Figuring Out AI: Two Axes, Two Systems, Two Environments
By Joe Nalven + Claude + Gemini
A Note for Those Asking What AI Is
People who ask “What is AI?” usually expect a single answer. There is no single answer. “AI” is a name for a family of computer systems that work in different ways and in different settings. A program that plays the board game Go, a camera system that recognizes pedestrians, and a chatbot that drafts a letter share some techniques, but they differ in how they reach their answers and in how far those answers can be trusted.
A more useful starting point than “Is it intelligent?” is two narrower questions. First, what kind of world does the system work in? Second, does the system give the same answer every time it is asked the same question? This essay turns those two questions into two axes. Along one axis are two kinds of systems. Along the other are two kinds of environments. Crossing the axes produces four quadrants, and most AI systems, or parts of them, can be placed in one of the four.
The First Axis: Two Kinds of Systems
The first axis describes how a system produces its output.
A deterministic system always gives the same output for the same input. A pocket calculator is deterministic: 2 + 2 produces 4 every time.
A stochastic system includes a deliberate random step, so the same input can give different outputs on different occasions. (“Stochastic” is a technical word for “involving chance.”) Rolling dice is stochastic.
Probability can enter an AI system in two different ways, and the two should be kept apart. A system can estimate probabilities, for example by calculating that a position in a game has a 70 percent chance of being won. Or a system can sample, which means choosing its output by a random draw in which more probable options are more likely to be picked. A system can estimate probabilities and still be fully deterministic, because the same input always produces the same estimates. Only sampling makes a system stochastic. This axis is about sampling.
The Second Axis: Two Kinds of Environments
The second axis describes the world the system works in.
A closed environment has rules that are fully known in advance, such as a board game or a tax code. Every possible situation follows from those rules.
An open environment has rules that are incomplete, ambiguous, or changing, such as city traffic or human language. New situations keep arising that no rule anticipated.
What This Framework Borrows and What It Adds
Neither axis is new. Stuart Russell and Peter Norvig’s textbook Artificial Intelligence: A Modern Approach, the standard text in the field, classifies the environments that AI systems work in along several dimensions. Their distinction between known and unknown environments is close to this essay’s distinction between closed and open. They also distinguish deterministic from stochastic, but they apply those terms to the environment: whether the world itself behaves predictably. This essay applies the same terms to the system: whether the system’s own procedure for producing an answer includes a random step. Keeping the two apart separates two questions that are easily confused, namely how predictable the world is and how predictable the system is.
The environment axis also has an older ancestor in economics. In Risk, Uncertainty and Profit (1921), Frank Knight distinguished risk from uncertainty. Under risk, the possible outcomes can be listed and their probabilities can be known or calculated. Under uncertainty, they cannot. A closed environment resembles Knight’s risk; an open environment resembles his uncertainty.
This essay adds one further point to these earlier frameworks. Deterministic does not mean verifiable. A system that gives the same answer every time has not shown that the answer is correct, and it has not shown that anyone can inspect how the answer was reached. This point matters most in the final section.
Quadrant 1: Deterministic Systems in Closed Environments
Classical computer programs belong here. Examples are tax-preparation software and the flight-control software in an airliner, which in the most demanding cases is checked by formal verification, a mathematical proof that the code does what its specification says. The rules in these programs were written by people, line by line. As a result, the system is both repeatable and inspectable: a person can read the rule that produced any given output.
Lethal autonomous weapon systems (LAWS), weapons that can select and engage targets without a human decision for each engagement, show both the appeal and the limit of this quadrant. Designers try to keep the logic that authorizes an attack in Quadrant 1. That logic consists of geofences (fixed geographic boundaries the weapon may not cross), thresholds for which kinds of targets qualify, and rules of engagement written as explicit conditions. However, the component that recognizes a target in a camera or radar image is often a neural network, which belongs in Quadrant 2. A rule that says “engage only vehicles of type X inside this boundary” is only as reliable as the component that decides what counts as a vehicle of type X.
Quadrant 2: Deterministic Systems in Open Environments
A neural network is a computer system that learns to perform a task from examples instead of following rules written by a programmer. It consists of millions or billions of adjustable numbers, called weights. During training, the network is shown a large number of examples, such as photographs labeled “pedestrian” or “no pedestrian,” and its weights are adjusted step by step until its outputs match the labels.
A trained image classifier, a neural network that sorts images into categories, belongs in this quadrant. The training process uses randomness. Once training is finished and the weights are fixed, however, running the network on an image is a fixed calculation, and the same image always produces the same label. The world the network classifies is open, because photographs of streets vary without limit, but its calculation is deterministic.
Unlike a Quadrant 1 program, this system cannot be read rule by rule. No person wrote the rule that turns a pattern of pixels into the label “pedestrian.” That rule exists only as a pattern spread across millions of learned weights. The system repeats itself, but no one can read its reasoning the way one can read a tax code.
Self-driving cars, such as those operated by Waymo, span more than one quadrant, and they show how the quadrants can fit together inside a single machine. The car works in an open environment: city streets contain construction zones, double-parked trucks, hand signals from police officers, and pedestrians who step out without looking. Within that environment, the car’s software performs three different jobs.
The first job is perception. Neural networks interpret the data from cameras, lidar (a sensor that measures distance with laser pulses), and radar, and they label the objects around the car: a cyclist, a traffic cone, a child. Like the image classifier described above, these networks are deterministic once trained, and they cannot be read rule by rule.
The second job is prediction. The prediction component estimates several possible futures for each road user and how likely each future is. A cyclist might continue straight, swerve left, or stop. This component works with probabilities because the behavior of other people cannot be known in advance.
The third job is committing the vehicle to a path. This layer is held to deterministic constraints based on physics and safety rules, such as limits on speed, braking distance, and separation from other road users. No designer leaves the final steering command to a random draw when the system controls a two-ton vehicle at highway speed.
The self-driving car is therefore an early working example of the combined design described at the end of this essay. It also shows where that design is weakest. The safety rules in the third layer can be written out and tested, but they act on whatever the first two layers report. If the perception layer mislabels a pedestrian as a shadow, the safety rules will be applied correctly to a false picture of the street.
Quadrant 3: Stochastic Systems in Closed Environments
The game of Go is the clearest example. The board and the rules are completely known, and the game contains no element of chance: the same sequence of moves always leads to the same position. Yet the number of possible games is far too large for any computer to examine every one.
AlphaGo, the program that defeated the world-class player Lee Sedol in 2016, combined two kinds of tools. Neural networks estimated which moves looked promising and how likely each position was to be won. A method called Monte Carlo Tree Search then tested those candidate moves by exploring a sample of possible continuations instead of all of them. (The method is named after the Monte Carlo casino because it relies on random sampling.) In the original AlphaGo, part of that search involved playing out quick, randomized games to the end to see which side tended to win.
Here, random sampling is a tool for working within a fully defined world. The result is a strong move, not a proven best move. Go has not been solved, so no one knows the best move in most positions.
Quadrant 4: Stochastic Systems in Open Environments
Generative AI belongs here. Generative AI is AI that produces new text, images, or sound, as when a large language model (LLM), the kind of system behind chatbots, drafts an essay. Language has no closed set of legal moves, and for most writing tasks there is no single correct answer, because the conventions of language depend on context and change over time.
An LLM does not work with words directly. Before the model processes any text, the text is broken into small pieces, usually whole words but sometimes parts of words or punctuation marks. Engineers call each piece a “token.” Every piece in the model’s fixed vocabulary, which typically holds tens of thousands of entries, has its own identification number. Inside the model, each of those numbers is converted into a long list of numbers, and the model calculates with those lists. For the rest of this essay, “word” stands for one of these pieces.
An LLM writes one word at a time. At each step, it calculates a probability for every word in its vocabulary and then samples one. A setting controls how much randomness that sampling allows. Engineers call it “temperature”; this essay calls it the randomness setting. When the randomness setting is high, the model often picks less likely words, which makes its writing more varied. When it is low, the model sticks closely to the most likely words. When it is set to zero, there is no randomness at all: the model always picks the single most likely next word.
This shows that a system’s quadrant depends on how the system is run, not only on what the underlying model is. If the randomness setting is turned to zero, the same LLM becomes deterministic, giving the same answer to the same question every time, and it moves into Quadrant 2. The model’s calculation of probabilities was deterministic all along. Randomness enters only at the final step, when one word is selected.
The Neuro-Symbolic Direction
The framework points to a central problem in the design of AI systems: how to combine the strengths of Quadrant 4 with the strengths of Quadrant 1. Quadrant 4 systems handle ambiguous situations and natural language well. Quadrant 1 systems can be checked.
Determinism alone does not solve this problem. An LLM with its randomness switched off gives the same answer every time, but that answer is the one its training made most likely, not one that has been checked against the facts. If that answer is false, the model will repeat the same false answer every time it is asked. Consistency is not correctness.
What Quadrant 1 offers that the other quadrants lack is explicit rules that a person can read, test, and, in the best cases, prove correct. Systems that learn from data handle perception, ambiguity, and language well, but they are unreliable at strict logic and factual accuracy. Systems built from written rules can be inspected, but they fail when the world presents a case their authors did not anticipate.
Neuro-symbolic design tries to keep the strengths of both. “Neuro” refers to neural networks, which learn from data. “Symbolic” refers to systems that operate on explicit rules and logical statements written by people. In a neuro-symbolic design, the neural network handles perception and language, and decisions with serious consequences pass through components whose rules are written out. These include constraint solvers, which are programs that check whether a proposed action satisfies a stated set of rules, and safety kernels, which are small, rigorously checked programs that can block an action.
The self-driving car and the autonomous weapon described above are both attempts at this arrangement, and each is only as trustworthy as the point where its two parts meet. The written rules can be verified. The information those rules act on, however, comes from a neural network that cannot be verified in the same way.
A Closing Note for Those Asking What AI Is
For anyone trying to understand a particular AI system, three questions are more useful than “Is it intelligent?” Which quadrant does the system, or each of its parts, belong in? Which of its parts were written by people, and which were learned from data? And at what point does the output of a learned part become the input to the written rules? The answers will not say whether the system is intelligent. They will say what kind of mistakes the system can make, and who, if anyone, is in a position to catch them.
A further note: This framework describes AI systems as they are built today; as the systems change, the quadrants may need to be redrawn.
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References
Knight, Frank H. Risk, Uncertainty and Profit. Boston: Houghton Mifflin, 1921.
Russell, Stuart, and Peter Norvig. Artificial Intelligence: A Modern Approach. 4th ed. Hoboken, NJ: Pearson, 2020. Chapter 2, “Intelligent Agents.”
