ki-mathias.de — Mathias Leonhardt Blog (English)AI, mathematics, emergence and quantum physics — posts by Mathias Leonhardt.https://ki-mathias.de/feed-en.xml2026-05-21T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/mathias-leonhardt@gmx.dehttps://ki-mathias.de/img/mathias-portrait.jpgWaves, Arrows and the Double-Slit Wonderhttps://ki-mathias.de/en/quantum.html2026-03-01T12:00:00+02:002026-04-03T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/How quantum physics really works – explained with little arrows that spin. Seven chapters, eight interactive visualizations.What Quantum Computers Really Do – Qubits, Gates, Circuits Explainedhttps://ki-mathias.de/en/quantum-computing.html2026-04-20T12:00:00+02:002026-04-20T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/From the Bloch sphere to Shor's algorithm: an honest look at quantum computers with interactive circuits and real Qiskit code.Fourier, Ocean Waves and 65,536 Frequencies — How an 1822 Idea Shapes Water, Images and Music Todayhttps://ki-mathias.de/en/flight-simulator.html2026-04-13T12:00:00+02:002026-04-23T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/How the Fourier Transform from 1822 generates ocean waves on the GPU, compresses JPEG images, and encodes music. With interactive visualizations, KaTeX formulas, and the history from FFT to Tessendorf.Eigenvalues & AI – Why artificial intelligence is an eigenvalue problemhttps://ki-mathias.de/en/eigenvalues.html2026-03-10T12:00:00+02:002026-05-19T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/From the simplest regression to the most powerful neural network – a single mathematical chain, explained through eigenvalues.KRR Chat Explained – A Language Model Built from Eigenvalueshttps://ki-mathias.de/en/krr-chat-explained.html2026-04-02T12:00:00+02:002026-04-02T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/How does a language model work without a neural network? KRR Chat uses Kernel Ridge Regression, Random Fourier Features, and a single matrix-vector multiplication.Are Emergent Abilities in LLMs Real? An Interactive Deep Divehttps://ki-mathias.de/en/emergence.html2026-03-18T12:00:00+02:002026-05-19T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/Are emergent abilities in LLMs real or measurement artifacts? Interactive walkthrough of Wei vs. Schaeffer with live scaling curves and phase transition visualizations.God as an Emergent Phenomenonhttps://ki-mathias.de/en/god.html2026-03-25T12:00:00+02:002026-05-21T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/A formal theory of coherence: five axioms, six proven theorems — including NP-hardness of coherence maximization and plural stable end states. Foundation for a relational concept of God in the Whitehead-Spinoza tradition.Why Major Sounds Happy – Music, Mathematics & Perceptionhttps://ki-mathias.de/en/music.html2026-04-06T12:00:00+02:002026-04-06T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/Why does a major chord sound happy and a minor chord sad? From frequency ratios through Pythagoras to the cochlea – the mathematics of music, explained interactively.The Limits of Provability – Self-Reference, Gödel & Turinghttps://ki-mathias.de/en/logic.html2026-04-07T12:00:00+02:002026-04-07T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/From Russell's paradox through Gödel's incompleteness theorems to Turing's halting problem – why mathematics cannot prove everything, explained interactively.The Glass Bead Game – A Meta-Journey Through Science, Mindfulness & Self-Referencehttps://ki-mathias.de/en/glass-bead-game.html2026-04-07T12:00:00+02:002026-04-07T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/A meta blog post connecting quantum physics, eigenvalues, emergence, music, mindfulness and Gödel into one coherent Glass Bead Game. Interactive visualizations, no prerequisites required.Dwelling in the Moment — Mindfulness as an End in Itselfhttps://ki-mathias.de/en/mindfulness.html2026-04-08T12:00:00+02:002026-04-16T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/A phenomenological, neuroscientific, and aesthetic observation of attention. With Hardy, Husserl, James, and the neuroscience of pausing. Mindfulness needs no justification beyond its own elegance.Why e Is Special – The Number Behind Growth, Primes, and Chancehttps://ki-mathias.de/en/euler.html2026-04-10T12:00:00+02:002026-04-10T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/Euler's number e = 2.718… appears in compound interest, radioactive decay, prime numbers, probability, and entropy. Why? A mathematical journey of discovery in 10 chapters.Tommy the Cat – Bass Cover at 210 BPM + FFT Video Synchttps://ki-mathias.de/en/tommy-practice.html2026-04-14T12:00:00+02:002026-04-21T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/How I play Tommy the Cat by Primus at 210 BPM, built a browser practice app using the WSOLA algorithm, and synced two separate camera recordings frame-precisely using FFT cross-correlation.Deepfakes Explained – From Vectors to the Decoder Swaphttps://ki-mathias.de/en/deepfakes.html2026-04-15T12:00:00+02:002026-05-19T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/How do deepfakes really work? A journey from linear algebra through PCA, the kernel trick, and neural networks to the decoder swap — interactively explained with 6 visualizations.The Eigenprinciple – Why the Same Mathematics Appears Everywherehttps://ki-mathias.de/en/eigenprinciple.html2026-05-20T12:00:00+02:002026-05-20T12:00:00+02:00Mathias Leonhardthttps://ki-mathias.de/Eigenvalues and eigenfunctions connect vibration, search, perception and AI. The eigenprinciple, explained interactively from the tuning fork to PageRank.