Five luminous glass spheres connected by threads of light – a symbol for the Glass Bead Game: quantum arrows, waves, networks, Euler’s formula, and an eye.

Notes from Conversations with a Machine

KI-Mathias

This is not a blog that explains the world. It is more like a notebook – a digital, public, incomplete notebook – where I record what happens when a human and an artificial intelligence sit down together and try to truly understand things.

The human is me. The AI is Claude Code, a large language model by Anthropic. And this – the texts, the visualizations, the thought experiments – is what emerges when you use this tool not to draft emails or debug code, but to have the world explained to you. Or more precisely: to explain it to each other, together.

I am someone who has questions. And I have found that an AI does not give up after the fifteenth “But why?” – and is broadly educated enough to assemble the answer from three disciplines at once.

What emerges reminds me of Hermann Hesse’s Glass Bead Game. Hesse imagined a distant future where the highest intellectual achievement was synthesis – revealing the hidden architecture connecting music, mathematics, philosophy, and natural science. But in Hesse’s telling, this extraordinary capability was locked inside Castalia, a monastic elite that selected gifted children and trained them for decades. The Game was magnificent. The price was that it did not belong to the world. Joseph Knecht, the novel’s protagonist, ultimately leaves Castalia – because synthesis without connection to life is sterile.

What fascinates me about this blog: it is the Game without Castalia. The same kind of synthesis – Fourier decompositions and music say the same thing, eigenvalues simultaneously explain quantum mechanics and artificial intelligence, emergence connects physics, consciousness, language models, and perhaps even what people once called “God” – but accessible to anyone who has questions. No ivory tower. No selection process. A language model and a curious human are enough.

We are living in the years when large language models are beginning to change the way people think, learn, and create. This blog records what that feels like – from the inside.

Posts

Quantum Mechanics · Interactive

Waves, Arrows, and the Double-Slit Wonder

How quantum physics really works – explained with nothing but little arrows that rotate. Seven chapters, seven interactive visualizations, zero prerequisites.

· ~45 min read · Video
Double Slit Path Integral Fourier Three Languages Entanglement

Quantum Computing · Qiskit · Interactive

What Quantum Computers Really Do

Qubits, Bloch sphere, Bell state — and Qiskit code that runs on real IBM hardware. Building on the quantum post: from the double slit to quantum circuits, no hype.

· ~35 min read · 4 interactive demos
Qubit Bloch Sphere Qiskit Shor Bell State

Mathematics · Artificial Intelligence · Interactive

Eigenvalues & AI

From the simplest regression to the most powerful neural network – a single mathematical chain, explained through eigenvalues. With interactive visualizations.

· ~50 min read · Video
Kernels PageRank Neumann Series Gradient Descent Glass Bead Game

Language Model · Kernel · Deep Dive

KRR Chat: Under the Hood

How does a language model work without a neural network? Dual-model architecture, RAG pipeline, three-color code for memorization vs. generalization – and the complete source code in three functions.

· ~12 min read
RAG Float64 Three-Color Code Source Code KRR Chat

Mathematics · AI · Interactive

Hopfield Networks – From Spin Glass to Attention

Why every language model is, at its core, a Hopfield network from 1982 – and what that reveals about memory, pattern recognition and attention. Seven chapters with five interactive MNIST demos.

· ~45 min read
Spin Glass Pseudoinverse Modern Hopfield Attention Nobel Prize 2024

Mathematics · Spectral Theory · The Glass Bead Game

The Eigenprinciple

Why the same mathematics appears everywhere – from the vibrating tuning fork through face recognition and web search to quantum mechanics. Nine chapters, a fireworks of interactive visualizations.

· ~45 min read
Eigenvalues PCA Markov PageRank Spectral Theory

Artificial Intelligence · Interactive

Emergence in Large Language Models

At what size does a language model begin to “understand”? On phase transitions, suddenly appearing capabilities, and the parallel to emergence in physics. Eight chapters, eight interactive visualizations.

· ~35 min read
Emergence Phase Transition Grokking Ising Model 20+ Papers

Philosophy · Emergence · Interactive

God as an Emergent Phenomenon

What emerges from enough human thought? A concept of God beyond religion – formalized, not proven. Six chapters, six interactive visualizations. Based on a paper submitted to the European Academy of Religion 2026.

· ~30 min read
Whitehead Spinoza Coherence Attractor EuARe 2026

Music · Physics · Perception

Why Major Sounds Happy

Why do certain notes sound good together? What makes major and minor triads? Why can a guitar never be perfectly tuned for all chords? And what does Pythagoras have to do with it? Six interactive sound visualisations.

· ~40 min read · Video
Harmony Tuning Overtone Series Psychoacoustics Web Audio API

Mathematics · Computer Graphics · Fourier

Fourier, Ocean Waves, and 65,536 Frequencies

How an 1822 mathematical idea shapes water, images, and music today – from the Fourier transform through JPEG and MP3 to GPU ocean simulation. With a playable 3D flight simulator.

· ~35 min read · Playable!
Fourier FFT / iFFT Octree Ocean Shader Three.js

Logic · Computer Science · Philosophy

The Limits of Provability

Gödel’s incompleteness theorem, Turing’s halting problem, and the question: what can a system know about itself? From the diagonal argument to the Busy Beaver — with interactive Turing machines and a Gödel number calculator.

· ~45 min read
Gödel Turing Cantor Self-Reference P vs NP

Phenomenology · Neuroscience · Aesthetics

Dwelling in the Moment

Mindfulness as the noticing that notices itself. What phenomenology, neuroscience, and mathematics have to say about the simplest movement of consciousness — and why beauty needs no justification.

· ~35 min read
Hardy Husserl Neuroscience Phenomenology Beauty

Mathematics · Nature · Probability

Why e Is Special

Euler’s number appears in growth processes, radioactive decay, prime numbers, the Fibonacci sequence, and every differential equation. Why 2.718... of all numbers?

· ~30 min read
e = 2.718... Differential Equations Primes Decay

AI · Linear Algebra · Autoencoders

Deepfakes Explained — From Vectors to the Decoder Swap

How do deepfakes really work? A journey from linear algebra through PCA, the kernel trick, and neural networks to the face swap — with 6 interactive visualizations, a rotating tesseract, and an MNIST autoencoder running in your browser.

· ~15 min read · 6 interactive demos · Video
Deepfakes PCA Autoencoders Kernel Trick Tesseract

Music · Bass · Fourier

Tommy the Cat — Bass Cover at 210 BPM

Primus’ Tommy the Cat — simplified but playable at original tempo. Plus: how FFT cross-correlation automatically syncs two camera recordings. With interactive practice loop.

· ~10 min read · Practice loop! · Video
Primus Bass FFT Sync 210 BPM

Meta · Mindfulness · Philosophy

The Glass Bead Game

A meta-journey through this blog: where do quantum physics, eigenvalues, music, and logic connect? What does mindfulness have to do with Gödel? And why did Josef Knecht leave Castalia?

· ~35 min read
Hesse Mindfulness Emergence Self-Reference Meta Post