The math behind ContextCrunch
Six interactive concepts. Each fully separated into two tailored tracks — simple English for immediate intuition, and technical formulas for engineering implementation. Live demos powered by a real Python backend, showing code alongside equations.
Tokens & context windows
What is a token? Why do sessions fill up even on Pro accounts? How Claude, ChatGPT, and Gemini each tokenize differently. Interactive subword pill offset inspector.
Lesson 02Embeddings & similarity
How does AI represent meaning, not just letters? Compute real cosine similarities on sentence pairs and hover matrix cells to visualize vector angle rotations programmatically.
Lesson 03Entropy & information
How do we measure information versus redundancy? Paste text to measure Shannon entropy, character probability histograms, and lossless compression limits in real time.
Lesson 04Quantization precision
Float32 to Int8: 4x smaller storage with less than 0.5% loss. Slide a precision slider to quantize a real 10D vector and view Mean Squared Error and cosine retention.
Lesson 05Attention & latency
Why does attention scale quadratically? N tokens mean N² calculations. Move a slider to draw a causal-masked turns attention grid heat-map showing softmax decay.
Lesson 06Prompt efficiency
Paste any system instruction or prompt. The Groq Llama 3.3 70B engine rewrites it, highlighting removed polite fillers and redundant clauses in a visual strikethrough diff editor.