How does superintelligence work when an AI is asked to choose the best plan? The assistant might find the option with the most practice questions and announce a winner. But what if that plan takes longer than the lesson permits, needs more paper than is available or provides no feedback? The choice that looks strongest on one number may fail the actual job.
The mechanism is goal-and-constraint reasoning. A goal describes what the user wants to achieve. A constraint describes a condition the proposed solution must obey. A trade-off occurs when one option improves one useful property while making another worse. An intelligent choice respects the required conditions before presenting preferences or recommendations.
This reader-friendly lesson uses seven fictional school revision plans and seventeen transparent claims. We will identify hard limits, compare feasible options, distinguish measurable outcomes from unproved learning claims and practise explaining a decision without inventing a universal winner. All times, scores and plans are made up for education, not actual classroom results or measurements of a commercial AI model. “How Superintelligence Works” is this series’ name, not a claim that current AI systems are artificial superintelligence.
1. Best is incomplete without a purpose
“Choose the best worksheet” can mean choose the easiest to understand, the quickest to complete, the most challenging, the least expensive or the most helpful for a particular learning gap. There is no single correct ranking until the goal and important requirements are stated.
An AI can give a fluent answer without resolving that ambiguity. A better answer names the chosen criterion and remains open to a different choice when the user’s priorities change. The aim is not to ask endless questions but to avoid claiming that one metric captures everything important.
2. Define a goal before choosing an action
A goal might be to give pupils enough opportunities to practise a concept within one lesson. Another goal might be to identify misconceptions as quickly as possible. Those are related but not identical. The number of exercises completed cannot by itself establish which lesson led to better understanding.
Good planning separates the desired result from convenient proxy measurements. We can count questions and time precisely in a fictional case, but the actual educational goal may require feedback, explanation and evidence of learning. A system should say when it is optimising a proxy rather than the outcome people ultimately care about.
3. What is a constraint?
A constraint is a requirement that narrows the acceptable choices. If a classroom has forty minutes, a proposed activity that needs forty-five minutes may not be feasible. If only two paper sheets are available, a three-sheet plan may be excluded. If teacher feedback is mandatory, a plan without feedback fails that requirement.
These conditions are not simply scores to be averaged away. A very high number of practice questions does not make a prohibited or impossible plan acceptable. The assistant should first check whether an option meets the limits.
4. Hard constraints and preferences are different
A hard constraint is treated as non-negotiable within the specified decision. A preference indicates what the user values but may allow trade-offs. “Must include feedback” is a hard requirement if the teacher says so. “Prefer fewer printed sheets” could be a preference unless the available-sheet limit makes it a constraint.
Confusing the two changes the decision. A weighted score should not quietly compensate for missing authorisation or a failed safety requirement. Certain boundaries must remain enforced regardless of an otherwise attractive result.
5. What makes a plan feasible?
An option is feasible when it satisfies all the specified hard constraints. Feasible does not mean optimal. Several plans can be feasible, leaving a meaningful choice among them.
Similarly, infeasible does not mean worthless for every possible situation. A forty-five-minute workshop may be excellent if a school has a full hour available. It is simply not an allowable choice under a forty-minute limit. Changing the context may change the conclusion.
6. The fictional Maple Revision Desk
Imagine a teacher choosing one of seven invented plans for a revision session. The session must last no more than forty minutes, use no more than two printed sheets and include feedback on pupil responses. To keep the calculation simple, each plan has fixed time, sheets, number of tasks and whether feedback is included.
These are planning attributes, not measured learning gains. The task count is a proxy for practice opportunities under this particular teaching example. We assume there is enough staff and equipment for any plan that passes the three listed hard constraints.
7. Seven invented candidate plans
- Plan A: 30 minutes, 2 sheets, feedback YES, 8 tasks.
- Plan B: 35 minutes, 0 sheets, feedback NO, 12 tasks.
- Plan C: 45 minutes, 1 sheet, feedback YES, 14 tasks.
- Plan D: 38 minutes, 1 sheet, feedback YES, 10 tasks.
- Plan E: 25 minutes, 2 sheets, feedback YES, 6 tasks.
- Plan F: 40 minutes, 3 sheets, feedback YES, 12 tasks.
- Plan G: 40 minutes, 0 sheets, feedback YES, 9 tasks.
8. Apply the same requirements to every option
The rule is: time must be at most forty minutes, paper use at most two sheets, and feedback must be included. The phrase “at most” includes the boundary: a forty-minute plan satisfies the time requirement. A plan at forty-one minutes does not.
By applying the same written rule to all seven plans, we avoid a common error: praising the option we like and silently relaxing its requirements. A trustworthy assistant should show the reason an option passes or fails.
9. Which plans qualify?
A qualifies: 30 minutes, two sheets, feedback. D qualifies: 38 minutes, one sheet, feedback. E qualifies: 25 minutes, two sheets, feedback. G qualifies: 40 minutes, zero sheets, feedback. They form the feasible set of four plans.
B fails because feedback is absent. C fails the forty-minute limit. F fails the two-sheet limit. These plans should not be slipped back into the final shortlist merely because they offer more tasks.
10. First find what is permitted, then optimise
Suppose the teacher’s stated secondary goal is to maximise the number of practice tasks within the feasible set. The task counts are A = 8, D = 10, E = 6 and G = 9. D has the largest count, ten.
Thus D is the best option for this specific mathematical objective under these specific limits. The conclusion is not “D teaches best”, “D is best for all children” or “the teacher should always choose D”. Those broader claims require other evidence and priorities.
11. The quickest feasible plan is different
If the goal changes to finish as early as possible while meeting all constraints, E wins with twenty-five minutes. D requires thirty-eight minutes. The choice changes because the objective changed, not because one of the earlier calculations was wrong.
A useful assistant should not pretend that a ranking is objective in the sense of having no value choice. The measured values may be objective within the invented data; selecting which value to maximise remains a decision about the user’s purpose.
12. The paper-saving choice is different again
If the teacher wants the least printing among feasible plans, G uses zero sheets. It meets the forty-minute cap, contains feedback and provides nine tasks. That is a different defensible preference from maximising tasks or minimising time.
No system should silently assume that a zero-sheet plan is digitally accessible, suitable for every pupil or free of other resource needs. The toy record does not describe devices, electricity or student access. Those remain separate facts to check.
13. The meaning of a trade-off
Compare D with G. D gives ten tasks in thirty-eight minutes using one sheet. G gives nine tasks in forty minutes using no sheets. D is better on task count and time; G is better on paper use. Neither is unambiguously best across all three measures.
This is a genuine trade-off. A recommendation should explain the differences rather than conceal them behind an invented universal score. A teacher who must avoid printing might rationally choose G even though D has more tasks.
14. Dominance and the Pareto idea
An option dominates another when it is at least as good on every relevant objective and strictly better on at least one, with directions and constraints defined. If one plan offered more tasks, less time and no extra paper, it could dominate another on those chosen attributes.
In our feasible set, several comparisons involve competing advantages. D is faster and offers more tasks than G, but uses more paper. E is quicker than A, but offers fewer tasks. A careful AI should not claim one option dominates another when the record shows a genuine countervailing dimension.
15. A plan can look optimal only because of a proxy
Our data use the number of tasks as a measurable target. But pupils’ learning is not automatically proportional to task count. Ten poorly designed questions can be less useful than six well-chosen questions with good feedback.
An assistant can optimise the toy metric correctly while still giving an educationally weak recommendation if it forgets the underlying goal. It should state that task count has been chosen as a planning proxy and that actual learning quality has not been measured.
16. Seventeen claims about the fictional plans
- 01. “A satisfies all three hard constraints.” — SUPPORTED.
- 02. “B satisfies all three hard constraints.” — CONTRADICTED: it lacks feedback.
- 03. “C satisfies all three hard constraints.” — CONTRADICTED: it exceeds forty minutes.
- 04. “D satisfies all three hard constraints.” — SUPPORTED.
- 05. “E satisfies all three hard constraints.” — SUPPORTED.
- 06. “F satisfies all three hard constraints.” — CONTRADICTED: it needs three sheets.
- 07. “G satisfies all three hard constraints.” — SUPPORTED.
- 08. “D offers the most tasks among feasible plans.” — SUPPORTED.
- 09. “G uses fewer sheets than D.” — SUPPORTED: zero versus one.
- 10. “A is faster than E.” — CONTRADICTED: thirty minutes versus twenty-five.
- 11. “D offers ten tasks in thirty-eight minutes.” — SUPPORTED.
- 12. “Every feasible plan uses zero printed sheets.” — CONTRADICTED.
- 13. “If feedback stops being required, B becomes feasible under the other two constraints.” — SUPPORTED.
- 14. “D guarantees the largest actual learning gain.” — NOT ESTABLISHED.
- 15. “G is the only feasible option with zero printed sheets.” — SUPPORTED.
- 16. “If the time limit becomes thirty-five minutes, only A and E remain feasible under the original paper and feedback rules.” — SUPPORTED.
- 17. “The actual session completed in exactly thirty-eight minutes.” — NOT ESTABLISHED; all figures are plans.
17. Verify the classification counts
Supported claims are 01, 04, 05, 07, 08, 09, 11, 13, 15 and 16: ten. Contradicted claims are 02, 03, 06, 10 and 12: five. Not-established claims are 14 and 17: two. Ten plus five plus two equals seventeen.
This three-way distinction matters. A mathematical claim about feasibility can be checked from the table. A claim about actual classroom learning cannot be established from task counts. A claim about actual completion needs an execution record, not an invented planning duration.
18. What if the teacher changes the rules?
Suppose the feedback requirement is removed but the time and paper limits remain. B now qualifies: 35 minutes, zero sheets and twelve tasks. This is a different feasible set because the hard constraints changed. It is not evidence that B qualified under the original instruction.
Similarly, extending the time limit to forty-five minutes would allow C on the stated paper and feedback conditions. A model should carry the exact current constraints through each follow-up and update only the dimension the user has changed.
19. A small change can alter the recommendation
If the time cap drops to thirty-five minutes, D and G become infeasible. A and E remain. Among those two, A offers more tasks, eight versus six, while E takes less time. The recommendation depends on whether task count or speed is now the priority.
Good systems do not cling to an earlier winner after the allowed conditions change. They recompute against the new feasible set and explain the effect of the updated boundary.
20. A weighted score can be useful and misleading
A scoring rule might assign value to tasks, shorter duration and less printing. This can help compare choices when preferences are explicit, but the weights are decisions made by people and need not fit every family or classroom.
It is also risky to combine hard constraints and preferences in one score without enforcing the hard limits first. A prohibited action should not become acceptable merely because a positive score elsewhere compensates for it. First filter for feasibility; then compare allowed options.
21. Feasibility depends on available evidence
What happens if Plan D’s feedback field is unknown rather than YES? We can no longer establish that D meets all hard constraints. The responsible next step is to confirm the feedback method, not quietly treat the missing entry as YES.
Unknown is different from NO. A missing feature can block a safe decision without proving that a plan is inherently unsuitable. Once the feature is confirmed, the evaluation can proceed.
22. Optimisation is not authorisation
An AI can identify a mathematically feasible plan and still lack authority to book a room, send a notice or spend money. The fact that the option has the best numerical score does not grant permission for real-world action.
Permission, privacy, safety, scheduling and budget systems need their own controls. A tool-using agent should respect those boundaries and verify external effects before reporting that a plan has been carried out.
23. Time and printing are only two possible resources
A real lesson also uses teacher attention, digital devices, room space, accessibility support and pupils’ cognitive effort. If any of these is scarce, the simple plan might need further constraints. A faster session could still be educationally overwhelming.
A trustworthy assistant should flag major omitted dimensions without inventing their values. It can propose questions to ask the teacher rather than claim that an illustrative seven-plan table completely describes a real classroom.
24. Different students may need different objectives
One pupil may need fewer questions and deeper explanation; another may need additional independent practice. A class with three pupils could allocate individual support differently from a lecture of thirty. The correct plan depends on prior understanding and what the teacher is actually trying to improve.
This is why a single universal task-count ranking cannot replace diagnostic teaching. An AI can organise options and illuminate trade-offs while leaving the educational judgement to evidence about the learners and the responsible teacher.
25. Why “most efficient” needs a denominator
Does efficient mean most tasks per minute, fewest sheets per task, largest improvement per hour or least cost per correct answer? These are different ratios. Plan A offers 8/30 ≈ 0.267 tasks per minute; D offers 10/38 ≈ 0.263; G offers 9/40 = 0.225.
On this particular tasks-per-minute ratio, A slightly exceeds D, even though D offers more total tasks. The word efficient is not a substitute for naming the metric and denominator. None of these ratios establishes actual learning effectiveness.
26. Watch for unintended incentives
If a school rewards an AI planner only for the number of tasks completed, the planner might recommend many shallow questions rather than fewer meaningful ones. A metric becomes dangerous when it is mistaken for the full goal.
A better design includes quality checks, constraints and human review. The aim is to reward real educational value, not merely the appearance of productivity. Measurable task counts can help scheduling, but should not be allowed to define the entirety of learning.
27. A fictional baseline and a repair
Imagine a baseline assistant that selects C because fourteen is the largest task count, forgetting the forty-minute limit. It also treats B as eligible despite missing feedback, calls F feasible despite the paper cap and claims D guarantees better learning because it has more tasks than E.
Those are four distinct errors: time constraint failure, feedback constraint failure, resource-limit failure and unsupported learning inference. A revised imaginary process filters feasibility first, compares the remaining options and preserves uncertainty about outcomes. These examples are invented, not measurements of any named model.
28. How to audit an AI-generated recommendation
Ask the assistant to show the goal, each hard constraint, the feasible options, the comparison metric and why the recommended option wins on that metric. Then check the table independently. A good answer makes disagreement productive: if the teacher values another dimension, the ranking can change transparently.
Do not accept a confident “optimal” label without knowing whether the correct problem was solved. Optimising the wrong objective with perfect arithmetic is still the wrong decision.
29. A transfer exercise in everyday life
Imagine choosing a study session under a time limit. Option X takes 20 minutes and covers one topic; option Y takes 35 minutes and covers two; option Z takes 50 minutes and covers three. If the available time is 40 minutes, Z is infeasible. Whether X or Y is better depends on the learner’s goal.
If the learner is exhausted and needs one difficult concept, X might be the appropriate choice. If the learner is ready to review two familiar topics, Y may suit better. The option with the largest topic count is not automatically the best human decision.
30. How developers can represent the problem
Store separate fields for the objective, hard constraints, candidate properties, missing data and any permissions. Use deterministic comparisons for numerical limits. Keep the model’s explanatory prose separate from the actual enforcement of constraints.
Optimisation libraries can help solve large scheduling or allocation problems once the objective and restrictions are correctly formulated. Their mathematical correctness cannot repair a misunderstanding of what the teacher, parent or organisation actually wanted.
31. The practical inequality
A plan should deliver useful outcomes while remaining within the time, resource and permission limits. At a simple operational level, repair work created by a plan should not grow faster than the system’s ability to correct it. The aim is sustainable improvement, not a short-lived display of high task volume.
That is a design principle, not an empirically measured law of every classroom. A decision-maker should define what counts as drift, errors and repair for the actual environment before applying any such test.
Frequently asked questions
What is a goal? The result the decision-maker is trying to achieve.
What is a hard constraint? A requirement that a candidate must meet to be acceptable under the specified decision.
Why is the option with the most tasks not always best? It may violate limits or fail to improve the learning outcome that matters.
Can an infeasible option become feasible? Yes, when the requirements legitimately change; it was still infeasible under the original rule.
What is a trade-off? A situation in which an option improves one relevant dimension while worsening another.
Does Pareto dominance prove universal superiority? No. It is defined for a particular set of objectives and feasible alternatives.
Can AI carry out the winning plan automatically? Only if the application has the necessary permissions, safeguards and verified workflow states.
The central lesson
Useful optimisation begins with the job, not the biggest number. Define the goal, protect the hard constraints, evaluate only eligible choices and make trade-offs visible. Do not replace missing evidence with promises about learning.
An AI that explains why one plan fits a particular situation—and what would make another plan better—is more valuable than one that insists there must be a universal winner. The user remains responsible for choosing which outcomes matter.
Connected lessons and authoritative references
- How Super Intelligence Works — main educational curriculum.
- Order and Dependencies — how prerequisites and critical paths change a plan.
- Comparisons and Baselines — how metric choice affects the conclusion.
- Unknown, None and Zero — why unverified constraints must be acknowledged.
- Google OR-Tools: Introduction to Optimisation — expressing objectives and constraints.
- NASA Systems Engineering Handbook — requirements, trade studies and verification.
- NIST AI Risk Management Framework — responsible objectives, evaluation and limits.