Daniel sent us this one — he's noticed that the word "model" has become completely colonized by AI. You hear "model" and your brain immediately goes to machine learning, large language models, neural nets. But clinicians have been using pharmacokinetic models for decades — plug in age, body weight, renal function, and the model spits out a drug dosage. No training data, no loss function, no GPU. His question is: how do we actually define these different things in opposition to each other, where do the boundaries lie, and why does everyone now assume "model" means AI?
This is one of those semantic problems that sounds pedantic until you realize people are making million-dollar purchasing decisions based on it. And clinical decisions.
A hospital buys a "clinical decision support model" thinking they're getting interpretable pharmacokinetics and instead they get a black-box gradient-boosted tree that nobody can explain.
That's not hypothetical. We'll get to Epic's sepsis model. But first we need to actually define our terms — because the word model is doing an absurd amount of heavy lifting in 2026.
Doing the semantic equivalent of carrying a sofa up six flights of stairs by itself.
It's been doing that for decades before anyone uttered the phrase "large language model." The OSI networking model, the relational model in databases, the waterfall model in software development — none of these have anything to do with machine learning. The term "model" in computing predates AI as a commercial category by something like forty years.
Let's establish the taxonomy. What are we actually distinguishing here?
First, classical mathematical models — and I want to use the pharmacokinetic model as our anchor example throughout because it's concrete and life-saving and zero percent AI. Second, machine learning models — neural networks, gradient-boosted trees, transformers. Third, algorithms — which are often confused with models but are fundamentally different. An algorithm is a procedure, a step-by-step recipe for computation. A model is a representation.
The differential equation describing how a drug concentration decays in the bloodstream is a model. The Runge-Kutta method you use to solve that equation numerically is an algorithm.
And the trained weights of a neural network are a model. The backpropagation and gradient descent that produced those weights — those are algorithms. This distinction sounds tidy but it gets messy fast because people routinely say "the GPT-4 model" and "the training algorithm" in ways that collapse the boundary.
The word is like a rental tuxedo — it fits everyone passably but nobody perfectly.
Let's start with the pharmacokinetic model, because it's the clearest example of what a non-ML model actually is, and it's been saving lives since long before anyone thought to train a neural network.
Walk me through it.
A pharmacokinetic model is a system of differential equations. The simplest is a one-compartment model where you assume the body is a single well-stirred container. The core equation is dC over dt equals negative k times C — the rate of change of drug concentration is proportional to the concentration itself. First-order elimination. You solve that and you get an exponential decay curve.
"k" is what, exactly?
The elimination rate constant. It's estimated from patient-specific variables — renal function, liver function, age, body weight. In a two-compartment model, which is more realistic, you have a central compartment representing the bloodstream and a peripheral compartment representing tissue. The drug distributes between them at certain rates. You end up with a system of two coupled differential equations.
How many parameters are we talking about?
A typical two-compartment PK model has four to six parameters — volume of distribution in the central compartment, intercompartmental clearance, elimination clearance, things like that. Each parameter has a physical meaning. You can point to clearance and say "that's the rate at which the kidneys are removing this drug from the blood." It's not an abstract weight in a matrix. It's a measurable physiological quantity.
This produces deterministic outputs?
Given the same inputs, yes. Plug in the same patient characteristics, you get the same predicted concentration-time curve. There's no sampling from a distribution, no probabilistic output layer. The uncertainty comes from measurement error in the inputs and model misspecification — the fact that no real human body is exactly two compartments — not from the model itself being stochastic.
Now contrast that with a machine learning model doing the same job — predicting drug concentrations.
This is where it gets interesting. You could train a neural network to predict drug concentrations given the same input variables. Feed it age, weight, renal function, dose, time since administration. Train it on thousands of patient records. It would learn some function mapping inputs to outputs. But that function would have potentially millions of parameters — weights in the network — and not a single one of them corresponds to a physical process. You can't point to layer three neuron seventeen and say "that's the renal clearance parameter.
It's the difference between a map and a photograph. The PK model is a map — simplified, schematic, but every symbol means something. The ML model is a photograph — high-resolution, potentially more accurate in distribution, but you can't point to a pixel and ask what it represents.
That's a really useful distinction. And it gets at something deeper about how these models are constructed. A classical PK model is theory-first. You start with known physiology — how drugs distribute, how kidneys filter, how the liver metabolizes. You derive equations from first principles. Then you fit the parameters to data using something like nonlinear least squares. But the structure of the model comes from theory, not from data.
Whereas the ML approach is data-first.
You start with a flexible function approximator — a neural network, a random forest — and you train it on data to minimize prediction error. The model discovers patterns in the data, but it has no built-in knowledge of physiology. It doesn't know that drug concentration should decay exponentially. It might learn something approximating exponential decay from the data, or it might learn something else that works well on the training distribution but fails catastrophically when you extrapolate.
That extrapolation point seems critical.
It's arguably the most important practical difference. A PK model, because it encodes physical laws, can extrapolate beyond its fitting data with some confidence. If I've fitted my PK model to patients with normal renal function, I can still use it to predict what happens in a patient with kidney failure — because the model explicitly represents renal clearance as a parameter. I can set that parameter to near zero and the equations still make physical sense.
The ML model trained only on patients with normal kidneys —
Has no idea what to do with a kidney failure patient. It's never seen that region of input space. It might output something nonsensical, like a negative concentration or a concentration that increases over time. And because it's a black box, you might not even know it's failing until the patient is harmed.
We've got two things that are both called models, both take inputs and produce outputs, but they're epistemologically different species.
Completely different species. And this isn't just an academic taxonomy problem — the FDA recognizes this distinction explicitly. In 2023, they issued draft guidance on physiologically based pharmacokinetic models — PBPK models. The guidance requires model developers to submit the actual differential equations and parameter values. The FDA reviewers can inspect the equations, verify that they represent known physiology, check the parameter values against published literature.
For AI and ML models?
The 2024 framework for AI slash ML-enabled medical devices is a completely different document with completely different requirements. They ask for training data provenance, performance across subpopulations, robustness testing under distribution shift. They don't ask to see the equations, because there are no equations in any meaningful sense — just a massive matrix of weights.
Same regulatory body, same word "model," fundamentally different standards.
That's appropriate. The risks are different. A PK model fails interpretably — you can diagnose why the prediction is wrong by checking each parameter. An ML model fails opaquely — you get a wrong output and you have to investigate whether it's a training data issue, a distribution shift, or something else entirely.
Let's talk about the algorithm boundary, because that's the third leg of this stool and it's where I see people get confused most often.
The confusion is understandable because we use "model" and "algorithm" interchangeably in casual speech. But they're different categories of thing. An algorithm is a procedure — a finite sequence of well-defined steps for solving a problem. Sort this list using quicksort. Solve this differential equation using fourth-order Runge-Kutta. Find the shortest path using Dijkstra's algorithm.
A model is a representation of something.
The PK model is a representation of how a drug behaves in the body. The neural network is a representation — a very complex, opaque representation — of patterns in the training data. Neither is an algorithm. But here's where it gets tricky: the process of training a neural network is an algorithm. Gradient descent is an algorithm. Backpropagation is an algorithm. But the trained network itself is not an algorithm — it's a model.
When someone says "the GPT-4 algorithm," they're committing a category error.
GPT-4 is a model. The transformer architecture plus the training procedure produced it, but the thing you interact with is a model — a set of learned weights that represent patterns in text. The inference procedure that generates tokens one by one is arguably algorithmic, but the model itself is not.
This reminds me of the distinction between a recipe and a cake. The recipe is the algorithm. The cake is the model.
That's a solid analogy. And a classical PK model is more like a chemical formula for a cake that's derived from the physics of baking — you can write down why each ingredient does what it does. An ML model is a cake produced by a machine that reverse-engineered millions of cakes and can now produce something cake-like, but nobody can tell you exactly what's in it or why it works.
The FDA's 2023 PBPK guidance versus their 2024 AI framework is basically the difference between demanding the recipe and demanding the health inspection records of the factory.
And both are called "model validation." Same phrase, completely different activities.
Let's drill into a concrete comparison. You mentioned the Epic sepsis model earlier.
This is a perfect case study because it involves two "models" for the same clinical task — predicting which patients will develop sepsis — that are radically different under the hood. The qSOFA score is a simple logistic regression model. It uses exactly three variables: respiratory rate, systolic blood pressure, and altered mental status. That's it. Three inputs, a simple scoring system, and a threshold. You can write the entire model on a Post-it note.
It's validated, transparent, anyone can understand how it works.
It was developed from known pathophysiology — sepsis causes tachypnea, hypotension, and confusion. The model encodes medical knowledge. Then there's Epic's sepsis prediction model, which was deployed in hundreds of hospitals. It uses over three hundred features and a gradient-boosted tree. It's a machine learning model. And a 2021 study found that in practice, it had a positive predictive value of about three percent.
For every hundred patients it flagged as likely to develop sepsis, three actually did. The qSOFA score, using three variables and no machine learning, performs comparably or better in many settings. But Epic's model was sold as this sophisticated AI system, and hospitals bought it.
Both are called "sepsis prediction models.
Both are called models. One is a transparent, theory-driven scoring system. The other is a black-box ML system trained on historical data. A clinician looking at the qSOFA score knows exactly why a patient was flagged — their respiratory rate is elevated, their blood pressure is low, they're confused. A clinician looking at the Epic model's alert sees a risk score and has no idea which of the three hundred features drove it.
This is where the semantic collapse becomes actively dangerous. A hospital administrator hears "model" and assumes a certain level of interpretability, a certain standard of validation, because that's what "model" meant in medicine for decades.
The vendor is using "model" in the ML sense, where interpretability is not guaranteed and validation means something completely different. The expectations are completely misaligned, and the word "model" is what enables that misalignment.
It's the linguistic equivalent of a bait and switch.
Unintentional, usually, but yes. And it's not just healthcare. Weather forecasting has the same tension. Traditional numerical weather prediction is a classical model — you take the Navier-Stokes equations for fluid dynamics, the thermodynamic equations, you discretize them on a grid, and you solve them forward in time on a supercomputer. It's physics all the way down.
Then there's Google's GraphCast.
GraphCast is a machine learning model trained on forty years of historical weather data from ECMWF. It doesn't solve any fluid dynamics equations. It learns patterns from the historical record and predicts future weather states directly. And it's remarkably good — competitive with or better than operational numerical weather prediction on many metrics.
Both are "weather models.
Both are called weather models. And here's the thing — GraphCast doesn't know about conservation of mass or energy. It might produce a forecast that looks plausible but violates fundamental physical constraints. The numerical weather prediction model, by construction, conserves mass and energy because the equations it solves enforce those constraints.
If you're trying to predict a hurricane's path in unprecedented conditions — climate change is producing situations that aren't well represented in the historical record — which model do you trust?
That's the extrapolation problem again. The physics-based model has theoretical grounds for extrapolating. GraphCast is interpolating within the distribution of its training data. If you give it conditions it hasn't seen before, all bets are off. And you might not know the bets are off because the model will happily produce a forecast that looks confident.
This brings me to a question I've been chewing on. Is the difference between classical models and ML models a difference in kind, or a difference in degree?
I think it's a difference in kind, and the key is where the knowledge lives. In a classical model, the knowledge is in the structure — the equations, the choice of which variables to include, the form of the relationships. The data is used to estimate parameters within that structure, but the structure itself comes from theory. In an ML model, the knowledge is entirely in the data. The structure — the neural network architecture — is deliberately generic. It's designed to be a flexible function approximator that can learn anything from data.
It's theory-first versus data-first, as you said. But what about the hybrid approaches?
This is where the boundary gets genuinely blurry, and it's probably the most exciting development in scientific computing. Physics-informed neural networks — PINNs — embed differential equations directly into the neural network's loss function. The network is penalized not just for prediction error but for violating the known physics.
You're training a neural network, but you're constraining it to obey the PK equations?
The network learns to approximate the solution to the differential equations while also fitting the data. You get the flexibility of ML with the physical constraints of a classical model. The resulting model has millions of parameters like an ML model, but it respects conservation laws and other physical constraints like a classical model.
What do you call that thing?
That's the question. Is it a classical model with a neural network implementation? Is it an ML model with physics constraints? The vocabulary hasn't caught up. People say "hybrid model" or "physics-informed ML," but these are placeholder terms for something that doesn't fit neatly into either category.
This isn't just academic — these hybrid models are starting to show up in drug development, in engineering, in climate science.
Neural ODEs are another example — neural ordinary differential equations. Instead of a discrete sequence of layers, you define a continuous dynamics specified by a neural network. The model is literally a differential equation where the right-hand side is a neural network. It blurs the line between classical differential equation models and deep learning in a way that's mathematically elegant and practically useful.
We've got three categories we're trying to keep distinct — classical models, ML models, algorithms — and the cutting edge is actively blending the first two.
Which makes precise language more important, not less. If the boundaries are blurring, you need to be able to say exactly what you mean.
Let's talk about the practical consequences of getting this wrong. You mentioned hospital purchasing. What does that look like on the ground?
Imagine you're the chief medical information officer at a mid-sized hospital. A vendor comes in and says "we have a clinical decision support model that predicts patient deterioration." The word "model" triggers your mental schema from medical training — you think of something like a risk score, validated in peer-reviewed literature, with transparent inputs and known performance characteristics.
The kind of thing you learned about in medical school.
You sign the contract. What you actually get is a gradient-boosted tree trained on the vendor's proprietary dataset, with feature engineering that nobody outside the vendor understands, and performance characteristics that were measured on a dataset that may not resemble your patient population at all. When it fails — and it will fail — you can't debug it because you can't see inside it.
The liability question is completely different.
If a PK model gives a wrong dose because someone entered the wrong weight, that's a data entry error. If an ML model gives a wrong prediction and a patient is harmed, who's responsible? The vendor who built the model? The hospital that deployed it? The clinician who relied on it without understanding its limitations? The legal frameworks haven't caught up.
Because the law assumes "model" means something you can reason about.
Or at least something with a clear chain of causation. With an ML model, you have a prediction that emerged from a high-dimensional interaction of hundreds of features through multiple layers of nonlinear transformations. Good luck establishing causation in a malpractice suit.
What should an engineering team or a product team actually do when someone says "we need a model"?
This is where the practical takeaways start. The first question should not be "what data do we have" — which is the reflexive ML-first question. The first question should be "what kind of model are we building, and why?
Theory-driven or data-driven.
That choice has massive downstream implications. If you choose theory-driven, you need domain experts who understand the underlying physics or biology or economics. Your timeline involves literature review, equation derivation, parameter estimation. Your validation involves checking against known physical constraints. If you choose data-driven, you need large, representative datasets. Your timeline involves data cleaning, feature engineering, hyperparameter tuning. Your validation involves holdout sets and distribution shift testing.
The skills, the budget, the timeline, the failure modes — all completely different. And it all hinges on which sense of "model" you're using.
Here's the thing — in many cases, the theory-driven approach is simpler, cheaper, and more reliable. The WarfarinDosing website is a perfect example. It uses about ten variables and a linear regression to predict warfarin dosing. No machine learning. It incorporates known pharmacogenomic factors — CYP2C9 and VKORC1 gene variants — plus age, weight, and other clinical variables. It's interpretable, it's been validated in multiple populations, and it works.
You could train a deep learning model to do the same thing. It might even be marginally more accurate on some metric. But would it be worth the loss of interpretability?
In most clinical settings, absolutely not. The ability to explain why you're recommending a particular dose — to a colleague, to a patient, to a malpractice attorney — is worth more than a fraction of a percent improvement in some accuracy metric.
Let me try to crystallize the definitional boundaries we've been circling. A classical mathematical model is a collection of formulae that represent a system, derived from theory, with interpretable parameters, producing deterministic or statistically well-characterized outputs. A machine learning model is a function approximator with learned parameters that have no necessary physical interpretation, trained via optimization on data, typically producing probabilistic outputs. An algorithm is a step-by-step procedure for computation — it's the process, not the representation.
That's a clean summary. And I'd add: a classical model can be wrong in ways you can diagnose. You can check each parameter, each equation, each assumption. An ML model can be wrong in ways that are much harder to diagnose — distribution shift, spurious correlations in training data, adversarial examples. The failure modes are different because the epistemology is different.
The word "model" is doing something similar to what happened to "cloud" — it started as a specific technical term and expanded until it meant everything and therefore nothing.
" Everything is a platform now. Your toaster is a platform.
The toaster is a thermal-gradient breakfast platform.
This semantic drift isn't harmless. When the EU AI Act classifies "models" by risk tier, it's using "model" in a way that lumps together things that have fundamentally different risk profiles. A PK model deployed in a hospital poses different risks than an LLM deployed in a chatbot. But the regulatory language uses the same word for both, which creates pressure to either over-regulate the classical models — requiring documentation that makes no sense for a differential equation — or under-regulate the ML models — applying standards designed for interpretable systems to black boxes.
What's the fix?
I think we need to be more precise in technical communication. Instead of saying "we built a model," say "we built a pharmacokinetic compartment model" or "we trained a gradient boosting regressor" or "we implemented a physics-informed neural network." The extra words do real work — they set expectations about interpretability, validation, and failure modes.
That requires the speaker to actually understand what they built.
Yes, and that's a feature, not a bug. If you can't name what kind of model you're using, you probably don't understand it well enough to deploy it responsibly.
There's a knock-on effect here that I want to pull on. The AI industry has an incentive to call everything a model because "model" sounds scientific, rigorous, validated. It borrows the credibility of centuries of mathematical modeling and applies it to a neural network that was trained last Tuesday on a dataset nobody's audited.
That's a sharp point. The term "model" carries connotations of scientific rigor that don't automatically transfer to ML systems. When a physicist says "our model predicts," they're making a claim backed by theory and validated through experiment. When an AI company says "our model predicts," they might mean "our neural network produced this output on a benchmark dataset." The epistemic weight is completely different, but the language obscures that.
It's the rhetorical equivalent of wearing a lab coat to sell supplements.
The arXiv alone had over forty thousand papers with "model" in the title in 2025, spanning physics, biology, computer science, economics. The word is doing so much work across so many disciplines that it's essentially lost its ability to convey specific meaning without additional qualification.
Let's get practical. You mentioned three questions people should ask when evaluating any model. Let's lay them out.
First: is it theory-driven or data-driven? This tells you where the knowledge comes from and what happens when you extrapolate. Second: are the parameters interpretable? Can you point to a specific parameter and say what it means in the real world? Third: what guarantees does it provide about behavior outside the training data? Can it extrapolate, or is it only reliable within the distribution it was fitted or trained on?
Those three questions will catch most of the dangerous category errors before they happen.
For teams that are building or buying models, I'd go further — create a model taxonomy document. For every model in your system, classify it by type, by validation method, and by known failure mode. Is it a compartment model validated against published pharmacokinetic data? Is it a random forest validated on a holdout set with known performance degradation under distribution shift? Is it a hybrid PINN that enforces conservation laws but still has millions of uninterpretable parameters?
This sounds like paperwork, and engineers hate paperwork.
It is paperwork, and it's paperwork that prevents you from deploying a model that kills someone in a way you can't explain. In regulated industries — healthcare, finance, autonomous systems — this kind of documentation should be non-negotiable.
The Epic sepsis model story makes that case better than any argument we could make. Three hundred features, gradient-boosted trees, three percent positive predictive value in practice. If someone had asked "what kind of model is this and how was it validated" before deploying it across hundreds of hospitals, a lot of false alarms could have been avoided.
False alarms in a clinical setting aren't just annoying — they cause alarm fatigue. Clinicians start ignoring the alerts. Then when a real case comes along, they miss it. The model doesn't just fail on its own terms; it degrades the entire clinical system around it.
Where does this leave us? The word "model" isn't going anywhere. We're not going to successfully rename neural networks to "function approximators" or PK models to "differential equation systems" in common parlance.
No, and we shouldn't try. Language evolves organically. But we can be more precise in contexts where precision matters — technical documentation, regulatory filings, procurement contracts, clinical decision-making. And we can train ourselves to hear "model" and immediately ask "what kind?
The hybrid models make this both more urgent and more complicated. If we've got physics-informed neural networks that blend classical differential equations with deep learning, the old categories start to break down.
This is the forward-looking question I find fascinating. As scientific machine learning matures, we're going to need new vocabulary. A PINN isn't just a classical model with a neural network implementation, and it isn't just an ML model with some physics sprinkled on top. It's a new kind of thing that inherits properties from both traditions.
It's interpretable at the level of the physics constraints but opaque at the level of the neural network representation.
You know it conserves energy because you built that into the loss function. But you don't know exactly how the network is representing the solution internally. It's a partial interpretability that doesn't fit neatly into either the classical or the ML bucket.
Which means the regulatory frameworks need to evolve too. If the FDA's PBPK guidance asks for the differential equations and the AI framework asks for training data provenance, what do you submit for a PINN that does both?
Currently, nobody knows. And that's a problem because these hybrid models are moving from research into practice. There are PINN-based models being explored for drug development, for medical imaging, for patient-specific surgical planning. The regulatory frameworks are still organized around a distinction that the technology is actively erasing.
The semantic problem and the regulatory problem are the same problem. We need words that capture the actual properties of these systems — not just "model" with an adjective, but a richer vocabulary that communicates interpretability, causal structure, extrapolation guarantees, and failure modes.
That vocabulary is going to have to emerge from practice. Standards bodies, regulatory agencies, professional societies — they need to develop taxonomies that are precise enough to be useful without being so complex that nobody uses them.
Given all this, what should someone actually do differently on Monday morning?
One: in your next design doc or technical spec, ban the word "model" without a qualifier. Say "logistic regression classifier" or "transformer-based language model" or "two-compartment PK model." Two: for every model in your system, write down the three answers — theory-driven or data-driven, interpretable parameters or not, extrapolation guarantees or not. Three: if you're buying a model from a vendor, ask for these answers in writing. If they can't provide them, that's a red flag.
If you're a clinician, when someone says "the model recommends," ask which kind of model and what validation it's undergone.
The qSOFA score versus Epic's sepsis model comparison should be required reading for anyone who deploys clinical decision support. Three variables, transparent scoring, validated in multiple populations — versus three hundred features, proprietary training, three percent positive predictive value. The simpler model won.
Simpler model, same word. That's the whole problem in a sentence.
Where does this leave us? The word "model" isn't going anywhere, but maybe it should come with a warning label. "This term may refer to anything from a four-parameter differential equation to a one point eight trillion parameter transformer. Ask for details.
The nutritional label for models. I'd buy that.
The open question I keep coming back to is whether the hybrid approaches will force a genuine linguistic innovation. When PINNs and neural ODEs become standard tools, will we settle on a new term that captures the blend of theory and data? Or will "model" just expand its semantic range even further until it's truly meaningless?
My bet is on the latter. Semantic expansion is easier than coining new terms. But maybe that's the pessimist in me.
The other frontier is the legal question of what constitutes a model change. If you retrain an ML model on new data, is it the same model? Most regulatory frameworks assume a model is a stable artifact. But ML models in production are often retrained continuously. For a PK model, changing a parameter is a deliberate, documented update. For an ML model, retraining might shift the behavior in ways nobody fully understands.
The legal frameworks assume a world of classical models — stable, documented, interpretable. The technology has moved on. The law hasn't.
That gap is going to produce some fascinating court cases in the next few years. When an ML model makes a harmful decision and the vendor says "that was version three point two, we're on version three point four now, and version three point two no longer exists" — what does liability look like?
It looks like a very expensive seminar in semantic precision for everyone involved.
If this episode changed how you think about the word "model" — or if you've got other terms that you think need semantic rescue — leave us a review and tell us about it. We read them.
Now: Hilbert's daily fun fact.
Hilbert: In the 1840s, European explorers in South Sudan documented the Shilluk people's "king's knot" — a complex lashing technique used to bind ceremonial spears that produced a joint stronger than the wood itself. The technique was considered extinct by 1900, but a 2023 archaeological dig near Malakal recovered a preserved binding that matched the explorers' sketches exactly.
Stronger than the wood itself. That's a heck of a knot.
This has been My Weird Prompts. I'm Corn.
I'm Herman Poppleberry. Find us at myweirdprompts dot com, or wherever you get your podcasts.
