index e11ddc3..d17848b 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. [[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.
+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. [[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.
@@ -45,15 +45,15 @@ the math pipeline:
2. **filtering** removes artifacts and noise
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 same [[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.
+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|counting and measurement]] problem, but for consciousness.
## medical statistics
-clinical trials are [probability](/wiki/immediate/probability-in-daily-life) in its highest-stakes application. does this drug work, or did we get lucky with our sample? p-values, confidence intervals, randomization, blinding — the entire machinery of evidence-based medicine is statistical.
+clinical trials are [[probability-in-daily-life|probability]] in its highest-stakes application. does this drug work, or did we get lucky with our sample? p-values, confidence intervals, randomization, blinding — the entire machinery of evidence-based medicine is statistical.
-and the errors are consequential. p-hacking (running many statistical tests until one comes out significant) has contributed to a replication crisis across biomedical research. base rate neglect in diagnostic testing (see [probability](/wiki/immediate/probability-in-daily-life)) leads to unnecessary procedures and missed diagnoses. getting the math right literally saves lives.
+and the errors are consequential. p-hacking (running many statistical tests until one comes out significant) has contributed to a replication crisis across biomedical research. base rate neglect in diagnostic testing (see [[probability-in-daily-life|probability]]) leads to unnecessary procedures and missed diagnoses. getting the math right literally saves lives.
## the deep point