Robert

Avid Annual Report Reader & Macro Trader. Views are of my own opinion, and not to be taken as financial advise.

[Luiz Pessoa @PessoaBrain]

𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴 𝗱𝘆𝗻𝗮𝗺𝗶𝗰𝗮𝗹 𝘀𝘆𝘀𝘁𝗲𝗺𝘀 𝗶𝘀 𝗵𝗮𝗿𝗱
But lots of progress being made; this one looks very interesting.
https://t.co/OkBDB8qaKS

[Mathelirium @mathelirium]

The Wavefunction Opens Vortex Holes

A 2D quantum harmonic oscillator is prepared as a superposition of exact eigenstates,

Ψ(x,y,t)=Σcₙₘφₙ(x)φₘ(y)e⁻ⁱ⁽ⁿ⁺ᵐ⁺¹⁾ᵗ

As the phases separate, the probability density surface |Ψ|² develops moving dark holes where the complex wavefunction vanishes, while the colour tracks arg Ψ and reveals the phase winding around each node.

Every lobe, fold, and vortex comes directly from the analytic quantum evolution.

#QuantumMechanics #Wavefunction #Physics #Mathematics #QuantumArt #ScienceVisualization

[Mathematica @mathemetica]

Take a look at Alain's curve, defined by the equation (x² - y²)² = a²x² - b²y².

The image plots it with b = 1.2 and a ranging from 0.4 (green, forming inner loops) to 1.3 (producing outer branches), showing the effect of a on the shape.
The curve results from projecting the intersection of an elliptical cone and a hyperbolic paraboloid onto the xy-plane.

Algebraic curves like this are used in computer-aided design and visualization tools to model intersections of surfaces in engineering and graphics applications.

[Night Sky Today @NightSkyToday]

“My brain is only a receiver, in the Universe there is a core from which we obtain knowledge, strength and inspiration. I have not penetrated into the secrets of this core, but I know that it exists.”

~ Nikola Tesla

[Bluntly Put Philosopher (BPP) @SocraticScribe]

Fascinating, imagines the universe less like a machine and more like a living flow. Gravity pulls inward, expansion pushes outward, and everything in between becomes part of a continuous cycle of energy, information, and transformation. An endless loop

[Denistratos @Denistratos]

Buffett. Munger. Soros. Dalio. Ackman. Icahn. Paul Tudor Jones. Howard Marks.

And dozens of other names investors repeat like a mantra.

They read their books.

They dissect their interviews.

Their investor letters are treated like textbooks.

Every 13F filing is scrutinized.

Their words are treated as gospel.

The problem?

The last 15 years have been one of the greatest bull runs in market history.

Yet a large part of the active management industry failed to outperform a simple S&P 500 ETF.

That’s why I’ve always found it strange that investors keep looking for answers from Wall Street’s media “gurus”.

Because the greatest track record in market history didn’t come from Wall Street at all.

Continued ↓

[World of Science @Science_TechTV]

Isaac Newton's college notebook, handwritten by the genius himself around 1664.

[Kekius Maximus @Kekius_Sage]

Ask a physicist what quantum mechanics means and watch the room fall apart.

Bohr: "There is no reality until you measure it."

Einstein: "Something is missing. God doesn't play dice."

Heisenberg: "You can't know everything about a particle. Not because your tools are bad. Because nature won't let you."

Everett: "Everything happens. The universe splits every time."

Bohm: "The particle always had a position. You just can't see the hidden layer."

They all use the same math. Get the same predictions. And completely disagree on what's actually going on.

90 years later, nobody's won the argument.

[Space Explained @SpacedExplained]

🚨: You’re 400 million times closer in size to the observable universe than to the Planck length.

Let that sink in.

[Shounak Das @TheScienceLoop]

The Hopf fibration. Take every single point on a sphere and "lift" each one into a full circle living in 4D. Project that down to 3D and the circles interlock into these nested tori, where no two ever touch. This is what topology looks like when it stops being abstract.

h: S³ → S², each fiber is a circle.

#math #GenerativeArt #simulation

[kynd.info @kyndinfo]

Principal Component Analysis 主成分分析
[Math short write-up]
https://t.co/CKulZU34GM

[Cosmos Archive @cosmosarcive]

A few matrices, a strange-looking equation, and a prediction that rewrote physics.

The Dirac equation remains one of the most beautiful examples of mathematics uncovering reality.

[Cliff Pickover @pickover]

Math. Symphony of Symmetry: 12 Masterpieces of Graph Theory.

Gallery of "named graphs": Markström graph, McGee graph, Meredith graph, Moser spindle, Sousselier graph, Poussin graph, Robertson graph, Sylvester graph, Tutte's fragment, Tutte graph, Young–Fibonacci graph, Wagner graph. https://t.co/7R8MwZhRPk

[JJ @JosephJacks_]

How a memory gets physically written into your brain — at the molecular level:

ACTIVATION …

The synapse fires, a glutamate signal arrives, then the NMDA receptor opens and Ca²⁺ floods into the post-synaptic spine.

Calmodulin — a small dumbbell-shaped sensor protein — cradles four Ca²⁺ ions, two per lobe. Loaded calmodulin clamps onto CaMKII, the central memory enzyme of the brain.

CaMKII isn’t one kinase. It’s a holoenzyme: 12 kinase domains arranged as two stacked hexagonal rings of 6, all radiating from a violet hub.

When Ca²⁺/calmodulin binds, the kinase arms swing out from their folded inactive state into the activated starburst.

Then each kinase autophosphorylates its neighbor at Thr286. That single modification locks the enzyme ON — even after Ca²⁺ leaves. The switch is now a latch. The memory trace begins here.

DOCKING …

A microtubule is a hollow cylinder built from α/β-tubulin dimers — 13 protofilaments, 25 nm outer diameter, 15 nm inner lumen. The tubulins tile its surface in a near-hexagonal lattice.

CaMKII’s hexagonal foot is ~20 nm across. The numbers aren’t coincidence — the kinase hexagon matches the tubulin lattice exactly.

When activated CaMKII lands on a microtubule, six of its kinase feet contact six tubulins arranged in a hexagonal ring around one untouched central “address” dimer.

Complementary surface charges hold it in place with 6 to 36 kcal/mol of electrostatic attraction — strong, specific, reversible.

The enzyme isn’t just sitting on the lattice. It’s registered to it. Like a print head locking onto paper.

ENCODING — the write step

Now CaMKII writes…

Each of the six feet transfers a phosphate group (one ATP per contact) onto its target tubulin’s C-terminus — or doesn’t. Six independent decisions. Six bits. One byte.

The phosphorylation sites are real and identified:

Thr312 and Ser444 on βIII-tubulin.

Each phosphate flips that tubulin into a glowing amber conformational state, distinguishable from the unphosphorylated teal/indigo dimers around it.

The information capacity is staggering:

•A-lattice binary (β-tubulin only): 2⁶ = 64 states per byte

•A-lattice ternary (α or β phosphorylation): 3⁶ = 729 states per byte

•B-lattice 9-dimer (ternary, 6 of 8 dimers writable): 5,281 states per byte

Multiply that across the billions of tubulins in every single one of our neurons and you get memory density that dwarfs anything we build in silicon.

COMPUTATION — the pattern isn’t inert; it computes…

The phosphorylation pattern isn’t a passive record. It actively shapes the microtubule lattice, and thus the cell:

C-terminal tails flip between up/down conformations, seeding hexagonal Turing waves that propagate the pattern across the lattice.

MAPs (microtubule-associated proteins) dock preferentially at amber phospho-sites, templating bundle architecture and synaptic stability.

Kinesin — the two-legged molecular motor — reads the amber path and walks cargo vesicles along it. The memory becomes a routing map for transport.

The whole lattice resonates at MHz frequencies — millions of state updates per second. Storage and processing collapse into the same substrate.

The brain may literally write in hexagonal bytes!

Craddock, Tuszynski & Hameroff (2012), PLoS Comput Biol 8(3):e1002421 — https://t.co/InJdmdYv8d

[Peter Berezin @PeterBerezinBCA]

My model, which consists of several hundred leading indicators for the stock market, is getting nervous. If the economic activity component deteriorates further, the z-score could fall below -1, a critical threshold that has reliably predicted bear markets in the past.

[Cosmos Archive @cosmosarcive]

Consciousness is a hyperstructure of the nervous system.

We are the macroscopic proof of phase-coherent thought.

A localized rebellion against entropy where simple synaptic firing scales into the infinite complexity of the human experience.

[Stephen Wolfram @stephen_wolfram]

What happens when agents with all possible strategies compete? That's a question for ruliology. With some surprising answers...
https://t.co/5RdL27qQc3

[Science Simplified @Scivf4]

This is what the AI brain looks like.

[Cliff Pickover @pickover]

Mathematicians dream of π.

Let's imagine handing this to space-faring extraterrestrials as a gift, or to determine how many of these they have discovered themselves.

This equation set is circulating widely on the web. Example: https://t.co/nU4QkAg1ig