MODEL SCALE
Model train · 1:64
64 = 2⁶. A real dimension written as x A8/31 becomes the same coefficient x A8/25 in a 1:64 model.
Same shape. Same coefficient. Six rungs smaller.
One ladder. Pick the rung. State the rung. Stay on the rung.
Changing rungs changes the size of the measuring step — not the object, trip, speed or laws of physics.
Nature on one A8 scale
The same exact doubling rule can be followed from atomic structure to people, landscapes and larger motion scales. The picture below uses the current working A8/31 ≈ 1.14988 legacy m stake and simply asks where familiar physical scales fall. It does not make those objects new authorities.
What would A8 look like at “quantum scale”?
There is no single quantum length. Atomic quantum structure, nuclear structure and the Planck scale are radically different sizes.
On the current A8 ladder, the Bohr radius lies near A8/−3, the proton charge radius near A8/−19,
and the Planck length near A8/−85. These are comparison placements, not new A8 definitions.
Comparison values: 2022 CODATA / NIST —
fundamental constants.
The basic idea
Io, Europa and Ganymede recover the primary natural timebase. Mintaka independently witnesses Earth's stellar rotation against that timebase, while Mean-Sun recurrence supplies the working civil-day duration authority.
Quartz supplies a microscopic geometric witness. Earth supplies a macroscopic geometric witness. A8 brings both toward human scale on the same doubling ladder and compares where they meet.
A full turn is represented as 512 A8 angle units. The circle, π, trigonometry and the physical world do not change; only the ruler used to label the turn changes.
Once distance and time exist independently, speed follows. Ships, aircraft and rockets can all be expressed on the same ruler architecture; application-specific rung choices remain open until they are deliberately tested and selected.
The length “barbell”
You do not have to be a crystallographer or geodesist to understand the working experiment. Reduce each 3-D witness to a reproducible length comparison, bring the tiny one up and the huge one down, then see where the common human-scale ruler settles.
Legacy metre values are comparison bridges. The current working A8 statement is simply A8/31 = 1 human A8 length.
The part that makes scaling easy
Every step on the length ladder is exactly twice the step below it. Nothing fancy happens between rungs.
Each rung = ×2
Ten rungs = ×2¹⁰ = ×1024
A8/31≈1.15 m
/32×2
/33×4
/34×8
/35×16
/36×32
/37×64
/38×128
/39×256
/40×512
A8/41≈1.177 km
On a small screen, slide the ladder sideways.
A8/41 = 1024 × A8/31 ≈ 1,177.47 legacy metres ≈ 1.177 km
1Pick a useful rung
2State the rung
3Stay on it for the instrument
Why change rungs at all?
For the same reason people do not normally measure a continent in millimetres. The rung selects a useful numerical scale and useful resolution. The ladder preserves the exact relationship between every scale.
HUMAN SCALE
A8/31 · human rung
The current working stake is 1 A8/31 ≈ 1.15 legacy m. It is a convenient human-size anchor in the general length ladder.
This is the ladder reference, not a claim that every object must be one rung long.
EARTH NAVIGATION
A8 NAV · ships & routes
Navigation keeps its Earth-derived ruler: mean Earth circumference ÷ 32,768. That is ≈1.222 legacy km.
Cross-check: 1 A8 NAV ≈ 1.03779 A8/41. Almost A8/41 — not forced to equal it.
LARGER SCALE
Aircraft & rockets
The same exact ladder can scale to larger distances and faster motion when needed. No aviation, rocket or Mach-test rung is assigned on this introduction page.
Application scale remains an open engineering choice. The ladder exists first; a specific working rung is selected only when the instrument is actually defined.
Scale models make the idea obvious
A8 scaling is especially easy to see with trains because common model scales are already powers of two. A 1:64 model is exactly six binary rungs smaller than the real object.
REAL TRAINdimension = x A8/31
÷64 →six rungs down
1:64 MODELsame coefficient x A8/25
Same object proportions + same numerical coefficient + different rung = exact scale relationship
Speed works the same way
Speed is just distance over time. Once the time ruler and length ruler are established, the instrument chooses a sensible distance rung for the job. A8 does not need a completely different physics system for a ship, airplane or rocket.
Use A8 NAV
For terrestrial navigation, keep the Earth-derived route ruler and express motion as A8 NAV over a stated A8 time interval.
Aviation already fits the ladder
A representative Airbus ACJ319 long-range cruise of 447 knots is about 827.8 legacy km/h. In one A8 HOUR that aircraft covers about 620.9 km, or approximately 32.96 A8/45 per A8 HOUR. A8/41 remains a useful route-scale length neighborhood; no separate aviation ruler is required.
Example only · Airbus ACJ319 long-range speed 0.78 Mach / 447 kts.
Lunar-mission motion fits the ladder too
NASA reports Apollo 17 — the last crewed lunar landing mission — at 1,484,933.8 legacy miles traveled over 12 days 13 hours 52 minutes. Its whole-mission average is about 7,916.6 legacy km/h, equivalent to about 5,937.5 km per A8 HOUR or 39.39 A8/48 per A8 HOUR.
Mach remains a dimensionless ratio to the local speed of sound. A8 can express the underlying distance and elapsed time without turning Mach into a new ruler.
Whole-mission average only — not launch, translunar, lunar-orbit, return-entry or peak velocity.
Same ruler. Different rung. Useful resolution.
A model train does not become a different kind of geometry. A ship does not sail farther. An aircraft does not fly faster. A rocket does not change its trajectory. Only the measuring step changes.
A8 NAV is close to A8/41 — but they are not the same definition
≈1.150 mcurrent legacy comparison for 1 A8/31
≈1.177 kmA8/41 = 1024 × A8/31
≈1.222 km1 A8 NAV from Earth circumference ÷ 32,768
A8/41 comes from the general exact doubling ladder. A8 NAV comes independently from dividing the mean Earth circumference by 32,768 (= 2¹⁵ = 8⁵). The present cross-check is approximately 1 A8 NAV = 1.03779 A8/41. Their closeness is observed; it is not forced.
A8 does not claim that Nature is binary everywhere.
Natural phenomena come first. Binary and octal are engineered ways to represent, divide and count them. A finite register or ladder is a ruler placed on Nature; it is not Nature itself.
The useful feature is exact scaling: every rung relationship is known without inventing another unrelated unit. If finer resolution is needed, move down the same ladder. If numbers become too large, move up the same ladder.
What is fixed, and what is still experimental?
Mathematically fixed: the exact doubling relationship between A8 length rungs; the 512-state angular representation; and the 32×64×64 civil-day representation.
Current working stake: A8/31 = 1 native human-scale length, with a present legacy comparison of approximately 1.15 m (engineering comparison ≈1.14988 m).
Application choices: aviation, rocket, machining and other instruments may later select a useful rung from the same ladder. No application-specific rung is assigned here.
Experimental: physical realization, uncertainty, refinements of the quartz/Earth comparison, and independent replication. A better physical measurement may refine the legacy comparison without breaking the ladder.
Research status: A8 is an experimental COSIGO Labs project. Software demonstrations test architecture and usability. Physical metrology claims require physical realization, uncertainty analysis, independent measurement and replication. No declaration is above reproduction.
See it, then inspect it
The public pages teach the ruler first. The engineering laboratory exposes the recovery, comparison and experimental machinery underneath.