Complexity in the Wake of Artificial Intelligence

Theodore Modis

REVIEW 3 major objections 4 minor 4 references

Complexity in the Wake of Artificial Intelligence

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The human system's complexity has reached its peak and will now decline, with the next major milestone due around 2050–2052.

desk verdict A readable, honest extension of Modis's own logistic model that gives specific forecasts for the peak and decline of human complexity, but the equal-importance assumption in the core measurement equation is load-bearing and unvalidated, so the central claim is plausible but not established. read the letter →

arxiv 2506.04269 v2 pith:7MJCP6TV submitted 2025-06-03 physics.soc-ph physics.app-ph

Theodore Modis This is my paper

classification physics.soc-phphysics.app-ph

keywords complexityentropylogisticgrowthevolutionarymilestonesartificialintelligencebabyboomworldpopulationtechnologicalforecasting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish quantitatively that the complexity of the human system has traced a bell-shaped curve across 700,000 years and is now at its top, about to start declining. It derives complexity values from the timing of 14 canonical evolutionary milestones, from the domestication of fire to AI in 2023, taking each milestone's added complexity to be inversely proportional to the time until the next milestone. A logistic life-cycle fit to those values places the maximum at the present and forecasts the next milestone of comparable importance around 2050–2052, adding less complexity than AI but more than nuclear energy, DNA, and the transistor combined. If the forecast is right, complexity will keep arriving at longer and longer intervals, and the baby-boom generation's lifespan coincides with the peak.

What carries the argument

The central object is the canonical milestone sequence together with the inverse-time rule of Equation (1), $\Delta C_i = I/\Delta T_i$, which assigns each milestone a complexity equal to a constant importance divided by the wait until the next milestone. That rule transforms a list of event dates into a quantitative complexity series, and the paper fits this series to the logistic life cycle—the derivative of the logistic function—using the sequential milestone number as the time axis. The governing identity is that if entropy follows an S-shaped curve, complexity, being its time derivative, follows a bell-shaped curve; the fitted bell then yields both the current peak and, through the same inverse-time rule, the dates at which future milestones should appear.

What would settle it

A concrete falsifier would be a clearly canonical milestone arriving before 2050 whose inverse-time complexity is larger than the fitted declining curve predicts; alternatively, recomputing the fit with only the six most recent milestones and showing the implied peak shifts by more than a generation would undercut the forecast.

Watch

Extended reading notes

Core claim

The paper's central claim is that complexity grows on a unimodal curve: it rose through human history, reaches its maximum around the present, and then falls. With the inverse-time rule $\Delta C_i = I/\Delta T_i$, where $I$ is a shared importance and $\Delta T_i$ the interval to the next canonical milestone, the paper converts the 14 milestone dates into a sequence of complexity increments, then fits those increments to the derivative of a logistic function on a milestone-number axis, obtaining $R^2 \approx 0.985$ for all milestones and 0.980 for major milestones. The fit puts the peak of complexity at the present day, assigns the 15th canonical milestone to 2050–2052 with a lower complexity increment than AI, and says the next increments will be progressively smaller. The paper also claims the declining branch is consistent with entropy being an S-shaped curve and complexity its derivative, that the complexity peak falls inside the baby-boom generation's lifespan, and that the peak in world population growth preceded the complexity peak by about 25 years.

Load-bearing premise

The load-bearing premise is that the 14 canonical milestones are approximately equal in importance, so each one's added complexity is a shared constant divided by the time to the next milestone; if some milestones matter more than others, the complexity values and the forecasts shift.

Editorial extensions

If this is right

Future evolutionary milestones will arrive at increasingly longer intervals and will each add less complexity than the one before it.
The world population growth rate, which peaked around 1997, acts as a leading indicator: complexity and innovation should decline roughly 25 years after a peak in population growth.
The baby-boom generation will have lived through the full complexity peak, making its members witnesses to more historical complexity than any generation before or after.
Slowing the rate of change of complexity—through practices like minimalism, slow living, or degrowth—should flatten the bell curve and yield a larger cumulative complexity over a longer period.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural test of the equal-importance assumption would be to reweight the 14 milestones using expert surveys or archival frequency data and see whether the bell-shaped fit and the 2050–2052 forecast survive.
If complexity is generally the derivative of entropy, the same bell shape should be observable in other large coupled systems, so one could search for analogous 25-year demographic leads in technological or ecological time series before 1950.
The proposed link between population growth rate and innovation suggests country-level predictions: nations whose working-age population is now shrinking should show a measurable decline in milestone-class inventions within roughly a generation.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is a clear and candid extension of Modis's earlier logistic-growth work on complexity. New here: AI is treated as milestone 14, the dataset is updated, and the forecasts are specific—peak complexity around now, next milestone 2050–2052, baby-boom overlap, and a 25-year lead of world population growth. The writing is transparent, the data are in an appendix, and the logistic fits are decent (R² ≈ 0.98). The robustness section honestly acknowledges subjectivity and historical perspective bias. Credit where due: the paper does not hide its warts.

The soft spot is exactly what the stress-test note says, and it is the crux. Equation (1) defines the complexity values that are then fitted: ΔC_i = I/ΔT_i, with a single importance I for all 14 canonical milestones. The paper itself says some milestones are "obviously more important than others" and then proceeds to approximate them as equal. The later discussion tries to defuse this by arguing that the fit is dominated by recent milestones, but those are precisely the ones where importance varies most (Internet vs. AI vs. modern physics). No sensitivity analysis is offered, and systematic errors are explicitly disclaimed. So the fitted peak location and the 2050 date are outputs of the equi-importance assumption, not robust measurements.

Also, the complexity the paper lists for AI is not a data point—it is read off the fitted curve. That is a forecast, not a measurement, and it is presented as both. The declining half of the bell curve is entirely extrapolation from the assumed logistic life cycle. The author is upfront that complexity is taken to be the derivative of entropy, but that relationship is argued qualitatively and not derived from fundamentals. So the central claim, that complexity has peaked and will now decline, is a model output, not an empirical finding.

That said, the paper is not incoherent or dishonest. It is a provocative, well-written piece of quantitative futurology. Who gets value from it? Researchers in futures studies, complexity, and maybe demography who want a concrete, citable model with explicit dates. It deserves a serious referee—the methodology is specific, the data are available, and the forecast is falsifiable in principle. But a solid referee would push hard for a sensitivity analysis that varies the importance weights, or at least a more rigorous defense of equi-importance. My own verdict is skeptic, but I would send it out rather than desk-reject.

Referee Report

3 major / 4 minor

Summary. This paper constructs a quantitative measure of 'complexity' for human evolution by assigning equal importance to 14 canonical milestones and setting ΔC_i = I/ΔT_i (Eq. 1). It fits a logistic life-cycle (Eq. 2) to the first 13 complexity values, obtains a peak near milestone 13.75 (present), and forecasts that AI's complexity contribution is 0.0350 with the next comparable milestone around 2050-2052 (Table III). The paper then links this bell-shaped curve to the baby-boom generation and to the rate of growth of world population, and recommends flattening the complexity curve.

Significance. The forecast is potentially striking, and the paper has some virtues: the data are tabulated in Appendix A, fit parameters and goodness-of-fit statistics are reported, and two versions (all milestones and major milestones) give similar results. The comparison with the 2002 study is a useful consistency check. However, the quantitative machinery rests on two unvalidated choices: the equal-importance assumption in Eq. (1) and the logistic-derivative functional form in Eq. (2). The paper does not provide sensitivity analyses for these choices, and its own text acknowledges that some milestones are 'obviously more important than others' and that the complexity-entropy derivative relation 'cannot be rigorously generalized.' Under the stated assumptions the arithmetic may be correct, but the paper does not establish that its complexity values are measurements rather than definitions.

major comments (3)

[Section 3, Eq. (1)] The assumption that all 14 canonical milestones are of equal importance is asserted without independent support and is contradicted by Section 2, which states that among the milestones 'some of them obviously more important than others.' Since every data point fitted by Eq. (2) is defined as I/ΔT_i, any variation in true milestone importance changes the complexity values and therefore the fitted peak (x0 ≈ 13.75) and all Table III forecasts. No sensitivity analysis is provided, and Section 4 explicitly disclaims systematic error estimation; this makes the central claim unsupported.
[Section 3.1 and Table III] The paper states that the complexity of the 14th milestone (AI) cannot yet be calculated because the date of the 15th milestone is unknown, yet Table III lists a complexity of 0.0350 for AI in 2023 and derives future dates. The inversion of Eq. (1) to turn forecast complexity into inter-milestone intervals requires a numerical value for the arbitrary constant I, but I is never reported or calibrated; the paper should show, for example, how I is fixed by milestone 13 and how uncertainty in that calibration propagates to the 2050 date.
[Section 3 and Eq. (2)] The logistic life-cycle is adopted because complexity is asserted to be the derivative of entropy, but Section 5 itself notes that this relation 'cannot be rigorously generalized in all cases.' With only 13 data points and the entire declining branch outside the fitted range, the high R² on the rising branch does not validate the extrapolated decline or the 2050-2052 forecast; the fit is a model of the data under the assumed form, not a test of the form.

minor comments (4)

[Tables I and II] The displayed algebraic expression for the fitted function is garbled in the PDF (the denominator and the exponential terms are not rendered correctly); the reader cannot verify Eq. (2) from the table headers.
[Section 5.1] The statement that the baby-boom span 'coincides squarely' with the complexity peak is a post-hoc visual alignment; no quantitative test of the overlap is given, and the life-expectancy assumption of 80 years is arbitrary.
[Section 4.1] The discussion of remembering and forgetting is a useful caveat, but the claim that selecting only the highest-importance milestones makes the timing immune to the perception bias is itself an assumption; the text should flag it as such.
[References] The reference list contains typos: 'Edenm A. H. et al' should be 'Eden, A. H. et al.' and 'Hubermann and Hog' should be 'Huberman and Hogg.'

Circularity Check

3 steps flagged · score 6.0 of 10

The complexity measure is defined by Eq. (1) as the reciprocal of inter-milestone intervals, and the logistic-life-cycle model is imported from the author's own prior entropy-derivative claim, so the 2050 forecast and the peak/decline conclusion are partly restatements of the fitted assumptions.

self citation load bearing [Section 3 (Eq. (2)); Section 5; refs [Modis, 2022, 2024]]
"Given that our data depict a rate of growth – i.e. complexity change per milestone – we expect their trend to follow the time derivative of the logistic function, i.e. the logistic life cycle. We therefore fit to the expression: f′(x)=... With information-related definitions for entropy and complexity, a simple mathematical relationship between them has been established, namely the latter being the time derivative of the former. It follows that if entropy traces out an S-shaped curve, complexity will trace out a bell-shaped curve.[Modis, 2022, 2024]"

The declining branch of the fitted curve is not present in the 13 data points, which increase monotonically as inter-milestone intervals shorten; the peak and the decline are produced by the logistic form. That form is justified by the claim that complexity is the time derivative of entropy, which is cited to two of the author's own prior papers and which the text admits cannot be rigorously generalized in all cases. Without that self-cited premise, Eq. (2) is an arbitrary ansatz, so the central conclusion (peak near x0 about 13.75 and decline after AI) rests on an unverified self-citation chain.
self definitional [Section 3, Eq. (1); Section 3.1, Table III]
"Assuming that milestones are approximately of equal importance, and according to the above definition of importance, we can conclude that the increase in complexity ΔCi associated with milestone i of importance Ι will be inversely proportional to the time period to the next milestone. We can thus quantify the complexity of milestone i as follows: Δ𝐶𝑖 = 𝐼 / Δ𝑇𝑖 (1) ... The forecasted complexity of future milestones can be translated to dates using Equation (1)."

The quantity being fitted, ΔC_i, is not an independent observable; it is defined as I divided by the interval to the next milestone. The forecast dates for milestones 15-19 are then computed by inverting exactly this defining equation. Consequently, the 2050-2052 date and the claim that the next milestone adds less complexity than AI are not independent predictions: they are the reciprocal of the extrapolated curve fitted to reciprocals of the input intervals. The only substantive input, the equality of I across milestones, is asserted without independent support and even contradicted by the text's own statement that some milestones are obviously more important than others.

1 more flagged steps

self definitional [Sections 1 and 5; refs [Modis, 2022]]
"entropy reflects the accumulation of complexity.[Modis, 2022] ... With information-related definitions for entropy and complexity, a simple mathematical relationship between them has been established, namely the latter being the time derivative of the former. It follows that if entropy traces out an S-shaped curve, complexity will trace out a bell-shaped curve.[Modis, 2022, 2024]"

If entropy is defined as the accumulation of complexity, then saying that complexity is the derivative of entropy is true by definition; it is not an empirical regularity that can independently support a bell-shaped forecast. The paper uses this self-cited identity to move from an assumed S-shaped entropy to the logistic-life-cycle fit, so the conclusion of a present peak and imminent decline is built into the definitions and the self-cited relationship rather than derived from measured complexity data.

full rationale

The paper is not wholly without content: it compiles milestone dates, fits them, and compares the resulting curve with baby-boom and population data. However, the central quantitative chain is partially circular. Equation (1) defines the complexity data from the same inter-milestone intervals that the forecast dates recover by inversion, so the Table III dates are a restatement of the fitted curve under the equi-importance assumption. The choice of the logistic life cycle is justified by the complexity-is-the-derivative-of-entropy relation, which is imported from the author's prior work and is conceded to be non-rigorous in general; the data themselves show only an increasing trend, so the declining branch and the 'peak now' conclusion come from that self-cited model assumption. The population and baby-boom correlations are external but do not validate the complexity measure. Because the central claim depends on a self-citation chain and on definitionally constructed data, a score of 6 reflects partial circularity rather than a completely equivalent derivation.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central quantitative outputs, including the location of the complexity peak and the 2050-2052 forecast, depend on three fitted logistic parameters, the assumed equal importance of milestones, and the subjective choice of milestone dates. No new physical entities are introduced, but the empirical grounding is weak because the data are selected and the model form is assumed rather than independently validated.

free parameters (7)

M (all milestones) = 0.1945
Fitted in Table I to the 13 canonical complexity values; sets the overall scale of the bell-shaped complexity curve.
alpha (all milestones) = 0.7907
Fitted in Table I; controls the width and steepness of the complexity curve and strongly influences the forecast dates.
x0 (all milestones) = 13.75
Fitted in Table I; places the complexity peak just after milestone 13, which implies decline begins after AI.
M (major milestones) = 0.8119
Fitted in Table II for the major-milestone subset; used as a robustness check.
alpha (major milestones) = 0.1849
Fitted in Table II for the major-milestone subset; used as a robustness check.
x0 (major milestones) = 13.71
Fitted in Table II for the major-milestone subset; used as a robustness check.
I (common milestone importance) = arbitrary units, assumed equal for all milestones
Introduced in Equation (1) to convert complexity values into time intervals. It is not measured or fitted independently; the paper assumes equal importance across the 14 canonical milestones.

assumptions (5)

domain assumption Entropy grows monotonically along an S-shaped logistic curve, and complexity is the time derivative of entropy, so complexity must be bell-shaped.
Invoked in Sections 3 and 5 to justify fitting the logistic life cycle. This thermodynamic analogy is applied to human social history without independent evidence.
ad hoc to paper The 14 canonical milestones are of comparable importance, so the complexity added by each can be written as I divided by the time to the next milestone.
Appears in Section 3, Equation (1). Without this approximation, the complexity values entering the fit have no quantitative meaning.
domain assumption The selected milestone dates, defined as when impact began to be felt, are accurate enough for quantitative fitting.
Stated in Section 2. The dates come from a subjective compilation by the author, Nobel laureates, and ChatGPT, and only statistical errors are estimated.
domain assumption Milestones before the Renaissance follow a purely exponential trend and do not bias the bell-shaped fit.
Discussed in Section 4. The fit is heavily influenced by the six most recent milestones, so the older data do little to constrain the peak or the decline.
domain assumption The logistic function is the correct natural-growth curve for accumulated human complexity.
Stated in Section 3 as 'it is reasonable that a logistic function could be suitable.' No alternative functional forms are tested against the same data.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Complexity in the Wake of Artificial Intelligence." pith.science (2026). https://pith.science/paper/7MJCP6TV

@misc{pith2026250604269,
  author       = {Pith},
  title        = {Pith review of: Complexity in the Wake of Artificial Intelligence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7MJCP6TV}},
  note         = {Machine review of arXiv:2506.04269}
}

read the original abstract

This study aims to evaluate quantitatively, albeit in arbitrary units, the evolution of complexity of the human system since the domestication of fire. This is made possible by studying the timing of the 14 most important milestones, breaks in historical perspective, in the evolution of humans. AI is considered here as the latest such milestone with importance comparable to that of the Internet. The complexity is modeled to have evolved along a bell-shaped curve, reaching a maximum around our times, and soon entering a declining trajectory. According to this curve, the next evolutionary milestone of comparable importance is expected around 2050 and should add less complexity than AI but more than the milestone grouping together nuclear energy, DNA, and the transistor. The peak of the complexity curve coincides squarely with the life span of the baby boomers. The peak in the rate of growth of the world population precedes the complexity peak by 25 years, which is about the time it takes a young man or woman before they are able to add complexity to the human system in a significant way. It is in society's interest to flatten the complexity bell-shaped curve to whatever extent this is possible in order enjoy complexity longer.

Figures

Figures reproduced from arXiv: 2506.04269 by the authors.

**Figure 1.** A histogram of the 128 milestones with geometrically increasing time bins as we go back in time. The thin black line is superimposed to outline the peaks that define the dates of the “canonical” milestone set. On the horizontal axis, we read the dates of these peaks determined as described in the text. The breadth of each cluster helps define the error on each date. 2.2 The major milestones In [PITH_FULL_IMAGE:figu… view at source ↗

**Figure 2.** A histogram of 56 major milestones with geometrically increasing time bins as we go back in time. On the horizontal axis, we read the average date of the milestones in each bin. There is no overlap between adjacent milestones. 3. The Analysis It is easy to quantify the complexity of a simple system like a fair dice.[Modis, 2024] But it seems hopelessly unrealistic to quantify complexity for humans and their environm… view at source ↗

**Figure 2.** [ [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗

Figures from the paper (1 more)

**Figure 7.** Figure 7: The gray line is a logistic fit to the world population data (black dots.) We can now compare in [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

4 extracted references · 3 canonical work pages

[1]

Aaronson, S., Carroll, S., Ouellette, L. (2014). Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton. Cornell University arXive. https://www.researchgate.net/publication/262677209 Adami C. (2002). What is complexity? Bioessays 24, pp 1085–1094 Bostrom, N. (2014). Superintelligence: Paths, Dangers, Strategies (p. 352). Oxfor...

work page arXiv 2014
[109]

A., Hogg, T

Huberman, B. A., Hogg, T. (1986). Complexity and Adaptation. Physica D. 22, 376-384. Kauffman, S. A. (1993): The Origins of Order: Self Organization and Selection in Evolution. Oxford University Press. Kauffman, S. (1995). At Home in the Universe: The Search for the Laws of Self-Organization and Complexity (1st ed., p. 336). Oxford University Press. Kelly...

1986
[176]

https://doi.org/10.1016/j.techfore.2021.121457 Modis, T. (2024). The Relationship between Entropy and Complexity Quantitatively: The Case of Throwing a Fair Dice in the Very Long Run. Journal of Biological Physics and Chemistry 24, 124–129 doi:10.4024/22MO23A.jbpc.24.3/4. Preprint archived at https://osf.io/bxr3h/. Sagan, C. (1986). The Dragons of Eden: S...

work page arXiv 2024
[1995]

Scientific American, 272 (6), June 1995, 104-

From Complexity to Perplexity. Scientific American, 272 (6), June 1995, 104-

work page 1995

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Aaronson, S., Carroll, S., Ouellette, L. (2014). Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton. Cornell University arXive. https://www.researchgate.net/publication/262677209 Adami C. (2002). What is complexity? Bioessays 24, pp 1085–1094 Bostrom, N. (2014). Superintelligence: Paths, Dangers, Strategies (p. 352). Oxfor...

work page arXiv 2014

[2] [109]

A., Hogg, T

Huberman, B. A., Hogg, T. (1986). Complexity and Adaptation. Physica D. 22, 376-384. Kauffman, S. A. (1993): The Origins of Order: Self Organization and Selection in Evolution. Oxford University Press. Kauffman, S. (1995). At Home in the Universe: The Search for the Laws of Self-Organization and Complexity (1st ed., p. 336). Oxford University Press. Kelly...

1986

[3] [176]

https://doi.org/10.1016/j.techfore.2021.121457 Modis, T. (2024). The Relationship between Entropy and Complexity Quantitatively: The Case of Throwing a Fair Dice in the Very Long Run. Journal of Biological Physics and Chemistry 24, 124–129 doi:10.4024/22MO23A.jbpc.24.3/4. Preprint archived at https://osf.io/bxr3h/. Sagan, C. (1986). The Dragons of Eden: S...

work page arXiv 2024

[4] [1995]

Scientific American, 272 (6), June 1995, 104-

From Complexity to Perplexity. Scientific American, 272 (6), June 1995, 104-

work page 1995