Draft: a measurable definition of "entering the singularity"

Status: draft for me's review, 2026-10-07. Not adopted. Not part of methodology version 2. Written after I noticed that a top comment on r/accelerate ("any prediction made right now about the next 5 years is gonna look stupid in retrospect") matches one of the standard definitions of the singularity, and asked whether the idea could be made into a definition, a progress measure and a mark to cross.

1. The problem with the existing definitions

Three definitions have been in use since the 1990s (Yudkowsky's 2007 "three schools"):

Each one, used alone, has a known false positive:

• Accelerating change alone fires on any sector having a fast decade. Moore's law was a steady exponential for fifty years and nobody called it a singularity.
• Event horizon alone fires in every technological revolution as felt from inside. Five-year forecasts about the internet made in 1995 look stupid in retrospect too. It is also a claim about the forecasters, not about the world.
• Intelligence explosion alone cannot be measured from outside the labs, and a high share of AI-written code in a slow-moving field would not be a singularity.

The proposal: define entry as all three being true at once, and staying true.

2. The three legs

One capability measure, chosen and frozen in advance, anchors legs A and B. The working candidate is the length of task (in human-hours) that the best public AI system can complete unaided at a stated success rate, as published by METR. It is chosen because it has not saturated the way benchmarks do. A successor rule is needed for the day it does saturate: the replacement measure must be named before the old one stops moving, and the overlap period published.

Let C(t) be that measure at time t.

Leg A: pace is accelerating

Doubling time T(t) is how long C takes to double, estimated over a trailing window of W months (W = 12 to start):

T(t) = ln 2 / (slope of ln C over the trailing W months)

A steady exponential has constant T. The singularity signature is T falling over time.

• Threshold: T(t) at or below T* (placeholder: one month) and still falling over the last two windows.
• Gauge (0 to 1): g_A(t) = clip((T_ref − T(t)) / (T_ref − T*), 0, 1), where T_ref is the doubling time in a frozen reference year (placeholder: 2019).

Leg B: forecasts have stopped working

For forecasts of C made at time s with lead d (that is, about C(s + d)), the skill score against the trend-extrapolation baseline is

S(s, d) = 1 − (mean squared error of the forecasts, log scale)
            / (mean squared error of extrapolating the trend as of s, log scale)

The baseline is trend extrapolation, not "no change". In a world of steady fast progress, "no change" loses badly but the trend wins, and that world is Kurzweil's, not Vinge's. The event horizon is the point where even the trend breaks.

The forecast horizon H(s) is the largest lead d at which S(s, d) is still above zero.

• Threshold: H(t) at or below one year.

• Gauge: g_B(t) = clip((H_ref − H(t)) / (H_ref − 1 year), 0, 1), with H_ref the horizon in the reference year.

• Direction is recorded, not just size. Were the forecasts too slow or too fast? Milestones from the 2016 Grace survey mostly arrived early. "Consistently too slow" is a claim about the world; "unpredictable" hides it.

• Lag. H(t) can only be computed once t + d has passed, so leg B is confirmed in arrears. The real-time stand-in is revision velocity: with M(t) the consensus arrival date for human-level AI (surveys, Metaculus, Manifold, all already in data/aggregates.csv), let D(t) = M(t) − t be the years remaining. If M is constant, D falls one year per year. Excess pull-in is

    v(t) = −dD/dt − 1

  which is zero when the date is standing still and positive when the date is being pulled in faster than time passes. Sustained positive v is the leading indicator that forecasts are failing in the slow direction. It is reported beside g_B, never substituted for it.

Leg C: AI is doing the improving

Let f(t) be the share of inputs to frontier AI progress (code, experiments, research ideas) supplied by AI systems rather than people, from the best measurement available. Candidate sources: lab self-reports of AI-written code share, surveys of frontier researchers on time saved, and the AI-contribution disclosures that some venues now require on papers.

• Threshold: f(t) at or above one half.
• Gauge: g_C(t) = clip(f(t) / 0.5, 0, 1).
• This is the weakest-measured leg and the draft says so. Every f value carries its source and whether it is a self-report.

3. The mark

We have entered the singularity, as defined here, when all three gauges equal one for four consecutive quarters. Any leg dropping back below its threshold resets the count. This is the same shape as the three-month persistence rule in the vocabulary ledger (methodology section 8).

The status at any date is one of: not entered; approaching (all three gauges above one half); mark crossed, under persistence test (count in progress); entered (count complete, with the quarter it completed).

4. Progress toward it

The three gauges are published separately, each in its own panel. If a single number is wanted:

P(t) = min(g_A(t), g_B(t), g_C(t))

The smallest gauge, not the average. The definition requires all three, so the weakest leg is the honest distance remaining. An average would let one runaway leg hide two stalled ones. This also keeps methodology section 9's rule: series are never combined into an index. A minimum is not an index; it is the definition's own bottleneck.

5. Tests the definition must pass before adoption

1. Backward test. Run on every year from 1995 to 2019 with the best data available, it must return "not entered". Specifically, 1995 to 2000 (internet) should fire leg B and nothing else; 2012 to 2017 (deep learning) should fire leg A weakly and nothing else. If it fires on those periods, the thresholds are wrong.
2. Preregistration. The capability measure, the reference year, T*, the one-year horizon, the one-half share and the four-quarter persistence are set and frozen before any current-period value is published. Changing any of them afterwards is an amendment entry.
3. Self-reference. If leg B is true, forecasts of when the mark will be crossed are themselves unreliable. The mark is therefore observed, never forecast. The project publishes status, not an arrival date.
4. What it does and does not claim. Crossing the mark establishes that the singularity as defined here has been entered. It does not settle which of the three schools was right, and it does not establish that the world is now unknowable. It establishes that three stated measurements crossed three stated lines and stayed there.

6. Relation to the tracker

The Zeitgeist tracker measures what people believe. This definition measures the world. They are kept apart on purpose, and the interesting chart is the two side by side: the share of statements claiming we are in or near the singularity (streams E, F and the vanguard sub-series) against P(t). Divergence in either direction is a finding. The hedging rule (R3) in the vanguard codebook already gives a proxy for a community's sense of its own forecast horizon, and can be charted against g_B.

7. Open questions for me

• Is METR's task horizon the right anchor for C, and what is the successor rule?
• Placeholders to set: T* (one month?), reference year (2019?), persistence (four quarters?). Each needs a one-line reason recorded here.
• Should an economic leg (Hanson's world-output doubling time) be added as a fourth, lagging confirmation, or does it belong in a separate "has it mattered yet" measure?
• Where does the data for leg C come from in a form that is not pure self-report?

Rendered from docs/singularity-entry-definition-draft-2026-10-07.md at version a7bd17a.