Work Classification Layer
Compare Works
Pick two or more works to set their attribute fingerprints, dimension-by-dimension passages, and shared school embodiments side by side. Especially useful for author-stage comparisons (Wittgenstein early vs late) and for setting a single tradition's foundational texts against each other.
Elements
There is no royal road to geometry — the most successful textbook in the history of mathematics
Attribute Fingerprint
Rows where works disagree are highlighted in gold. The full ontology grid is shown.
| Attribute | Elements |
|---|---|
| Time · Extent | Infinite |
| Time · Ontological Status | Substantival |
| Time · Grain | Continuous |
| Time · Freedom | Deterministic |
| Time · Traversability | Linear |
| Time · Dimensionality | One |
| Time · Direction | Uni-directional |
| Space · Extent | Infinite |
| Space · Ontological Status | Substantival |
| Space · Curvature | Flat |
| Space · Dimensionality | Three |
| Space · Locality | Local |
| Matter · Extent | not engaged |
| Matter · Ontological Status | not engaged |
| Matter · Conservation | not engaged |
| Matter · Dimensionality | Three |
| Matter · Locality | not engaged |
| Observer · Time Instance | Single |
| Observer · Space Instance | Single |
| Observer · Knowledge Extent | Immediate |
| Observer · Knowledge Retainment | Total |
| Observer · Physicality | Disembodied |
| Observer · Agency | Active |
| Observer · Number | Plural |
| Observer · Metaphysical Agency | not engaged |
| Observer · Moral Authority | Reason |
| Observer · Theological Method | — |
| Energy · Extent | not engaged |
| Energy · Ontological Status | not engaged |
| Energy · Conservation | not engaged |
| Energy · Dispersibility | not engaged |
| Information · Ontological Status | Substantival |
| Information · Cosmic Conservation | Conserved |
| Information · Personal Conservation | not engaged |
| Information · Granularity | Continuous |
Dimension-by-Dimension Evidence
What each work's passages reveal about its stance on each of the six dimensions.
Time
Elements
Mathematical truths are eternal and a-historical. The Pythagorean theorem is as true today as in 300 BCE. Time is presupposed but not theorised.
Space
Elements
Space is Euclid's subject: infinite, flat (the fifth postulate ensures Euclidean flatness), three-dimensional (Books XI–XIII). The parallel postulate implicitly defines flat space.
Matter
Elements
Not addressed. Geometric objects are ideal — points have no extension, lines no breadth.
Observer
Elements
The geometer has immediate access to truth through rational intuition and deductive proof. In a sense disembodied: geometric truths do not depend on sensory experience.
Energy
Elements
Not addressed. The Elements is pure mathematics, not physics.
Information
Elements
Mathematical information is conserved and cumulative. Each theorem adds to the stock of known truth. The axiomatic method is an information-conservation technology.
Internal Tensions
Where each work's argument pulls against itself.
The status of the fifth postulate: it does not feel self-evident, and Euclid delays using it until I.29. Twenty-two centuries of failed attempts to prove it led to non-Euclidean geometry and ultimately to Einstein's curved spacetime.