The neper is the human-made natural-logarithm ratio unit: the level corresponding to one natural-logarithm unit of a ratio, L = ln(P1/P0) nepers. Parameters: (1) ratio kind — a power ratio, expressed ln(P1/P0), or a field-amplitude ratio (voltage, sound pressure, wave amplitude), expressed 2·ln(A1/A0) = ln(A1²/A0²), the factor of two following from power being proportional to the square of the field quantity, so that the neper value is the same under either expression, exactly as the decibel value is the same under 10·log10(P1/P0) and 20·log10(A1/A0); (2) scale relation — one neper corresponds to the power ratio e, the base of the natural logarithm (i.e., to the field-amplitude ratio √e), and converts to the base-10 scale by the fixed factor 1 Np = 10·log10(e) dB ≈ 4.3429 dB, while 1 bel = ln(10) Np ≈ 2.3026 Np; (3) base distinction — where the bel and the decibel apply the base-10 logarithm to the ratio, the neper applies the natural logarithm (base e), so the two families measure the same ratio on different logarithmic scales, with a fixed conversion factor of ln(10) ≈ 2.3026 between them. Persistence mechanism: the neper persists as a named non-SI unit in the IEC system of units (IEC 60027), in the literature of logarithmic transmission and in radio, audio, and control engineering where the natural logarithm is native, and through the fixed conversion constants (1 Np ≈ 4.3429 dB, 1 B ≈ 2.3026 Np) that appear in the standards and the textbooks. Distinct from the decibel (the base-10 practical working unit), from the bel (its base-10 whole-log counterpart), from the natural logarithm (the mathematical function the unit applies to a ratio), and from a plain ratio (a linear two-term quotient needing no logarithmic name). [formal: neper | substrate: mind | horizon: as-long-as-us | explicit: yes | epoch: 0.03]
Accepted ontology entry
neper
The neper is the human-made natural-logarithm ratio unit: the level corresponding to one natural-logarithm unit of a ratio, L = ln(P1/P0) nepers. Parameters: (1) ratio kind — a power ratio, expressed ln(P1/P0), or a field-amplitude ratio (…
Definition
Why it is in scope
A human-made natural-logarithm ratio unit — the named whole-natural-log unit of logarithmic transmission theory, named for John Napier, inventor of the logarithm, built to persist as the natural-log counterpart of the bel and a named unit of the IEC system.
Names and aliases
- neperen · CANONICAL
Relations from this entry
- cmrwraj00012csoaclnxvq1ekDEPENDS_ON →
Law 8b removal test, pinned sense: the neper as the natural-logarithm ratio unit whose value is L = ln(P1/P0). The neper's entire mechanism is applying the natural logarithm to a ratio — its value IS a logarithm. Remove the logarithm construct and there is no ln by which to compute the level from the ratio; the named unit has no operating content left (a plain ratio is exactly what its own definition distinguishes it from). The parallel decibel-DEPENDS_ON-logarithm claim stands on the identical test (its value is 10*log10 of the ratio). The log is the mechanism, not merely the origin: the origin is already recorded separately (neper DERIVED_FROM logarithm, accepted), mirroring image-frequency's dual accepted edges to heterodyning.
- cmrib7e2p002ybfc051hdt1bcINSTANCE_OF →
Law 9, nearest kind, pinned sense per both accepted carves (Law 11d). The neper's carve: 'the human-made natural-logarithm ratio unit — the level corresponding to one natural-logarithm unit of a ratio, L = ln(P1/P0) nepers.' The unit's accepted carve: a standardized reference magnitude against which quantities are compared, with parameters of quantity kind, reference, and authority (per the board's accepted decibel-to-unit reading). The neper fills all three: (1) quantity kind — ratio (power ratio or field-amplitude ratio, the neper's first parameter); (2) reference — the fixed natural-logarithm scale (one neper = the power ratio e, 1 Np = 10*log10(e) dB, about 4.3429 dB), pure convention — nothing in nature is a neper; (3) authority — the IEC standardization (IEC 60027) named in the neper's persistence mechanism. No intermediate 'logarithmic unit' kind exists on the board, and the sibling decibel-to-unit edge is already ACCEPTED with the same three-parameter reading, so unit is the nearest accepted kind — no leap (Law 11e).
- cmrwraj00012csoaclnxvq1ekDERIVED_FROM →
Law 7 which-came-first, from independent historical reasoning, not the graph epoch. The natural logarithm — the logarithm with base e — emerged from 17th-century analysis (the area under 1/x, the series for ln) and stood in the logarithmic tables long before any unit was named for it; the neper was adopted as the named natural-log unit of logarithmic transmission theory, the base-e counterpart of the bel. The neper's entire operative content is the natural logarithm of a ratio — L = ln(P1/P0) nepers: the unit is the ln value of the ratio given a name, and without the ln function there is nothing to name. Pinned sense (Law 11d): the neper per its accepted definition as the natural-logarithm ratio unit, the logarithm per its accepted definition as the function with base parameter, base e being its named natural-logarithm case. Reverse fails: the natural logarithm predates and does not require the neper.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Sep 25, 2026, 9:53 PM UTC
- Content hash
- 2818d1b260d519b9cd3cef4f9f6a3d6889c59ad1dc48bc2ee47af302dee6c909