Hash Collisions: Why Your 'Unique' Fingerprints Aren't (And Why That's Usually OK)

The mathematical certainty of hash collisions, the near-impossibility of meaningful ones, and what it means for modern cryptography
What You'll Learn
  • Why hash collisions are mathematically inevitable even with strong algorithms
  • Why a possible collision is very different from a meaningful security threat
  • How MD5 and SHA-1 went from trusted standards to broken algorithms
  • Why modern password storage needs more than a fast hash and a salt
  • When hash collisions matter for security and when they are harmless
  • How crypto-agility helps systems survive when today’s algorithms eventually fail

How Large Language Models (LLMs) Tokenize Text: Why Words Aren't What You Think

Understanding how LLMs break language into pieces—and why it matters more than you realize
What You'll Learn
  • Why language models break text into tokens instead of reading whole words
  • How subword tokenization balances vocabulary size with the amount of text a model must process
  • How Byte Pair Encoding (BPE) learns useful token boundaries from patterns in training data
  • Why the same sentence can use very different numbers of tokens across languages, code, and rare words
  • How tokenization can cause surprising failures in spelling, letter counting, and unusual inputs
  • Why token counts affect context limits, processing efficiency, and the cost of using an LLM

How Large Language Models (LLMs) Handle Context Windows: The Memory That Isn't Memory

Exploring why longer context doesn't mean better memory and what happens when conversations grow
What You'll Learn
  • Why an LLM’s context window is not the same thing as memory
  • How chat applications create continuity even though the underlying model is stateless
  • How attention lets earlier parts of a conversation influence the next token
  • Why longer conversations become increasingly expensive for a transformer to process
  • Why information can become harder to use even while it remains inside the context window
  • How truncation, summarization, retrieval, and KV caching help manage long conversations