If a language model were a classical calculator, much of what it does would be hard to explain. It isn't, and Friction Theory predicts which limits show up.
The default mental model of a language model is something like a very fast deterministic engine: feed it tokens, get tokens out, bounded only by clock speed and parameter count. Under that model, more context should always help, more explanation should always teach better, and the model's stated confidence should track correctness. None of those follow. The empirical record across the Friction Theory paper series points in a consistent direction: LLMs display systematic cognitive limits that closely mirror patterns long documented in human cognition. The working hypothesis is that this is because they share a structural feature with us: race-architecture probabilistic computation under finite bandwidth, though independent replication is still in early stages.
The list below collects findings that would be hard to predict from the calculator model, and trivial to predict from the friction model.
Things a calculator wouldn't do
Information overload
A calculator gets monotonically more accurate as you give it more relevant information. Language models don't. Beyond a model-specific threshold, accuracy on a target task degrades as context grows, even when the added context is on-topic and non-contradictory. This is not the long-context attention problem — it appears well below the model's nominal context window and tracks the friction profile of the added material rather than its raw token count.
Source: Paper 4b (in preparation)
The overexplanation effect
Adding more thorough explanation to a worked example can decrease a learner's ability to apply the underlying principle to a new problem. The effect appears in LLM fine-tuning trajectories with the same shape that Sweller and colleagues report in human learners: redundant elaboration competes with the schema being acquired. Sender-side completeness and recipient-side learnability are not the same property and trade off against each other.
Source: Paper 4b (in preparation)
Completeness is a sender virtue; learnability is a recipient property
These two are systematically conflated in pedagogical practice (and in LLM prompt engineering). They are not the same: maximising the information density of a message is a property of the sender; whether the recipient can encode it under finite resolution-bandwidth is a property of the recipient. A message that is perfectly complete can be unlearnable, and a message that is incomplete can be highly learnable, depending entirely on the recipient's friction-budget for the encoding task.
Source: Paper 4b (in preparation)
Anchoring — the first token shapes the rest
A calculator's first output digit has no causal relation to the second. In a language model the first committed token constrains the distribution from which every subsequent token is drawn, with the effect propagating tens of tokens downstream. This is anchoring in the Tversky & Kahneman sense, observable directly in the logprob trajectory: the same prompt with a different first-token commit reaches different answers at non-trivial rates.
Two identical training datasets administered in different orders produce different fine-tuned models, with measurable performance differences on held-out evaluation. This is path-dependence in the strict thermodynamic sense: the system's end state is not a function of its input alone but of the trajectory through input-space. The same property is the reason humans show order-of-acquisition effects in skill learning.
Tell a child "don't think of a pink elephant" and the child immediately thinks of a pink elephant. The instruction itself activates the route it tries to prevent. The same architectural fact shows up in language models: instructions are inputs that activate competing routes in the substrate, alongside whatever the model was going to do. When you demand "just yes or no" from a model trained to elaborate, format-violation experiments (n=50 per condition × 3) show accuracy collapsing from 70% to 48%. The model isn't being defiant; the instruction has added a route the model now has to manage. RLHF-trained models show this more strongly than base models, because RLHF makes them more responsive to instructions in general, including the unhelpful ones. Reactance is not a prompt-engineering failure. It is a structural consequence of an architecture that resolves competing routes, since instructions are routes too.
Yerkes-Dodson: performance is maximal at intermediate task difficulty and degrades both when the task is too easy and when it is too hard. Originally observed in mice in 1908, now empirically present across slime moulds, C. elegans, mammals, and language models. Paper 10 organises this under a race-architecture vocabulary: it reads as a kernel-conditional inverted-U (a scope condition Wallace notes), the profile a finite-bandwidth race system tends toward under the race-axioms, rather than a contingent property of nervous systems.
The 1/e secretary — an intrinsic 37% exploration rate
The secretary problem has a famous solution: sample the first 1/e ≈ 37% of candidates, then commit to the next one exceeding the best sampled so far. Base language models (before RLHF) converge to roughly this sampling fraction across a range of decision tasks. The convergence is not because they were trained on the secretary problem; it is because 1/e is the friction-optimal exploration rate for any race-architecture system with finite horizon. RLHF then partially flattens this signature.
Confident-wrong — low friction does not entail correct
Low logprob friction (the model is "sure" about its next token) and accuracy are correlated but the relationship is far from monotonic. A non-trivial fraction of model errors are produced under low-friction conditions: the model is calibrated-confident in a wrong answer. This is the failure mode that bounds the reachable ceiling of friction-based selectors from above — you cannot catch confident-wrong errors by looking at friction, because by definition there isn't any.
Worked-example scaffolding helps novices and hurts experts — a fifty-year-old finding in human learning (Sweller, Kalyuga) that reproduces cleanly in fine-tuned language models. Llama-3.3-70B drops from 73% to 50% to 61% as in-context examples increase from 0 to 1 to 3 shots on a target task: more guidance, worse performance, then partial recovery. A classical calculator has no analogue for this; a race-architecture system necessarily has one.
Source: Paper 4b (in preparation)
Why these aren't accidents
The Friction Theory prediction is structural, not contingent. Any system that (i) maintains multiple candidate continuations in parallel, (ii) accumulates evidence against a finite resolution-bandwidth, and (iii) commits irreversibly to one outcome at a time will display these signatures. They are consequences of the architecture, not effects of training. The shared signatures across slime moulds, mammals, and transformers are evidence for the architecture, not coincidences of biology.
The calculator model fails because LLMs are not unbounded. They are bandwidth-limited probabilistic resolvers, and the limits show up as recognisably cognitive phenomena. The papers in this series develop the formal apparatus, the empirical signatures, and the falsification criteria for that claim.