index 67fd2d2..e11ddc3 100644
@@ -13,7 +13,7 @@ the lotka-volterra equations model predator-prey interactions:
- predators grow when prey are abundant
- the system oscillates: more prey → more predators → fewer prey → fewer predators → more prey → ...
-this is a pair of coupled differential equations, and the oscillating solution explains real population cycles (like the famous lynx-hare cycle in canadian fur trapping records). the math predicts the qualitative behavior — boom and bust — without knowing anything about the specific animals.
+this is a pair of coupled differential equations, and the oscillating solution explains real population cycles (like the famous lynx-hare cycle in canadian fur trapping records). the math predicts the qualitative behavior — boom and bust — without knowing anything about the specific animals. [[structural/calculus-as-thinking|calculus]] is the language here: growth, decay, rates of change, equilibrium points — all the core concepts show up in biological modeling.
more sophisticated models handle competition, mutualism, migration, and age structure. conservation biology uses these to predict extinction risk and design nature reserves.
@@ -24,7 +24,7 @@ the SIR model (susceptible → infected → recovered) is the foundation of epid
- dI/dt = βSI - γI (infected people either infect others or recover)
- dR/dt = γI (recovered people are immune)
-the basic reproduction number R₀ — how many people one infected person infects on average — determines whether an epidemic grows or dies out. R₀ > 1 means epidemic; R₀ < 1 means it fizzles.
+the basic reproduction number R₀ — how many people one infected person infects on average — determines whether an epidemic grows or dies out. R₀ > 1 means epidemic; R₀ < 1 means it fizzles.
during COVID, everyone suddenly cared about these models. "flatten the curve" was a mathematical statement: reduce β (through masking, distancing) to keep the infection peak below hospital capacity. the math was simple; getting people to act on it was the hard part.
@@ -43,8 +43,9 @@ in my research on anesthetics and brain monitoring, the raw data is EEG signals
the math pipeline:
1. **fourier analysis** decomposes the signal into frequency bands (delta 0.5-4 Hz, theta 4-8 Hz, alpha 8-13 Hz, beta 13-30 Hz, gamma 30+ Hz)
2. **filtering** removes artifacts and noise
-3. **feature extraction** computes statistics (power spectral density, coherence between channels, entropy measures)
-4. **classification** — in our case, a CNN trained on spectrogram images to detect depth of anesthesia
+3. **classification** — in our case, a CNN trained on spectrogram images to detect depth of anesthesia
+
+the same [[stem/engineering-and-modeling|signal processing techniques]] used in engineering — fourier transforms, wavelets, spectral methods — are critical here.
the goal: can we tell from brain signals alone how deeply anesthetized a patient is? too light and they might wake up during surgery. too deep and you risk complications. the math turns a subjective clinical judgment into an objective measurement — exactly the [counting and measurement](/wiki/immediate/counting-and-measurement) problem, but for consciousness.