number line led him to develop Chaitin’s constant. The value-object of transcendental infinitesimals is the ability to encoding functions that would nominalize them. The impossibility of one is the impossibility of the other.

So I would see different sets as being collections of value-objects all belonging to the same functor. Under Axiom of Choice, the recognition of the ability to collect any arbitrary set matches our inability to ascribe limits to any given process-function (that could name/output/phenomenologize value-objects). So when I match sets to sets through pataphor it would be through different ᶠ and ᵍ, even though we are looking at A, B and C. What obscures our thinking in this way for set theory is the same problem with venn diagrams. Presenting the collections through either ST or VD assumes that the domain is the same when it’s not. You’ve alluded through to this issue with multi-dimensional venn diagrams. We’d have to assume that the spacial dimensional representations/set theory collections are non-relational — but from some obscure accident — at least partially compossible, at least where the pataphor coincides. Thinking about ST or VD in this way makes them appear more like manifolds… which, I think, is our dumb way of Euclid-alizing more complex topographies so that we can compare them and more intuitively grasp them.

So this is a little beyond pataphors, but I figure I’d share my own approach, since that’s how I understood many of the links you’ve included including the very exciting programming discussions.

This is what I would find astounding about Karan Barad’s work. It’s oblique but the inevitable frame for me is that all knowledge is process-generated-knowledge. All capturable/nominalizable difference requires navigating a value-tree to encounter it… the “dumbest” value-tree that is still navigable is a numeric list. But there are other procedural trees. Lawyers have terms that are meaningful only within the frame of navigating court procedure, which includes how they deal with clients and conflicts of interest (which, when extended maximally includes law procedures and policy lobbying). Building code, contractors and architects likewise have terms that are only meaningful within a given frames of finance, material construction, fire-safety regulations, “design languages/schools” and so on. In that sense, each piece of knowledge/jargon is its reified ontology given its ontic-historic branch (which is the originary procedure to encounter it).

Metaphors become copulas when we accept them as literal === knowledge becomes nominalized as knowledge when signifiers at milestones become indicators of decision-vectors within our material/processing. I make a living as a real estate broker, mortgager and building inspector (as well as a programmer) so all the jargon and legal, finance, banking issues are all be mappable in this way for me.

In that sense, pataphor IS the reality that we live and navigate in.

In 2007, the California code required accessible showers to be a minimum of 48″ x 42″. The Federal requirements were either 30″ x 48″ or 36″ x 48″. Each of these specified different locations for grab bars, controls and so on. So good luck finding a manufacturer of prefabricated showers that were an amalgamation of these two standards, which is a meta-metaphor of sorts.

Likewise, how we get a PDF from a website accessible only on a desktop/laptop computer (say a website that listed property for sale) to WeChat which only takes images (our client uses WeChat but doesn’t have email, or anything else), is a pataphorical tracing in terms of form… which we don’t think about because as humans (or investors/agents) we are focused solely on content.

I think that as humans, we can encounter difference in conversation and map them back and forth to have a conversation. Our approaches are different in many ways, yet we can still have a conversation. AI can’t do this; because it can’t distinguish/extract/ construct content from what is literally a pataphorical presentation. If we talk enough, we would calibrate each other’s thoughts so that the pataphor would become more stable, maybe as a metaphor or even as a literal allegory.

I’d say that our high level abstract commenting is a pataphor as well, between each of our different collections of methodological experiences. =)

]]>I think I see your point about chaos theory, but disagree. I agree that concepts like attractors and feedback loops are metaphorical in nature, and so can be applied in many different settings. And due to sensitivity to initial conditions, we can only a vague analogical sense say that two chaotic systems have the ‘same’ nonlinear properties. But it seems that because of this sensitivity to initial conditions, chaotic systems can’t handle substitution, *à la* tortoise → slug in allegory. For example, if you replace the ‘seed’ shape of a fractal, it becomes a completely different fractal. Thus I’m inclined to think of chaos theoretic concepts as also metaphorical — so there’s no ‘phase transition’ to allegory. Chaos theory is perhaps the closest that metaphors can get to allegory before they break down. I’d say this breakdown of allegorical structure is why chaos theory never caught on in economics.

Your characterization of pataphor as a Venn diagram is interesting—I hadn’t thought of that. One can think of **B** as a kind of ‘tangent point’ where the edges of **A** and **C** overlap. However, this approach plays down the differing natures of *f* as metaphorical/metonymic and *g* as non-figurative. Even using a 3D diagram, I don’t think there’s any way to account for this.

In your point about content and form, I take it you’re defining *f* as form and *g* as content? I think this works. Of course the hard part is finding what counts as **B**.

Your point about pataphor being applicable to cryptography and hackers is right-on. There’s actually a field called cryptographic mechanism design, since the concerns of the two fields so often overlap. (Just think of hacking as trying to game the system.) There’s a lot of hype about ‘cryptoeconomics’ right now in relation to blockchain-based technologies, but the really deep crypto-related stuff is happening in mechanism design. Still, this might be a nice way to sell this idea to non-economists. Thanks for the reminder.

I’m afraid your points about Skolem’s paradox, Badiou, and the axiom of choice go over my head, as I’ve read very little on any of them. Due to the above point about Venn diagrams, I’m a bit suspicious about viewing pataphor using sets. Still, it’s all very alluring, and if you care to elaborate I’d be quite interested.

As for category theory, someone once proposed the notion of ‘patamorphism’, facetiously defined as “a patatoid in the category of endopatafunctors.” I can’t really follow their argument, as most of it is in Scala code, but it would be really cool to explicitly formulate this idea.

Curiously, pataphors live in a quite different universe than categories because by definition they don’t obey the rule that given arrows A—ᶠ→B and B—ᵍ→C, there must be a composite arrow A—ᵍ∘ᶠ→C. That is, the diagram for a pataphor doesn’t commute; only meta-metaphors have this composite arrow. A category must also have an identity (here, the zero-pataphor ₱) such that ₱ ∘ P = P and P ∘ ₱ = P — but as you’ve seen, even making sense of that is a struggle. So while I think it’s too strong to say that ‘pataphysics provides an “inverse” of category theory (‘patagories?), we might think of pataphor as a bizarre, non-commuting variant of categories. I wish I knew more category theory — it would help a lot, especially since meta-metaphor only makes sense in terms of diagram-chasing.

It’s really exciting to think of how pataphor can be applied in other contexts. So far I’ve found that hyperstition has a pataphorical structure. Christian Bök’s xenotext project (in which he encodes a poem into DNA and injects it into a virus, which then writes a ‘poem’ of its own in the form of a protein) can also be viewed as pataphorical. Perhaps one day people will recreationally create pataphorical structures in their discipline the same way programmers write quine programs for fun.

]]>– Chaos Theory is the difference between allegory and metaphor (as defined above). Chaos theory is the union of many expressed particular (metaphors) that fit an allegorical form.

– At first I was thinking a pataphor as being a venn diagram of A and B where there is no A+B; but then it’s better to say that we can map a *p* that is in A and also in B.

– Then I was thinking *p* could be an element Skolem’s Paradox of both A and B, where some subset of items *a* = *p* and some subset of items *b* = *p*.

– A pataphor is a way to bridge content and form. It’s the non-connection between the semantics of a Word document and the encoded binary (or any particular api level and another api level).

– Given the above; “hackers” can work through Skolem’s Paradox. They can find a “key” that belongs but is uncountable — in cryptography. But another concrete way is to use those belonging items (but are uncountable) to jump between secure domains. InfoSec would want to create a secure domains. But hackers use the pataphorical translations that aren’t categorical in themselves, but defy categories through their particularity. So they can use your DMV records to get access to your IRS records, which unlocks your bank account. Another more concrete expression: here.

– Given Badiou’s *Being & Event II: Logic of Worlds* in how he defines a “world” each world’s local zero is a zero-pataphor. Žižek uses Objet petit a in this way, but he conflates zero-pataphors as being the same.

– Also, this gets outside of logic into process theory,* but I think that if we assume that each set is in fact selected from multitudes of undifferentiated difference (to use early Deleuze’s language), the “axiom of choice”—the “process” that creates each set—is equivalent to a combination of its “axiom(s)”. In that sense, inverse pataphors can make sense… but we are really just expanding the generalizations of the items that may be selected for.

In that sense, the family of pataphysics as an inverse of category theory (an inverse of the selection process of kind and type) can show us the omega of differentiation/ differenciation — where being-as-countable becomes being-in-kind.

I think the family of pataphysics can also be used to describe consciousness as “design space” to match material agency with semantic “cuts,” but I’m still trying to make that connection more coherent, since there are implications for programming, culture language and gene chunking — which is done naturally… as a function of entropy (energy) and energy (information).

*I would also suggest that philosophical process theory includes Karen Barad’s agental realism. Barad’s book is worth reading if you haven’t yet, but her writing is pretty atrocious. Like Kant she tries to express complex ideas but doesn’t yet have the language to outline the differences. So she keeps recycling the same words in different ways, making it monotonous and hard to understand.

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