Symbols
This is the active inventory of marks and diagram conventions used by the four-face Obelisk prototype. An entry records what a mark is intended to represent, how the surrounding pictures attempt to teach it, and where interpretation can fail.
The inventory now includes arithmetic, geometric, physical, and material-process conventions. Presence here means the symbol appears in the prototype. It does not mean that unbriefed-reader testing has validated it.
Numerals and operations
0
Represents: absence of counted objects.
Teaching method: an empty outlined tray is placed beside filled trays before zero participates in equations.
Redundancy: 1 + 0 = 1, 1 - 0 = 1, and complete removal producing an empty tray.
Risk: an outline may be read as an object rather than a container.
1–9
Represents: discrete quantities.
Teaching method: each numeral is paired with the same number of recognizable stones; later rows pair objects, tally marks, and numerals.
Redundancy: the numerals recur in groups, grids, lengths, balances, and repeated trials.
=
Represents: equal quantity or matching relationship on both sides.
Teaching method: stones are connected one to one with tally marks and the same numeral before different expressions are compared.
Redundancy: level balances, mirror halves, equal pendulum intervals, and arithmetic identities repeat the idea physically.
Risk: the reader may initially interpret it as a divider or connector.
+
Represents: combination.
Teaching method: two trays visibly converge into one tray containing every original object.
−
Represents: removal or separation from a quantity.
Teaching method: nine stones visibly branch into six retained stones and three removed stones before 9 - 3 = 6 appears.
Revision: this replaces the arithmetic source’s conflicting tally example.
*
Represents: repeated equal groups.
Teaching method: three trays holding two stones each are paired with 2 + 2 + 2 = 6 and then 2 * 3 = 6.
Risk: rotational symmetry can make the mark look decorative; equal-group pictures carry the meaning.
/
Represents: equal sharing and later ratio.
Teaching method: six objects divide into two equal trays before 6 / 2 = 3. The same mark then compares distance with repeated time intervals.
Risk: the slash is more abstract than the initial operations and needs behavioral testing.
1/2 and 1/4
Represents: equal parts of a whole.
Teaching method: two half-tiles reconstruct one tile; a full turn is divided into four square corners; half-width grid cells have one quarter the unit area.
Redundancy: symmetry, turn fractions, scale, and area reuse the fractions.
Ten-object enclosure and ten-by-ten grid
Category: numeral structure.
Represents: decimal grouping and one hundred as ten groups of ten.
Teaching method: bounded boxes contain exactly ten objects; two bundles and three loose objects produce 23; a 10 × 10 array produces 100.
Revision: the prototype grounds tens and hundreds before invoking larger magnitudes.
Direction and reading
Arrow
Represents: change, movement, process order, or transfer.
Teaching method: arrows first follow stones physically moved from separate trays into a combined tray.
Redundancy: rolling, pouring, heating, filtering, and rearrangement all preserve recognizable objects across the arrow.
Risk: arrows have several related uses. Object continuity must distinguish process from force or travel.
Numbered cartouche
Represents: panel position in the curriculum.
Teaching method: consecutive panel numbers repeat in a corner; each panel ends with a small arrow and the next number.
Risk: ordered navigation is itself a convention and has not been tested without instruction.
One to four face dots
Represents: arithmetic, geometry, physics, or chemistry face.
Teaching method: every panel on the same physical face repeats the same dot count; the subject matter provides secondary confirmation.
Geometry conventions
Peg and taut cord
Represents: a point, fixed center, straight segment, or repeatable length.
Teaching method: a visibly slack cord between two pegs is contrasted with the same cord pulled straight, then repeated end to end.
Tick mark
Represents: equal intervals along a line.
Teaching method: a single cord length is copied repeatedly between marks and counted.
Small corner square
Represents: a square corner, perpendicular directions, or one quarter turn.
Teaching method: folding a rectangle produces the corner; hanging cord and still water reproduce perpendicular references later.
Tiled square
Represents: area measured in repeated square units.
Teaching method: a rectangle’s boundary count is separated from the count of interior tiles.
Gridded cube
Represents: volume measured in repeated cubic units.
Teaching method: visible unit cubes are stacked in counted layers. An unfolded six-square net separately represents surface area.
Fine construction line
Represents: reference, correspondence, or a measured relation rather than a material object.
Risk: line-weight differences are vulnerable to erosion and need fabrication testing.
Physical conventions
Ground line with hatching
Represents: a fixed surface and down direction.
Teaching method: falling stones approach the line; hanging objects settle perpendicular to it.
Balance and fulcrum
Represents: comparison of weight or turning effect.
Teaching method: equal reference stones produce a level equal-arm beam. Unequal arms then balance one weight at twice the distance against two weights at one distance.
Pendulum positions
Represents: successive states and a repeatable time interval.
Teaching method: the same hanging stone returns to its starting side; repeated complete returns are counted.
Risk: multiple drawn positions are temporal samples, not multiple stones.
Wavy horizontal line
Represents: a free liquid surface.
Teaching method: it remains horizontal across different vessels and changes height when an object is submerged.
Flame and radiant sun
Represents: familiar sources of heat.
Teaching method: each appears beside observable melting, evaporation, drying, or material change.
Risk: the source alone does not specify temperature or duration.
Hand
Represents: deliberate human action such as moving, pulling, rubbing, shaping, or plucking.
Risk: it is a pictogram and assumes recognition of a simplified hand outline.
Matter and process conventions
Circles and squares as persistent material kinds
Represents: two distinguishable types of component.
Teaching method: the shapes are sorted physically, then reused in the final rearrangement model while the count of each shape remains constant.
Limit: they do not identify real chemical elements.
Filter triangle
Represents: woven or porous material retaining coarse insoluble grains while liquid passes through.
Teaching method: recognizable grains remain above the mesh and drops collect below.
Limit: no panel claims that filtered water is safe to drink.
Evaporation and condensation path
Represents: transfer of liquid through vapor and back to liquid.
Teaching method: vapor traces rise from a heated open vessel; drops form on a cool sloped surface and collect separately.
Closed vessel
Represents: a boundary preventing material from entering or leaving during the comparison.
Teaching method: the same sealed vessel rests on one balance beam before and after internal mixing.
Subdivision bridge and particle diagram
Represents: a proposed finer-grained model of matter.
Teaching method: the same sample is repeatedly divided into smaller cells before a magnified circle encloses repeated component marks.
Limit: this is the least secure bridge in the current system. Subdivision motivates a model but does not prove atoms or bonding.
Status
These symbols are now encoded in prototype one. They remain experimental until readers unfamiliar with the design can reproduce the pictured operations and predict new examples. Failed interpretations will remain part of the record and may require new redundancy, reordered lessons, or removal of the symbol.