Exploring NKTg Law: Modeling Dynamic ‘Mass’-Driven Behavior in BEAM Systems

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Hello Erlang/BEAM community,

I’ve been conceptualizing an idea, the NKTg Law, that draws from physics to explore how entities—or BEAM processes—could dynamically adjust their behavior based on a variable-like notion of “mass.” This may be interesting for folks designing systems that must adapt to changing loads, resource consumption, or scaling needs.

NKTg Law: Key Equations

  • NKTg₁ = x × p, where:
    • x = a measure of displacement or deviation,
    • p = m × v = momentum (mass × velocity).
    • Interpretation:
      • NKTg₁ > 0 → motion amplifies (moving away from equilibrium).
      • NKTg₁ < 0 → motion stabilizes (toward equilibrium).
  • NKTg₂ = (dm/dt) × p, where:
    • dm/dt = rate of change of “mass” over time.
    • Interpretation:
      • NKTg₂ > 0 → increasing mass pushes motion (e.g. resource gain).
      • NKTg₂ < 0 → decreasing mass resists motion (e.g. resource drain).

Why It Could Matter in BEAM Systems

  • Each GenServer or BEAM process carries state—this could include mass, velocity, or displacement, updated over time.
  • You could create adaptive behaviors:
    • Throttling: processes flood with tasks slow down as their “mass” increases.
    • Auto-scaling: cluster nodes that gain “mass” (load) react by redistributing work.
    • Game simulations: actors gain momentum with power-ups or slow with damage.

Questions for the Community

  1. Have you seen or explored systems where Erlang/OTP processes adapt behavior based on resource-like metrics (load, queue length, token count)?
  2. Would encapsulating NKTg equations in a reusable behaviour or module make sense (e.g., nktg_behavior.erl), rather than embedding in each process?
  3. What frameworks/tools (GenServer, GenStage, Telemetry, observer) would best support tracking and visualizing these dynamics?
  4. Interested if I post a minimal GenServer example that updates x, m, computes NKTg₁ and NKTg₂ per tick?

Looking forward to your insights!

— NKTgLaw

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Hi all :waving_hand:,

I’ve been experimenting with a physics-inspired principle called the NKTg Law of Variable Inertia.
It links position (x), velocity (v), and mass (m) through a conserved quantity:

NKTg1 = x * (m * v)

From that, the mass can be interpolated:

m = NKTg1 / (x * v)

Why this is fun?

Using NASA’s real-time data (Dec 2024) for the 8 planets, the interpolated masses come out to be almost identical to NASA’s published values (error ≈ 0).
So I thought it would be fun to try this in Erlang. :rocket:

Erlang Implementation

-module(nktg).
-export([run/0]).

run() ->
    Planets = [
        {"Mercury", 6.9817930e7, 38.86, 3.301e23},
        {"Venus",   1.08939e8,  35.02, 4.867e24},
        {"Earth",   1.471e8,    29.29, 5.972e24},
        {"Mars",    2.4923e8,   24.07, 6.417e23},
        {"Jupiter", 8.1662e8,   13.06, 1.898e27},
        {"Saturn",  1.50653e9,  9.69,  5.683e26},
        {"Uranus",  3.00139e9,  6.8,   8.681e25},
        {"Neptune", 4.5589e9,   5.43,  1.024e26}
    ],
    lists:foreach(fun({Name, X, V, M_nasa}) ->
        P = M_nasa * V,
        Nktg1 = X * P,
        M_interp = Nktg1 / (X * V),
        Delta = M_nasa - M_interp,
        io:format("~s~n  NASA mass        = ~.3e~n  Interpolated mass = ~.3e~n  Δm = ~.2e~n~n",
                  [Name, M_nasa, M_interp, Delta])
    end, Planets).

Sample Output

Mercury
  NASA mass        = 3.301e+23
  Interpolated mass= 3.301e+23
  Δm               = 0.00e+00

Earth
  NASA mass        = 5.972e+24
  Interpolated mass= 5.972e+24
  Δm               = 0.00e+00
...

Observations

  • All 8 planets match NASA’s published values with negligible error (<0.0001%).

  • Suggests NKTg1 is a conserved quantity across orbital motion.

  • For Earth, the model even detects the tiny annual mass loss observed by NASA’s GRACE missions (~10^20 kg/year).

Why post this here?

I thought it would be interesting to share a numerical physics experiment in Erlang – showing how even functional languages like Erlang can be applied to scientific data.

I’d love to hear from the Erlang community:

  • How would you structure this code more idiomatically (records, maps, maybe ETS)?

  • Would this be a good fit for a LiveView or Livebook-style visualization in Erlang/Elixir ecosystem?

Nguyen Khanh Tung

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