Open Letter to Garrett Lisi on E8 and Special Systems Theory

Jun 05 2011


Garrett Lisi

Garrett Lisi



Garrett Lisi–

Just thought I would contact you and let you know that your theory and mine have connections.

My theory is called Reflexive Autopoietic Dissipative Special Systems Theory, and connects to yours via the Freudenthal–Tits magic square ( E8 is the limit of that square. My theory is about the mathematical and physical basis of Consciousness, Life and Society based on anomalous structures that have unexpected and ultra-efficacious properties.

Basically the theory is this:

There are two schemas Systems and Meta-systems (environments, ecosystems, media, situation, context)

Systems are wholes greater than the sum of their parts and Meta-systems are wholes less than the sum of their parts (whole full of holes, like a sponge). Systems are Turing Machines and Meta-systems are Universal Turing Machines.

But there is a possibility that there are wholes exactly equal to the sum of their parts, like perfect numbers which are anomalies.

It turns out that there are three kinds of systems that are exactly equal to the some of their parts. These are related to the perfect, amicable and sociable numbers and other mathematical structures like hypercomplex algebras.

Thus the structure of this meta-theory is as follows:

  • Meta-systems (whole less than sum of parts), i.e. environments, ecosystems etc De-emergent, numbers less than whole, deficient
    • Reflexive Social Special System = sociable numbers = octonions = hyper kleinian bottle = super breather (cf O’Malley, Sandywell reflexive social theory) Consciousness
      • Autopoietic Symbiotic Special Systems = perfect numbers = quaternions = kleinian bottle = breathers (cf Maturana and Varella autopoietic theory) Life
    • Dissipative Ordering Negentropic Special Systems = amicable numbers = complex numbers = mobius strip = solitons (cf Prigogine, Adrian Bejan nb. construcal theory) Social
  • System (whole greater than the sum of parts) Emergent, numbers greater than whole, excessive

The Special Systems have the property of being ultra-efficacious because they are the emergent levels of negative entropy, thus entropy is lifted as a constraint ever so slightly in a local envelope of a far from equilibrium energy/matter flow.

The Special Systems combine together with the normal System to produce the Emergent Meta-system and that system I believe has its constraint in the Freudenthal–Tits magic square of which E8 is the limit.

Thus your physics is the limiting case of the Emergent Meta-system structure. That structure is as follows:

  • Seeds in a pod = traces (seeds)
    • Creation Operation = Lose unity of real numbers which gives complex conjugates = Complex Numbers
  • Monads in a Swarm = eventities (leaves)
    • Mutual Action Operation = Lose commutative property = Quaternions
  • Views in a Constellation = perspectives (flowers)
    • Schematization Operation Lose associative property = Octonions
  • Candidates in a Slate = genetic algorithm produced variations (fruits)
    • Annihilation Operation = Lose Division Property = Sedenions
  • Seeds in a pod = traces in nondual emptiness or void

The Emergent Meta-system is a structure that is relaxing to lower and lower energy levels, and it is bound and given its finite limits by the Freudenthal–Tits magic square which in turn is limited ultimately by E8.

So in effect your theory of particles is the theory of the limits of the Emergent Meta-system cycle, and thus that cycle and the Special Systems fills in the stages related to that limit which allows Consciousness (dissipative ordering), Life (Autopoietic Symbiotic) and Society (Reflexive Social) to exist as ultra-efficacious, i.e. hyper-effective and hyper-efficient processes as described by the constructal theory of Bejan.

For more information see Reflexive Autopoietic Dissipative Special Systems Theory at, also Reflexive Autopoietic Systems Theory at that same site. See also my dissertation called Emergent Design at or See also and my blog at where  copy of this letter will also exist as a blog post.

I was fascinated by your theory based on E8, and I thought that I should tell you about my theory of Special Systems which I realized connected to your own theory as its ultimate limit. It is interesting that the ultimate limit that describes the properties of the fundamental particles is the limit of the Emergent Meta-systems’s energy well. The universe with its dark energy and dark matter is itself a far from equilibrium system we have recently discovered, that it is accelerating in its expansion. Therefore these Special Systems that give us the possibility of Consciousness, Life and Society, as ultra-efficacious structures are part of the structure of the universe itself acting locally as anomalies, for instance in the self-organization of Galaxies on the macro scale.

See also my theory of General Schemas which identifies the ontological emergent levels of projection which are pluriverse, kosmos, world, domain, meta-system, system, form, pattern, monad, and facet. These are different from the ontic emergent levels like quark, fundamental particle, atom, molecule,  macro-molecule, virus, cell, multi-cell organism, species, societies.

System and Meta-system are the central schemas in the list of Schemas we project, and the Special Systems exist as partial thresholds between these two schemas. The set of schemas themselves form Autopoietic Reflexive ring like structure, and thus our projected templates of understanding at various scopes is itself based on the special systems, that describe anomalous phenomena in society (reflexive structures), psychology (Jung archetypes), biology, physics. This theory comes from a study of Plato’s Cities which is found in my Fragmentation of Being and the Path Beyond the Void ebook. Thus these special systems were known earlier in our tradition and in other traditions. I have found many precursors where these special systems were known previously. One example that stands out is Acupuncture Theory that is based on Autopoietic Symbiotic special systems organized structures that give a theory of the virtual flow of Chi in the Body. It is that Chi that you actualize when catch a wave and remain in its flow as you surf those waves that so fascinate you.

Anyway, perhaps this very brief survey of the theory of Special Systems will pique your interest.
Kent Palmer



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