Programming-Language Atlas
Normalized information distance, approximated with LZMA compression across 100 carefully sampled programming-language corpora.
A comparison view of the same 100 corpora, fitted from eight compression and distributional instruments.
100 corpora LZMA NCD 4 repository-disjoint folds 64 KiB per object
100 corpora 8 instruments 4 repository-disjoint folds 128 KiB per view
Select a language to inspect its full-space density and nearest neighbours.
The default view is an ordinal display of the full normalized compression distance matrix. Screen-space whitespace is not direct evidence of an information gap.
Method
From NID to a computable map
What the comparison measures
Normalized information distance is a universal theoretical distance between objects. It is uncomputable, so this atlas uses normalized compression distance as a practical approximation.
NID
Kolmogorov complexity K measures the length of the shortest program describing an object. Up to logarithmic terms, the normalized distance is:
NID(x,y) = [K(xy) - min(K(x), K(y))] / max(K(x), K(y))
NCD
Because K cannot be computed, compressor length C is substituted. LZMA is order-sensitive, so this experiment conservatively takes the larger concatenation length:
NCD_C(x,y) = [max(C(xy), C(yx)) - min(C(x), C(y))] / max(C(x), C(y))
Corpus
Each language contributes four repository-disjoint, source-only objects of exactly 64 KiB. The displayed matrix averages all cross-fold NCD comparisons, reducing dependence on any single repository draw.
Map
The full NCD matrix is converted to a three-dimensional ordinal embedding. The fit seeks to preserve the rank ordering of distances. Thin lines are the minimum spanning tree of the raw matrix, and point size is median raw NCD to the five nearest languages.
Read carefully
This display preserves much, but not all, of the full NCD ordering. NCD remains compressor-dependent, and screen-space whitespace is not direct evidence of an information gap.
This is a map of sampled code corpora, not a map of programming languages in the abstract. Nearness means that corpora were measured as similar across the fitted compromise of the retained instruments.
Sample
Each language contributes four repository-disjoint folds. Every source, lexeme, and normalized-token object is exactly 128 KiB and uses the same framed logical chunks. Repository contribution is capped to limit domination by a single codebase.
Measure
Three held-out order-4 finite-context excess-code-length instruments are combined with five square-root Jensen-Shannon divergence instruments. Source-only LZMA normalized compression distance remains a comparator, not an oracle.
Fit
The eight rank-normalized dissimilarity matrices fit a shared 10-dimensional compromise. This page applies classical multidimensional scaling to the full compromise matrix for a three-dimensional view. Thin lines show the consensus minimum spanning tree computed in full space.
Read carefully
The projection preserves much, but not all, of the full-space ordering. Point size reports local five-neighbour radius: smaller points sit in more granular regions, while larger points are more isolated.
Current finding
A strong signal, conditional geometry
A continuum, not a set of chasms
LZMA NCD strongly distinguishes repeated samples of the same language from samples of different languages: within-versus-between AUC is 0.9946. Delete-one-fold tests preserve pairwise ranks at a median 0.987 and five-neighbour overlap at 0.843.
That supports an exploratory map, but not a claim of canonical coordinates. LZMA also missed one synthetic Markov-relation check, while the PPMd alternative badly violated self-identity. The global NCD signal is stronger than any exact local reading.
The broad granular-to-isolated ordering recurred under a second repository sample. Exact nearest neighbours were less stable, the shared geometry failed its held-out-instrument criterion, and no full-space edge passed the robust-gap rule in either run.
Whitespace in this view is therefore not evidence of a gap. Treat local structure as an exploratory hypothesis and the density continuum as the stronger result.