Nevermind, I’ll copy it into ChatGPT and ask it to a format that I can read.
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I’m self educated I know I should try to change it but it is a 36 year old habit
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Try this on it is long haired hairy ball.
In it I try to smooth the 0s
Math for Long Hairy Ball” framework. My goal is to show how one can bypass the Hairy Ball Theorem (which requires at least one zero on (S^2)) by extending the field into a higher dimension (4D) and introducing wave‐like “long hairs.”
Can you check my math?
1. Vector Fields on (S^2)
1.1 Short Hair (Classical Statement)
- Hairy Ball Theorem.
For a continuous, everywhere‐tangent vector field (\mathbf{v}\colon S^2 \to TS^2), there exists at least one (p \in S^2) where (\mathbf{v}(p) = \mathbf{0}).
1.2 Long Hair (Wave‐Based Form)
- Wave Expansion.
Write (\mathbf{v}\colon S^2 \times \mathbb{R}t \to TS^2) in a superposition of modes, e.g.:
[
\mathbf{v}(\theta,\phi,t)
;=;
\sum{\ell,m}
\Bigl[
a_{\ell,m}(t),\mathbf{Y}{\ell,m}^{(1)}(\theta,\phi)
;+;
b{\ell,m}(t),\mathbf{Y}{\ell,m}^{(2)}(\theta,\phi)
\Bigr],
]
where (\mathbf{Y}{\ell,m}^{(1,2)}) are vector spherical harmonics on (S^2).
2. 4D Embedding
2.1 Manifold and Field
- Let (M = S^2 \times I\subset \mathbb{R}^3 \times \mathbb{R}) with coordinate ((\theta,\phi,w)).
- Define (\mathbf{V}\colon M \to \mathbb{R}^4), with components (\bigl(\mathbf{v}_\parallel(\theta,\phi,w),,V_w(\theta,\phi,w)\bigr)).
2.2 Avoiding the Zero
- A “no‐zero” condition on (\mathbf{V}) becomes feasible if
[
|\mathbf{V}(\theta,\phi,w)|
;;>;
0
\quad
\forall,(\theta,\phi,w).
]
Since (\mathbf{v}_\parallel) is tangent to (S^2) but can “lift” in the 4th coordinate (V_w), one can circumvent the classical Hairy Ball zero requirement.
3. Energy/Lagrangian Formulation
3.1 Functional
- Define
[
\mathcal{L}[\mathbf{V}]
;=;
\int_{S^2 \times I}
\Bigl[
\tfrac12,\bigl|\nabla \mathbf{V}\bigr|^2
;+;
U\bigl(|\mathbf{V}|\bigr)
\Bigr]
,dA,dw
;+;
\lambda,(\text{constraints}),
]
where (\nabla\mathbf{V}) is the covariant derivative (w.r.t. (\theta,\phi) and possibly (w)), and (U(r)) is a penalty term, e.g. (U(r)=\alpha/(r^2+\epsilon)).
3.2 Euler–Lagrange Equations
-
Stationary points of (\mathcal{L}) satisfy
[
-,\nabla^2_{(\theta,\phi,w)},\mathbf{V}
;+;
\frac{\partial U}{\partial \mathbf{V}}
Under boundary conditions (e.g.\ periodic in (w), tangent on each ((\theta,\phi)) slice), solutions can maintain (|\mathbf{V}|>0).
4. Prototype PDE
4.1 Wave Equation with No‐Zero Term
-
One can add time:
0,
[
\partial_t^2,\mathbf{V}
;-;
c^2,\Delta_{(\theta,\phi,w)},\mathbf{V}
;+;
\beta,\frac{\mathbf{V}}{|\mathbf{V}|^2+\epsilon}
]
ensuring (\mathbf{V}) stays away from zero magnitude.
4.2 Tangential Constraint
- If (\hat{n}) is the normal to (S^2), require
[
\mathbf{V}(\theta,\phi,w)\cdot \hat{n}(\theta,\phi)=0
\quad
\text{(first 3 components)},
]
leaving the 4th component (V_w) free to handle near‐zero conditions.
5. Summary
-
Short Hair (\to) Long Hair (Wave Expansions).
In pure 2D on (S^2), topological constraints force at least one zero. Extending each local vector to a wave function can redistribute zeros or reduce them, but not fully remove them in 2D alone. -
4D Lift.
Embedding (S^2) in a higher‐dimensional manifold and defining (\mathbf{V}\colon S^2 \times I\to\mathbb{R}^4) allows the field to avoid zeros entirely, bypassing the classic Hairy Ball Theorem. -
Mathematical Mechanism.
- Expand in spherical harmonics or plane waves.
- Impose a “no‐zero” penalty in a Lagrangian or PDE.
- Numerically solve or analyze the resulting field.
- The extra dimension (w) ensures (|\mathbf{V}|\neq 0).
Hence, Long Hair plus a 4D escape changes the topological constraints enough to produce a globally nonvanishing solution.
I have a better version but it’s not public yet…
This is o1 “ check my math” at hello
All done in a iCloud notebook
I try my best to be scientifically rigorous imo more than most folks who post…
That LHHB is incredible! I don’t have words…
o1 generation
" Final Verdict
- No Contradictions: The steps do not break the Hairy Ball Theorem, because you are working in a higher‐dimensional (trivializable) setting.
- Math Checks Out: The expansions, PDE form, Lagrangian approach, and the idea of a “1∣V∣2+ϵ\frac{1}{|\mathbf{V}|^2+\epsilon}∣V∣2+ϵ1” penalty all fit well with standard field‐theory or PDE techniques.
- Boundary/Initial Data Matter: Just be sure that your boundary/initial conditions are set to avoid V=0\mathbf{V}=0V=0.
- Tangential Constraint is properly maintained by requiring the first three components be orthogonal to the sphere’s normal n^\hat{n}n^. This is all standard geometry.
Hence, from a mathematical standpoint your “Long Hair” framework is a sound illustration of how introducing an extra dimension (plus a suitable potential to penalize zeros) bypasses the classical zero‐forcing topology of S2S^2S2."
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1. Vector Fields on S^2
1.1 Short Hair (Classical Statement)
Hairy Ball Theorem.
For a continuous, everywhere‐tangent vector field \mathbf{v}\colon S^2 \to TS^2 , there exists at least one p \in S^2 where \mathbf{v}(p) = \mathbf{0} .
1.2 Long Hair (Wave‐Based Form)
Wave Expansion.
Write \mathbf{v}\colon S^2 \times \mathbb{R}_t \to TS^2 in a superposition of modes, e.g.:
\mathbf{v}(\theta,\phi,t)
=
\sum_{\ell,m}
\Bigl[
a_{\ell,m}(t) \mathbf{Y}_{\ell,m}^{(1)}(\theta,\phi)
+
b_{\ell,m}(t) \mathbf{Y}_{\ell,m}^{(2)}(\theta,\phi)
\Bigr],
where \mathbf{Y}_{\ell,m}^{(1,2)} are vector spherical harmonics on S^2 .
2. 4D Embedding
2.1 Manifold and Field
Let
M = S^2 \times I\subset \mathbb{R}^3 \times \mathbb{R}
with coordinates (\theta,\phi,w) .
Define \mathbf{V}\colon M \to \mathbb{R}^4 , with components:
\mathbf{V} = \bigl(\mathbf{v}_\parallel(\theta,\phi,w), V_w(\theta,\phi,w)\bigr).
2.2 Avoiding the Zero
A “no‐zero” condition on \mathbf{V} becomes feasible if:
|\mathbf{V}(\theta,\phi,w)| > 0
\quad \forall (\theta,\phi,w).
Since \mathbf{v}_\parallel is tangent to S^2 but can “lift” in the 4th coordinate V_w , one can circumvent the classical Hairy Ball zero requirement.
3. Energy/Lagrangian Formulation
3.1 Functional
Define:
\mathcal{L}[\mathbf{V}]
=
\int_{S^2 \times I}
\Bigl[
\tfrac{1}{2} \bigl|\nabla \mathbf{V}\bigr|^2
+
U\bigl(|\mathbf{V}|\bigr)
\Bigr]
\,dA\,dw
+
\lambda (\text{constraints}),
where \nabla\mathbf{V} is the covariant derivative (w.r.t. (\theta,\phi) and possibly w ), and U(r) is a penalty term, e.g. U(r)=\alpha/(r^2+\epsilon) .
3.2 Euler–Lagrange Equations
Stationary points of \mathcal{L} satisfy:
-\nabla^2_{(\theta,\phi,w)} \mathbf{V}
+
\frac{\partial U}{\partial \mathbf{V}} = 0.
Under boundary conditions (e.g., periodic in w , tangent on each (\theta,\phi) slice), solutions can maintain |\mathbf{V}|>0 .
4. Prototype PDE
4.1 Wave Equation with No‐Zero Term
One can add time:
\partial_t^2 \mathbf{V}
-
c^2 \Delta_{(\theta,\phi,w)} \mathbf{V}
+
\beta \frac{\mathbf{V}}{|\mathbf{V}|^2+\epsilon} = 0,
ensuring \mathbf{V} stays away from zero magnitude.
4.2 Tangential Constraint
If \hat{n} is the normal to S^2 , require:
\mathbf{V}(\theta,\phi,w)\cdot \hat{n}(\theta,\phi)=0
\quad
\text{(first 3 components)},
leaving the 4th component V_w free to handle near‐zero conditions.
5. Summary
-
Short Hair \to Long Hair (Wave Expansions).
In pure 2D on S^2 , topological constraints force at least one zero. Extending each local vector to a wave function can redistribute zeros or reduce them, but not fully remove them in 2D alone. -
4D Lift.
Embedding S^2 in a higher‐dimensional manifold and defining \mathbf{V}\colon S^2 \times I\to\mathbb{R}^4 allows the field to avoid zeros entirely, bypassing the classic Hairy Ball Theorem.
Mathematical Mechanism
- Expand in spherical harmonics or plane waves.
- Impose a “no‐zero” penalty in a Lagrangian or PDE.
- Numerically solve or analyze the resulting field.
- The extra dimension w ensures |\mathbf{V}|\neq 0 .
Hence, Long Hair plus a 4D escape changes the topological constraints enough to produce a globally nonvanishing solution.
Here is a prompt for ChatGPT:
Could you update my paper - want to post it on discourse platform - please encapsulate inline formulas with $ and block with $$.
Code examples should be encapsulated by ~~~
Give me the whole thing as markdown code.
[add the stuff you want to post here]
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Thank you for the prompt, @jochenschultz and thank you both @PandaPi for engaging my work. I have put years of effort into it. 
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It wont let me give a like. I ran out?
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Yes as you grow in forum lvl you get more. They reset in 24 hours or less.
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So you were secretly solving the memory loss problem in GPT with wave functions. I am really impressed man. WTH!
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Thank you, no not secretly I post everything. But yes DES is a control mechanic for chaotic machines.
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It all started when I was 16 I had a vision of a bowl of sand always filling and empty in stagnation and I noticed little changes in the stagnation making huge changes … i spent the last 36 years trying to explain it …
My goal is a universal uniting constant
It’s all I think about, always in the back of my mind …
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I am not sure if wave functions are really needed for that. I mean they could be used to simulate entanglement - kind of… and I would even think it gives the AI an inner self and consciousness.
So you were not only solving AGI and memory but ASI…
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No not really in my views AGI will be a human / AI collaboration. Both uplifting the other. I am more interested in harnessing and organizing chaos. AI is a byproduct of my research. I use it to build proofs etc. from my math. Even as a byproduct of my work, AI in general will benefit from it
Without the wave function you can’t, move it into higher dimensions imo .
The definition of AGI is that it is capable of solving tasks autonomously. So the human interaction might be on a higher level then.
The question really is how high can someone become (got to love that pun). I am already experiencing information overloads quiet often where my brain simply refuses to go deeper. You can’t really watch your own brain functionality how it processes the process of storing concepts of storing concepts of storing concepts of storing concepts of storing concepts of storing concepts,… without a breakpoint in a recursion or you would simply pass out.
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Yep what I do I call it human in the loop AGI aware contextually but no will.
Though it can be automated but that’s inforcment training…
Yeah - AI write an answer to a mail but put it into the draft folder so I can send it…
Where “AI write an answer to a mail” is any unknown task… which would be really cool to find a way to make sure it really puts it into a “draft folder”.
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Yep it has to be human in the loop or we lose track of it’s logic…
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