The science behind the practice

Research & evidence

Practise holding a model in mind, finding its relationships and recognising the same structure in a new world.

This collection maps encouraging research findings to the operations you practise: generating analogies, aligning roles, explaining relationships, imagining consequences and updating memory.

Explore the studies ↓ New research connections How the Da Vinci method fits

Connect the research to your practice

What each mode asks you to do

Mode 1 · Relational reasoning

Use the Da Vinci cross-domain method to build and compare relationships in different imagined worlds, keeping the supplied compass relationships intact. Give five answers: three statement matches, whether the conclusion follows, and whether the complete triad matches the correct earlier trial.

Integrate several relationships.
Separate a valid conclusion from a familiar one.
Track roles through changed letters and wording.

Research connection: generate possible interactions between the entities, then assemble and check a coherent model. Relational encoding improved immediate insight solutions. Relationships and creative insight.

Read Mode 1 research →

Mode 2 · Ontological integration

Keep categories and perspectives attached to the correct ends of each relationship. More advanced variations ask you to coordinate different facets of one entity and structures inside larger worlds.

Preserve category–perspective–role bindings.
Align complete structures across trials.
Coordinate relationships at more than one level.

Research connection: use categories to retrieve relevant relationships. Guided category-building improved spontaneous structural retrieval. Category learning and retrieval.

Read Mode 2 research →

Other training · Ordered N-back

Listen to or view digits, update the remembered sequence, and recognise a number only when it returns in the same position exactly N trials later.

Update information as each new trial arrives.
Keep item identity tied to sequence position.
Reject familiar digits in the wrong place or trial.

Research connection: inspect mistaken matches as well as successful detections. An older-adult N-back intervention improved discrimination on an untrained variant, with benefits retained three months later. Durable memory discrimination.

Read N-back research →

Read the mappings as operations you can practise: build a meaningful world, reconstruct it in a distant domain, explain the shared rule, predict a consequence and retain the right earlier trial. The links identify the research behind each operation.

Turn the evidence into a useful exercise

What this suggests for practice

These are proposed applications of the research to this game. Each example keeps the actual scoring rules intact while making the thinking more deliberate.

Carry a relational rule into another world

Suppose A is north of B and B is east of C. At 8 directions, A is northeast of C. Now give the entities meaningful jobs while keeping those positions.

Imagine a chain C → B → A: tank → pump → sprinkler. Rebuild it as author → relay → reader. Explain the shared source–intermediary–receiver roles and predict what happens if the middle link is blocked. State your added rule: this is the only route from C to A. The compass clues alone do not establish it.

The game still scores the supplied directions and historical matches. An old claim that A is west of C remains false, however familiar it feels.

Explicit comparison and transfer

Make a category into a working role

For Outer Connection H, imagine H as a station connected to another station; then as a cell connected to another cell. The connected-member role stays, although its embodiment changes.

Carry over every other endpoint job and compass direction too. If H has a second facet, it is the same entity doing another job. Explain what stays fixed before calling the whole world a match.

Comparison and role-based categories

Remember the slot and the right round

At 2-back, imagine round 1 is [3, 8], round 2 is [6, 2], and round 3 is [3, 5]. Compare round 3 with round 1: only the first position matches.

For the next round, round 2 becomes the target. Ask “Which number, in which slot, in which round?” A familiar number alone does not answer that question.

Item–context binding and updating

Make the mapping more precise

What changes, and what carries over?

A new domain, a new combination and a later attempt each ask something different of a learned rule. A review of transfer research makes the useful case for naming these differences. The examples below combine that framework with specific findings to suggest ways to deepen your practice. Barnett & Ceci, 2002.

Proposed reflection exercises for both main modes
Change	Keep or inspect	Try it	Research connection
Move to another domain	Preserve the functional roles and supplied relationships.	Start with “something sends, something receives.” Find a different system that performs those jobs.	Function-first imagination
Combine familiar parts in a new way	Check the meaning of each component and its attachment.	In Mode 2 reflection, vary one category or perspective at a time; then explain an unfamiliar combination.	Learning reusable components
Change a condition of the imagined world	Ask which dependency still holds under the new condition.	Give the source a second working route to its receiver. Explain how this changes your prediction about blocking the first route.	Context-sensitive reuse
Return after a break	Identify which relation you can reconstruct and which needs checking.	Explain the world before rereading it. Use a missing or mistaken relationship to choose what to practise next.	Monitoring and targeted restudy

Use these as optional reflection exercises. A changed category or dependency creates a comparison case; check it against the original rather than assuming it is a match. The supplied compass relations, endpoint descriptors and historical matching rules still determine the scored answers.

Combine the findings

These research-informed prompts deepen the Da Vinci practice in both main modes. Use them during reflection or a practice break. The combination is a proposed application of the studies.

Build a bridge to a distant world. If a correspondence is unclear, establish it in a familiar example, then carry it into a more distant domain. Progressive alignment.
Keep both the scene and the rule. Describe the imagined mechanism, express its roles and constraints in one sentence, then rebuild it with different objects. Concrete examples and abstraction.
Explain, then inspect. Say why the entities occupy their roles. In Mode 2, also check every endpoint category and perspective against the trial. Rule discovery and detail.
Make a useful near-miss. Compare several embodiments of one role, then change the defining relationship. Identify exactly why the changed example fails. Comparison across examples.
Connect imagination with experience. Use the common rule from two imagined worlds to recall a real event. Check the correspondence in that third example. Retrieving relational memories.
Return and reconstruct. Later, recall a checked principle and apply it to a fresh problem. Reveal the example afterward and correct missing relationships. Delayed retrieval and transfer.
Construct a new event from familiar pieces. Combine a person, setting and object from different experiences. Make their interactions express the required relations. Imagination-based event construction.
Try a contrasting condition. Identify a property your explanation depends on and explore its opposite, then intermediate or mixed cases where meaningful. Predict before checking. Opposites and hypothesis testing.

Help a useful rule come to mind

Describe a relational family. For example, “delivery depends on one intermediary.” Decide which cases fit and explain why. This gives you a relational category to search with. Learning a usable category.

Search deliberately. Recall a case with that organization. Compare its roles and conditions with your current problem before borrowing its explanation. Prompting distant retrieval.

Create another problem. Invent a different domain’s version of the unsolved problem. Preserve its goal and constraints, then bring a useful solution back. Learner-created analogies and transfer.

Make the imagined rule do real work

For the tank → pump → sprinkler and author → relay → reader examples above, name the rule: a source reaches a receiver through one required intermediary. A direct source-to-receiver route breaks that requirement. Blocking the middle should interrupt delivery in both worlds under the stated rule; if it does not, explain the difference and repair the analogy.

Choose between two explicit models: C reaches A only through B, or C also has a working direct route to A. Blocking B separates their predictions. Use this contrast to explain which rule your analogy represents. Choosing an informative intervention.

Within each model, compare B working with B blocked while keeping the other conditions fixed. This isolates what the intermediary changes. Derive imagined outcomes from your stated rules; use observed evidence when testing a real system. Controlled comparisons.

Then inspect the actual trial: did each entity keep its compass relationships and, in Mode 2, its endpoint descriptors? A meaningful analogy and an accurate formal match each need their own check.

Feature by feature

Why these demands are worth practising

Find a feature, see the researched operation it draws on, then use the practice connection. Select a named source for its findings and study context.

Training features, research findings and practical connections
Feature	Reason to practise	How closely the evidence fits	Read the source
Mode 1 · Relational reasoning across domains
Generating and comparing relationships across domains	Construct two different systems, identify corresponding entities and roles, and explain the shared relationship or rule. Use that rule to make a prediction. Changing the objects alone leaves out the comparison.	Related analogy paradigms Explicit comparison supported transfer of learned principles; distant-analogy generation improved relational responding on subsequent tasks. Apply those operations by generating an embodiment, mapping each role and explaining the shared rule.	Gentner et al., 2003 Gick & Holyoak, 1983 Vendetti et al., 2014 Du & Sun, 2022
Integrating directional clues and separating truth from memory	Combine relations to judge whether the conclusion follows. Judge historical matches separately: a repeated conclusion can still be false. Both reasoning interventions and direct reasoning practice offer encouraging precedents.	Related paradigm Reasoning practice improved immediate deduction compared with no intervention in a randomized app study. Combining premises and checking a conclusion are the shared operations applied here.	Mackey et al., 2011 McLoughlin et al., 2022 Cortes et al., 2023
Separating logical validity from what feels believable	Test the conclusion against the supplied relations. Distant-analogy generation has helped reasoners overcome belief-based responding in a transitive task.	Related paradigm An immediate reasoning effect supports this practice idea. Belief conflict and recognition of an old trial are distinct challenges.	Andrews & Vann, 2019 Szmalec et al., 2011
One consistent letter map, even after equivalent wording reversals	Follow who occupies each role while surface wording changes. Relational language and structure mapping provide a useful rationale.	Related paradigm + theory Relational language helped learners identify corresponding roles; structure-mapping theory describes shared organization across different representations. Apply that principle by keeping each entity’s role consistent through equivalent wording.	Loewenstein & Gentner, 2005 Gentner, 1983
Expose a misleading analogy by aligning its roles	During reflection, compare two domains side by side. Trace each role to its counterpart, then identify the relationship that a tempting alternative breaks.	Related instructional paradigmSupported mathematics comparisons improved transfer and reduced misleading mappings. Explicit correspondence is the proposed practice connection.	Richland & McDonough, 2010
Distinguish relation inference from memory retention	In reflection, solve a fresh example with its clues visible, then reconstruct it from memory. Identify whether an error concerned the inference or recall.	Related reasoning interventionA randomized child study found different transfer patterns after reasoning and working-memory practice, motivating separate checks of these operations.	Bergman Nutley et al., 2011
Integrate the model before retrieving its pieces	During reflection, reconstruct how the premises connect. Explain why the candidate follows or does not follow, then check the complete model.	Related learning paradigmsIntegrated sentence retrieval supported delayed deduction; explanation-directed retrieval supported delayed comprehension. These findings motivate recalling connected reasons as well as answers.	Eglington & Kang, 2018 Hinze et al., 2013
Compare two valid routes to a judgment	Derive the conclusion by combining the premises, then check it by expressing the relations from the opposite endpoint. Explain why both routes agree.	Proposed strategy applicationComparing algebra solutions improved procedural flexibility. Applying that comparison to inference strategies is a proposed extension.	Rittle-Johnson & Star, 2007
Retrieving the exact N-back trial	Keep the relevant memory available as new information replaces old information. Updating training can transfer to another updating task; an imaging-based synthesis also found related-task gains.	Component task Transfer to related updating tasks supports practising accurate retrieval and replacement. The application is to the memory operation shared by all three training areas.	Dahlin et al., 2008 Pahor et al., 2022 Pappa et al., 2020
Learn a causal pattern across several systems	During reflection, compare worlds built around an explicit causal rule. Use that pattern to predict a new case, then examine an exception.	Related causal-learning paradigmExperience across causal systems supported predictions from sparse new evidence. The proposed Da Vinci application is to learn a reusable dependency and specify when it applies.	Kemp et al., 2010
Generate interactions that can form a solution	Explore how pairs of imagined entities could interact. Combine useful interactions into an explanation, then check the supplied relationships.	Related insight experimentGenerating relationships between problem elements improved immediate solutions against baseline and memory-task comparisons. This directly motivates making imagined interactions explicit.	Kurtz et al., 2025
Learn a comparison procedure and revisit it later	Identify similarities and differences, select the relevant comparison, and check the rule on a new example. Later, reconstruct the procedure.	Related reasoning interventionA primary child study found matrix-reasoning gains and six-month transfer favoring inductive subtests. It adds design and retention detail to the programme discussed by Klauer and Phye’s existing review.	Klauer et al., 2002
Mode 2 · Keeping meaning attached to the right relationship
Six endpoint category–perspective bindings	Remember which aspect belongs to each end of each statement. Updating an item together with its context creates demands beyond remembering the item alone.	Proposed extension Laboratory binding findings motivate precise attachments. Extending them to semantic endpoint roles and this six-endpoint design is a design inference.	Chuderski, 2014 Kessler et al., 2023
Multiple facets of one stable entity	Keep one entity's identity stable while distinguishing its jobs. For the imagined embodiment, examine an object's parts and properties instead of allowing its usual name to dictate its only possible role.	Proposed extension Generic-parts instruction improved insight problem solving. Its practical connection is active reinterpretation: describe an entity’s parts, properties and possible jobs, then explain which aspect each relationship uses.	Chuderski, 2014 McCaffrey, 2012
Nested worlds and complete inner structures	Coordinate relations inside each world with relations between whole worlds. In the imagined model, explain which dependency supports the predicted consequence.	Mechanism + proposed extensionExperiments found that connected relational systems guide analogy and inference. Nested worlds apply this principle at two levels while retaining the complete inner structures.	Clement & Gentner, 1991 Gentner, 1983 Halford et al., 1998 Krawczyk et al., 2011
Learning a category through its relational role	Compare what an entity does in two different worlds. Explanation and explicit correspondence mapping can help learners recognize relational categories beyond familiar objects.	Related paradigm The research studied role and causal-system categories. Using it to give the nine game categories concrete meanings is a proposed application.	Goldwater & Gentner, 2015 Goldwater et al., 2016
Explain the role, then audit the exact attachment	Explain the assigned role, then check that each category and perspective stays attached to the correct entity through equivalent wording reversals.	Related category-learning paradigmsExplanation supported rule discovery and children’s relational matches. Preserving individual details was a distinct demand, motivating this second check.	Williams & Lombrozo, 2010 Brockbank et al., 2023
Make a category label carry a consistent meaning	Explain what the category names in each imagined world. Check that the same label identifies corresponding roles, then verify each formal endpoint descriptor.	Related transfer paradigmRelational labels supported transfer when examples aligned. The connection is understood role correspondence across embodiments.	Son et al., 2010
Learn a family of roles and a close alternative	Compare an airport hub with a communication hub as Inner Connection examples. Then contrast a hub with an individual connected member: the role changes.	Category-learning applicationGroup comparison supported rule discovery. Other experiments distinguish practice that reveals commonalities from practice that highlights category differences.	Edwards et al., 2019 Carvalho & Goldstone, 2014
Ask which relationship would settle the comparison	When two interpretations seem plausible, ask which role or attachment distinguishes them. Check that specific relationship against the trial.	Proposed information-search applicationExplanatory prompts helped older children ask more useful feature-based questions. That operation motivates a targeted question during reflection.	Ruggeri et al., 2019
Manipulating a model while preserving its bindings	In the practice break, change the requested directions and work out the new consequence while retaining the endpoint jobs. Structured manipulation is a more specific demand than rereading a list.	Mechanism + related intervention Mechanism research distinguishes retaining a structure from transforming it. Some working-memory training components also transferred to reasoning. The proposed application is to change a relation deliberately and recompute its consequences.	Kroger & Kim, 2022 von Bastian & Oberauer, 2013
Checking the whole pattern and its local details	Describe the overall world, then audit each endpoint and inner world. A broad pattern and its precise attachments answer different parts of the matching problem.	Proposed extension Distant-analogy generation shifted attention toward global visual patterns. A proposed extension is to describe a world’s overall organization, then inspect its individual role bindings.	Li et al., 2024 Krawczyk et al., 2011
Nine categories and the inner-world output rule	Use explicit definitions and a stated rule to make a complex comparison checkable: a valid inner candidate projects outward; an invalid one receives inward.	Custom game rule The nine categories and output rule are author-defined parts of the game. Research on meaningful labels and relational category learning motivates using explicit definitions and concrete examples to make their roles understandable.	Loewenstein & Gentner, 2005 Gentner & Namy, 1999
Separate an entity from the role it fills	Track the same entity through its different facets. Compare examples to identify the role, while retaining which entity fills it.	Computational accountDORA models how comparison extracts reusable relations while preserving participant bindings. This supplies a mechanism for role–entity separation.	Doumas et al., 2008
Learn components before testing a new combination	In reflection, explain a category and perspective separately, then check a new combination and its endpoint attachment.	Related generalization experimentFactor-separated curricula improved performance on unseen combinations. Applying that progression to ontology components is a practice proposal.	Dekker et al., 2022
Track the scope and order of a composed rule	For nested worlds, identify the inner structure, its output, and the outer relation using that output. Preserve each level’s attachments.	Human composition experimentAdults applied miniature-language functions to unfamiliar arguments and longer compositions. The relevant operation is tracking what each rule acts on.	Lake & Baroni, 2023
Use category membership to retrieve a relationship	Summarize a family of cases and explain why a new example belongs. Use its defining relationship to look for useful prior knowledge.	Related retrieval experimentsGuided category-building improved spontaneous transfer and structural retrieval beyond comparison conditions. The proposed connection is actively learning and applying category membership.	Snoddy & Kurtz, 2021
Connect a category’s structure, behavior and use	Explain who relates to whom, what the stated rule predicts, and how an action changes the result. Carry that organization across imagined domains.	Nonrandomized category-learning interventionCombined analogy instruction and systems teaching showed larger recognition gains. Associations with controlling new systems depended on achieved-learning subgroups, guiding a proposed practice direction.	Kessler et al., 2023
Other N-back and shared challenge settings
Ordered number slots	Keep a digit tied to its position. A familiar number in another slot must not substitute for the remembered ordered sequence.	Component + proposed extension Item–context experiments identify a specific binding demand. The game's one-to-three-digit matching rule remains an extension.	Kessler et al., 2023 Dahlin et al., 2008
Familiar but incorrect lures	Retrieve the correct context when an item feels familiar. N-back experiments show that interference can prompt more context-sensitive responding.	Component task Temporal and semantic interference were studied directly. Slot and ontology lures are extensions; maximum interference was not shown to be the best training level.	Szmalec et al., 2011 Salminen et al., 2012
Replacing obsolete information without losing what still matters	When the target advances, retain the trials you will still need and let the expired trial leave the active queue. Updating research identifies selective removal as a distinct operation.	Component mechanism Experiments studied removal and partial updating. The N-back queue offers a related demand, rather than the identical laboratory procedure.	Ecker et al., 2014
Returning to practice across days	Distribute learning opportunities and rebuild the skill on another day. Selected follow-up comparisons in one randomized child study favoured reasoning transfer from the most spread-out updating schedule.	Preliminary related intervention The study varied days between sessions and used child participants. The overall distribution trend was weaker than the selected follow-up results; the finding supplies a preliminary rationale for distributed practice.	Wang et al., 2014
Spoken stimuli	Auditory presentation offers another way to encode the sequence. Clear, complete speech makes the actual memory task accessible.	Related paradigm Laboratory dual N-back used auditory and visual streams. The relevant connection is encoding and updating information presented through different senses; clear speech supports access to that task.	Jaeggi et al., 2008 Li et al., 2021
Maintaining an advancing sequence	Keep the relevant recent trials available as new items arrive. Distinguish the memory lag from the number of digits within each trial.	Related training paradigmAdaptive dual N-back improved an untrained running-span task, connecting training with retention of a changing sequence.	Lilienthal et al., 2013
Carrying updating across sensory formats	Check whether you can preserve the exact-N and same-slot rule when the digits are heard or read.	Related near-transfer resultVisual-location N-back training transferred to auditory-letter N-back relative to an active control. This motivates examining a shared updating operation across formats.	Buschkuehl et al., 2014
Learn a reliable compare-and-update procedure	Explain how you keep trial identity and digit position separate. Practise that procedure, then check its accuracy with unfamiliar items.	Related strategy interventionStrategy instruction improved transfer to harder letter and color N-back tasks beyond identical practice without instruction.	Laine et al., 2018
Identify the particular interference operation	A wrong-slot lure calls for context checking. Ask which competing response a challenge creates and which rule resolves it.	Proposed control-training directionTraining a different response-inhibition rule improved resistance to irrelevant speech. This motivates studying control ingredients separately; it does not establish an optimal lure setting.	Kattner, 2021
Connect transfer tasks through their shared operations	When comparing practice formats, identify whether each requires maintaining order, replacing contents or checking a past item.	Related updating interventionA three-task programme transferred to selected memory tasks. Its authors proposed shared updating operations as an explanation; the study did not isolate task variety.	Waris et al., 2015
N-back difficulty and practice dose	Watch whether learning improves as difficulty rises. Protect accurate reconstruction instead of treating a higher N or more minutes as the only goal.	Mixed component evidence Some studies link training gains to transfer; the meta-analysis found no reliable dose moderator. No optimal schedule is established here.	Jaeggi et al., 2011 Soveri et al., 2017
Knowing what makes a problem harder	Distinguish additional relations, spatial axes, memory delay and endpoint bindings. These demand different operations, so inspect which operation caused an error.	Task-design evidence Research separates premise integration, updating and supervisory control. Use these distinctions to identify which operation needs practice and choose a manageable challenge. The cited task study measured difficulty.	Cortes et al., 2021 von Bastian & Oberauer, 2013
Select the relevant memory at the right time	Separate encoding the current digits from selecting the exact earlier trial that controls the answer. Recheck that procedure when task demands change.	Related memory-control mechanismRepeated cue-first task structure improved initial performance. Transfer costs after a structural change show why a learned procedure needs a fit check.	Bhandari & Badre, 2018
Make the attachment part of the decision	Reject familiar digits in wrong slots; in Mode 2, inspect familiar categories attached to different entities. Practise identifying the changed binding.	Visual-memory mechanismMaking conjunctions more task-relevant improved detection of recombined visual features. Temporal slots and semantic endpoints are proposed applications of that principle.	Cao & Deouell, 2025
Review a strategy between practice sessions	After practice, identify a useful strategy, the error it missed, and one adjustment to try next time.	Related coached interventionAdding structured planning, monitoring and evaluation to memory training improved children’s three-month memory gains. This motivates reflective practice; the study included coaching and workbooks.	Jones et al., 2020
Check whether discrimination lasts	Review accurate detections and mistaken matches. Revisit the task later and inspect accuracy with unfamiliar stimuli.	Related active-controlled interventionOlder adults retained better discrimination and fewer false alarms on an untrained N-back variant after three months. The result supports checking precision over time.	Jaeggi et al., 2020
Keep still-needed contents accessible	Use available maintenance time to revisit relevant trial–slot contents. In Mode 2, include the remembered category and its entity attachment.	Selective maintenance mechanismCombined results across six experiments favored recall of contents selected by external attention cues. This motivates selective attention to needed bindings; self-directed use remains a proposed extension.	Souza et al., 2018
Shared Da Vinci practice · Construct, compare and revise
Comparing worlds and extracting their common rule	Map one world onto another, then state the shared solution pattern without either world's surface details. Comparing two examples can support a transferable schema: a reusable relational template.	Related paradigm Comparing examples supported transfer of the learned solution principle. The corresponding Da Vinci operation is to identify each shared role and state the reusable rule.	Gentner et al., 2003 Kurtz et al., 2001 Gick & Holyoak, 1983
Progress toward distant correspondences	Clarify a difficult role correspondence in familiar examples, then preserve it across increasingly different domains.	Related developmental paradigmSuccessful simpler comparisons supported children’s later cross-dimensional relational matching. This motivates a bridge toward distant analogies.	Kotovsky & Gentner, 1996
Move from an imagined scene to a portable rule	Describe the meaningful scene, compress its roles and constraints, then reconstruct them in another domain.	Proposed imagination applicationConcrete-to-idealized simulations supported transfer of a scientific principle. The scene–rule–scene loop applies that progression to reflection.	Goldstone & Son, 2005
Use comparison to find a relevant memory	Compare two imagined situations and seek an earlier experience sharing their rule. When stuck, compare two unresolved examples to clarify the needed structure.	Related retrieval paradigmsComparison improved retrieval of structurally matching past events and use of previously learned solutions in new problems.	Gentner et al., 2009 Kurtz & Loewenstein, 2007
Generating a distant analogy yourself	Invent a fitting world in a different domain and specify its correspondences. Several experiments found advantages for generating distant analogies over evaluating supplied analogies or generating nearer ones.	Close related paradigm Outcomes include subsequent relational mapping and integration. These are immediate effects with differing comparisons; the proposed repeated-training benefit remains to be tested.	Vendetti et al., 2014 Du & Sun, 2022 Du & Sun, 2026
Find shared meaning across different actions	Explain the common relation across different imagined actions and where their meanings diverge. Keep Mode 2’s formal category and perspective labels exact when scoring.	Analogy mechanismExperiments show that relational meaning can support analogy across different vocabulary. Applying this as deliberate reflection is a proposed extension.	Gentner & Kurtz, 2006
Improve the quality of a generated world	Inspect your first analogy, compare its correspondences with a checked example, and repair the unclear relationship.	Classroom learning precedentStudents’ generated analogies improved during guided biology practice. This motivates assessing how well a world expresses the relationship.	Tise et al., 2023
Detailed, coherent imagination	Specify entities, events and relevant steps, then use the imagined scene to work out a solution.	Related paradigm Brief episodic-detail inductions increased relevant solution steps in means–end problem solving and supported divergent idea generation. This provides a precedent for deliberately reconstructing useful scene details.	Madore & Schacter, 2014 Madore et al., 2015
A metaphor that compresses several relevant features	Create a short description that captures how the imagined system works, then unpack its exact correspondences. Distant-analogy generation has increased metaphor use on later topics.	Related creative outcome Distant-analogy generation increased later metaphor production. Apply this creative outcome by making a compact description, then explaining and checking the relationships it expresses.	George et al., 2025
Counterfactual probes and repairing an inconsistent explanation	State the imagined mechanism, change one relationship and predict the consequence. Compare predictions across domains; explain and repair a mismatch.	Mechanism + related experimentSimulation research models causal judgments. Familiar bodily thought experiments with comparison prompts improved immediate judgments, supporting deliberate prediction checks.	Gerstenberg et al., 2021 Bascandziev, 2024
Reflection, inference and active explanation	Work out the missing relationship before revealing the answer. Explain why it follows and why a close alternative fails. Self-explanation and inference-based category learning offer positive precedents.	Related learning paradigms Self-explanation supported learning across instructional studies; inference-based category learning helped learners discover relations and learn in new contexts with feedback. Use the same active sequence: attempt, explain, check and revise.	Needham & Begg, 1991 Bisra et al., 2018 Goldwater et al., 2018
Carry a story’s principle into another setting	Explain why events in an imagined scene illustrate its rule, then show the same principle with a different cast and setting.	Related developmental paradigmExplanation helped children recognize a story lesson in new contexts despite distracting surface similarities.	Walker & Lombrozo, 2017
Retrieve a checked principle after a delay	Revisit a completed example later. Reconstruct its principle before revealing it, then apply the checked rule in a fresh domain.	Related transfer paradigmRepeated testing with feedback supported new cross-domain inferences one week later; transfer questions cued the relevant concept.	Butler, 2010
Prepare a question that feedback can answer	Attempt a model and compare a contrasting case before consulting the explanation. Identify what the correction teaches, then use it on a fresh example.	Related learning paradigmsContrast analysis and invention prepared students to learn from later explanations or worked examples. The relevant sequence includes that corrective resource.	Schwartz & Bransford, 1998 Schwartz & Martin, 2004
Choose a test and predict before checking	State competing rules, choose a change that separates their predictions, and explain the outcome before checking it.	Related causal-learning paradigmsChoosing interventions and generating predictions supported learning in tasks providing outcome evidence. Imagined deductions here follow the rules you explicitly supply.	Sobel & Kushnir, 2006 Brod et al., 2025
Revisit a reasoning strategy and check what lasts	Return to a learned rule after a break and apply it to a fresh example. Track reconstruction and later use alongside today’s score.	Long-term related interventionOlder adults retained targeted reasoning benefits years after instruction and refresher practice. This motivates checking the durability of learned strategies.	Rebok et al., 2014
Corrective feedback	Notice the error, inspect the correct relationship and revise your explanation. Feedback can reduce learning of attractive wrong alternatives.	Related paradigm The cited experiment tested factual learning, so explanatory correction is the relevant connection.	Butler & Roediger, 2008
Invent the world from its required functions	Start with the jobs and relationships the world must contain. Invent entities that can fulfil them, then inspect every supplied relation.	Related imagination experimentAbstract survival requirements produced more novel imagined creatures. Function-first construction is the proposed bridge to meaningful category-role worlds.	Ward et al., 2004
Explore adding and removing a condition	Add a possibility to generate alternatives; remove an assumption and work through the consequences. Keep each imagined rule explicit.	Related immediate task effectsAdditive and subtractive counterfactual primes favored different subsequent tasks: creative generation and analytical solving. Alternating these operations is a proposed reflection exercise.	Markman et al., 2007
Change the imagined viewpoint as well as the setting	Place the relation in another time or an unfamiliar situation. Describe the whole scene from an observer’s perspective, then check its correspondences.	Related creative outcomeDistant simulation combined with observer instructions improved immediate originality. This adds a concrete way to vary imagined embodiments.	Toyama, 2024
Use reconstruction to choose the next practice target	After a break, reconstruct a checked world. Identify the uncertain relation or endpoint and revisit that part.	Related learning mechanismDelayed reconstruction helped students identify weaker texts, choose restudy and improve comprehension. Apply the diagnostic step to your relational model.	Thiede et al., 2003
Deliberately search for an analogous case	During reflection, ask which remembered situation shares the problem’s relationships. Check its conditions before using it to explain the current world.	Prompted retrieval experimentsExplicit analogy-search instructions improved distant retrieval during argumentation and explanatory-hypothesis generation. The proposed practice supplies that retrieval prompt deliberately.	Trench et al., 2026
Invent a counterpart before solving the problem	Create another domain’s version of an unsolved problem. Preserve its goal, roles and constraints, then use the counterpart to seek a solution.	Related interdomain-transfer experimentInventing an analogous target problem improved application of a previously learned solution. Structural correspondence makes the generated comparison useful.	Minervino et al., 2017
Assemble a new event from separate experiences	Combine a person, setting and object from different memories. Make their actions express the required relationships in a coherent scene.	Event-construction experimentAn imagination-based induction increased specific details in later remembered and imagined events. This supplies a method for constructing richer relational embodiments.	Madore et al., 2019
Generate a contrast that tests the rule	Identify a condition your explanation relies on. Explore a contrasting case and predict its outcome before checking.	Related rule-discovery experimentInstruction in identifying properties and testing their opposites improved numerical rule discovery. Use contrasts to examine boundaries, then explore intermediate cases where relevant.	Branchini et al., 2025
Isolate the relationship behind a consequence	Change one relevant condition while keeping the others fixed. Explain what the comparison allows you to infer.	Related scientific-reasoning interventionExplicit instruction plus probe questions improved children’s learning and transfer of controlled comparisons. The imagined-world application uses that same comparison logic under stated rules.	Chen & Klahr, 1999

Shared practice

The Da Vinci / World Building method

Give the symbols meaning, then carry the relationships into a different domain. A useful imagined world must obey the supplied constraints.

Build. Give each letter a concrete role. Imagine one coherent scene in which the required relationships hold.
Explain. Identify what depends on what, which direction the relationship runs, and which detail would change the answer.
Transfer. Rebuild the same structure using distant subject matter—for example, an ecosystem, a transport network or a team.
Check. Keep the same roles and relationships. Name a point where your analogy would stop working.

Preserve the relationship through the change

A branching river and a distribution network can both carry something from one source to several destinations. The objects change; the one-to-many flow can remain. A loop that returns to its source has a different structure, even if it uses the same objects.

In both modes, preserve the supplied compass relations while comparing the worlds’ meaningful roles and rules. Those directions constrain the scored problem; they are only one part of the cross-domain exercise.

If you add a causal mechanism, state it as a rule of your imagined world. Compass positions alone do not supply that mechanism. The game scores the written pattern; use these checks to assess your own imagined scene.

The research connections are concrete: generation asks you to construct an analogy, comparison exposes a common rule, explanation makes the rule explicit, and prediction checks how well your imagined system works. These are the operations the Da Vinci method brings together.

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Follow every claim to its source

The research collection

Choose a mode or search for a skill. Each paper appears once in the collection, even when it relates to several modes.

Experiments test a task or intervention. Observational studies examine relationships or mechanisms. Meta-analyses combine results from studies; reviews and theory explain the wider evidence or a model.

Component task means research on an ingredient such as N-back. Related paradigm means a different task with a relevant demand. Proposed extension means applying that idea to a new feature here. The study context records the population, comparison and outcome so you can see the basis for each application.

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Enable JavaScript to search the full collection. You can still read these original sources: Pahor, Seitz & Jaeggi (2022), N-back transfer; Soveri et al. (2017), N-back meta-analysis; Dahlin et al. (2008), working-memory updating.

Make the practice count

Aim to understand and preserve the relationships. Increase difficulty while you can still explain the model and distinguish a close non-match. Treat your game scores as practice measures; check broader progress with unfamiliar problems and new domains.

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