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A fundamental distance unit

A length unit defined purely from fundamental physics, with exactly one human choice: how many dozenal steps to climb to reach human scale. Everything else is fixed by nature.

The definition

unit = 12^N × ℓ_P

where ℓ_P is the Planck length (≈ 1.616×10⁻³⁵ m) and N is an integer — the only free, human-chosen number. The unit is literally "N dozenal hops up from the Planck length." Because it's a pure multiple of a physical length, stating it needs no metre, no second, no frozen reference — only N and nature.

The guiding rule: 12 is principled, the Planck length is fixed by nature; the only arbitrary thing is the number of ×12 hops — nothing more. (On base 12, see Dozenal.)

Why the Planck length — it gives the unit a floor

Build on any everyday length — a foot, an atom — and you can always ask "what about half of that?" The scale floats: there's no natural bottom, so where you call "1" is arbitrary, stuck somewhere in the middle of an endless ladder running down forever.

The Planck length is different. It is (expected to be) the smallest length that physically means anything — below it, the very notion of distance stops working. Anchor there and the unit gets a natural floor: its "1" (N = 0, one Planck length) is the smallest meaningful length in the universe, and "less than 1" isn't a small number, it's nothing — physically impossible. The whole ladder grows upward from the true bottom of reality, instead of floating in the middle of it.

That floor — not precision, not elegance — is the decisive reason to anchor on the Planck length.

Honest caveat: a minimum length is the strong, mainstream expectation from quantum gravity (the generalized uncertainty principle, discreteness in loop quantum gravity, a minimal length in string theory) — not a proven theorem. The floor argument rests on that expectation.

What it is on your hand

The unit jumps by ×12 per step, so its human rungs are fixed:

N size hand reference
31 4.60 cm finger, knuckle → tip
one step down 3.84 mm finger crease mark
32 55 cm arm reach
33 6.6 m room

The everyday unit is N = 31 ≈ 4.60 cm — finger-scale. The rule for picking the rung: it should not exceed a stretched hand span (~22 cm) and should stay within an order of magnitude of it, because the hand is our manipulation scale, the thing always in view. N=32 (55 cm) overshoots the hand and feels awkward; N=31 is the only fundamental rung that fits under it. So the reference is a part of the hand — the index finger, knuckle to tip — and the unit's twelfth (3.84 mm) lands on a finger crease, so the unit and its subdivision read off the same finger. (Finger and thumb units have deep precedent: the inch is a thumb, the "digit" a finger-width.)

A typical adult, in these units: hand span ≈ 5, foot ≈ 6, reach ≈ 12 (one dozen), height ≈ 38.

Why nothing lands exactly at hand size

No fundamental anchor places a rung at a whole hand (~22 cm). The atomic family clusters its rungs at ~27 cm and ~2.3 cm (because α ≈ 1/144 = 12⁻²); Planck at ~4.6 cm and ~55 cm. A rung sitting right on the hand would need a tuned multiplier — the forbidden fudge — so finger-scale is the honest best fit.

The objections, answered

Doesn't every unit secretly rely on arbitrary numbers? — no frozen numbers here

The SI defines the metre via a frozen value of the speed of light, the kilogram via a frozen Planck constant, and so on. Those "exact" constants are conventions fixed by committee (2019) — fixing them created no physical accuracy, it merely relocated the uncertainty. Only dimensionless constants (the fine-structure constant α, mass ratios) are convention-free physics.

This unit uses no frozen number: it's a pure multiple of a real physical length, the only chosen input being the integer N. That's the cleanest a dimensional unit can be — you can't avoid leaning on physical constants to build one, but you can drive the arbitrary choices down to a single integer.

Isn't the Planck length badly measured? — the precision trade

Yes. The Planck length contains G, the gravitational constant — the worst-measured constant in physics (~2×10⁻⁵; gravity is too weak to measure precisely and offers no exact quantum effect to exploit). So the unit's value in metres is known only to ~5 figures, sharpening as G improves.

This is accepted on purpose: the definition is exact; only the realization is finite — honest, not faked, precision. And ~10⁻⁵ is already far beyond any human or engineering need (nobody measures a length better than parts-per-million), so the imprecision never bites in practice.

Why not a precise atomic anchor instead? — and the harmon's fudge

You could anchor to a precisely-known atomic length — the Rydberg length 1/R∞ is known to ~10⁻¹² (a million times better than the Planck length), and the electron is perfectly universal (no less fundamental — Planck itself leans on the contingent G). But the atomic anchor has no floor: atoms and nuclei sit far below it, so its "1" is arbitrary. Maximal fundamentality — the floor — is weighted over realizable precision.

The existing dozenal Harmonic System shows the trap. Its length unit, the harmon = 272.35 mm, is (dozenal 1,001,700;) ÷ Rydberg constant. A clean 12⁶ ÷ R∞ would give 272.09 mm — but the harmon nudges that by +0.09% so that 100 yards ≈ 240 harmons, a cubic half-harmon ≈ 2/3 US gallon, and so on. That deliberate fudge toward legacy units is exactly what this proposal forbids: the only freedom allowed is the integer hop, never a fitting factor.

Sources: The Harmonic System — Dozenal Wiki · Universal Unit System (asahi-net dd6t-sg).