Paisaje celeste y arqueoastronom\'ia: las iglesias hist\'oricas como indicadores de la planimetr\'ia de una ciudad ideal

Alejandro Gangui

REVIEW 3 major objections 3 minor 3 references

Paisaje celeste y arqueoastronom\'ia: las iglesias hist\'oricas como indicadores de la planimetr\'ia de una ciudad ideal

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read The grid of San Cristóbal de La Laguna is better explained by solar-oriented churches than by a Platonic ideal-city blueprint.

desk verdict A persuasive takedown of two over-the-top geometric theories of La Laguna's design, undermined by its own missing dataset and an untested histogram. read the letter →

arxiv 1908.09792 v1 pith:3MGMAMF6 submitted 2019-08-26 physics.hist-ph astro-ph.IM

Alejandro Gangui This is my paper · ORCID

classification physics.hist-phastro-ph.IM

keywords archaeoastronomychurchorientationurbanplanimetrySanCristóbaldeLaLagunaidealcitysolardeclinationcolonialurbanismCanaryIslands

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

San Cristóbal de La Laguna has often been described as an 'ideal city' founded in 1500 according to a precise geometric plan inspired by Plato's Laws and a Vitruvian eight-wind octagon. This paper tests that story with archaeoastronomical measurements of 21 historic churches and chapels. Their axes, converted into absolute astronomical declinations, produce a single prominent histogram peak just below 20°, which the author associates with the Sun's position on the feast of San Cristóbal (July 25 or July 10) at the founding epoch. On this basis the paper argues that the city's planimetry can be explained by simple, well-attested solar-orientation practices, making the earlier Platonic and geometric blueprints unnecessary.

What carries the argument

The machinery is the conversion of each church's doorway-to-altar axis into an absolute astronomical declination. In the field the author measures azimuth and horizon height; after removing local magnetic declination and atmospheric refraction, these local coordinates become a declination that is independent of the measuring site. Plotting the normalized histogram of absolute declination for the 21 churches reveals the dominant peak near 20°, which is then compared with the Sun's annual declination range and with the calendar of saints' feasts around the 1500 founding epoch. The histogram is the object that carries the argument.

What would settle it

Measure the axes of the city's original street grid from Torriani's 1588 plan and compare them with the 21 church axes; if the two sets of directions do not agree, the churches cannot serve as indicators of the planimetry. Alternatively, recover the pre-reconstruction orientations of the churches damaged by fire, such as the Cristo sanctuary before 1810 and Santa Clara before 1697: if the declination peak near 20° disappears when only original, unrebuilt axes are counted, the central claim collapses.

Watch

Extended reading notes

Core claim

The central discovery is that the orientation pattern of La Laguna's surviving historic churches is dominated by one solar declination, not by solstitial or equinoctial peaks. Measuring the axes of 21 churches and chapels from door to altar, correcting for magnetic and refraction effects, and plotting the normalized frequency of absolute declination yields a prominent peak at a declination just below 20°, close to the Sun's declination on the feast of San Cristóbal de Licia in the early sixteenth century. The author takes the churches, taken together, as indicators of the city's planimetry and concludes that the city's layout is adequately understood through ordinary archaeoastronomical principles. Consequently, the paper maintains, the proposed Platonic, Vitruvian, solstitial, or golden-triangle schemes lack support.

Load-bearing premise

The load-bearing premise is that the axes of the churches as they stand today faithfully record the original layout of the city from around 1500, even though several of these buildings were rebuilt or reoriented after fires and the paper does not demonstrate that their axes coincide with the street grid.

Editorial extensions

If this is right

If the interpretation is correct, La Laguna's regular grid should be understood primarily as the cumulative result of solar-oriented religious construction, not as the realization of a Platonic or Vitruvian master plan.
The solstitial and equinoctial alignments proposed by earlier authors would be subdominant features, not organizing principles, since the histogram shows them weaker than the peak just below 20°.
The feast of San Cristóbal, the city's patron, would be the most plausible calendrical anchor for the orientation pattern at the founding epoch.
The same orientation-based approach could be extended to other colonial Spanish towns with surviving historic churches to test whether their plans also follow solar alignments rather than ideal-city blueprints.

Reading between the lines

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

A testable extension the paper leaves implicit: check whether other early colonial towns dedicated to San Cristóbal show the same declination cluster near 20° in their churches; if they do, the pattern would suggest a broader regional convention for siting churches.
The paper never directly compares church axes to street-grid axes; a careful statistical comparison would either confirm the proxy assumption or reveal that churches and grid were oriented independently.
If each church's declination corresponds to a feast day, the width of the histogram leaves enough scatter that individual foundations cannot be dated precisely; a future high-precision survey of the surviving original buildings could sharpen the peak.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

You should read this one as a cautionary example of a good idea running ahead of its evidence. Gangui is right to be skeptical of the Navarro Segura Vitruvian octagon and the Herráiz Sánchez golden-triangle scheme; neither is backed by documents, and the church-axis data do suggest something less exotic. The paper does that part well, and the archaeoastronomical framing is clear and honest. He states straight out that the solar-orientation of churches is his starting hypothesis, which I respect. The historical summary is also useful if you don't know the La Laguna literature.

The problem is the positive claim. The whole case rests on Figure 5: a histogram of 21 absolute declinations with one peak just under 20°, which he ties to San Cristóbal's feast. But there is no table of measurements, no uncertainties, no stated binning, no significance test against uniform azimuth. With N=21, subtracting a uniform distribution from a histogram can create impressive-looking peaks by chance. The author himself calls the result 'sugerente' and admits the peak is not narrow enough to select a precise date. Then he offers two possible feast dates, July 10 or July 25, which makes the identification look post-hoc. The reader's concern about rebuilt churches is also real, but I agree with the stress-test that it is secondary: even perfectly preserved original axes would not rescue a peak that might be a binning artifact. And the paper explicitly says the full dataset is in a 'trabajo en preparación' (Gangui and Belmonte 2017), so the reader cannot check anything.

Where does that leave the paper? The historical critique stands; it is not original in the sense that many have doubted these schemes, but Gangui marshals the evidence well. The empirical contribution would be new if it held up, but as presented it is not yet a result. He needs to publish the axis table, horizon heights, final declinations, the binning rule, and a proper test against the uniform null. He should also address the rebuilt-church question directly, otherwise the chain from present-day axes to sixteenth-century planimetry stays unanchored.

If an editor sent me this, I would send it out for review, because the question is worth asking and the author is not a crank. But I would expect major revisions before publication: the quantitative core has to be put on the table. For your own use, it is a useful source for the skepticism of the geometric theories, but I would not cite the histogram result until the measurement paper appears.

Referee Report

3 major / 3 minor

Summary. El manuscrito de Gangui examina la planificación urbana de San Cristóbal de La Laguna (Tenerife) y critica las propuestas anteriores de un diseño geométrico basado en Platón, Vitruvio o la sección áurea. A partir de mediciones de orientación de 21 iglesias y ermitas históricas, el autor convierte los ejes a declinaciones astronómicas y presenta un histograma (Fig. 5) con un pico alrededor de 20°, que interpreta como la declinación solar en la fiesta de San Cristóbal (25 o 10 de julio) en la época fundacional. Concluye que la planimetría de la ciudad puede entenderse mediante principios simples de orientación solar, sin necesidad de hipótesis geométricas complejas. El artículo reconoce explícitamente que el pico no es lo suficientemente preciso y que el resultado es solo sugerente.

Significance. De ser robusto, el resultado ofrecería una explicación arqueoastronómica más parsimoniosa que las anteriores y conectaría la orientación de las iglesias con el trazado urbano. Sin embargo, la evidencia cuantitativa presentada es insuficiente: el histograma carece de barras de error, prueba de significación y especificación del procedimiento de normalización; el tamaño muestral es pequeño; y no se demuestra que las orientaciones actuales reflejen las originales. Por lo tanto, el valor principal es programático: señala una dirección de investigación, no una conclusión establecida.

major comments (3)

[Iglesias históricas como indicadores de la planimetría de la ciudad (Fig. 5)] La Figura 5 y el texto que la acompaña no especifican el ancho de los bins, el origen de los bins, ni el procedimiento exacto de la 'frecuencia relativa normalizada' que sustrae una distribución uniforme. Con N=21, un pico visual puede deberse a artefactos de binning, y no se ofrece ningún test estadístico (por ejemplo, Rayleigh, Kuiper o Monte Carlo) contra la hipótesis nula de ausencia de orientación preferente. Sin estos elementos, el pico a ~20° no puede considerarse una evidencia sólida de la orientación solar propuesta.
[Párrafo posterior a la Fig. 5 y sección Discusión] La identificación del pico con la fiesta de San Cristóbal es post-hoc: el propio autor admite que el pico no es lo suficientemente angosto para seleccionar una fecha precisa, y se ofrecen dos fechas posibles (10 y 25 de julio) y una época de fundación. No se presenta un cálculo de la declinación solar para esas fechas en el año 1500, ni una comparación con otras fechas candidatas dentro del rango que el histograma no puede excluir. La afirmación de que las orientaciones solsticiales y equinocciales son 'subdominantes' tampoco se basa en un test cuantitativo.
[Iglesias históricas como indicadores de la planimetría de la ciudad y descripción de las iglesias] El manuscrito no demuestra que los ejes actuales de las iglesias reconstruidas o remodeladas sean proxies fiables de la planimetría original. Por ejemplo, el Real Santuario del Cristo fue reconstruido tras el incendio de 1810 y el convento de Santa Clara tras el de 1697. Si estas orientaciones son decisiones posteriores, la inferencia desde el pico de declinación hacia el diseño de la ciudad de 1500 se debilita. El artículo debería analizar por separado las iglesias originales (como la Concepción) y las reconstruidas, o justificar por qué la reconstrucción preservó los ejes originales.

minor comments (3)

[Discusión] La conclusión final de que 'no hay necesidad de proponer hipótesis extrañas' es excesiva respecto a la evidencia presentada, que el propio autor califica de 'sugerente'.
[Referencias y datos] El texto se refiere a 'Gangui y Belmonte 2017, trabajo en preparación' como fuente de los datos completos; esto impide la verificación de los resultados. Se deberían incluir los datos en una tabla o apéndice, o al menos las incertidumbres de las mediciones.
[Fig. 5] La Figura 5 carece de etiquetas claras en los ejes y de una leyenda que explique las líneas verticales; la línea continua se identifica como solsticio y la discontinua como Luna, pero no se indican los valores exactos de declinación correspondientes.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured histogram is an independent empirical input, and the San Cristóbal interpretation is an explicitly cautious post-hoc comparison, not a construction-level reduction.

full rationale

The paper's derivation chain is: (1) field measurements of 21 church axes; (2) correction for magnetic declination and refraction and conversion to absolute astronomical declination; (3) a histogram of absolute declinations showing a prominent peak slightly below 20°; (4) comparison of that peak with the Sun's declination on the feast of San Cristóbal; (5) the suggestion that the city plan may be understood through simple solar-orientation principles. None of these steps reduces to its own input by construction. The hypothesis that churches are oriented with the Sun is explicitly declared as a starting assumption ('nuestra suposición de que las iglesias se orientan con el Sol (esa es nuestra hipótesis de partida)'), not as a conclusion derived from the data. The histogram peak is a measured feature; it is not generated by selecting the feast date. The identification of the peak with San Cristóbal is presented cautiously as 'podría estar asociado' and the paper concedes that the peak is 'no lo suficientemente preciso (angosto)' to select a precise date. This is a post-hoc interpretive comparison, not a formal derivation. The only notable self-citation is to Gangui y Belmonte 2017, listed as 'trabajo en preparación', but the present paper itself contains Figure 5 and describes the measurement procedure, so the central empirical claim does not reduce to that citation. Concerns about missing raw data, absence of a significance test, binning choices, and later rebuilding or reorientation of some churches are validity and robustness risks, not circularity. There is no equation, definitional identity, or fitted parameter renamed as a prediction that would make the central inference equivalent to its inputs.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical or conceptual entities; it reads an existing architectural ensemble as an archaeological record. The ledger is dominated by interpretive choices: which feast date to match to the peak, how to bin the histogram, and which assumptions (solar orientation, churches as planimetry proxies) carry the inference. No free parameters are fitted to data in the numeric sense, but the date selection and histogram construction are effective degrees of freedom.

free parameters (2)

Feast date and calendar epoch for the San Cristóbal identification = July 25 (or July 10), with an unspecified Julian/Gregorian treatment
The broad histogram peak near 20° does not determine a unique date; the author matches it to the patron's feast and offers two candidate dates in Fig. 5's caption, and the epoch astronomy is asserted without showing the calculation.
Histogram binning and baseline subtraction for Fig. 5 = not stated
The 'frecuencia relativa normalizada' is obtained by subtracting a uniform azimuth distribution, but the bin width, the number of bins, and the normalization are not specified; these choices determine whether a peak appears.

assumptions (3)

domain assumption Historic Christian churches are oriented toward solar-rising points; a church whose declination falls inside ±23.5° is treated as solar-oriented.
Stated explicitly in section 'Iglesias históricas como indicadores de la planimetría de la ciudad': 'nuestra suposición de que las iglesias se orientan con el Sol (esa es nuestra hipótesis de partida)'. This is the standard archaeoastronomical prior for Christian churches, but it is an assumption, not a demonstrated fact for La Laguna.
domain assumption Church axes measured today are reliable indicators of the city's original 1500 planimetry.
The paper uses the churches as 'elemento indicador de la planimetría de la ciudad' without showing that the axes align with the street grid, and despite several churches being rebuilt after fires (Cristo in 1810, Santa Clara in 1697). This premise is necessary for the conclusion about the city's design.
ad hoc to paper After subtracting a uniform distribution, the residual peak at ~20° with n=21 is meaningful without a significance test.
The paper draws its conclusion from the shape of the normalized histogram in Fig. 5 but reports no statistical test of the peak against the null hypothesis; with 21 data points, the peak's interpretation depends on this unstated statistical judgment.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Paisaje celeste y arqueoastronom\'ia: las iglesias hist\'oricas como indicadores de la planimetr\'ia de una ciudad ideal." pith.science (2026). https://pith.science/paper/3MGMAMF6

@misc{pith2026190809792,
  author       = {Pith},
  title        = {Pith review of: Paisaje celeste y arqueoastronom\'ia: las iglesias hist\'oricas como indicadores de la planimetr\'ia de una ciudad ideal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3MGMAMF6}},
  note         = {Machine review of arXiv:1908.09792}
}

read the original abstract

According to popular tradition, the Canarian city of San Cristobal de La Laguna, a World Heritage Site by UNESCO since 1999, emerged in the early sixteenth century with a novel organization, in line with a new peaceful social order inspired by the religious doctrine of the millennium and its expression through urban design [...] In this paper we briefly discuss some details of these ideas, which propose a planned geometric origin for the city, and the original sources on which they are based. We then look for other indications that in a simpler way might explain some of the notable characteristics of the order and design of La Laguna, where over time a model of traditional Canarian architecture was installed that, during the 17th century, was populated with civil and religious constructions (churches, chapels and convents) with notable creations in carpentry of Mudejar origin, for example coming from the lower Andalusia. To conclude, we show our precise analysis of the orientation of almost all the historical churches and chapels of the city, taken together as an indicator of its planimetry. This study employs the usual tools of archaeoastronomy as a complement to the historical and cultural research of religious constructions. We will see then that a new -- and simpler -- interpretation of the spatial distribution of the city is possible.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

Ciudad de Paz

1 PAISAJE CELESTE Y ARQUEOASTRONOMÍA: LAS IGLESIAS HISTÓRICAS COMO INDICADORES DE LA PLANIMETRÍA DE UNA CIUDAD IDEAL ALEJANDRO GANGUI De acuerdo a la tradición popular, la ciudad canaria de San Cristó bal de La Laguna, Patrimonio de la Humanidad por la UNESCO desde 1999, surg ió en los inicios del siglo XVI con una organización novedosa, acorde con un nue...

work page 1999
[1717]

Por su valo r artístico se destaca la cubier ta de la capilla mayor, con una armadura ochavada, también de influencia mudéjar

La iglesia es de nave única, con presbiterio rectangular, al que se accede por un arco de medio punto. Por su valo r artístico se destaca la cubier ta de la capilla mayor, con una armadura ochavada, también de influencia mudéjar. De más está decir que los ejemplos abundan, como estos dos que acabamos de enumerar. Ya se trate de la ermita de Nuestra Señora...

work page 2000
[2014]

locales" (acimut y altura) nos permiten conocer exac tamente

En nuestro estudio, esta última posibilidad también será tenida en cuenta, pues la orientación a poniente es característica en los tiempos iniciales del Cristia nismo y, asimismo, se ha repetido en zonas ya estudiadas del norte del África que son posibles regiones de origen de la población canaria nativa (Esteban et al. 2001; Belmonte et al. 2007). En nue...

work page 1986

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Ciudad de Paz

1 PAISAJE CELESTE Y ARQUEOASTRONOMÍA: LAS IGLESIAS HISTÓRICAS COMO INDICADORES DE LA PLANIMETRÍA DE UNA CIUDAD IDEAL ALEJANDRO GANGUI De acuerdo a la tradición popular, la ciudad canaria de San Cristó bal de La Laguna, Patrimonio de la Humanidad por la UNESCO desde 1999, surg ió en los inicios del siglo XVI con una organización novedosa, acorde con un nue...

work page 1999

[2] [1717]

Por su valo r artístico se destaca la cubier ta de la capilla mayor, con una armadura ochavada, también de influencia mudéjar

La iglesia es de nave única, con presbiterio rectangular, al que se accede por un arco de medio punto. Por su valo r artístico se destaca la cubier ta de la capilla mayor, con una armadura ochavada, también de influencia mudéjar. De más está decir que los ejemplos abundan, como estos dos que acabamos de enumerar. Ya se trate de la ermita de Nuestra Señora...

work page 2000

[3] [2014]

locales" (acimut y altura) nos permiten conocer exac tamente

En nuestro estudio, esta última posibilidad también será tenida en cuenta, pues la orientación a poniente es característica en los tiempos iniciales del Cristia nismo y, asimismo, se ha repetido en zonas ya estudiadas del norte del África que son posibles regiones de origen de la población canaria nativa (Esteban et al. 2001; Belmonte et al. 2007). En nue...

work page 1986