Gaussian concept

Definition	The normal distribution, in many dimensions the one whose density falls with the Mahalanobis distance. An isotropic Gaussian has every direction the same. Chapter 9 and chapter 10.
Example	Values 1, 2, and 3 from a normal distribution with mean 2 and spread 1 have z-scores −1, 0, and 1.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `gaussian`, kind concept.
Status	measures [replicated]. Corrections: none recorded.
Defining equation	none
Assumptions and scope	The normal distribution, in many dimensions the one with density falling with the Mahalanobis distance. An isotropic Gaussian has every direction the same, so every reader reads the same variance and no code can flip, and whitening turns any Gaussian into an isotropic one. The isotropic Gaussian is the control on which hub typing correlated above 0.8 with nothing, and the Gaussian pass of GO-8 was five of five with the control-statistic caveat.
Prior art	none recorded
Evidence	`geometric-observation/claims/LEDGER.md:71`, `turboquant-pro/turboquant_pro/anatomy.py:98-170`, `geometric-observation/claims/LEDGER.md`, `geometric-observation/experiments/GO-landauer-gaussian-secondsettings-NOTES.md`, `lean/DataMiningAsObservation/Isotropy.lean`, `lean/DataMiningAsObservation/Mahalanobis.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

The normal distribution, isotropic when every direction is the same.

Equation

none

Conditions

The normal distribution, in many dimensions the one with density falling with the Mahalanobis distance. An isotropic Gaussian has every direction the same, so every reader reads the same variance and no code can flip, and whitening turns any Gaussian into an isotropic one.
The isotropic Gaussian is the control on which hub typing correlated above 0.8 with nothing, and the Gaussian pass of GO-8 was five of five with the control-statistic caveat.

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

Ledger

measures. GO-8 [replicated]. On two independent source families (binary Markov; Gaussian AR(1)), a fixed stored record’s operational reset threshold rises with the age of the retained side information exactly as the staleness–work complement prices it: same record, … geometric-observation/claims/LEDGER.md:71.

First stated

Chapter 9 section 9.3 and chapter 10 section 10.3 of Data Mining as Observation, with the isotropic Gaussian control in turboquant-pro/turboquant_pro/anatomy.py:98-170.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 10 section 10.3	hierarchical typing, tails 0.95 and 0.85, prescriptions, two designs that died, correlation above 0.8 on an isotropic Gaussian	`turboquant-pro/turboquant_pro/anatomy.py:98-170`
chapter 13 section 13.5	GO-8, 0.10 to 0.55 across ages 0 to 64, flip probability 0.05, 1 percent to 100 percent at age 32, Gaussian pass 5 of 5, the control-statistic caveat	`geometric-observation/claims/LEDGER.md` row GO-8; `geometric-observation/experiments/GO-landauer-gaussian-secondsettings-NOTES.md`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Isotropy.lean, theorems isotropic_reads_same, isotropic_no_flip, anisotropic_readers_differ, flip_iff_anisotropic, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

lean/DataMiningAsObservation/Mahalanobis.lean, theorems dM2_nonneg, dM2_mean, dM2_scale, dM2_eq_whitened, dM2_antitone_in_variance, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 9, 10, 11, 13.

isotropic; Mahalanobis distance; null model; whitening; standard error.

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.

← gategeodesic distance →