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Andrius Kulikauskas

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Andrius Kulikauskas: Welcome! This is where I record my latest research notes.

The relation between {$CT$}-groups and Clifford algebras in terms of their representations gives a way of looking at the symmetries in a new way where the locations on the Clifford clock are shifted by {$+2$}. That may be related to this link between structure and recurring activity, how they evoke each other. The quantum symmetries are defined with two different interpretations and that is what the operation {$+2$} may be all about.

Conjugation of an element of complex numbers can be related to reflecting a Clifford algebra generator. Think of a Clifford algebra generator as being a complex number, an imaginary number.

When we keep adding generators {$+1$} how does {$M_2(C)$} express itself? What is used as {$i$}? And what is this third generator that squares to {$+1$}? How do these generators relate to {$C, iC, iCT$} for the CT-groups? Going in the positive direction, when you get to {$M_2(H$)}, what is the {$i$} and {$j$} inside? How is that expressed? How are {$i,j$} are getting expressed especially when the generators are squaring to {$+1$}?

Consider how divisions of everything are defined in terms of the complementary perspectives given by the generators squaring to {$+1$}. How does that relate to the sevensome, sixsome, fivesome. How do the antiautomorphisms convert over?

For the super division algebras consider that the generators square to {$-1$} or to {$+1$}. Compare that with the {$8$} different inner products to see if the {$p,q$} may yield all {$8$}.

The automorphisms in Todd Trimble's discussion of super division algebras can basically be thought of as antiautomorphisms so I need to see how they relate to reversing, conjugating, involution. I need to understand the particular automorphism in the complex periodicity case because that will link in with the spinors and make the picture complete.

Schroedinger's equation includes the complex number {$i$}. So how does that relate to the {$i$} in the equation {$H=im$}? I should put {$im$} as a solution into the Schroedinger's equation and see what it says about {$m$}.

Try to interpret the imaginary number {$i$} as a perspective like {$J_1$}. What is it doing to go from {$m$} to {$H=im$}? What does it mean in the reverse direction? {$H$} has real eigenvalues, {$m$} has pure imaginary eigenvalues (rotations). Is {$m$} like imaginary energy? What does that mean? How does that relate to imaginary time?

The skew-symmetry constraint is in addition to the constraints given by {$J_1,J_2,\cdots$}. So think how that interacts. And to realize that skew-symmetry is for all of them. So when we just have skew-symmetry that means we have no additional restriction.

  • Skew-symmetric matrices have pure imaginary eigenvalues. These eigenvalues are fourth roots of unity, at least the imaginary number {$i$} is, and that's the fourfold periodicity. And then with spinors it gets twisted so that if you go around you get the opposite state so that gets multiplied by two and that gives us Bott periodicity. So that should be the heart of it, interpreting the fourfold turn by {$i$} and the spinor twisting.

Analyzing twofold complex Bott periodicity. We end up with matrices that are two copies of themselves. In what case is that a collapse? If the original case was multiple copies, perhaps infinite copies, then we just got back to where we started.

  • The key being that if you have infinitely many copies for yourself. That may be fine for a user requirement, for things that aren't. Whereas it would be a problem for things that are.
  • Making two copies is reproduction so it is interesting how that relates to biological reproduction.

A Hamiltonian is a perspective in that it is left over as we go deeper, commuting further and further, it is what does not commute, so it is part of the division of everything, what gets divided away. Whereas the thing that commutes with everything would be a zero.

The Hamiltonian is maybe giving the view from outside (the operation +1) of the division of everything, so it is looking into everything that it commutes with. How does that shift the starting point? Why is it that these linear complex operators jump in from the very beginning? Would complex numbers be like {$aI + bJ_1$}? Are they aligned up correctly? I have to think about that.

The generators of the symmetric group where you have tuples, 1 goes to 2, i goes to i+1, these commute if they aren't adjacent, and if they are adjacent they join together to make a larger link. (i i+1)(i+1 i+2)(i i+1) = (i i+2). So the bring to mind the chains of simple roots in the Dynkin diagrams.

The Hamiltonian doesn't commute with {$J_4$} and then the higher perspectives (it does commute with them) but when you restrict to that subspace then because its an isometry it can't fit in that subspace. So it can't be taken as an operator as itself. So that may be like the level "whether", the base level which is not accessible but it reaches out into the other subspace as the isometry. Think about that as a general concept.

Parity symmetry when it exists is {$J_2J_3$} and then {$J_4J_5$} where these are the highest possible shifts. And then I should check if it could equal {$J_6J_7$} and {$J_8J_1$} if that could mean anything.

Generally, {$H=J_1m$}, with {$J_1$} the first perspective, all the way up to experiencing the final perspective, which could be considered {$m$}. So {$H$} is the shift in perspective from the beginning to the end. And {$m=HJ_1^{-1}$} could be thought of as {$H$} with {$J_1$} modded out.

Usually complex numbers commute. So you could think of linear complex structures as identifiable with {$i$}. So they should all commute. But actually they all anticommute. Similarly, the quaternions {$i$} and {$j$} anticommute. Are they all antilinear? (What is {$i$}? and that is linear with regard to itself.) We're looking for something that would commute with the Hamiltonian, which they generally do, but that would be linear (?)

A Hamiltonian is a self-adjoint operator, equals its conjugate transpose, so the conjugate equals the transpose. There are two different ways of giving the same information. This is what the two minds are striving for, this self-adjointness, and the third mind is this self-adjointness. I should put that in the Theory Translator. And this could be extradynamical culling by which a Hamiltonian evolves over time as a subsystem of a whole system.

The point of linear algebra is that you can express in either way: the transpose externally switches the arrow of the entry, and the conjugate switches internally the sign algebraically, positive or negative. So you have both options.

The Dynkin diagrams for the onesome and the twosome has no shift in perspective. For the threesome there is a single dot, meaning a single shift in perspective, but there is no extra shift in perspective noted. And for the foursome there are two shifts in perspective but there is no link. What does that mean?

In the Dynkin diagrams {$B_k$} has an angle of 135 degrees between two shifts in perspective. And that angle functions like an additional perspective looking upon the shift between shifts in perspective.

For the Hamiltonian, the conjugate and the transpose are the same thing, but they are two different expressions. Conjugation will make it antilinear and transposing it will make it transposed. Depending on which expression you use, you will get a different symmetry.

Perspectives are fermionic whereas views are bosonic. There can be many views with the same perspective.

John distinguishes the classical world (local) and the quantum world (global). Globalness is like God's (spirit's) togetherness and localness is like human's (essence's) separateness. That is the relationship between God and human but also between the quantum world and the classical world.

Hamiltonian is the final generator, for example, {$J_7$}, and the initial generator {$J_1$} expresses {$i$}, the real structure (as with {$J_2J_4J_6$}), and is also important.

Hamiltonian is a self, the last perspective in a division of everything, expressing the whole of the previous division, the the outcome of the operation {$+1$}.

Study time reversal and how it expresses antilinear behavior and how that can be gotten by the product {$J_2J_4J_6$}.

{$J_1, J_2, J_1J_2$} expresses the quaternions and perhaps {$J_5, J_6, J_5J_6$} expresses the

  • The quaternions should be related to {$J_1, J_2, J_1J_2$} and to {$J_5, J_6, J_5J_6$}, whereas {$2\times 2$} real matrices should be related to {$J_3,J_4$} and the isometry {$J_3J_4$}, and likewise with {$J_7,J_8$} and the isometry {$J_7J_8$}.

Line up charge conjugation, time reversal, and symmetric and anti-symmetric bilinear forms, and the antiautomorphisms reversing and conjugation.

Relate John's ideas of measurement (with probes) with the idea of probing in the Yoneda lemma with regard to topological spaces.

If you have one shift or two shifts and you go through them, then you end up in a different place. If you have three shifts or no shifts then you stay where you are. So three shifts (or no shifts) is like a three-cycle, it keeps you where you are.

In the Chevalley action, a single generator of U acts on lists of shifts in perspective by adding a minus sign to each generator, which keeps it the same if there is an even number of shifts, and switches the sign if there is an odd number of shifts. And compare this with the effect of real structure, which distinguishes between generators in the vector subspace where the real structure doesn't change the sign, and where it doesn't. This suggests that it establishes a real structure.

Look for relations between catastrophe theory (in bifurcation thoery and singularity theory) and divisions of everything and the ways that classical root systems describe the symmetry of counting backwards and forwards.

See also hysteresis.

Quantum symmetry C is commuting with the Hamiltonian which is iM and m and H are broken up by J_k because it commutes with H and anti-commutes with m. Here we have the quantum symmetry acting on the eigenvector of H. We need to compare that action with the actions of the various automorphisms and antiautomorphisms of the Clifford algebra and what are they acting on.

Chevalley action of V=W+W'+U. A single generator of the one-dimensional subspace U acts on lists of shifts in perspective by adding a minus sign to each generator, which keeps it the same if there is an even number of shifts and negative if there is an odd number of shifts. Compare this action with real structure, which distinguishes between generators in the subspace which doesn't change the sign and the subspace where it does change the sign. So this suggests that this involution automorphism establishes a real structure.

Are the 4 quantum symmetries (identity, time reversal, charge conjugation, involution) related to the 4 classical Lie algebras and their Dynkin diagrams, their widgets at the end of the chain?

My proposed talk considers Bott periodicity of spin representations to further distill the underlying mechanisms and how they express the conceptual frameworks. Here are some pages where I'm working on that.

The orthogonal group {$O(n)$} has two connected components. But the indefinite orthogonal group {$O(p,q)$} where {$p,q\geq 1$} has four connected components, which are images of the four quantum symmetries: identity, time reversal, space reversal and their combination (charge conjugation).

Varlamov 2001, page 7, expresses the quantum symmetries in terms of the representation of a Clifford algebra generator.

  • Involution {$A^\star = WAW^{-1}$} where {$W=\rho(\omega)$} and {$\omega=e_1\cdots e_n$} is the volume element.
  • Reversion {$\widetilde{A} = EA^TE^{-1}$} where {$E$}, the matrix of the antiautomorphism, satisfies {$\rho(e_i)=E\rho(e_i)^TE^{-1}$} and {$E^T=(-1)^\frac{m(m-1)}{2}E$}.
  • Conjugation {$\widetilde{A^\star} = CA^TC^{-1}$} where {$C=EW^T$} and {$\rho(e_i)=-C\rho(e_i)^TC^{-1}$} and {$C^T=(-1)^\frac{m(m+1)}{2}C$}.

Note that these mappings, when taken to define symmetries on the generators, accord with the quantum symmetries on the Hamiltonians, for {$UU^\dagger=I$} thus {$U^\dagger = U^{-1}$} for unitary matrices. And also {$H=im$} and so the imaginary number {$i$} gets conjugated, making the Clifford algebra generator change sign.

Bott periodicity quadratic reciprocity. Compare {$\frac{(p-1)(q-1)}{2}$} with {$\frac{(n)(n-1)}{2}$} so that {$p=q+1$}.

Analytic Discrete Self-Similar Solutions of Einstein-Klein-Gordon at Large D Could this relate to singularity theory and Bott periodicity at large dimensions?]]

A permutation corresponds to a pair of standard tableaux of the same shape. Among permutations, involutions are those pairs which have the same standard tableaux twice. (Write out the numbers 1 2 3 4 5... and then keep the fixed points fixed but swap the paired numbers as 1 3 2 4 5... indicating (23) and then insert in that order, popping up as needed.) Then one standard tableaux is a geometric construction, recording how it was built. And the other standard tableaux is understood as an algebraic labeling of the sequence that triggers the algorithm. And the algorithm ends up placing those labels in accord with the construction, if the permutation is an involution.

Condensed mathematics

Robert P. Langlands. Representation Theory: Its Rise and Its Role in Number Theory.

Generating all mathematical functions with {$\textrm{eml}(x,y)=\textrm{exp}(x)-\textrm{ln}(y)$} and {$1$}.

  • {$\textrm{eml}(x,1)=\textrm{exp}(x)$}
  • {$\textrm{eml}(1,x)=e-\textrm{ln}(x)$}
  • {$\textrm{eml}(\textrm{eml}(1,x),1)=e^{e-\textrm{ln}(x)} = \frac{e^e}{x}$}
  • {$\textrm{eml}(1,\textrm{eml}(1,x),1)=e-\textrm{ln}(\frac{e^e}{x})=e-(e-\textrm{ln}(x))=\textrm{ln}(x)$}

Mathematics in light of representation theory

Jordan algebras (ab+ba) and Lie algebras (ab-ba) may work together. The types of (Euclidean) Jordan algebras relate to R, C, H, O.

  • John Baez considers the octonionic qutrit.

The difference between semantic choice (left + right) and syntactic choice (include + exclude) is based on the difference between bosonic (commonness) and fermionic (separateness). And semantic choice expresses the second mind.

The number {$\binom{n+k-1}{k}$} counts the monomials of degree {$k$} which are built from {$n$} variables {$x_1,x_2,\dots,\x_n$}. This can be interpreted as

{$\binom{n+k-1}{k}= \sum_{k=1}^n\binom{n}{j}\binom{k-1}{k-j} = \sum_{k=1}^n\binom{n}{j}\binom{k-1}{j-1}$}

We choose {$j$} of the variables and we choose {$j-1$} of the {$k-1$} possible placeholders which tells us how to assign the extra powers so that we get {$k$} powers in all.

A. Clark, K. Friston & S. Wilkinson. Bayesing Qualia: Consciousness as Inference, Not Raw Datum.

https://sites.google.com/view/berkeley-cs294-158-sp20/home

Relate double cover with reflection and two minds

The two kinds of free energy and the Bayesian revolution

Luca M. Possati. Markov Blanket Density and Free Energy Minimization.

Think of randomness of spin, etc., as a conservation law that applies to the entire universe, that the total of the possibilities has to be conserved. If it happens one way in one instance, then it needs to happen in the other way in another instance. Although this is the basis for primitive thinking about probabilities.

Camilo Miguel Signorelli, Joanna Szczotka, Robert Prentner. Explanatory profiles of models of consciousness - towards a systematic classification

suspense and PTSD: defensive pessimism

How can you use a tetrahedron to untangle a trefoil knot in four dimensions? And why would that be important?

Orthogonal Sheffer polynomials

  • The only difference between A(t) and u(t) is multiplying by x.
  • x takes us across the plane. No x: do not cross the plane. Also: odd powers vs. even powers. Spinors?
  • What is encoded by the roots? by the eigenvalues? (Yoneda lemma)
  • Can imagine A(t) is compartmentalized (compact), or not (noncompact), or mixed. What do these interpretations look like?

Physical processes that can be measured have natural randomness due to measurement and have fivefold "canonical links" related to the presumptions of measurement.

Entropy

Arnold Silverberg. Psychological Laws. About Norman Anderson's theory. I photographed a copy.

Time reversal symmetry

Physics has two frames, absolute and relative

  • position is absolute
  • momentum is relative
  • charge conjugation swaps them, time reversal makes relative negative
  • time is focused on the relative arrow, its direction with regard to itself

Jere

  • quaternions, attaching meaning to +1 (past) and -1 (future) and 0 (present)
  • word - language. World - whole.

Bott periodicity

  • Look for exact sequences - chain complexes (divisions of everything) in symmetric spaces and Lie groups.

Ergodic theory

  • Time evolution of a system. Never do we see states that are invariant in time but not constant in space.
  • You can replace time averages with ensemble averages.
  • Link density of states with averages.
  • Ergodic hypothesis and maximum entropy = statistical physics

Daniel's paper?

  • inference = atomic investigation = third mind
  • fourth mind = 24-fold system of third mind

Yoneda lemma

  • kaip išreiškia atspindžius kategorijų teorijoje?

Bott periodicity

  • J_1 anticommutes with U(8), whereas J_5 anticommutes with U(2) but furthermore everything prior to it

Graphical explanation for length contraction

https://thoughtforms.life/suti-the-search-for-unconventional-terrestrial-intelligence

https://thoughtforms.life/why-the-tight-clustering-of-mathematical-constants/

https://grahampriest.net paraconsistency in philosophy, time

information-theoretic derivation of the prime number theorem

You lose perceived time when you lose ability to see the sensory information.

Eckehart Kohler. Why von Neumann rejected Carnap's dualism of information concepts.

Compare derivation (product rule) in:

  • Kalman filter (though it has a denominator)
  • entropy - operads
  • energy as the sum of two terms

And does this say anything about the three minds or comparing the first two minds?

https://pubmed.ncbi.nlm.nih.gov/29292362

Wikipedia: Spin-statistics theorem

Several forms of the three minds - quantum symmetries, quantum foundations (states, observables, measurements), energy and entropy (knowledge lens vs. knowledge gained) predate biology, chemistry and natural selection.

On the fundamental group of {$RP^2$} being {$\mathbb{Z}_2$}. I visualize it as a point moving on either side of a half-disk, or alternatively, as an axis moving. If I move the point to the opposite side (arriving at the same point) then I have a commitment, an obligation, to be at that point. But if I concatenate with another such path ending up back to the original side, then the obligation goes away, and so there is nothing to keep me from shrinking the resulting loop. The obligation relates the initial point and final point, not any point in the middle.

Cross-entropy is what I am equating with energy.

The form {$Q(x)\ln\frac{1}{P(x,y)}$} expresses that the probability {$Ω(x)$} may equal zero (and thus models an observer) whereas the probability {$P(x,y)$} may not equal zero (and thus models the observed). This is one way to distinguish an observer and an observed.

Think through inverse temperature (which is the relevant concept, rather than temperature) as "perturbability", "sensitivity", "receptivity" or "confusion" (increase in ambiguity per energy).

Energy, entropy, free energy relate the observer (knowledge lens) and the observed (knowledge gained). Disequilibrium is required for there to be useful work. Because it means that there is recoding of one system in terms of another. Recoding a system into itself is useless, thus is entropy. Learning, gaining knowledge, making Q(x) more specific, increases entropy.

Connectomic traces of Hebbian plasticity in the entorhinal-hippocampal system

Stephen M. Fleming, Nicholas Shea. Quality space computations for consciousness.

Eleonora Grasso, Maria Corteze, Helene Schmidt. Connectomic traces of Hebbian plasticity in the entorhinalhippocampal system.

Elliott Hauser. Facts in the machine: Systems of record and the performance of sociotechnical truth

https://www.cisek.org/pavel

synchronization manifold

cognitive modeling

  • reinforcement learning
  • expected utility theory
  • cognitive architecture modeling
  • signal detection theory
  • probabilistic Bayesian modeling
  • variational Bayesian predictive processing
  • control theory and cybernetics
  • sequential sampling modeling
  • dynamical systems modeling
  • connectionism
  • rule-based and heuristic modeling
  • quantum-inspired models
  • logic-based models

Manuel Gustavo Isaac. Conceptual Engineering: A Systematic Unified Framework.

Wolfram Physics technical introduction

Luke Darlow, Ciaran Regan, Sebastian Risi, Jeffrey Seely, Llion Jones. Continuous Thought Machines.

{$Rec \equiv \varnothing'''$} relates, for each x such that {$W_x$} is recursive, two machines, one that halts when the other does not, and vice versa. These two machines are entangled, as when one particle is spin up and the other is spin down.

Nancy Kanwisher. The Human Brain. MIT Videos.

Roly Perera: Subjectivity via Self-Simultation: Virtualising the Cartesian Theater. (About heterophenomonelogy - our inner subjective life).

Wikipedia: Entscheidungsproblem: Quantifier_prefix is a section on the undecidability of the form "for all there exists for all there exists"

Kevin Kelly. Notes on Computability

Daniel Ari Friedman. On Cognitive Art & Science: Toward Wholeness From Both Sides

Chris Fields, Karl Friston, James F. Glazebrook, Michael Levin. A free energy principle for generic quantum systems.

Noah Chrein. Yoneda Ontologies.

Chris Fields: If Q1 and Q2 cannot be deployed or measured simultaneously, because they don't commute, then they must be implemented by compartments that communicate classically. So this explains how linear complex structures can be modeling compartments, and says that means they are to be interpreted classically.

Róbert Szőke. Quantization of compact Riemannian symmetric spaces.

  • John Baez: Symmetric spaces give the ways of quantization, in my words, of choosing a Lie subgroup from a Lie group.
  • Geometric quantization

Paul Badcock. The Zone of Bounded Surprisal: Raising further questions

  • Vervaeke's 4P's / ways of knowing: propositional, procedural , perspectival, participatory.

A taxonomy of surprise definitions

Héctor M. Manrique, Michael J. Walker. To copy or not to copy? That is the question! From chimpanzees to the foundation of human technological culture.

Closed-loop control theory

Karl J. Åström and Richard M. Murray

Adam Safron

Karl Friston: Can only know itself through acting.

Adam Safron - quasi-Cartesian interpretations. Bayesian blur problem (Andy Clark). The lived body vs. the mind's eye.

Susan Hasty: ​Yes, my focus is on participatory underwriting that reduces prediction errors (anticipatory) vs traditional underwriting that reduces consequences of losses. Underwriting relative to cumulative tradeoffs, please.

How quantum is life

Think of how to construct the {$J_i$} in a step-by-step way by twisting and permuting as necessary. Relate this to John Baez's forgetful-free adjunction for representations of Clifford algebras.

  • “Bayesian Statistics the Fun Way” by Will Kurt
  • “Foundations of the Theory of Probability” by A.N. Kolmogorov
  • “The Scientific Image” by Bas Van Fraassen
  • “An Introduction to the Philosophy of Science” by Kent W. Staley
  • “The Philosophy of Language” by Aloysius Martinich
  • “The Semantic Conception of Truth and the Foundations of Semantics” by Alfred Tarski
  • “Tractatus Logico-Philosophicus” by Ludwig Wittgenstein
  • “Logical Investigations” by Edmund Husserl
  • “An Introduction to Non-Classical Logic” by Graham Priest
  • “Modern Multidimensional Calculus” by Marshall Munroe
  • “Axiomatic Set Theory” by Paul Bernays
  • “Computational Modeling of Cognition & Behavior” by Simon Farrell and Stephan Lewandowsky
  • “Math for Deep Learning: What You Need to Know to Understand Neural Networks” by Ronald T. Kneusel,
  • “The Neurobiology of Neural Networks” by Daniel Gardner
  • “Multilevel Structural Equation Modeling” by Bruno Silva
  • “A Course in Time Series Analysis” by Daniel Pena

Spinoza's Ethics in the spirit of triangle geometry.

Janna recommends

There are some nice d3.js courses in udemy.

Frequentist, looking to the past - the answering mind. Bayesian, looking to the future - the questioning mind. Postdiction - predicting the past, the uncertainty in the past - is perhaps the investigatory mind. That allows for changing one's mind, one's mental model, and not just one's belief.

Quantum computing forums

Three-cycle has us choose a particular statement from within our generative model that we want to put to the test. That is Willful Inference.

A shift in perspectives is the reinterpretation of active inference as passive inference. And this can form a stable three-cycle which allows us to stably distinguish willful (taking a stand), active (following through) and passive (reflecting). The stability of the three-cycle is the stability of the two eigenspaces {$V_+$} and {$V_-$}.

Relational symmetry paradigm - linear relation is continuous and emblematic of the unconscious, the answering mind.

Association for the Scientific Study of Consciousness 2025 Conference Program

Bernd Anton Schmeikal. Logic Quaternions.

Michael Levin: Cells creatively interpret DNA and their situation. (Third mind.)

David Spivak: Attending, caring.

David Spivak: Computation happens only if somebody has an interest, expends energy, to make it happen.

Robert Rosen

David Hyland. ResearchGate. Oxford University. Active Inference.

Steven Rude. Insight Meditation and Reality Alignment: The Neuroscience of Predictive Brain Processing vs. Present Moment Sensory Updating.

Bosons (photons) traveling at the speed of light don't have passage of time, don't have any notion of time. So they don't have a problem with "spooky action at a distance". It is only fermions that have a problem. Fermions are the basis for space-time.

Wave function - double slit experiment: interference pattern comes from all of the particles that will go through the slits in a time period which may extend into the future - the time period is determined by the carving up of time - as carved up by the sublattice symmetry.

Maximize entropy to understand causes and minimize entropy to protect self from diffusion.

Antonio Garcias, Friston coauthor, billionaire

Lower bound on expenditure of energy: switching a single bit, a quantum of information. Landau's principle.

Precision and uncertainty: precision-weighted prediction error. Attention.

Two kinds of expected surprise

  • expected surprise as uncertainty
  • expected surprise as avoiding bad things (which I may know precisely)

homeorhesis, allostasis

Giulio Ruffini computational neurology

Tim Mauldlin. Time reversal is complex conjugation because you fix position but reverse momentum.

Majid Beni. Carving teleology at its joints.

Karl Friston. Perception and self-organized instability.

Karl Friston. Path integrals, particular kinds and strange things.

Karl Friston. A variational synthesis of Evolutionary and Developmental Dynamics

Karl Friston. A free energy principle for a particular physics.

  • Explains the renormalization group.
  • Gives a scale-free aspect from all the way up to all the way down.

Chris Fields

  • Separability, Contextuality, and the Quantum Frame Problem

Chris Fields. Michael Levin. Minimal physicalism as a scale-free substrate for cognition and consciousness.

  • Stygmergic memory.

E.T.Jaynes The Minimum Entropy Production Principle

Carlo Rovelli looking at self-organizing systems.

Jeremy England ratcheting of levels of self-organization

Ping Ao

Two track mind - next word vs. next idea - comparing the two streams.

Conference: Metaphysics and the Matter With Things. Thinking With Iain McGilchrist.

Michael Levin. David Resnik. Technological Approach to Mind Everywhere: A Framework for Conceptualizing Goal-Directedness in Biology and Other Domains

Hernan A. Makse, Paolo Boldi, Francesco Sorrentino, Ian Stewart. Symmetries of Living Systems: Symmetry Fibrations and Synchronization in Biological Networks.

https://www.theguardian.com/technology/2025/jun/09/apple-artificial-intelligence-ai-study-collapse

Artificial super intelligence alliance dedicated to decentralized Artificial General Intelligence (AGI). Formed in April 2024, the ASI Alliance unites SingularityNET, Fetch.ai, and Ocean Protocol, with CUDOS joining as a network member shortly after. The unified token $FET underpins a collaborative framework designed to scale open-source AI research, infrastructure, and development.

Outreach

David Albert on the arrow of time, distinguishing dynamical laws from initial conditions.

Qualia Research Institute

Veronica Pasquarella. QFT from Category Theory | Particle Physics for Mathematicians. (Part 1)

Klein-Gordon equation for a single particle gives the expected answer for probability current. But for probability density, it says it is proportional to the energy, which can be positive or negative. But then a negative energy implies a negative probability density. Does this relate to the pf"holes"?

Are branes related to the choicę framework of an observer?

Pamela Lyon, Fred Keijzer, Detlev Arendt, Michael Levin. Reframing cognition: getting down to biological basics basal cognition, primitive version of cognition

The Need for a More Complete Model of Intelligence

Consider determinism in terms of the choice frameworks. If the choice framework does not have us carve up space, then it proceeds deterministically, according to nature. But it could be that when the choice framework carves up the space, then this carving up is super deterministic, and to balance that out, it opens up an indeterminacy, which manifests itself probabilistically with regard to the Born rule. In this situation of "the process of measurement", the process is partly creative, because it is superdeterministic.

Relate the measurement problem (states, observables, measurements) and the three minds with the kinds of choice frameworks, whether we are carving up space or not.

Carboxylic acid is the bookend for the Krebs cycle. Is it related to the foursome, relating the two branches as two shifts? What is its role in amino acids?

https://en.wikipedia.org/wiki/Donald_D._Hoffman interface theory

Berggruen Prize for Philosophy and Culture laureates

  • Charles Taylor (2016); Onora O’Neill (2017); Martha Nussbaum (2018); Ruth Bader Ginsburg (2019); Paul Farmer (2020); Peter Singer (2021); Kojin Karatani (2022); and Patricia Hill Collins (2023).

https://en.wikipedia.org/wiki/The_Order_of_Time_(book) Carlo Rovelli

Gabriele Carcassi. Why time is not an observable.

Pru Mendez. The Aiwon Code - Unveiling the Infinite Layers of E = mc².

Michael Levin https://files.osf.io/v1/resources/5g2xj_v3/providers/osfstorage/67a6189f05e0091426af4497?action=download&direct&version=1

Mathematical fonts

https://deepfunding.ai/terms/ gobbledygook

Overview, make sense of, and structure the purposes of the various neurotransmitters, human hormones and other physiological forms of signaling.

Obisidian organizing thoughts

Simon Grant. Types of thing in the world. Including links to ontology projects, his own and others.

John A. Shuster. “HeartMinds” in HeartMind space.

Wikipedia: Symmetry-protected topological order: A complete classification of 1D gapped quantum phases (with interactions)

Eckhard Meinrenken. Clifford algebras and Lie groups. Chapter 1. Symmetric bilinear forms., Chapter 2. Clifford algebras.

Marc Lachieze-Rey. Spin and Clifford algebras, an introduction.

John Baez explains in his notes on the tenfold way how the classical Lie groups (in the geometric embeddings) can be defined as the "unitary" elements of Clifford algebras, where the latter are {$*$}-algebras, where {$*$} maps generators {$e_i$} to {$-e_i$} and maps {$ab$} to {$b^*a^*$}. But this becomes tricky to calculate...

We have that Lie groups are the "unitary" subgroups of Clifford algebras (generated by {$e_i$} with {$e_i^2=-1$}) considered as "*-algebras" (* is conjugation). As we grow the Clifford algebras, the even part of the Clifford algebra equals the preceding one. So how is it that the Lie groups can be thought of as subgroups, in the opposite direction? What is the role of the halving of dimension? What is the role of commutation by the generator {$e_i=J_i$}? What is the role of anticommutation?

Are Rumyin's four real representations related to the Dynkin diagrams of the classical Lie groups (and how they interpret the symmetry in counting)?

Economics

  • Wanting to develop an alternative to a monetary system, we need to negate the functions of money, having what is not storable, not a focus of authority, not measurable, not a medium of exchange.
  • Subculture economics is a way of becoming inclusive and it is a meaningful inclusion because it is a subculture inclusion.
  • What Marcus pays attention to, which is solved in his dreams, can be something trivial or profound, and it is his choice which to focus on, just as a person who starts to think independently can choose between the current thought and an earlier thought she saved.
  • The four functions of money are based on ownership for the ideal participant, who is sovereign over the property of value and the sign of their authority gives where they are in the system.
  • How does the shrinking of the dimension of the Lie group relate to John's concept of culling and the factor 2?

In the ways of figuring things out, in the system 4+6 you go from the question to the answer so the arrows move from Why to How, What and Whether.

Algorithmic probability, a mathematical method of assigning a prior probability to a given observation.

Ray Kurzweil - cortical layers

Octonions are alternative and thus ŽDŽDŽ is associative but ABC... is not.

Geometry based on projective modules.See Daniel Chan on vector bundles.

How do classifying spaces relate to my video on Sheffer polynomials as space builders?

Building up Bott periodicity is a lot like building up a basis. The first vector can be anything. But with each new basis vector you have to check that its not dependent on the other ones. Similarly with the linear complex structures, or with the generators of a Clifford algebra, or in the iterated loop space, they come in sequence.

A circle is really a line with a point of infinity. It should be understand as a map relating to a point. And that point which is involved in that map, and the circle, they have a relationship. And together that seems what a perspective is all about.

A projective line is nondirected but it can be broken down into a line going forward and a line going backward. It is the same topologically as {$S^1$} but that is the difference being captured.

Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called asymptotic freedom. (Comparw with threesome or fivesome)

Are symmetric spaces (quotients of Lie groups) related to Lie algebras and how?

Rudolf Steiner. Human and Cosmic Thought. Lecture II.

Daniel Friedman's relationship with truth relates the first mind's truth and the second mind's truth.

Clean Up

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This page was last changed on August 02, 2026, at 08:31 AM