claim

active

claim:for-a-given-task-the-number-of-all-sequences-which-work-is-tiny-by-comparison-with-the-huge-number-of-all-possible-sequences-less-than-a-trillionth-of-all-6-10-23-possible-sequences-actually-work-well-enough

For a given task, the number of all sequences which work is tiny by comparison with the huge number of all possible sequences; less than a trillionth of all 6 × 10^23 possible sequences actually work well enough.

A combinatorial argument that good sequences are astronomically rare, emphasizing the difficulty of discovery.

Neighborhood — ranked by edge-count

Concepts (1)

concept

Partial Order of Steps
supports
Mathematical representation of precedence relations among steps: which centers must be in position before another can be formed, defining good sequences as linearizations that minimize backtracking.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Less than a trillionth of all the 6 × 10^23 possible sequences actually work well enough to allow smooth unfolding.quote0.883
Alexander's striking quantification of the rarity of good sequences, underscoring why finding the right order is so difficult and precious.
Half a dozen sequences taken together can have a very big effect on the environment and show a wholly new way of conceiving space.claim0.814
Highlights the emergent power of even a small network of interlinked sequences.
There are fewer representations competent for N tasks than M<N tasks, so training more general models should yield fewer possible solutionshypothesis0.801
Selective pressure toward convergence via task generality
There appears to be a systematic relationship between the frequency of concepts and the dictionary size needed to resolve features for them.claim0.798
Feature presence depends on concept frequency in training data, with a threshold scaling inversely with alive features.
Parallel sub-tasks within skills and across skill families should produce parallel outputs for legibility.claim0.792
A skill's output length should match task complexity—short tasks produce short reports, long tasks produce structured hierarchical reports.claim0.790
Digital minds with humanlike capabilities could think at least thousands of times, and perhaps millions of times, faster than humans given sufficient hardwarehypothesis0.783
Grounds the subjective speed dimension of super-beneficiary status
Roughly 2,000 long sequences, each containing ~20 smaller snippets, thus about 40,000 short sequences could completely transform the built environment.claim0.780
Quantitative estimate of the scope of the gene pool needed for a living world.