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Bott Periodicity

The Bott Periodicity is hypothesized to apply to the cognitive states, and the +1/+2/+3, and hence the quest to understand it very well.

With the Bott Periodicity — groups of actions — Z2 is on/off switch, Z is integers, 0 is trivial. There is that pattern across the 8’s. Taking the matrix of Clifford Algebra, and looking at Matrix characteristics/size.

In the Split-Complex number — getting Z+Z. One of the Z’s goes away and you get the Z.

Particle-Whole, CPT, Time-reversals — these are like coming out of nowhere. And they seem related to 2some, 3some, 4some. If they could align.... For now though lost.

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Bott Periodicity Models Consciousness? Preliminary Exploration⁠

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8 cycle. 8 years now for AK since 2016. Now learning enough — Lie groups (of actions) are embedded (these are continuous groups of actions, like rotating a circle which can be summated). These can be real, Complex, Quaternion. There is high level of symmetry, e.g. like higher spheres.

These worlds, and the movement from→to. E.g. huge rotations in 16 dimensions. Add a linear complex structure (squaring to -1) — it adds structure, while also being symmetry-breaking. That leads to 8x8 complex output. Keep adding those linear complex operators, and as long as they are Mutually Non-Commuting (Clifford Algebras) — you don’t need to know about them, they determine the sequence of cycling of embeddings.

Then at the bottom — taking a world, and having it and having it and having it (refining the self?). “This part of myself is part of the world, this part is deeper”. Then when you get to the bottom of the 8 — you get back to the similar starting point (from the outside, the behavior, Yoneda lemma

Category Theory⁠

Now with some new tutorial — AK working on going Backwards — Sphere is symmetric in a more total way than a Cube. Let’s say you want to get back to the Sphere, after adding 3. Now trying to remove/restore 3, adding the structures back into the bigger place. This is where

Cognitive Frameworks⁠

come into play — the 3cycle, 4some, 5some. The evidence is building that these are natural modes of recovery.

If you are a little space, Dividing everything (between Total and Your space) — how to arrange the 4 perspectives, and so on.

It is all about the 2x2 matrices, and John Harland’s work on the extradynamical evolution as per

Biology⁠

Quantum⁠

and JH-AK interests are connecting.

deling Introspected Contexts With Mutually Anticommuting Linear Complex Structures⁠

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Application of mutually anticommuting linear complex structures to the orthogonal group O(16r)

Groups compose of actions

Lie groups — continuous actions, like rotation. Circle/Sphere can rotate, and also rotate across, and invert through (like sphere). It turns out, Orthagonal group are these possbilities. The group divides into 2 types, Reflections & Rotations. Once you reflect, you can’t get there from rotation. There is a metaphor that this is like mental rotation.

Rotation, as the least structured.

Adding a linear complex structure, multiplying by a big matrix (with i-acting blocks on diagonal) — interacting with this operator, everything will either commute or not. Rotations commute, the other ones do not because they have the reflection. So when this is applied, it throws away everything apart from rotation.

Continue with a mutually anti-commuting operator written in different Basis. Coming from different contexts, hence they see each other as different.

Build hierarchy — new linear complex structure, commuting with the 1st one, then commuting with the 2nd one (continuing to cut down by half). 2nd, complex symplectic Quaternion. Then 3rd, getting to two minds, which are related to each other as SPF2, .... — going 8 levels down, dimensions O(16) to single. Building blocks are the perspectives, filtering out the reflective parts.

Clifford algebras — quaternions with 2 building blocks — i and j squared go to negative one, and together ij go to negative 1, this is a 2-square (4D), and you can keep going. Linear complex structures are Clifford algebra generator. When you have 3, 4, etc. — divisions of everything are organized in a certain way like this.

Interpretation — divisions of everything

Imagine you have this thing of knowledge, what you know and do not know.

Reflection is coming from the 2nd mind, these are

Questions⁠

Start off that God knows everything. Then, he knows stuff about the Unknown (he knows the unknown and known). We are not interested in the 2ndhand knowledge, we want the directly knowable. Starting with all experience, then throw out the reflections, get to known of the known. Then K3 (known of the known of the known). Look at Clifford — as you are throwing away the reflective, 3rd level goes into 2 pieces, then 4th level, there are reflected/isometric parts.

If you throw the reflective stuff away, “I want the raw experience” — you’ve reduced yourself and the vector space is split into Unreflective and Reflective. Half the world is reflective, you can keep going deeper. Going 4 more times — you get this contradiction, no no no no is equal to the reflection. All is reflected and all is unreflected. You were out there looking for raw experience, and filtering out the heresay. And you get to the contradiction collapse point where everything is known and unknown

Three kinds of knowledge

Experience

2 - Unitary — when you know the know, you know the knower (you know the witness)

3 - If you know the knower’s knower — that is 4 steps in. Everything is converted into this knowledge.

If you start with Experience in general, or with “the knowledge that is known” — you get 8 fold thing. if you focus on the lived model of someone though, you get complex

Bott Periodicity⁠

not just the 8 cycle. You immediately split into 2.

We are going beyond ourself into God, and vice-versa, as knowers.

If you have a project of removing reflective knowledge. All this happens, and then it collapses. All the pieces of the

Wondrous Wisdom⁠

connect with

Bott Periodicity⁠

in this way.

There is a gap between

What/How — unconscious mind

Why/Whether — conscious mind

— like a gap or jump there.

Hypothesis within logic — something is known/unknown, supposed to be true/false. Then we’ve done that — if we observe the hypothesis, we have absorbed. My thoughts and emotions, as data arising from the experiment (not just the external data

Everything becomes knowledge

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