5.1 KiB
BioPhonon Translation Field Equations
Status: EQUATION_UPDATE Claim state: FORMAL_SCAFFOLD / ANALOGY_BOUNDED
This note defines the BioPhonon Translation Field: the class of evolved systems that convert mechanical wave propagation into actionable meaning. It includes percussive foragers, web/modal graph sensors, substrate vibration insects, seismic mammals, aquatic lateral-line systems, echolocators, and plant stress-ultrasound emission.
Boundary: this is not proof that plants have subjective experience or intentional speech. The plant-stress sound source is treated as an informative biomechanical emission term in a broader phonon-mediated translation equation.
1. Base BioPhonon field
Universal medium equation:
\mathcal{M}\ddot{u}
+
\mathcal{C}\dot{u}
+
\mathcal{K}u
+
\mathcal{N}(u,\nabla u)
=
S_a(x,t)
+
S_w(x,t)
+
N(x,t)
Observation equation:
y_i(t)
=
\mathcal{R}_i[u(x_i,t)]
+
\eta_i(t)
Translation equation:
P(z\mid y_{1:n},a)
\propto
P(y_{1:n}\mid z,a)P(z)
Action policy:
a^*
=
\arg\max_a
\frac{
I(z;y_{1:n}\mid a)
}{
E_{act}(a)+E_{move}(a)+C_{compute}(a)+C_{risk}(a)
}
2. Plant-stress ultrasonic emission term
The plant-stress source term adds an emitter that is not a moving animal sensor, but a biomechanical state-to-sound translator.
S_w(x,t)
\rightarrow
S_{world}(x,t)
+
S_{plant}(x,t;\sigma_h,w,i,\chi)
where:
σ_h = hydraulic / xylem tension stress
w = water deficit / dehydration state
i = injury or cutting state
χ = species / tissue / morphology parameters
The plant emission source can be modeled as a sparse ultrasonic pulse train:
S_{plant}(x,t)
=
\sum_k
A_k(\sigma_h,w,i,\chi)
\,g(t-t_k;f_k,Q_k)
\,\delta(x-x_{plant})
with event rate:
\lambda_{plant}(t)
=
\lambda_0
+
\lambda_w\,\Phi_w(w(t))
+
\lambda_i\,\Phi_i(i(t))
+
\lambda_h\,\Phi_h(\sigma_h(t)).
Interpretation:
Plant state -> ultrasonic event statistics -> receiver inference.
3. Cavitation-compatible source hypothesis
A conservative biomechanical source model treats plant sounds as cavitation-compatible xylem events rather than intentional vocalization:
\sigma_h(t) > \sigma_{cav}
\Rightarrow
\Delta P_{xylem}(t)
\Rightarrow
S_{plant}(t).
One possible event kernel:
g(t;f,Q)
=
H(t)e^{-\pi f t/Q}\sin(2\pi f t).
This keeps the plant term compatible with mechanical emission:
hydraulic stress / injury -> elastic release / cavitation-like pulse -> airborne ultrasound.
4. Receiver inference: who listens?
For any receiver organism r:
y_r(t)
=
\mathcal{H}_{air,plant\to r}[S_{plant}](t)+\eta_r(t)
and:
P(z_{plant}\mid y_r)
\propto
P(y_r\mid z_{plant})P(z_{plant}).
Receiver action:
a_r^*
=
\arg\max_{a_r}
\frac{
I(z_{plant};y_r\mid a_r)
}{
E_{move}(a_r)+C_{compute}(a_r)+C_{risk}(a_r)
}.
Examples:
moth: avoid oviposition on stressed host plant
bat/mouse/insect: detect ultrasonic environmental state
neighbor plant: possible stress preconditioning route, currently research-bound
farmer sensor: irrigation / stress monitoring
5. Updated universal BioPhonon translation equation
With plant-stress ultrasound included:
\boxed{
\mathcal{M}\ddot{u}
+
\mathcal{C}\dot{u}
+
\mathcal{K}u
+
\mathcal{N}(u,\nabla u)
=
S_{self}(x,t)
+
S_{prey}(x,t)
+
S_{mate}(x,t)
+
S_{predator}(x,t)
+
S_{plant}(x,t)
+
N_{env}(x,t)
}
Observation:
\boxed{
y_i(t)
=
\mathcal{R}_i[u(x_i,t)]
+
\eta_i(t)
}
Translation:
\boxed{
P(z\mid y_{1:n},a)
\propto
P(y_{1:n}\mid z,a)P(z)
}
Action:
\boxed{
a^*
=
\arg\max_a
\frac{
I(z;y_{1:n}\mid a)
}{
E_{act}(a)+E_{move}(a)+C_{compute}(a)+C_{risk}(a)+L_{FAMM}(a)
}
}
6. Stack translation
Plant-stress ultrasound adds a new category: passive biomechanical source emission.
not only: active probe -> response -> meaning
also: internal stress -> emitted phonon signature -> external listener inference
Compression analogy:
internal state strain -> sparse acoustic/phonon events -> classifier route -> FAMM scar/update
So the compression/semantic equivalent is:
route^*
=
\arg\max_{probe/listen}
\frac{
I(hidden\_state;response\mid probe/listen)
}{
C_{probe}+C_{listen}+C_{decode}+C_{interface}+C_{risk}+L_{FAMM}
}.
7. Warden boundary
Allowed:
Use plant-stress sounds as a biomechanical ultrasonic source term.
Use the term to expand BioPhonon translation to include passive stress emissions.
Use classifier/inference framing for animal, plant, or engineered receivers.
Blocked:
Do not claim plants intentionally scream.
Do not claim plant sentience or pain from ultrasonic emissions.
Do not claim plant-to-animal communication unless receiver behavior is empirically shown.
Do not promote BioPhonon claims outside the measured stress-sound/source-receiver boundary.
8. Source anchor
Primary source:
Khait et al. 2023. Sounds emitted by plants under stress are airborne and informative. Cell 186(7):1328-1336.e10. DOI: 10.1016/j.cell.2023.03.009