Length

Decided: the pace ≈ 1.4525 m, defined by c = 2 × 10^7 paces per blink (exact).

Why: the size is human: close to the Roman pace (Latin passus, ~1.48 m), a double step. Fixing c makes the definition exact, as in SI; making it round was the tie-breaker, and cost nothing human, since of the round values tried (table below) only this one gives a body-sized pace.

Advantage: length is exact in SI terms and still a comfortable body size.

Other round values of c were checked. Fewer paces per blink means a longer pace, so:

c (paces/blink) pace unc dig cub (≈ lib of water) vis (force) opus (energy)
1 × 10^7 2.91 m 24.2 cm 2.0 cm 14.2 L 342 N 993 J
2 × 10^7 1.45 m 12.1 cm 1.0 cm 1.77 L 21.3 N 31.0 J
4 × 10^7 73 cm 6.1 cm 5 mm 0.22 L 1.3 N 1.0 J

Rejected: both alternatives. 1 × 10^7 makes everything bigger (a 2.9 m pace and a 14 kg lib are too large for everyday use).

4 × 10^7, halving the pace so the base is a single step (72.6 cm), was looked at in detail (2026-10-05 CE) and rejected. With h re-rounded so a cub of water still weighs a lib, and e moved to 1 × 10^-15 so the riv is about an amp (1.02 A) and the imp 2.73 V, it has real attractions: the cub is about a cup (0.22 L), the lib about half a pound (0.22 kg), the opus about a joule, walking pace 8 steps per breath, and 1,000 base² (912 m²) about a quarter-acre block. But:

  • The dig stops being about a centimetre (it becomes 5 mm, and the next step down 0.42 mm), so rulers no longer read like metric ones: today the dig ≈ 1 cm and the tricia-pace ≈ 0.84 mm
  • The unc (6 cm) is no body measure; today's 12 cm unc is about a hand
  • Mass becomes pound-sized: halving length makes volume, and so the water-based lib, an eighth. A 70 kg person is 224 lib (316 dec) instead of 33;6
  • The vig drops to 2.8 W; today's 89 W vig is about a resting person's power
  • The gains are mostly available anyway as named sizes - the step is the gress (0;6 p), the cup is 0;2 cu - but the losses can't be won back in the halved system (a centimetre would be 2 digs, a hand 2 uncs, neither a prefix step)
  • Changing it would also mean recomputing almost every number in this spec

So the pace stays the base, and the half pace is named instead (gress, below).

Named sub-units (named because they're everyday sizes, like the inch and centimetre):

  • unc = 1/10 pace (1/12 dec) ≈ 12.1 cm
  • dig = 1/100 pace (1/144 dec) ≈ 1.01 cm

Decided: the span (symbol sp) = 0;2 pace = 2 uncs ≈ 24.2 cm, a hand's spread.

Why: a body-measure name like pace and dig, for the gap between the unc (12 cm) and the pace (145 cm); the old English span (9 in, 22.9 cm) is close. "Hand" was rejected earlier (the horse hand is 10.16 cm).

Advantage: a familiar body length for the 20-30 cm range, with no clash.

Decided: the ulna (symbol ul) = 0;4 pace = 4 uncs ≈ 48.4 cm, elbow to fingertip (a third of a pace).

Why: another body measure, filling the gap between the span (24 cm) and the pace (145 cm); it's also a handy length for a board ruler. Latin ulna is the forearm (and the forearm bone), and the old ell measure came from it. Rejected: cubit (Latin cubitum, elbow), which was liked, but its symbol would be "cu", the cub.

Advantage: fills the 30-90 cm gap with a body measure, and suits a board ruler.

Decided: the gress (symbol gs) = 0;6 pace = 6 uncs ≈ 72.6 cm, a single step (half a pace).

Why: the pace is the Roman passus, a double step (from one heel striking to the same heel striking again), but in English today "pace" usually means a single step, so someone pacing out a room would count twice as many paces as there are. The gress names the single step. Prior art: the Roman gradus (step) was exactly half a passus, about 74 cm. Latin gressus is also a step (as in progress, egress). Rejected: gradus (six letters, and its short form grad is the gradian), step (its symbols clash: st is the stone, sp the span), and halving the pace itself (c = 4 × 10^7 in the table above), which shrinks every unit built on it.

Advantage: distances can be paced out the way people walk them - one gress per step, two per pace - and the 60-90 cm range gets a body measure.

  • A gress is about an average adult walking step: men average ≈ 76 cm, women ≈ 67 cm (step length is roughly 0.41 × height). So "steps" is the everyday word for gresses, as "a k" is for a kilometre; the official name stays gress, because a step varies from person to person and the unit doesn't
  • Two gresses make a pace, so 1,000 paces (an iter) is 2,000 gresses (3,456 dec steps): a step counter reads distance directly
  • Today's "10,000 steps" goal (dec) ≈ 6,000 gresses (10,368 dec) = 3 iters ≈ 7.5 km

Decided: the iter (symbol ir) = 1,000 paces (1,728 dec) ≈ 2.51 km, the unit for distances.

Why: the Romans counted distance in thousands of paces (mille passus, the Roman mile), and the iter does the same in dozenal. It isn't the Roman mile's length: that was a decimal thousand paces (≈ 1.48 km), and the iter is a dozenal thousand (1,728 dec, 2.51 km), about 1.7 Roman miles. Latin iter means a road or journey (as in itinerary), and Roman route lists counted in milia passuum. Rejected: mille / mil (mi is the mile, mil is the thou), via (vi is the vis). League and stade were also considered; their clashes hardly matter since almost no one uses them now, but iter was preferred.

Advantage: a round distance unit with a long history, whose name means "journey".

Decided: iter is pronounced "EYE-ter", as in itinerary.

Why: a fixed pronunciation stops it being heard several ways ("IT-er", as in Latin, or "EE-ter"), and it's the sound people already know from itinerary.

Advantage: everyone says it the same way, using a sound they already know.

  • Defined by the speed of light: c = 2 × 10^7 paces per blink (exact)
    • = 2 × 10^8 paces per breath = 859,963,392 (dec) per breath
    • (equivalently 2 × 10^10 paces per day)
  • Light travels 2 × 10^8 paces in one breath ≈ 1,249,135 km (dec), about 3.25× the Earth-Moon distance
  • 1 iter = 1,000 paces = 2.51 km is literally a "thousand paces", counted in dozenal (the Roman mille passus was a decimal thousand, ≈ 1.48 km, a little longer than half an iter)
  • Half an iter, 0;6 ir (600 paces, 864 dec) ≈ 1.26 km, about a 15-minute walk, will be common. It needs no name of its own: halves are a single digit, and people already say "half a k" or "half a mile"
  • 15 iters ≈ 42.67 km ≈ a marathon (marathon = 14;99 iters)

Decided: the navis (symbol na) = 930 paces (1,332 dec) ≈ 1.935 km, the sea and air mile, replacing the nautical mile (1,852 m).

Why: the nautical mile exists because one nautical mile north or south is one minute of latitude (1/21,600 (dec) of a turn), so a navigator can measure distance off a chart's latitude scale. The dozenal version is 0;0001 turn of the Earth's meridian (1/20,736 (dec), four digits of a turn):

Advantage: navigators can still read distances straight off a chart's latitude scale.

  • Meridian (pole to pole and back) = 40,007.86 km (dec)
  • 0;0001 turn = 40,007,860 m / 20,736 = 1,929.4 m = 1,328.3 (dec) paces = 928;34 paces
  • A minute of latitude isn't constant (1,843 m at the equator, 1,862 m at the poles, as the Earth is flattened), so the nautical mile was fixed at a round 1,852 m in 1929 CE. The navis is rounded the same way
  • 928 paces is the nearest whole number (0.03% short); 930 was chosen as rounder (ends in 0) and it's only 0.3% long, well inside the ±0.5% that a minute of latitude itself varies
  • So 1 navis ≈ 0;0001 turn of latitude, and 10,000 navis ≈ once round the Earth through the poles
  • Name: Latin navis, a ship (as in navy, navigate). Symbol "na" follows the first-two-letters rule
  • Still open: a speed unit for ships and aircraft, to replace the knot (1 nautical mile per hour)

Imperial comparisons:

Imperial Paces Uncs Digs
6 ft 1;314 13;14 131;4
1 ft 0;263 2;63 26;3
6 in 0;131 1;31 13;1
1 in 0;026 0;26 2;6

Gravity

  • Would like g to be a nice dozenal number, but c and g have a fixed ratio (~2,559,X65 breaths), so only one can be exact.
  • With c exact: g ≈ 0;9926 paces/blink² (≈ 99;26 paces/breath², 117.2 dec)
  • g varies ~0.5% over Earth's surface anyway, so it's a poor basis for a definition.

Light distances

Light covers a round number of paces in every time unit, because c is fixed at 2 × 10^7 p/bl. So light times make handy yardsticks for big distances, as light-seconds and light-years do now:

Distance Paces Iters Light takes SI (dec)
Light-blink 2 × 10^7 p (exact) 20,000 ir 1 bl 104,095 km
Light-breath 2 × 10^8 p (exact) 200,000 ir 1 br 1,249,135 km
Earth-Moon (mean) 7;476 × 10^7 p 74,764 ir 3;84 bl (≈ 1;3 bt) 384,400 km
AU (Earth-Sun, exact in SI) 1;7E63 × 10^X p 17,E63,264 ir 9E;92 br (≈ X mt) 149,597,870,700 m
Light-day 2 × 10^10 p (exact) 2 × 10^7 ir 1 day 25.90 × 10^9 km
Light-year 5;0X6 × 10^12 p (exact) 5;0X6 × 10^E ir 1 year 9.461 × 10^12 km
Parax (see below) 3;2155 × 10^13 p 3;2155 × 10^10 ir 7;62 years 7.515 light-years, 2.304 pc
  • The light-year comes out exact and short: like SI's, it uses the Julian year of 265;3 days (365.25 dec), and light covers exactly 2 × 10^10 p a day, so a light-year is 265;3 × 2 × 10^10 = 5;0X6 × 10^12 p
  • The AU doesn't: it's fixed in metres (since 2012 CE), and the pace isn't a round number of metres

Star distances

Decided: the parax (symbol px), a dozenal parsec: the distance at which the Earth's orbit (1 AU, the Earth-Sun distance) spans 0;000001 turn (1/2,985,984 dec of a turn, 0.434 arcseconds).

Why: star distances come out as handy numbers - the nearest star is just under 1 (0;694), the centre of the Milky Way about 2,000 - and the distance is simply 1 over the parallax in millionths of a turn. 0;00001 turn was rejected because it makes star distances too large.

Advantage: star distances are small, handy numbers, read straight from the measured parallax.

The parsec is the same idea in degrees: the distance at which 1 AU spans 1 arcsecond (1/3,600 of a degree), so a star's distance follows straight from its parallax, the yearly shift in its position seen from either side of the Earth's orbit. That, not its size, is why astronomers use it: research papers give distances in parsecs (kpc, Mpc), star brightness is compared at a standard 10 parsecs (absolute magnitude), and the light-year is mostly for the public. The parsec is exact in SI (648,000/π AU), and this would be too:

  • 1 parax = 1,000,000 / 2π AU = 1X,E02;14 AU (475,234 dec) = 3;2155 × 10^13 p
  • = 2.304 parsecs = 7.515 light-years (dec)
  • Parallax in millionths of a turn gives the distance directly: a star that shifts 0;000004 turn is 0;3 px away
  • 0;00001 turn (5.2 arcseconds) would give 0.192 parsecs
Object Parsecs (dec) Parax
Proxima Centauri (nearest star) 1.30 0;694
Sirius 2.64 1;19
Pleiades 136 4E
Centre of the Milky Way 8,180 2,079
Andromeda galaxy 765,000 140,193

Decided: the name parax, symbol px.

Why: it's named after parallax, the way the parsec (parallax-second) is, so astronomers will recognise it. The root is Greek, but parallaxis was the word astronomers used when they wrote in Latin (Tycho Brahe, Kepler); classical Latin had no word for it, and the medieval diversitas aspectus ("difference of view") is too long to shorten well. Five letters, but the link to parallax is worth more than the rule. Symbol: "pa" is the pascal, so first and last letters; px is also the screen pixel, which isn't an SI or imperial unit. Rejected: sidus (Latin, a star; "si" reads as SI), caelum (Latin, the sky; too long).

Advantage: astronomers recognise it at once, and the name says how the distance is measured.