Ontological-Worlds
Each letter is one entity. Match its categories, perspectives and relationships together. Start with one descriptor, then add aspects or inner worlds.
Practice breaks pause the clock for a deduction, a change to the map and a new imagined world. They do not affect your N-back score.
Opens a separate full-screen number N-back trainer with 1–3 ordered numbers per trial, position-specific matching and dedicated cognitive-interference controls.
4 uses north, east, south and west. 8 adds northeast, southeast, southwest and northwest. 16 adds the intermediate directions. Cognitive interference changes lure difficulty, not compass resolution.
Select 4, 8 or 16 compass directions before starting Mode 1.
Controls partial statement matches, resolution-aware near-misses, relational reversals, surface-letter remapping and near-complete triads. At maximum, non-match trials strongly favour two-of-three statement matches with one exact relational conflict.
Every generated premise is supplied through visible text and optional speech using the same canonical content.
Mode 1 — Relational reasoning: how to play
Use the Da Vinci cross-domain method to imagine the same relationships in different worlds. Remember an old round. Then answer five questions.
1. Start small
The Da Vinci method: imagine the letters as things in one world, such as trees in a garden. Then rebuild the same relationships in a different world, such as parts of a machine. Keep every given direction and the same role for each letter. Use the two clues to check the final claim.
Choose Mode 1, 1-back and 4 compass directions. Try a short session, such as 3 minutes. Leave Audio-only display off so you can see the words. Read this guide, then press Start.
Each round has three lines, also called statements. The first two are clues. The last line makes a claim.
Think of the letters as name tags on a map. “A is north of B” means A is above B.
↑ UpWest
← LeftEast
Right →↓ Down
South
Later, 8 directions add corners such as northeast: up and right. With 16, there are more directions between those. Use the exact direction shown.
Use same-size steps for the two clues. In this game, each clue is one step of the same length, including diagonal steps. The last line asks for the direction between the two end letters; it does not say how many steps apart they are.
2. Pick the right old round
N-back tells you how far to look back. Count whole rounds, not the lines inside them. During play, the old round is not shown beside the new one. Keep it in your memory.
1-backThe round just before this one.
2-backTwo rounds ago.
3-backThree rounds ago.
At 2-back, round 3 goes with round 1. Then round 4 goes with round 2. Remember the newest round too: you will need it later.
3. Keep one set of name tags
The letters may change. Old C might become new X. That is fine! But C must mean X in every line of this comparison. Two old letters cannot share one new name.
Use one set of name changes that makes as many lines match as possible. Do not pick a different set for each line.
- The first two clues may swap places.
- The last line must match the old last line.
- “A is north of B” = “B is south of A.” Saying it backward is okay only when the direction flips too.
What if two name keys tie? Sometimes two ways of renaming make the same number of lines match, but disagree about which lines match. The game uses a fixed tie rule: compare their Yes/No answers from line 1 onward. At the first difference, choose the set with No.
For example, No, Yes, Yes takes priority over Yes, No, Yes when both are possible. Use the winning set for all three line answers. This rule settles the memory comparison; it does not change whether today’s last line is proved.
Remember the pattern of directions, not just the letters you see.
4. Give all five answers
The buttons show letters. Tap the button, or press its key if Keyboard controls is on.
| Question | Yes | No |
|---|---|---|
| 1. Does line 1 match one of the old first two clues? | A | S |
| 2. Does line 2 match the other old clue, using the same name changes? | D | F |
| 3. Does line 3 match the old last line? | H | J |
| 4. Do both clues prove line 3’s direction between the two end letters? This is “entailed”. | K | L |
| 5. Do all three lines match the old round together? This is the “complete triad”. | Space | N |
Question 4 is different. Use only the two clues on the screen now. Follow both clues from one end of the chain to the other. If they link A with B, then B with C, the two ends are A and C.
The last line must give the correct direction between those two end letters. Repeating just one clue is not enough. If the last line uses the wrong pair, is wrong, or is not proved by the clues, choose L.
For 16-direction play: use the nearest named compass direction after following the two equal steps. If the result falls exactly halfway between two compass points, choose the next point clockwise. For example, north plus north-northeast gives north-northeast under this game’s rule.
Each answer locks in as soon as you choose it. You get feedback straight away. Finish all five; the next round then starts by itself.
5. Let’s solve one together
Imagine this old round is the one you need to remember.
The old round
- A is north of B.
- B is north of C.
- A is north of C.
The round on screen now
- A is north of B.
- B is north of X.
- A is south of X.
Our name key: A stays A. B stays B. C becomes X.
- Line 1 matches. Choose Yes: A.
- Line 2 matches after C becomes X. Choose Yes: D.
- Line 3 changed from north to south. Choose No: J.
- Start at X. Go up to B, then up again to A. A is north of X, so the last line is wrong. Choose No: L.
- Only two lines match. The whole round does not. Choose No: N.
All five answers: A, D, J, L, N.
“Same as before” does not mean “true”. Suppose the old last line also said “A is south of C”. Both rounds would now have the same wrong claim. The whole round would match, but the claim would still not follow from the clues. You would choose L for question 4 and Space for question 5.
6. What about the first few rounds?
During the first N rounds, there is no old target yet. At 1-back, that means round 1. At 2-back, it means rounds 1 and 2.
Choose S, F, J and N for the four memory questions. Still check today’s clues and choose K or L for question 4.
These answers count. You must finish all five even on the first round.
7. Take your time and learn
There is no timer for each answer, but the session clock keeps running. Pause takes a break; Stop ends the session. P pauses or resumes and Esc stops, even when response keyboard controls are off.
A round is fully correct only when all five answers are right. Two matching lines do not make a whole match. Close-looking rounds are part of the game.
Want an easier start? Keep 1-back and 4 directions. The Cognitive interference setting is fixed; it cannot be lowered. Adaptive N is unavailable, so N will stay at your chosen level. Stop before changing your mode, N-back level or compass directions.
Right old round? → One name key? → Three line checks? → Is today’s claim proved? → Does the whole round match?
Back to game settings ↑Mode 2 — How to play
Imagine a little world. Remember who does what, where they are, and how the parts fit together. Does the whole pattern match the right old round?
1. Start small
Choose Mode 2, 1-back, 4 compass directions and One descriptor per entity for complexity. Try 3 minutes. Leave Audio-only display off so you can see the words. Keep Practice break after every 6 answers on while learning.
When that feels clear, try Multiple aspects per entity, the usual setting. An aspect, or facet, is one side or job of something: the same robot can send a message and also separate a part of itself. Worlds within worlds adds little worlds inside the bigger one.
Each main round has three lines. The first two are clues, called premises. The last is a claim to check, called a candidate conclusion. The group is a triad.
Think of the letters as name tags on a map. “H is south of D” means H is below D.
↑ UpWest
← LeftEast
Right →↓ Down
South
Eight directions add corners such as northeast: up and right. Sixteen add directions between those. Use the exact direction. The compass and the category do different jobs: north does not always mean one kind of thing.
Map rule: each of the two clues is one same-size step, including diagonal steps. The candidate gives the direction between the end letters, not their distance. In 16-direction play, use the nearest named direction; an exact halfway result goes to the next compass point clockwise.
2. Remember the right round
N-back tells you how far to look back. Count whole rounds, not lines. During play, the old round is not shown beside the new one. Keep it in your memory.
1-backThe round just before this one.
2-backTwo rounds ago.
3-backThree rounds ago.
At 2-back, compare round 3 with round 1. Then compare round 4 with round 2. Keep remembering each new round for later.
The first N rounds are for watching and remembering. At 1-back, watch round 1. At 2-back, watch rounds 1 and 2.
Match and No Match stay off. If speech plays, the game moves on shortly after it finishes. If speech is silent or unavailable, take time to read the whole world, then select Remember this world — Continue.
These setup rounds do not count toward your score.
3. Read both ends of every line
Outer Connection H is south of Projection D.
Read that as: “H, in its Outer Connection job, is below D, in its Projection job.”
All the words matter for matching. Keep the category, its Inner/Outer form, its letter and its place in the line together. Projection D and Outer Projection D name different aspects, even though D is the same entity.
One letter means one thing throughout a round. If H appears twice, it is still the same H in the same place. Its two jobs can differ with Multiple aspects per entity. They do not become two separate Hs, and the words do not silently make it move or change over time.
The letters can change between rounds. Use one name key for the entire comparison: if old H becomes new X, use X for H everywhere. Each old letter gets its own new name.
4. Try this 1-back example
This example uses Multiple aspects per entity. Watch round 1. On round 2, compare with round 1.
Round 1 — remember
- Outer Connection H is south of Projection D.
- Outer Projection D is south of Multiplication C.
- Candidate: Projection C is north of Inner Division H.
Round 2 — answer
- Multiplication Z is north of Outer Projection Y.
- Projection Y is north of Outer Connection X.
- Candidate: Inner Division X is south of Projection Z.
| Old name | New name |
|---|---|
| H | X |
| D | Y |
| C | Z |
The clues swapped order. Each line was said from the other end, so south became north, or north became south. Every job stayed with the correct entity and relationship.
Choose Match.
Check one line: old “Outer Projection D is south of Multiplication C” becomes “Outer Projection Y is south of Multiplication Z”. Saying “Multiplication Z is north of Outer Projection Y” gives exactly the same relationship.
5. The same words can be in the wrong places
Keep round 1 above. Now change round 2 to this:
- Projection Z is north of Outer Projection Y.
- Projection Y is north of Outer Connection X.
- Candidate: Inner Division X is south of Multiplication Z.
The directions are unchanged. All the same category words still appear. But Z’s Projection and Multiplication jobs have traded places between a clue and the candidate.
Choose No Match. Remember which job belongs to which link, not just a bag of words.
- The first two clues may swap places.
- A whole line may reverse only when its direction reverses too.
- Inner stays Inner. Outer stays Outer. Reversing a sentence does not change its jobs.
- The candidate must match the old candidate. It cannot trade places with a clue.
- All directions and all endpoint jobs must fit one name key.
A repeated claim can still be wrong. The first example puts C north of H. If its candidate instead said “C is west of H”, it would not follow from the clues. Yet two rounds can repeat that same wrong candidate and still be a memory Match.
Build your spatial world from the two clues. Hold the candidate as a claim to check; do not force a wrong claim to become a third fact.
6. Give one answer per memory round
Wait until the speech finishes and the answer buttons become available.
Match
The complete pattern fits the right old round: names, jobs, directions and line roles, all together.
Tap Match.
Keyboard: F or J.
No Match
No single name key preserves the complete pattern. One wrong binding is enough.
Tap No Match.
Keyboard: D or K.
Keys work when Keyboard controls is on. After your answer, the game shows feedback and moves to the next round.
There is no timer for each answer, but the session clock keeps running during the memory rounds. Pause takes a break; Stop ends the session. P pauses or resumes and Esc stops, even when response keyboard controls are off.
7. Make the words do something in your imagination
This is the Da Vinci cross-domain practice. A domain is a kind of world: a garden, a machine, a town, or a story. Choose concrete things that can do the jobs on the card.
- Build one scene. Keep each letter as one thing in its place. Make its different jobs work together.
- Give each job an action. For Projection, picture a source, a path and a destination. For Division, decide what is separated from what.
- Rebuild it in another kind of world. Preserve the relationships and jobs while changing their concrete form.
- Check a limit. Say what would have to change before the two worlds stopped sharing the same structure.
A garden example
Something creates more seeds. A carrier sends them outward. A receiving system isolates a part of itself.
A message-world example
Something creates more message copies. A broadcaster sends them outward. A receiving group separates one subgroup from itself.
These are starting ideas, not extra rules for the card. Fit your chosen things to all its endpoint jobs and compass positions. You can picture a fantasy machine if an everyday object does not fit.
State a rule before predicting what it causes. For example: “D is the only path by which C’s outputs reach H.” If D stops, new outputs from C cannot arrive at H along that path. Things already at H can remain.
A compass direction alone does not tell you what causes what. There is also no rule that adding two category words automatically creates a third.
The game checks the written pattern. It cannot see or score your imagined scene. Use the practice breaks to check whether you really built and transferred a connected world.
8. Choose how many things to hold together
One descriptor per entity
A letter keeps the same category and Inner/Outer/unmarked form wherever it appears. Learn the full matching rule here first.
Multiple aspects per entity
The same letter may have different jobs in different links, as H does in the example. All its facets share the same place. Match the exact job at each end of each link.
Worlds within worlds
Each outer letter contains its own little three-line world. Read those inner worlds as well as the three outer lines. A little world’s letter names are local to that world.
The explicit rule: if an inner world’s candidate follows from its two clues, that whole world projects outward. Otherwise, it receives inward.
For a Match, the inner worlds themselves must match under their own consistent name keys, and they must stay attached to the correct outer entities. Two different inner worlds producing the same outward result are not enough.
There is one inner layer. This is an added game rule, not a claim that one category can be calculated from other categories.
Complexity and N-back do different jobs. Complexity changes what is inside a round. N-back changes which old round you compare with. Increase one at a time while you can still build a clear world.
9. Use the short practice breaks
With Practice break after every 6 answers on, the game and session clock pause after six answered memory rounds. Setup rounds do not count toward those six. The break is not a new N-back round and does not move your memory history forward.
First, follow the two clues. Choose the direction of the candidate’s first letter relative to its second letter. Work it out from the clues; do not just copy the candidate’s direction.
Then try a changed version: reverse both clues’ compass directions, while keeping their letters and jobs in place. North becomes south; east becomes west. Where is the same first letter relative to the same second letter now? Choose that new direction.
This really changes the map. It is different from saying an unchanged relationship backward, where you swap the two ends as well as the direction. The candidate stays as written during practice.
Use the cross-domain prompts to rebuild the world, state a rule, predict a consequence and find a limit to the comparison. These are practice checks, separate from your N-back score. Select Check practice answers for feedback, then Continue training. You can also continue without answering or writing anything. Keep the next N-back target in mind.
Your first checked answer to each practice question goes into its separate practice result. You can try again after feedback to learn. Optional writing stays in the current open session; it is not graded or saved to History.
Stop the session before changing its complexity, N-back level, compass directions or practice-break setting. Cognitive interference is fixed; the game deliberately includes close-looking alternatives. Adaptive N is unavailable, so N stays at your chosen level.
10. A little dictionary of the nine jobs
Inner and Outer tell you which perspective on a job to imagine. Their exact meaning depends on the category. If neither word appears, use the plain form. All three forms are distinct for matching.
These are the operational meanings used for this game’s imagination practice. They are not arithmetic instructions or permanent meanings for compass directions.
All
Plain: the whole collection.
Inner: gather parts into one collection or whole.
Outer: make copies or likenesses of something.
Difference
Plain: a distinction between things.
Inner: locate or distinguish what is inside.
Outer: locate or distinguish what is outside.
Action
Plain: doing or changing something.
Inner: act upon yourself.
Outer: act from yourself upon something outside.
Division
Plain: separation into parts.
Inner: remove or isolate yourself, or a divided part of yourself.
Outer: subdivide, mark out or make several parts of something observed.
Connection
Plain: a link joining things.
Inner: the centre, hub or medium through which they connect.
Outer: the connected members or ends of that link.
Multiplication
Plain: making more or increasing.
Inner: support, strengthen, sustain or heal from within.
Outer: unfold, grow or blossom outward.
Projection
Plain: the span from a source, along a path, to a destination.
Inner: receive or converge toward yourself.
Outer: send or extend away from yourself.
Encompassment
Plain: surrounding or including.
Inner: push outward or expand from inside.
Outer: surround or engulf from outside.
Completion
Plain: reaching a whole or complete state.
Inner: become upright or sound in character within.
Outer: become sturdy in outward form.
Hold these jobs as meaningful parts of the world. A word moving to the wrong endpoint, or Inner changing to Outer, can turn a Match into a No Match even when the compass map stays the same.
Right old round? → One name key? → Right job at every endpoint? → Same directions and line roles? → Inner worlds too, if selected? → Match or No Match.
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