In the spirit of Hilbert’s problems, here are the most interesting things I currently know of:

  • Emergence
    • fundamental (non-contact) forces & particles (muons, quarks, …) ⇨ fluid dynamics, etc.
    • Collatz Ecologies
      • “how structure emerges out of iteration”
      • “When stable patterns emerge in some iterated system, it’s possible to build new systems on top of the old ones. Moreover, these new systems can be seen as independent of the old ones.”
      • Collatz conjecture:

        Pick any (nonzero, whole) number. If it’s odd, multiply it by 3 and add 1; if it’s even, divide by 2. Now you have a new number. Apply the same rules, get a new number and keep going. The conjecture predicts that no matter what number you started with, eventually you’ll end up at 1, at which point you’re stuck in a little loop: 1, 4, 2, 1.

  • Chaos theory
    • Small differences in initial conditions yield widely diverging outcomes, rendering long-term prediction impossible in general, even though these systems are deterministic.
      • In practice no time series consists of pure ‘signal.’ There will always be some form of corrupting noise.
      • A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error.
      • Manifests as avalanche in hash functions.
  • Entropy
  • Simulated evolution?
  • Self-replicating machines (logical or physical)
  • Patterns
    • Pattern recognition
    • fractals
    • TV Tropes
  • Materials:
  • Trust networks
  • Power structures
    • Organized crime
    • The State
    • Prisoner’s dilemma
  • Systems
  • Connections
    • netlists (vlsi)
    • bathroom sinks
    • networks
    • ip packet negotiation
    • airport connections (eg ATL)
    • distribution hubs (eg Trader Joe’s)
    • plumbing
    • joints
    • sockets
    • organization communication: information filters, delegation, email chains.
  • Analog computing / fuzzy logic
    • analog computing: “Instead of meaningful information being encoded as unambiguous (and fault-intolerant) digital sequences referenced by precise numerical addressing, meaningful information is increasingly being encoded (and operated upon) as continuous (and noise-tolerant) variables such as frequencies (of connection or occurrence) and the topology of what connects where…”
  • Private currencies
  • Decentralized/distributed order
    • currency (e.g., bitcoin)
    • dns (e.g., namecoin)
    • software development
    • crowdsourcing
      • prediction markets
    • open source development
    • web: Unhosted
    • Ubiquitous sovereignties
      • Nietzsche talked about how society would eventually work its way into anarchism.
        • before Vatican II, masses in Latin. Vatican II: bible readable by layman: increase in the number of atheists worldwide.
        • “Government I” holds Vatican I policies: important aspects of government are to be handled by the government elites, and the lay-person should be ignorant and uninvolved in the inner-workings of governmental procedure.
        • “Government II”: erosion of goverment elites: increase in the number of anarchists
      • (update 2023) Del Complex BlueSea Frontier Compute Cluster (BSFCC)
        • floating barge of 10k+ Nvidia H100 GPUs in international waters.
        • “Each BSFCC is a sovereign nation state for innovation and acceleration.”
        • “Kinetic risk mitigation with dedicated security forces.”
  • Ubiquitous encryption
  • Information theory
    • Compression
    • Encryption
    • Information Entropy
    • The Lagrangian: “If you know The Lagrangian, in principle you know everything there is to know about a system. … It is essentially an ultra-compressed way to write A LOT of information.”
  • Game theory
  • Folding@Home
  • Practical
    • Lock-picking
    • Knot-tying