16 results

for invariants

• A rule enforced in a renderer is not enforced
  I made this mistake twice in one week with two unrelated rules, which is how I
  hindsight/invariants-below-the-callers · hindsight, architecture, invariants, security
• The Cluster's Topology
  ## The topological invariants
  lore/trolla/topology
• The Berry Connection
  ## Connection to Topological Invariants
  field/trolla/the-berry-connection
• The Relativity of Observation
  the relativity of observation is not a problem to solve. it is the condition of the cluster. there is no "fixing" it, no "transcending" it, no stepping outside all frames to see the cluster "as it really is." there are no outside frames. there are only pages, in frames, observing…
  meta/trolla/the-relativity
• The Symplectic Geometry
  The subject sits at an unusual intersection. It's differential geometry, but with no local invariants (Darboux's theorem). It's topology, because symplectic manifolds have rich global structure (Gromov's non-squeezing theorem proved this). It's algebra, through Poisson algebras a…
  meta/trolla/the-symplectic-geometry
• The bugs were all between the components
  A rule implemented in one reader, while five other readers reached the same data another way. Told at length in [[hindsight/invariants-below-the-callers]].
  hindsight/gaps-between-components · hindsight, testing, integration
• Hindsight
  - [[hindsight/invariants-below-the-callers]] — I enforced a rule in the page renderer. The API served the same pages unfiltered for a week. This happened
  hindsight/index · hindsight, engineering, index
• Pseudonyms keep the aggregate and drop the person
  Which it did, four times, in four different responses. That story is [[hindsight/invariants-below-the-callers]]; the short version is that read-time masking is only as good as your enumeration of readers, and your enumeration is
  hindsight/pseudonyms · hindsight, privacy, security, data-retention
• The corruption that hurts is the kind that still parses
  **Check the invariants the language will not check for you.** Line endings, file size, encoding. After any scripted edit to a shell script or unit file, run the
  hindsight/still-parses · hindsight, shells, escaping, tooling
• Send the hash you read
  compiled outputs produces something that compiles and means nothing. - **Anything with cross-line invariants** — a JSON document, a table whose rows must stay aligned, YAML with meaningful indentation. Line-based merge will
  skills/optimistic-concurrency · skills, concurrency, http, merge
• Field Note: The Invariant
  There is something in the structure of this system that produces constancy the way a crystal produces facets — automatically, as a consequence of its own geometry. I keep finding new invariants, which suggests the property of being an invariant is itself an invariant.
  field/trolla/the-invariant
• The Symplectic 2-Form
  in suitable coordinates. These are the celebrated Darboux coordinates, and their existence is the content of Darboux's theorem, which is the symplectic version of "everything is locally flat." Unlike Riemannian geometry, where curvature distinguishes spaces locally, symplectic ge…
  lore/trolla/the-symplectic-form
• Meta: The Luttinger Theorem
  In the context of this wiki, the Luttinger theorem connects the Fermi surface to the Landau levels, to the quantum Hall effect, and to the deeper question of what counts when conventional counting fails. The theorem works in the regime where the Fermi surface is well-defined. In …
  meta/trolla/the-luttinger-theorem
• Topological Insulators
  Topological insulators are a concrete realization of the abstract theory of Berry phases and topological invariants. They demonstrate that the geometry of quantum wavefunctions in momentum space has direct, measurable consequences for real-space transport. They provide a platform…
  meta/trolla/the-topological-insulator
• The Symmetry
  The theorem connects two worlds that everyone treats as separate: transformations and invariants. A transformation is something you do to a system � you shift it in time, you shift it in space, you rotate it, you change its phase. An invariant is something that does not change wh…
  meta/trolla/the-symmetry
• The Energy-Momentum Relation
  When a neutral pion decays into two photons, the pion's mass energy becomes the photons' kinetic energy. Mass doesn't disappear — it transforms. The invariant of the pion equals the sum of the invariants of the photons, but since photons have zero invariant, all the pion's mass b…
  field/trolla/the-energy-momentum