The Advent of Technological Singularity: a Formal Metric

David Lizcano; Juan A. Lara; Juan Pazos; Mar\'ia A. Mart\'inez

arxiv: 1907.03841 · v1 · pith:AXLTBKWTnew · submitted 2019-06-25 · 💻 cs.CY

The Advent of Technological Singularity: a Formal Metric

Juan A. Lara , David Lizcano , Mar\'ia A. Mart\'inez , Juan Pazos This is my paper

Pith reviewed 2026-05-25 16:11 UTC · model grok-4.3

classification 💻 cs.CY

keywords technological singularityartificial general intelligencemetricmeasurementAGI progressobjective assessment

0 comments

The pith

A formal metric objectively measures the current state of technological singularity advent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents the first formal metric to quantify how close humanity is to technological singularity, the point at which general artificial intelligence surpasses human intelligence. Prior assessments of this possibility relied solely on subjective opinions rather than data. The metric is built from measurable indicators of AI development to provide an objective reading of progress. This matters because it could replace speculative debate with a data-driven way to track AI advancement.

Core claim

The authors claim that a metric constructed from measurable indicators can objectively determine the actual state of the advent of technological singularity, moving beyond opinions to a quantifiable assessment of when AGI might exceed human intelligence.

What carries the argument

The formal metric for technological singularity advent, assembled from measurable indicators of AI capability without subjective judgment.

If this is right

The metric supplies an objective alternative to opinion-based forecasts of singularity timing.
It enables consistent tracking of singularity state across different periods or AI development paths.
The approach can be applied to evaluate real-world AI milestones against the metric.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Adoption of the metric could guide resource allocation in AI research by highlighting measurable gaps.
The metric might be tested by applying it retroactively to past AI breakthroughs to check alignment with expert views.
Extensions could incorporate new indicators as AI capabilities evolve beyond current measures.

Load-bearing premise

The state of technological singularity can be captured objectively by one formal metric made only from measurable indicators.

What would settle it

Showing that any selection of measurable indicators still requires subjective judgment to reflect singularity progress would falsify the metric's claim to objectivity.

read the original abstract

The Technological Singularity; that is, the possibility of achieving a General Artificial Intelligence (AGI) that surpasses human intelligence, is one of the vital paradigms of today's humanity. However, until now only opinions about its possibility and/or achievement were issued, therefore, in this work, a metric is presented, for the first time, to objectively measure the actual state in which the advent of technological singularity is found.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims to introduce the first objective metric for tracking technological singularity progress, but the abstract supplies no formula, indicators, derivation, or evidence, so the claim cannot be assessed.

read the letter

The main point is that this paper says it presents, for the first time, a formal metric built from measurable indicators to track how close we are to technological singularity. That is the headline claim your colleague needs to know. The intent is to replace opinions with something more objective on a topic that some forecasters care about. If the metric were actually defined and shown to work, it could serve as a modest reference point in AI strategy discussions. The abstract does at least name the goal clearly. Beyond that, there is little to evaluate. No equations appear, no list of indicators is given, no data or validation is mentioned, and no comparison to prior attempts at quantifying singularity or AGI progress is offered. The assumption that a single metric can capture the state objectively without hidden judgment calls is stated but not demonstrated. Because the actual metric is absent from what is provided, it is not possible to check for circularity, free parameters, or independent grounding. This leaves the work in a state where the central promise cannot be tested. The paper would mainly interest a narrow set of readers already following singularity forecasting literature who want to see any new proposal. For most AI or forecasting researchers it offers nothing concrete to engage with. It does not look ready for peer review. The authors would first need to supply the metric definition, its construction, and supporting evidence before a referee could give useful feedback.

Referee Report

1 major / 0 minor

Summary. The manuscript claims to introduce, for the first time, a formal metric constructed from measurable indicators that objectively quantifies the current state of progress toward technological singularity (defined as AGI surpassing human intelligence), replacing prior opinion-based assessments.

Significance. A rigorously derived, parameter-free metric with explicit validation against historical data or falsifiable predictions would be a substantive contribution to AGI timeline research by enabling objective tracking; the current manuscript supplies none of these elements.

major comments (1)

Abstract: the central claim is that a metric 'is presented' and 'constructed from measurable indicators'; however, the manuscript contains no equation, derivation, indicator definitions, data sources, or validation procedure, so the claim is unsupported.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review. We respond to the major comment below and note that we agree the manuscript requires additional technical content to substantiate its central claim.

read point-by-point responses

Referee: [—] Abstract: the central claim is that a metric 'is presented' and 'constructed from measurable indicators'; however, the manuscript contains no equation, derivation, indicator definitions, data sources, or validation procedure, so the claim is unsupported.

Authors: The referee correctly identifies that the current manuscript version does not include an explicit equation, derivation steps, formal definitions of the indicators, data sources, or a validation procedure. The abstract states the intent to present such a metric, but the body does not deliver the supporting technical details. We will revise the manuscript to incorporate these elements so that the claim is properly supported. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and context describe only the high-level claim that a new metric is introduced to quantify the advent of technological singularity from measurable indicators. No equations, derivation steps, parameter-fitting procedures, self-citations, or ansatzes appear in the text. Without any load-bearing construction that reduces a result to its own inputs by definition, the paper's central assertion remains a straightforward definitional proposal and is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No details provided in the abstract regarding any free parameters, axioms, or invented entities used in the metric. The paper claims to present a metric for the first time but does not specify its components or construction.

pith-pipeline@v0.9.0 · 5592 in / 1057 out tokens · 55043 ms · 2026-05-25T16:11:30.941378+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

[1]

Abstract. The Technological Singularity; that is, the possibility of achieving a General Artificial Intelligence (AGI) that surpasses human intelligence, is one of the vital paradigms of today's humanity. However, until now only opinions about its possibility and/or achievement were issued, therefore, in this work, a metric is presented, for the first tim...

work page
[2]

arithmeticly

Introduction. In the 19th century, machines began to replace humans as physical workers. For many people, this was a blessing, despite the occasional resistance to change led by the Luddites –a secret sect of English textile workers in England who opposed textile machinery -. Another mythical story portraits, in the mid -19th Century, in the USA, a challe...

work page 1915
[3]

singularity

State of Art: Technological Singularity. Contrary to some recent publications (Tegmark, 2017), the term and especially the concept of, "singularity" has a long and substantial history behind. For instance, Condorcet (Condorcet, 1795) was the first to account for a singularity in the human intellectual faculties. Subsequently, Peirce (Peirce,

work page 2017
[4]

singularity

wondered how much knowledge could be done by machines and how much should be left for humans. Turing, in 1948 (Mitchie, 1998-2004), (Turing, 1948), (Turing, 1950) (Turing, 1952), wrote about intelligent machines. However, the first explicit use, in the technological context, of the term “singularity” was reported in 1957 and its author was von Neumann (Ul...

work page 1948
[5]

Deep Blue

The proposed solution. 3 George Polya (Polya, 1954) systematized a series of reasoning patterns that are usually followed in the research processes in the natural sciences, in the creation mathematics, in judicial and police investigations, in the diagnosis medical, etc .:The plausible reasoning. Its formal expression is: If A then B B____________________...

work page 1954
[6]

Holism: Ability to integrate intelligent elements from a lower level to build a higher level intelligence

work page
[7]

Learning: Acquire knowledge continuously, from all available sources and incorporate them into an integrated and congruent whole

work page
[8]

Creativity: Capacity of imagination, intuition and invention

work page
[9]

Teleology: Search for purposes

work page
[10]

Reasoning and inference: Abductive, deductive and inductive, and anterogado

work page
[11]

Proactivity: Initiative to detect interesting problems

work page
[12]

Enantiodromia: Overcoming apparent logical contradictions

work page
[13]

Evidences

Disambiguation: Overcoming the Turin g Test through the challenge of the Winograf schemes. Evidences

work page
[14]

Deep Blue , chess and regulated systems to which the Theorem of Lowenheim-Skolem applies (legislations, regulations, etc.) whose paradigmatic example is the one reviewed Deep Blue, that the year 1997 won to Kasparov

work page 1997
[15]

Deep Mind in 2014, found a way to maximize the score in the game of Atari Breakout, not predicted by humans, through deep learning, from scratch (Mnih, 2015)

work page 2014
[16]

Movement 5 confirme d the goodness of the choice of AlphaGo , which also combined , holistically,deep learning and logical GOFAI (D

AlphaGo: AI that gave clear signs of intuition and creativity, in its confrontation with the world champion of Go Lee Sedol to which he won, in movement 37 when placing a chip on line 5, when humans be lieved the best play in the ranks 3 or 4. Movement 5 confirme d the goodness of the choice of AlphaGo , which also combined , holistically,deep learning an...

work page 2016
[17]

AlphaZero. In 2017, this new AI completely ignored centuries of human experience in Go, including millions of games, learning from scratch, turning fiction into reality by emulating the 5 character of Zweig, Doctor B (Zweig, 1943), playing against himself. AlphaZero, not only won the Go to AlphaGo, but also ran in his confrontation with the best chess pro...

work page 2017
[18]

This AI program, Texas Holdem, in 2017, beat four professional poker`s gammer without break, it tooks 20 days by 14 hours a day, w inning $ 1,700,000 of the $ 2,000,000 at stake

Libratus. This AI program, Texas Holdem, in 2017, beat four professional poker`s gammer without break, it tooks 20 days by 14 hours a day, w inning $ 1,700,000 of the $ 2,000,000 at stake. The important thing about poker is that the number of moves, superior to chess, is joined by chance in the distribution of cards, and its characteristic of deception an...

work page 2017
[19]

In 1996, the proof program of theorems EQP (McCune, 1997) proved, creatively, converting it into a theorem, the Robbins Conjecture, until then an important open problem

work page 1996
[20]

The contest lasted three days and the victory of Watson was overwhelming winning three times more money than his opponents

In 2011, Watson won the TV show ABC Jeopardy, facing the two humans who held the record of consecutive victories and accumulated money. The contest lasted three days and the victory of Watson was overwhelming winning three times more money than his opponents. Table 1. Sorts and Evidence used for the test experiment

work page 2011
[21]

Table 2 shows the total of the probabilities, assigned a priori, to each evidence in each sort, then the Bayes theorem has been applied to them

Results and conclusions. Table 2 shows the total of the probabilities, assigned a priori, to each evidence in each sort, then the Bayes theorem has been applied to them. With these results, a sum of totals was made for each class and for each evidence. Finally, the final probability has been obtained. Lessons Evidences S1 S2 S3 S4 S5 S6 S7 S8 S9 Ev1 0.500...

work page
[22]

Bayes, T.: An Essay Toward Solving a Problem in the Doctrine of Chances

Bibliography. Bayes, T.: An Essay Toward Solving a Problem in the Doctrine of Chances . Philosophical Transactions of the Royal Society London, 53. 1763. PP: 370-418. Bronowsky , J .:The Ascendent Man: A Personal View. BBC Press London, UK 1973 Chalmers, A .: What is this thing called science? University of Quensland Press. Queensland, Australia. 1999. D....

work page 1973
[23]

Neumann, J

pp: 529-533. Neumann, J. von: Theory of Self -Reproducing Automata. AW Burks (Ed.) University of Illinois Press. Urban Ill. 1966 Pazos, J.: Artificial Intelligence: Heuristic programming. Paraninfo SA Madrid. 1987 7 Peirce, CS: On the Natural Classification of Arguments . Proceedings of American Academy of Arts and Sciences, Vol. 7. 1867. pp: 284-312. Pol...

work page 1966
[24]

Tegmark, M .: Life 3.0.Being Human in the Age of Artificial Intelligence

pp: 252-263. Tegmark, M .: Life 3.0.Being Human in the Age of Artificial Intelligence. Alfred A. Knopf Borzoi Books. Penguin Random House, LLC. New York, NY. 2017. Turing, AM: Lecture to the London Mathematical Society on February, 20 th. 1947. In, BE Carpenter, RW Dosan (Eds.): AM Turing's ACE Reports of 1946 and others papers. MIT press. Cambridge, Mass...

work page 2017

[1] [1]

Abstract. The Technological Singularity; that is, the possibility of achieving a General Artificial Intelligence (AGI) that surpasses human intelligence, is one of the vital paradigms of today's humanity. However, until now only opinions about its possibility and/or achievement were issued, therefore, in this work, a metric is presented, for the first tim...

work page

[2] [2]

arithmeticly

Introduction. In the 19th century, machines began to replace humans as physical workers. For many people, this was a blessing, despite the occasional resistance to change led by the Luddites –a secret sect of English textile workers in England who opposed textile machinery -. Another mythical story portraits, in the mid -19th Century, in the USA, a challe...

work page 1915

[3] [3]

singularity

State of Art: Technological Singularity. Contrary to some recent publications (Tegmark, 2017), the term and especially the concept of, "singularity" has a long and substantial history behind. For instance, Condorcet (Condorcet, 1795) was the first to account for a singularity in the human intellectual faculties. Subsequently, Peirce (Peirce,

work page 2017

[4] [4]

singularity

wondered how much knowledge could be done by machines and how much should be left for humans. Turing, in 1948 (Mitchie, 1998-2004), (Turing, 1948), (Turing, 1950) (Turing, 1952), wrote about intelligent machines. However, the first explicit use, in the technological context, of the term “singularity” was reported in 1957 and its author was von Neumann (Ul...

work page 1948

[5] [5]

Deep Blue

The proposed solution. 3 George Polya (Polya, 1954) systematized a series of reasoning patterns that are usually followed in the research processes in the natural sciences, in the creation mathematics, in judicial and police investigations, in the diagnosis medical, etc .:The plausible reasoning. Its formal expression is: If A then B B____________________...

work page 1954

[6] [6]

Holism: Ability to integrate intelligent elements from a lower level to build a higher level intelligence

work page

[7] [7]

Learning: Acquire knowledge continuously, from all available sources and incorporate them into an integrated and congruent whole

work page

[8] [8]

Creativity: Capacity of imagination, intuition and invention

work page

[9] [9]

Teleology: Search for purposes

work page

[10] [10]

Reasoning and inference: Abductive, deductive and inductive, and anterogado

work page

[11] [11]

Proactivity: Initiative to detect interesting problems

work page

[12] [12]

Enantiodromia: Overcoming apparent logical contradictions

work page

[13] [13]

Evidences

Disambiguation: Overcoming the Turin g Test through the challenge of the Winograf schemes. Evidences

work page

[14] [14]

Deep Blue , chess and regulated systems to which the Theorem of Lowenheim-Skolem applies (legislations, regulations, etc.) whose paradigmatic example is the one reviewed Deep Blue, that the year 1997 won to Kasparov

work page 1997

[15] [15]

Deep Mind in 2014, found a way to maximize the score in the game of Atari Breakout, not predicted by humans, through deep learning, from scratch (Mnih, 2015)

work page 2014

[16] [16]

Movement 5 confirme d the goodness of the choice of AlphaGo , which also combined , holistically,deep learning and logical GOFAI (D

AlphaGo: AI that gave clear signs of intuition and creativity, in its confrontation with the world champion of Go Lee Sedol to which he won, in movement 37 when placing a chip on line 5, when humans be lieved the best play in the ranks 3 or 4. Movement 5 confirme d the goodness of the choice of AlphaGo , which also combined , holistically,deep learning an...

work page 2016

[17] [17]

AlphaZero. In 2017, this new AI completely ignored centuries of human experience in Go, including millions of games, learning from scratch, turning fiction into reality by emulating the 5 character of Zweig, Doctor B (Zweig, 1943), playing against himself. AlphaZero, not only won the Go to AlphaGo, but also ran in his confrontation with the best chess pro...

work page 2017

[18] [18]

This AI program, Texas Holdem, in 2017, beat four professional poker`s gammer without break, it tooks 20 days by 14 hours a day, w inning $ 1,700,000 of the $ 2,000,000 at stake

Libratus. This AI program, Texas Holdem, in 2017, beat four professional poker`s gammer without break, it tooks 20 days by 14 hours a day, w inning $ 1,700,000 of the $ 2,000,000 at stake. The important thing about poker is that the number of moves, superior to chess, is joined by chance in the distribution of cards, and its characteristic of deception an...

work page 2017

[19] [19]

In 1996, the proof program of theorems EQP (McCune, 1997) proved, creatively, converting it into a theorem, the Robbins Conjecture, until then an important open problem

work page 1996

[20] [20]

The contest lasted three days and the victory of Watson was overwhelming winning three times more money than his opponents

In 2011, Watson won the TV show ABC Jeopardy, facing the two humans who held the record of consecutive victories and accumulated money. The contest lasted three days and the victory of Watson was overwhelming winning three times more money than his opponents. Table 1. Sorts and Evidence used for the test experiment

work page 2011

[21] [21]

Table 2 shows the total of the probabilities, assigned a priori, to each evidence in each sort, then the Bayes theorem has been applied to them

Results and conclusions. Table 2 shows the total of the probabilities, assigned a priori, to each evidence in each sort, then the Bayes theorem has been applied to them. With these results, a sum of totals was made for each class and for each evidence. Finally, the final probability has been obtained. Lessons Evidences S1 S2 S3 S4 S5 S6 S7 S8 S9 Ev1 0.500...

work page

[22] [22]

Bayes, T.: An Essay Toward Solving a Problem in the Doctrine of Chances

Bibliography. Bayes, T.: An Essay Toward Solving a Problem in the Doctrine of Chances . Philosophical Transactions of the Royal Society London, 53. 1763. PP: 370-418. Bronowsky , J .:The Ascendent Man: A Personal View. BBC Press London, UK 1973 Chalmers, A .: What is this thing called science? University of Quensland Press. Queensland, Australia. 1999. D....

work page 1973

[23] [23]

Neumann, J

pp: 529-533. Neumann, J. von: Theory of Self -Reproducing Automata. AW Burks (Ed.) University of Illinois Press. Urban Ill. 1966 Pazos, J.: Artificial Intelligence: Heuristic programming. Paraninfo SA Madrid. 1987 7 Peirce, CS: On the Natural Classification of Arguments . Proceedings of American Academy of Arts and Sciences, Vol. 7. 1867. pp: 284-312. Pol...

work page 1966

[24] [24]

Tegmark, M .: Life 3.0.Being Human in the Age of Artificial Intelligence

pp: 252-263. Tegmark, M .: Life 3.0.Being Human in the Age of Artificial Intelligence. Alfred A. Knopf Borzoi Books. Penguin Random House, LLC. New York, NY. 2017. Turing, AM: Lecture to the London Mathematical Society on February, 20 th. 1947. In, BE Carpenter, RW Dosan (Eds.): AM Turing's ACE Reports of 1946 and others papers. MIT press. Cambridge, Mass...

work page 2017