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nat concept

DefinitionThe unit of information measured with the natural logarithm, between 1.4426 and 1.4427 bits. Chapter 0 section 0.7.
Example0.10 nats is 0.144 bits, and 1 bit is 0.693 nats.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id nat, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • The unit of information measured with the natural logarithm, as a bit is measured with the logarithm to base two. The two conversions undo each other, the conversion is monotone, and one nat is between 1.4426 and 1.4427 bits.
  • The omission floor was measured at 0.10 nats against about six in ten million on sixteen of sixteen heads, and Landauer’s bound is stated per nat as kT and per bit as kT times the log of two.
Prior artnone recorded
Evidencereadscope/SPEC.md:653-680, geometric-observation/chapters/ch07_cost.md, geometric-observation/claims/LEDGER.md, lean/DataMiningAsObservation/NatUnit.lean, lean/DataMiningAsObservation/Bit.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
1 bit, 2 levels2 bits, 4 levels3 bits, 8 levels4 bits, 16 levelsone nat is 1.4427 bits, the natural logarithm's unit
Information in the natural logarithm's unit.

Equation

none

Conditions

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Chapter 0 section 0.7 of Data Mining as Observation, with the omission floor in nats in geometric-observation/chapters/ch07_cost.md.

Measurements

Where the book states it Numbers, as the book’s sources table records them Source
chapter 2 section 2.4 C-7, sixteen points in 128 dimensions, rank fifteen, near ten to the eleventh nats, refuses when samples do not exceed dimension, warns below five per dimension, loading is a property of two distributions readscope/SPEC.md:653-680
chapter 4 section 4.2 floor measured on 16 of 16 heads, naive assumption off 20 to 60 percent, about 100000 times, 0.10 nats against about 6e-7, first gate missed 0 of 16, NEG-13 geometric-observation/chapters/ch07_cost.md; geometric-observation/claims/LEDGER.md GO-P-2026-027 and NEG-13

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/NatUnit.lean, theorems log_two_pos, nats_bits, bits_nats, bitsOfNats_mono, one_nat_in_bits, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

lean/DataMiningAsObservation/Bit.lean, theorems levels_succ, levels_add, step_succ, sqError_succ, sqError_antitone, levels_zero, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation primer S, chapters 0, 2, 4.

Related

bit; budget; Landauer's principle; perplexity; KL divergence.

See also

Book equations stated beside the entry’s terms, not defining it: 0.15, 4.2, 0.16.

Ledger rows that cite the entry’s records without naming it: GO-7, NEG-13 → resolved.

Sources-table rows that share a record with the entry without naming it: chapter 2 section 2.4, chapter 2 section 2.6, chapter 4 section 4.2, chapter 8 section 8.4, chapter 11 section 11.3, chapter 11 section 11.7, chapter 11 section 11.9.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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