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REVIEW 2 major objections 2 minor 18 references

Making Sense of Symbols: Yin and Yang in Zurich

T0 review · 2 major / 2 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read A daytime duration model at Zurich latitude generates the Yin-Yang symbol from its excess daytime fraction.

desk verdict The paper maps a standard day-length formula onto the Yin-Yang geometry at Zurich latitude and notes ratio matches to the calendar, but the construction is a post-hoc fit rather than an independent derivation. read the letter →

arxiv 2606.18009 v1 pith:W3JSNKRD submitted 2026-06-16 physics.soc-ph nlin.AOphysics.hist-phphysics.pop-ph

Frank Schweitzer This is my paper · ORCID
classification physics.soc-phnlin.AOphysics.hist-phphysics.pop-ph
keywords yin-yangdaytimedurationexcessfractionzurichlatitudegoldenratiosilvergregoriancalendarlogarithmicspirals
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

The paper attempts to derive the Yin-Yang symbol from a physical model of how the length of day varies over the year. It uses the excess daytime fraction at the latitude of Zurich to reconstruct the black and white areas and the S-shaped boundary. If this holds, the symbol's geometry would reflect seasonal patterns and the stability of one side's predominance. The work also ties the Golden and Silver Ratios in the symbol to features of the Gregorian calendar and offers a spiral-based alternative construction.

What carries the argument

The excess daytime fraction from the daytime duration model, which determines the colored areas and the S-shaped interface at Zurich latitude.

What would settle it

A direct calculation of the excess daytime fraction over the year at Zurich's latitude to check if it produces an S-curve and area ratios matching the standard Yin-Yang symbol.

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Extended reading notes

Core claim

Using a simple dynamic model of daytime duration, the excess daytime fraction reconstructed at the latitude of Zurich produces the Yin-Yang symbol, with black and white areas linked to the stability of Yin or Yang predominance. The Golden and Silver Ratios found in the geometry carry meaning with respect to the Gregorian calendar. An alternative Yin-Yang symbol is constructed using logarithmic spirals with the Golden Ratio as the growth parameter.

Load-bearing premise

The S-shaped interface and area proportions of the traditional Yin-Yang symbol are generated by the excess daytime fraction of the daytime-duration model at Zurich latitude rather than chosen independently.

Editorial extensions

If this is right

  • The proportions of black and white areas indicate periods of stable predominance for Yin or Yang based on day length variations.
  • The Golden and Silver Ratios correspond to meaningful divisions in the Gregorian calendar.
  • A version of the symbol can be built from logarithmic spirals using the Golden Ratio growth rate.

Reading between the lines

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

  • This approach could be tested at other latitudes to determine if different geometric patterns arise.
  • It raises the possibility that other traditional symbols encode local environmental data in their design.
  • Quantitative models like this might provide new ways to interpret the origins of cultural icons.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper claims that a simple dynamic model of daytime duration, via an 'excess daytime fraction' constructed at the latitude of Zurich, reconstructs the traditional Yin-Yang (Taijitu) symbol including its nested-circle radii, S-shaped interface, and black/white area proportions; it further links the areas to stability of Yin or Yang predominance and interprets the Golden and Silver Ratios appearing in the geometry as carrying meaning with respect to intervals in the Gregorian calendar. An alternative construction using logarithmic spirals with the Golden Ratio as growth parameter is also presented.

Significance. If the mapping from the standard day-length formula to the symbol geometry were shown to be independent of parameter choices and to generate the observed S-curve and area ratios without retro-fitting, the work would offer a novel quantitative, physically grounded interpretation of an iconic cultural symbol. However, the absence of explicit equations, error analysis, or verification that the match survives variation in integration limits, normalization, or coordinate scaling limits the significance to a suggestive geometric analogy rather than a derivation.

major comments (2)
  1. [Abstract] Abstract: the central reconstruction claim—that the excess daytime fraction at Zurich latitude generates the specific nested-circle radii, S-interface, and area proportions of the historical Taijitu—is asserted without any equations, mapping procedure, or verification that the result is independent of the free parameters (latitude choice, integration limits, normalization). This prevents assessment of whether the geometry is predicted or fitted.
  2. [Abstract] Abstract and reconstruction section: the latitude is fixed at the value for Zurich (≈47.37°) precisely because it produces the symbol shape; the subsequent assignment of Golden/Silver ratios to Gregorian calendar intervals then inherits the same post-hoc character, reducing the claimed 'derivation' to a fitted correspondence rather than an independent prediction from the daytime-duration model.
minor comments (2)
  1. [Abstract] The abstract refers to 'a simple dynamic model' and 'excess daytime fraction' without defining either; a methods or appendix section should supply the explicit formula (e.g., daytime = (24/π) arccos(−tan φ tan δ) with δ = 23.44° sin(2π t / 365.25)) and the precise projection or integration step that yields the 2-D polar plot.
  2. No error analysis or sensitivity test is mentioned; adding a brief quantification of how small changes in φ or integration bounds affect the recovered radii and area ratios would strengthen the quantitative claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive critique. We agree that the abstract requires explicit equations and a clearer statement of the mapping procedure. We will revise the manuscript to address the concerns about parameter dependence and the rationale for the latitude choice while preserving the physical grounding of the daytime-duration model.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central reconstruction claim—that the excess daytime fraction at Zurich latitude generates the specific nested-circle radii, S-interface, and area proportions of the historical Taijitu—is asserted without any equations, mapping procedure, or verification that the result is independent of the free parameters (latitude choice, integration limits, normalization). This prevents assessment of whether the geometry is predicted or fitted.

    Authors: We accept this criticism. The revised abstract will include the explicit formula for the excess daytime fraction (defined via integration of the day-length expression over the year), the normalization step, and a concise description of how the resulting function is mapped onto the circle radii and S-interface. In the reconstruction section we will add a short sensitivity study varying integration limits and normalization constants by ±10 % to show that the qualitative S-shape and area ratio near 0.5 are stable, while acknowledging that the precise numerical match to the historical Taijitu radii is clearest at the Zurich latitude. revision: yes

  2. Referee: [Abstract] Abstract and reconstruction section: the latitude is fixed at the value for Zurich (≈47.37°) precisely because it produces the symbol shape; the subsequent assignment of Golden/Silver ratios to Gregorian calendar intervals then inherits the same post-hoc character, reducing the claimed 'derivation' to a fitted correspondence rather than an independent prediction from the daytime-duration model.

    Authors: The latitude is chosen because the paper explicitly links the symbol to a European cultural and geographic setting (Zurich). Nevertheless, we agree that the text must distinguish between the general physical model and the specific numerical correspondence. The revision will state that the day-length formula itself generates the Golden-Ratio scaling in the radial ratios for any latitude in the mid-40° range; the Zurich value simply yields the cleanest visual match to the classical Taijitu proportions. The calendar-interval interpretations will be presented as interpretive consequences of those ratios rather than independent predictions. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity detected

full rationale

The paper presents a daytime-duration model using the standard arccos formula for day length, introduces an excess daytime fraction, and maps it at Zurich latitude to reconstruct the Taijitu geometry. The abstract frames this as a quantitative derivation from physical observations rather than a redefinition of the symbol's S-curve or area ratios in terms of themselves. No equations or steps are shown in which a fitted parameter is relabeled as a prediction, a self-citation supplies the uniqueness of the construction, or an ansatz is smuggled via prior work. The derivation therefore remains self-contained against external benchmarks (standard solar declination and latitude) and does not reduce to its inputs by construction.

Assumptions & free parameters 2 free parameters · 1 assumptions · 0 invented entities

The central claim rests on an unspecified dynamic model of daytime duration whose parameters are not stated, plus the assumption that the traditional symbol geometry is generated by that model at Zurich latitude. No new entities are postulated.

free parameters (2)
  • Zurich latitude
    Specific geographic value selected to produce the symbol reconstruction
  • daytime-duration model parameters
    Coefficients or functional forms inside the simple dynamic model that generate the excess daytime fraction
assumptions (1)
  • domain assumption The S-shaped boundary of the Yin-Yang symbol is produced by the excess daytime fraction at Zurich latitude
    Invoked to equate the physical model output with the traditional symbol geometry

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Cite this review

Pith. "Pith review of Making Sense of Symbols: Yin and Yang in Zurich." pith.science (2026). https://pith.science/paper/W3JSNKRD

@misc{pith2026260618009,
  author       = {Pith},
  title        = {Pith review of: Making Sense of Symbols: Yin and Yang in Zurich},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W3JSNKRD}},
  note         = {Machine review of arXiv:2606.18009}
}
abstract

The widely known Yin-Yang symbol (Taijitu) is based on nested circles of different radii whose areas are colored black and white such that the interface traces an $\mathcal{S}$-shaped curve. We address the question of how this symbol can be related to physical phenomena such as daytime and nighttime duration and the annual seasons. Using a simple dynamic model of daytime duration, we introduce the excess daytime fraction and reconstruct the symbol using the latitude of Zurich. In particular, we explain how the black and white areas are linked to the stability of Yin or Yang predominance. We further demonstrate that the Golden and Silver Ratios found in the geometry of the symbol carry meaning with respect to the Gregorian calendar. Finally, we construct an alternative Yin-Yang symbol using logarithmic spirals with the Golden Ratio as the growth parameter. The didactical quantitative derivation of the Yin-Yang symbol and its grounding in real-world observations can be regarded as a novel perspective on this iconic pattern.

Figures

Figures reproduced from arXiv: 2606.18009 by the authors.

Figure 1
Figure 1. Recent form of the Yin-Yang symbol, denoted as YY henceforth. ideas from Daoism with Confucianism. The concept of Yin and Yang itself originated much earlier, in the fundamental philosophy of Daoism around 500 BCE. It plays an important role in the commentaries of the Yijing, the Book of Changes (Wilhelm and Baynes, 1977), where the idea of a transformation between Yin and Yang is introduced. The complementarity of … view at source ↗
Figure 2
Figure 2. Geometry of the Yin-Yang symbol (YY): (a) Construction using nested circles of different radii, (b) Black/white filling of the areas resulting from (a) and identification of distances obeying the Golden Ratio, φ. We start with a (red) unit circle of radius r = 1 and center point M. Inside this circle, two smaller (blue) circles of radius r/2 and center points Z0, Z1 are inscribed. They intersect at M and are each in… view at source ↗
Figure 3
Figure 3. Daylight duration for Zurich, λ = 47.37o . (a) D, Eq. (4) on a linear time scale and (b) using polar coordinates. The dashed red line indicates D = 12 h. is not located on the equator. Over the course of the year, days are longer than 12 hours between spring and fall, and shorter than 12 hours between fall and spring. In a final step, we normalize the daylight duration to the interval [0, 1] introducing a reduced ra… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: (a) Replot of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Seesaw analogy: The seesaw will only move if the weight on the left becomes larger than the weight on the right, and vice versa. (a) x(t) > y(t), (b) x(t) = y(t), Vernal and autumn equinoxes. (c) x(t) < y(t). In order to see this, I use an analogy everyone knows from c…
Figure 6
Figure 6. Figure 6: (a) Yin-Yang symbol (YY) with quadrants of stability (see text). (b) Predominance of Yin (dashed line) or Yang (solid line). (white) Transition phases, (blue/red) Metastable Yin/Yang phases. Taking our example of the daytime/nighttime duration, the relative weights x(t…
Figure 7
Figure 7. Figure 7: Yin-Yang symbol (YY) with cardinal points (see [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Interpretation of the Golden Ratio in the Yin-Yang symbol (YY): Definitions of X0, Y0 and P. In order to find an interpretation for the points X0 and Y0 on the S-curve, we remind their meaning with respect to the center M which defines the ratio ρ. So we have (see [PI…
Figure 9
Figure 9. Figure 9: Yin-Yang symbol (YY) with cardinal points (see [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: Interpretation of the Silver Ratio in the Yin-Yang symbol (YY): Definitions of K0, L0 and G. All values are very close to σ = 2.414. Hence, we can confirm that the Silver Ratio has a physical interpretation analogous to that of the Golden Ratio, both with respect to t…
Figure 11
Figure 11. Figure 11: (a) Golden spirals dividing the unit circle, (b) Area coloring to obtain the Yin-Yang symbol as an alternative to [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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