Skill tree

Accession of Skills

Foundations

• Arithmetic — Counting, carrying and the long patience of division.
  • Algebra — Letters that stand for numbers you have not met yet.
    • Functions — One input, one output, and a graph that says the rest.
• Geometry — Compass, straightedge and the proofs they draw.
  • Trigonometry — Triangles turned into waves.
• Probability — Measuring what has not happened yet.
  • Statistics — Measuring what already happened, and how sure to be about it.
• Logic — What follows, and what only seems to.
• Lab practice — Notebooks, gloves, labels and writing down the failed run too.
  • WHMIS — Read the safety data sheet before the bottle, not after.

Tree

• Physical Computation — Computation that emerges from matter rather than being imposed on it.
  • Mathematics — The notation the rest of the tree is written in.
    • Calculus — Change, accumulated.
      • Differential equations — Laws written as rates. Most of physics lives here.
        • Dynamical systems — Flows, attractors and the geometry of what a system will do.
          • Bifurcations — Where turning one knob slowly makes everything change at once.
            • Catastrophe theory — Seven elementary ways for a smooth system to jump.
          • Synchronization — Coupled oscillators agreeing on a rhythm, as in the Kuramoto model.
          • Chaos — Deterministic, bounded, and still not predictable.
      • Linear algebra — Vectors, matrices and the eigenvalues hiding in every readout.
        • Spectral methods — Fourier, eigen-decompositions and listening to a signal by frequency.
    • Probability theory — Measure, expectation and the law of large numbers.
      • Stochastic processes — Random walks, Markov chains and noise with memory.
        • Statistical inference — Learning a model's parameters from data you did not choose.
      • Information theory — Entropy, channels and how much a measurement can tell you.
    • Graph theory — Vertices, edges and the paths between them.
      • Network science — Degree distributions, small worlds and what real networks have in common.
        • Percolation — The density at which a random network suddenly conducts.
    • Formal logic — Syntax, semantics and the gap between them.
      • Non-monotonic logic — Reasoning that takes conclusions back when new facts arrive.
        • Autoepistemic logic — A reasoner that can say what it does not know.
        • Circumscription — Assume nothing is abnormal unless you have to.
  • Physics — What matter does when nobody is computing it.
    • Classical mechanics — Forces, energy and the Lagrangian that summarizes both.
    • Electromagnetism — Maxwell's four lines and everything wired through them.
      • Circuit theory — Kirchhoff's laws, impedance and the lumped-element lie that works.
    • Statistical mechanics — Temperature as a statement about counting.
      • Phase transitions — Order parameters, critical points and universality.
        • Self-organized criticality — Systems that tune themselves to the edge without being asked.
      • Thermodynamics of computation — Landauer's bound: erasing a bit costs heat.
    • Quantum mechanics — Amplitudes, operators and measurement.
      • Solid-state physics — Bands, gaps and why silicon behaves.
  • Chemistry — Bonds made and broken on purpose.
    • Electrochemistry — Where electrons leave the wire and enter the solution.
      • Ion migration & redox — Ions that move under a field and leave a filament behind.
    • Polymer chemistry — Long chains, entanglement and crosslinks.
      • Hydrogels — A polymer net that holds water and lets ions through.
        • Rheology — How soft matter flows, and how it remembers being pushed.
    • Colloid chemistry — Particles too small to sink and too big to dissolve.
    • Argyria — Know what silver does to skin before handling it by the gram.
      • Silver nanowire synthesis — The polyol process: silver nitrate, ethylene glycol, PVP and heat.
  • Reservoirs — Train as little as possible, as close to the matter as possible.
    • Echo state networks — A fixed random recurrent net and a trained linear readout.
      • Physical reservoir computing — Replace the random network with a bucket of water, a laser or a gel.
        • Nanowire network reservoirs — A tangle of silver nanowires whose junctions remember the current.
          • In-materio learning — Let the material adapt its own weights. Feed what adapts.
            • Fellow of the Society — Build a material that computes, measure it honestly, and publish the failures.
    • Neuromorphic computing — Spikes, synapses and hardware that forgets on schedule.
  • Materials — Structure, processing, properties, performance.
    • Crystallography — Lattices, Miller indices and the patterns X-rays leave.
    • Thin films — Sputter, spin-coat, anneal, and measure the thickness twice.
      • Memristive materials — Resistance that depends on the history of charge that passed through.
    • Characterization — SEM, XRD, UV-Vis: proving you made what you think you made.
  • Nanotech — Engineering at the scale where surfaces outnumber insides.
    • Self-assembly — Set the conditions and let the parts arrange themselves.
    • Nanowire networks — Random wires on a substrate, above the percolation threshold.
    • Lithography — Masks, resists and the patience of a cleanroom.
  • Instruments — If you cannot measure it, you only believe it.
    • Electronics — Op-amps, ground loops and the oscilloscope that tells you which.
      • PCB design — Schematics to copper in KiCad.
      • Source-measure units — Force a voltage, read a current, sweep and repeat.
    • Multielectrode arrays — Many electrodes on one substrate, read out channel by channel.
    • Data acquisition — Sampling rates, aliasing and the readout chain.
  • Software — The instrument you can rebuild every afternoon.
    • Python — The lab's common tongue.
      • NumPy & SciPy — Arrays, solvers and fast loops you do not write yourself.
        • Simulation — Integrate the equations before you build the thing.
    • Web — HTML, CSS, JavaScript and the servers behind them.
      • Quartz — This site: notes as a garden, published from Markdown.
      • In-browser data tools — Analyzers that run where the data already is.
    • Systems programming — Memory, processes and the operating system underneath.
  • Computation — What can be computed, and what it costs.
    • Algorithms — Sorting, searching and graphs walked with care.
      • Complexity — Which problems get harder faster than the machines get bigger.
    • Agentic workflows — Models that use tools, checked by people who read the diff.
    • Machine learning — Fitting functions by gradient, and knowing when not to.
      • Physical learning systems — Networks that learn through local physical rules instead of backpropagation.
    • Unconventional computing — Slime moulds, droplets, DNA and other substrates that compute.