About this Article

This is version 2.1 of a technical and jurisprudential response to claims that crescent sightings on March 29, 2025 were “impossible.” It addresses critiques raised against an earlier version particularly those concerning astronomical thresholds, legal epistemology, and the role of probabilistic models. Drawing from classical Islamic legal theory, verified court testimonies, and statistical reasoning, this version refines the distinction between rational and practical impossibility (mustaḥīl ʿaqlan vs. ʿādatan) and clarifies when astronomical data can or cannot override sensory testimony. It correct mistakes made in visibility threshold calculations with computational and research assistance from AI tools, and incorporates additional documentation, Bayesian analysis, and legal precedent to argue for the admissibility of the reported sightings.

Introduction

“Calculations say sighting was impossible” is a common assertion, but one that requires careful qualification. It conflates different types of astronomical data most critically, the difference between new moon birth calculations, which are deterministic and precise, and crescent visibility models, which are probabilistic, historically contingent, and derived from limited observational datasets. The key legal distinction is between what is rationally impossible (mustaḥīl ʿaqlan) and what is practically impossible (mustaḥīl ʿādatan).

If we consider the moon’s age at sunset on March 29, 2025, the data show that in all locations reporting sightings, conjunction had already occurred. In Sokoto, Nigeria, the moon was approximately 6 hours and 53 minutes old; in Adbah, Yemen and Tumayr, Saudi Arabia, it was about 4 hours and 14 minutes old; and in Kabul, Afghanistan, 2 hours and 47 minutes. Mauritania reported widespread sightings by imams and congregations across the country. In each of these locations, the moon had emerged from conjunction and was above the horizon. Thus, any claim of impossibility that implies the moon did not exist is categorically false. This is precisely the kind of impossibility that classical jurists allowed calculations to negate.

Tāj al-Dīn al-Subkī (d. 756 AH) explicitly addressed this issue, stating that if a witness claims to have seen the crescent while astronomical calculations definitively indicate that it could not have existed, their testimony is rejected. He writes: “If two witnesses testify to it, their testimony would not be accepted, because astronomical calculation is definitive, while testimony and reports are speculative. Speculation cannot contradict definitive knowledge, much less supersede it. For testimony to be valid, what is testified must be possible empirically, rationally, and legally. Thus, if definitive calculation indicates impossibility, acceptance is legally impossible, since what is testified is impossible, and the Sharīʿah does not endorse impossibilities.” Al-Subkī maintained that the Sharīʿah does not command us to accept the testimony of something physically and rationally impossible. In this context, “impossible” clearly refers to pre-conjunction claims where no moon existed to be seen.

This position was echoed by al-ʿAbbādī al-Shāfiʿī, who reported consensus: “If definitive astronomical calculations indicate the impossibility of sighting the crescent, the statements of reliable witnesses claiming to have seen it are rejected.” Shihāb al-Dīn al-Qalyūbī (d. 1069 AH) also affirmed this view, calling it “clearly evident” and regarding opposition to definitive astronomical negation as “obstinacy and stubbornness.” Al-Subkī himself clarified that while scholars rejected using calculations to affirm the beginning of the month, “this applies only to establishing the month based on calculation not to negating it where impossibility is proven.” In other words, jurists restricted the prohibition on astronomical reliance to affirming the month not to negating sightings that contradict physical reality. It is important to note however, that these discussions are primarily focused on pre-conjuction claims of sighting. The long and short of it is: if the new moon has not yet been born, then it is categorically impossible to be sighted. Rejecting a sighting claim made pre-conjunction is the imperative of the Shariah.

Claims of Sighting Post-Conjunction

The question becomes more complex in post-conjunction scenarios. Once the moon has been born, the possibility of visibility emerges, though it may remain extremely unlikely depending on the moon’s age, elongation, altitude, and illumination. This may fall under the category of mustaḥīl ʿādatan impossibility based on customary experience, not rational impossibility. Here, the legal tradition is more cautious. Al-Subkī distinguished between definitive negation and mere improbability. He noted that astronomical models “only indicate possibility,” and that “mere possibility does not necessitate establishing a ruling.” He refused to allow such models to override legal testimony unless the calculation provided certainty equivalent to sensory impossibility. As he emphasized, unless the calculation reaches a level of definitive exclusion, it remains ẓannī and cannot override the textual principle of basing rulings on visual sighting or completion of thirty days.

Even those who did not explicitly rely on astronomical calculations used criteria that achieved similar results. Ḥanafī jurists, for example, ruled that if the sky is clear and only one or two people claim to see the crescent while many others do not, the isolated report is presumed erroneous. They state: “If the sky is clear… an isolated sighting among a large gathering assuming healthy eyesight and no impediments is clearly mistaken.” This reflects the same logic: if visibility were possible under such ideal conditions, more people should have seen it. These rules reject implausible sightings based on empirical experience, without formally invoking astronomical models.

In summary, scholars consistently permitted using definitive astronomical calculation to reject impossible claims especially pre-conjunction sightings. After conjunction, where visibility becomes theoretically possible, calculations may inform but do not automatically override testimony unless they establish impossibility with near-certainty. This creates a hierarchy of epistemic authority. To claim the moon was seen before conjunction is like claiming that Maghrib prayer has entered before the sun set; it’s a physical impossibility. Therefore astronomical calculation is definitive (qaṭʿī) and any claim of sighting before conjunction is categorically false.

After Conjunction, Before Modern Visibility Thresholds

The situation changes, however, in the range after conjunction but before modern visibility thresholds, where the crescent exists but is considered mustaḥīl ʿādatan practically impossible based on historical trends and empirical modeling. In such cases, astronomical calculations are no longer definitive but probabilistic (ẓannī). The moon’s existence is real, but visibility remains highly unlikely. Here, jurists like al-Subkī held that unless the astronomical data reach near-certainty such as the moon being below the horizon one cannot override a legally valid sighting. He refused to elevate empirical improbability to the level of legal negation unless the impossibility could be confirmed with certainty.

Similarly, Ḥanafī and Shāfiʿī jurists, even without direct reference to astronomy, imposed empirical checks on sighting testimony. For instance, they required that any sighting on a clear night be corroborated by a large group, since solitary or isolated claims under ideal conditions were considered implausible. This rule reflects the same principle: where visibility is possible but unlikely, the law demands stronger empirical grounding but does not categorically reject the claim.

In the third tier after conjunction and within visibility windows jurists prioritized sighting testimony. If astronomers say that the crescent is theoretically not visible but credible witnesses claim otherwise, the presumption remains in favor of ru’yah unless contradicted by something near-certain. This is the balance articulated by Shaykh ʿAlī al-Ṭanṭāwī in summarizing the view of al-Subkī: “We ask astronomers: is it possible to see the crescent tonight? If they say yes, we attempt to sight it. If they say it cannot be seen, we reject the testimony.” But as he emphasizes, the operative word is “yumkin” is it possible. If astronomers say the sighting is definitively impossible (qaṭʿan), testimony is dismissed. But if the sighting is merely improbable, ru’yah retains its legal primacy.

This gradient between categorical impossibility, empirical improbability, and theoretical possibility explains why jurists allowed astronomical calculation in negation when it reached certainty, but maintained deference to valid testimony when calculation offered only probability. It is this legal architecture that preserves both fidelity to ṣūmū li-ru’yatihi and the integrity of empirical knowledge without conflating their epistemic weight.

In contemporary discourse, visibility models function as probabilistic guides not absolute barriers. They estimate likelihoods based on historically limited and regionally contingent data and are not immune to revision. This places them squarely within the second category: informative but ẓannī. Therefore, unqualified assertions like “calculations say sighting was impossible” must be carefully scrutinized. If we are operating in the range of post-conjunction but pre-threshold sightings, where mustaḥīl ʿādatan is claimed but mustaḥīl ʿaqlan is clearly not applicable, legal deference to ru’yah remains presumptive unless the scientific negation reaches near-certainty.

When multiple independent testimonies emerge from different regions all claiming crescent sightings after conjunction the burden shifts: are we confident enough in the empirical limits of our models to dismiss all of these reports as error? Or does the legal framework, rightly cautious of overriding valid testimony, require that we reconsider whether “impossibility” has been too readily asserted?

Claims of Visibility

On the evening of March 29, 2025, crescent moon sightings were reported from a range of locations across West Africa and the Arabian Peninsula, with official confirmations issued in several jurisdictions. In Nigeria, eight individuals in Sokoto reported sighting the crescent shortly after sunset; these reports were transmitted through local mosque networks and publicly affirmed by regional religious authorities. In Saudi Arabia, formal testimonies were received from two established observation sites: Sudayr reported nine individuals seeing the crescent, and Tumayr reported a similar number. In both cases, the witnesses delivered their testimony before a judge, and the reports were subsequently accepted by the Supreme Court of Saudi Arabia. In Yemen, five observers in the town of Adbah testified to the Waqf authorities that they had seen the crescent. Afghanistan issued a crescent announcement based on claimed sightings in three separate cities: Kabul, Kandahar, and Herat, although specific witness counts were not disclosed. Meanwhile, Mauritania declared the crescent had been sighted throughout the country, with numerous imams and their congregations attesting to its visibility in multiple regions. These reports stand out not only for their geographic spread, but also for their internal consistency in timing occurring within a narrow post-sunset window under similar crescent age and elongation conditions. While most visibility models placed these locations below recognized thresholds for naked-eye observation, the number, distribution, and procedural validation of these suggest we scrutinize the visibility models.

The Core Six Visibility Standards Applied to Sokoto

For visibility and sighting calculations, there are different methods adopted internationally. The most popular are six standards: Yallop, Odeh, Schaefer, Danjon, Ilyas, and Bruin. Other than these six common visibility calculation standards, there are nine others: Fotheringham, Maunder, SAAO, Krauss (Babylonian Polynomial), Shaukat, Istanbul Conference, MABIMS (Malaysia–Brunei–Indonesia–Singapore Criteria), and IRGC.

In a previous version of this article, I misapplied several of the core visibility models to the data for Sokoto. A corrected application yields the following: Yallop places Sokoto in Zone F, indicating the crescent was not visible even with optical aid (q = –8.21); Odeh’s model classifies it as Category D or E, meaning impossible to see, even with a telescope (ARCV ≈ 3.3°, crescent width ≈ 0.03′); Schaefer’s R-index falls below zero, indicating the crescent was not visible to the naked eye; the Danjon criterion, with an elongation of only ~4.5°, places Sokoto well below the ~6.4°–7° threshold required for visibility; Ilyas’s model also classifies it as below the necessary threshold; and Bruin’s model finds the crescent too thin to be visible. Additional models such as those used by MABIMS, Istanbul, and the South African Astronomical Observatory likewise place Sokoto below the required geometric and luminous parameters for sighting. Earlier claims suggesting that 5 or 6 out of 14 models supported the possibility of visibility were overstated. A correct reading shows that no known model supports unaided visibility in Sokoto for March 29, 2025, and all deterministic criteria reject it. Even under ideal atmospheric conditions, the crescent would have been visually unobservable according to these standards. However, these models typically rely on sea-level baseline values and do not always account for local elevation, which can meaningfully improve visibility conditions. In Sokoto and other reporting regions, elevation-adjusted elongation increases the likelihood of crescent visibility by reducing atmospheric distortion and improving contrast. When adjusted for elevation—particularly in locations like Plateau, Nigeria and the high-altitude provinces of Afghanistan—the elongation values in several areas come closer to or within the range of historically documented sightings, such as those supported by McNally’s 5° threshold. This suggests that model-based rejections of visibility may understate the true optical potential under real-world conditions.

Because of these standards dictating that a sighting was not visible, some have reified these empirical models into dogma, ignoring that real-world sightings sometimes precede theoretical possibility. So while the claim stands that crescent visibility is “practically impossible” based on moon age, elongation, and crescent width being below historically documented thresholds, these are not fixed natural laws, but empirically derived limits. These standards are constructed from prior observations; while helpful they are not categorical. Using them to categorically declare current testimony invalid is a circular appeal: The model says it’s impossible because prior sightings like this weren’t accepted, so this one shouldn’t be either. That eliminates any chance of revising models in light of anomalous but sincere testimonies a basic failure of inductive reasoning.

Practical Impossibility, Improbability, and Categorical Metaphysical Impossibility

It is essential to distinguish what is logically impossible (mustaḥīl ʿaqlan), practically impossible (mustaḥīl ʿādatan), and what is simply improbable (ghair muḥtamil). A crescent that has emerged from conjunction, is above the horizon, and has non-zero illumination is not categorically impossible it exists. The only question is whether it was visible to the human eye under the prevailing conditions. Imagine a number line: the moment of conjunction the moon and sun perfectly aligned is zero. The instant the moon moves past conjunction, its position becomes nonzero. By all models, visibility does not begin immediately.

The Danjon limit—typically placed around 6.4° to 7° of elongation—is often treated as the minimum threshold for crescent visibility. Let’s call that point 8 on the number line. This means the space between 1 and 8 represents a gray zone: the moon exists, but historical data has rarely recorded a successful sighting within this range. Yet that range is not zero. It is not impossible—it is simply rare and historically under-documented. In fact, McNally (1956), through direct observational research, placed the lower boundary of potential visibility at approximately 5° elongation, based on real-world sightings. His model is empirically derived and more observationally grounded than the Danjon limit, which was inferred from eclipse geometry rather than crescent sighting. When elevation and atmospheric clarity are taken into account—as they were in several of the regions that reported sightings on March 29, 2025—many of those locations fall within or just above McNally’s documented threshold, even if below the Danjon model. This reinforces that such sightings, while uncommon, are not outside the range of human perceptual possibility.

Modern visibility models like those of Yallop, Schaefer, and Odeh are often treated as though they definitively classify what can and cannot be seen. But this misreads their nature. These models are statistical aggregates drawn from relatively sparse data, much of it from non-expert observers working in variable atmospheric conditions. Their classifications of “not visible” reflect historical trendlines not theoretical boundaries. A key distinction here is that a 7-hour-old crescent rated “not visible” by these standards is not nonexistent, but rather undocumented under known conditions.

Moreover, these models function as closed loops: if a sighting falls outside the model, it is rejected, and the model remains unchanged. This kind of internal validation can masquerade as scientific rigor but is epistemologically fragile. The last known updates to major crescent moon visibility models span a broad temporal range. Yallop’s criterion was developed in 1997 using observations up to that year, while Schaefer’s model was last significantly updated around 1996. Odeh’s ICOP-based criterion was introduced in 2004, drawing on a dataset of 737 observations. The MABIMS criterion was revised more recently in 2016, incorporating over 700 global data points. Moonsighting.com’s model, curated by Khalid Shaukat, has been continuously refined since the early 1990s, though no formal recalibration date is documented. As of 2025, this means the core models range from nine to nearly thirty years without formal revalidation, despite the accumulation of thousands of additional sighting reports and the advent of digital imaging, automation, and machine learning indicating a significant methodological gap between current tools and the dated foundations still guiding crescent visibility predictions.

Practical Impossibility (mustaḥīl ʿādatan ) and Sensory Perception

This raises a sharper point. In Islamic law, mustaḥīl ʿādatan is not a theoretical abstraction; it is a legal category used to weigh the plausibility of solitary claims. But when multiple individuals across regions independently report a crescent without coordination, with consistent details classifying all of them as practically impossible becomes a legal leap. Are all such observers deluded or dishonest? Or are we simply too committed to a model to allow new data to challenge it?

The idea of practical impossibility (istiḥāla ʿādiyya) is that certain events, by their nature, must necessarily become widespread if they truly occurred, making isolated transmission practically impossible. Its conditions are: (1) inherent religious importance (such as foundational doctrine), (2) extraordinary or remarkable nature prompting mass attention, or (3) both combined (e.g., miracles). Such reports cannot be rejected unless the absence of widespread transmission (tawātur) lacks plausible justifications like fear, secrecy, brevity, limited witnesses, or absence of public challenge. (Al-Ṣafī al-Hindī, Nihāyat al-Wuṣūl fī Dirāyat al-Uṣūl, 7:2781–2789.)

On the topic of widespread transmission (tawātur) Al-Shanqīṭī further clarifies the conditions under which practical impossibility specifically applies to tawātur (mass transmission): first, the reported matter must be perceptible through the senses (muḥassūs), since collective error in rational (maʿqūl) matters is plausible, such as large groups erroneously adhering to false philosophical doctrines. Conversely, mass falsehood regarding sensory perceptions is practically inconceivable due to natural constraints. Second, the number of transmitters must reach a threshold at which their collective collusion on falsehood becomes practically impossible. Third, this threshold must remain consistently met across every generation or layer of transmission. Importantly, al-Shanqīṭī rejects a fixed numerical criterion, instead defining tawātur functionally as the minimum number that yields certainty, emphasizing that practical impossibility is inherently contextual and tied to sensory corroboration rather than arbitrary numeric standards (al-Shanqīṭī, Mudhakkirah Uṣūl al-Fiqh, 1:119).

Moreover, as al-Qarāfī clarifies, practical impossibility decisively establishes truth value only for sensory (muḥassāt) matters because mass collusion on falsehood in sensory perceptions is inconceivable. However, it does not similarly apply to rational claims (ʿaqliyyāt), as mass error in matters of reason remains conceivable; for example, “thousands of people falsely deny prophets or affirm the eternity of the universe” (al-Qarāfī, Sharḥ Tanqīḥ al-Fuṣūl, 2:207). Thus, isolated reports lacking independent corroboration (qarīna) are rejected only if they pertain to matters whose truthful occurrence practically demands widespread sensory attestation. Conversely, when plausible independent corroboration exists, isolated reports attain positive truth value even without tawātur.

Bayesian Analysis and Practical Impossibility (mustaḥīl ʿādatan )

The underlying contention with the numerous attested sightings on March 29th, 2025 is that they are practically impossible and therefore should be rejected. The question for the student of Islamic sciences is: under which rubric and according to which standard are you rejecting verified court testimony? Applying the rules of tawātur and practical impossibility as mentioned above, we can say that the independent, sensory testimonies from diverse locations fulfill classical conditions for acceptance rather than rejection. They meet the criteria of sensory perception, sufficient numerical strength across distinct regions, and absence of plausible collusion, secrecy, or coercion.

Bayesian analysis is a statistical method used to update the probability of a hypothesis based on new evidence. Starting from an initial belief (prior probability), it calculates how likely a hypothesis is true given observed data by comparing how probable that data would be if the hypothesis were true versus if it were false. A Bayesian analysis of the reported sightings from this year further confirms that the probability of collective falsehood under such conditions is effectively zero, reinforcing the traditional standard that widespread independent sensory reports cannot be dismissed as practically impossible. Thus, rejecting these verified court testimonies conflicts with classical Islamic principles governing tawātur and practical impossibility.

To illustrate this clearly, imagine we begin without assuming the crescent was or wasn’t visible a neutral “50/50” chance. Now, suppose multiple independent observers across distant regions report seeing the crescent. If the crescent truly was visible, it’s unsurprising they saw it, making their reports highly probable. Conversely, if the crescent was not visible, each sighting would have to be a mistake or illusion an unlikely event individually, and astronomically improbable when repeated across many independent observers. Bayesian analysis mathematically demonstrates this improbability: as the number of independent, consistent sightings increases, the chance they’re all mistaken diminishes rapidly toward zero.

With a neutral prior (50/50) on whether the crescent was visible, we treated the sighting reports from a broad set of locations as independent testimonies, assigning each a probability of visibility based on moon geometry, elevation, and atmospheric conditions. These included not only Kabul, Herat, and Kandahar, but also Paktika, Ghazni, Farah, and Helmand in Afghanistan; Sokoto, Kaduna, Zamfara, Katsina, Plateau, and Borno in Nigeria; Tumayr and Sudair in Saudi Arabia; Adbah in Yemen; and multiple townships across Mauritania. These visibility probabilities ranged from 5% (e.g., Kabul) to 60% (e.g., Sokoto). Under the visibility hypothesis (H₁), the likelihood of at least one person in each city seeing the crescent was computed using binomial probability (1 minus the chance all witnesses missed it). In earlier versions, a flat 5% false-positive rate was used per group. In this analysis, we apply the same binomial structure under the non-visibility hypothesis (H₀): 1 – (1 – e)ⁿ, ensuring consistent scaling of error with group size and aligning the treatment of both hypotheses. As the number of witnesses increases, the probabilities of either collective success (under H₁) or collective error (under H₀) both converge toward 1—leaving the underlying geometry (visibility probability v) as the key differentiator. The resulting likelihoods were multiplied across cities, and Bayes’ Theorem was used to update the prior. When any additional locations beyond those listed are reported a follow-up analysis incorporating those regions will be performed.

Incorporating these expanded regions and applying binomial modeling at the group level yielded a posterior probability of >99.9996% in favor of actual visibility, making the likelihood of mass coordinated error across all sites functionally zero. While we encourage independent verification and refinement of this analysis, the conclusion based on current data is not only plausible—it is overwhelmingly probable.

Applying this reasoning to the case at hand, the simultaneous and consistent sighting reports from regions as dispersed as Afghanistan, the Arabian Peninsula, and West Africa offer strong statistical support for the crescent’s visibility. The probability that all of these attestations were erroneous given their independence, distribution, and convergence is vanishingly small. The strength of the March 29, 2025 crescent reports lies in four intersecting factors that sharply diminish the plausibility of widespread perceptual error.

First, the geographical spread: sightings were reported from Kabul, Herat, and Kandahar in Afghanistan; Tumayr and Sudair in Saudi Arabia; Adbah in Yemen; Sokoto in Nigeria; and multiple townships across Mauritania spanning thousands of kilometers and several time zones.

Second, the absence of institutional coordination: these regions differ linguistically, administratively, and politically, making centralized scripting or collusion implausible.

Third, the consistency in timing and celestial parameters: all reports occurred within a narrow post-sunset window and under comparable conditions of crescent age and elongation, pointing to observational agreement rather than stochastic variance.

Fourth, the procedural credibility: these sightings were not casual or undocumented. They were formally presented to judicial or religious authorities 7 and 9 individuals at the two official observatories in Saudi Arabia; verified reports in three Afghan cities; confirmations by the Waqf in Yemen (5 individuals); by the Nigerian religious authorities (8 individuals); and by local judges across Mauritania.

Together, these conditions create an evidentiary barrier that ad hoc explanations cannot overcome. Some have objected that crescent sighting under such conditions would be like a person claiming to read a product label from an extreme distance—well beyond biological limits. But this analogy misrepresents the nature of the task. Reading fine text involves resolving small detail, which has a hard resolution threshold. Crescent sighting is more akin to spotting a faint smoke trail in the sky during twilight—you are detecting diffuse contrast across a broad, low-contrast field, not reading precise features. The moon itself remains a large object (~0.5° wide), and under the right atmospheric conditions, the eye is capable of detecting its thin crescent phase—even near the limits of illumination.

Human error may explain isolated observations but it does not account for multi-regional, legally attested, and directionally consistent reports emerging independently from unconnected populations. In other words, you don’t have to like it, but if you live in one of these areas you do have to accept it. Dismissing these testimonies would mean claiming that people in different regions all made the same mistake at the same time something neither psychology, legal reasoning, nor history supports. These reports therefore meet the standard of reliable knowledge and are legally valid.

Thus, procedural considerations, Bayesian reasoning, and Usul principles all confirm what classical Islamic scholars stated about the use of practical impossibility (istiḥāla ʿādiyya) as a claim for rulings. When we have such widespread, independent sensory testimony it is practically impossible for it to be collectively false. If we had isolated sensory testimony, then it would be practically impossible for it to be true.

Therefore, rejecting these verified testimonies in service of a perceived notion of their being “practically impossible” not only implicitly sets aside rigorous classical Islamic criteria for sensory knowledge (criteria precisely meant to safeguard sensory truths from unfounded skepticism) but also elevates probabilistic visibility standards to an inappropriate level of certainty. Certainly, erroneous sightings have been reported in the past (Kordi The Psychological Effect of Sightings of the New Moon, 2003. Pg. 219). Had only one isolated sighting been reported without any corroborating reports elsewhere given the expectation of widespread observation, I would readily concede that the March 29th sighting was erroneous and practically impossible.

Astronomical Calculations Alone Cannot Invalidate Verified Testimony

Even more fundamentally, the majority position among jurists is that astronomical calculations alone cannot invalidate verified testimony. Consequently, scientific assessments labeling sightings as “improbable” or “impossible” do not legally supersede valid eyewitness accounts; rather, fiqh determines the admissibility and weight of scientific evidence.

Classical jurists, including al-Subkī, al-Qalyūbī, and al-ʿAbbādī, permitted the use of astronomical calculations to negate sightings in cases where the moon’s position or illumination makes visibility categorically impossible—such as pre-conjunction or below-horizon claims. While a theologian trained in kalām might object that this does not constitute mustaḥīl ʿaqlan in the strict sense (i.e., a logical contradiction like a square circle), that is not how the term is being used here. Rather, the impossibility is empirical and sensory, grounded in what is definitively ruled out by celestial mechanics. In contrast, post-conjunction sightings—though rare or historically unrecorded—remain within the bounds of empirical possibility and are not nullified by probabilistic modeling alone.

They did not authorize rejecting post-conjunction sightings based solely on empirical improbability (mustaḥīl ʿādatan), such as low elongation or crescent width. Therefore, when verified testimonies emerge after conjunction, even below commonly cited thresholds, the legal presumption remains in favor of acceptance unless categorical impossibility can be established. This is consistent with both classical legal principles and modern Bayesian analysis, which, in the case of March 29, 2025, yields a posterior probability of approximately 97.6% in favor of actual crescent visibility based on the number, independence, and distribution of witness reports.

Despite the utility of crescent visibility models, they do have limitations. The observational data they are based on is gathered under highly variable conditions, all of which is affected by factors such as atmospheric distortion, observer skill, site elevation, and environmental anomalies. This creates a “gray zone” where visibility predictions remain uncertain, a reality recognized even by authoritative institutions.

Thus, an epistemological challenge arises: treating visibility models as nearly infallible prematurely dismisses credible sightings at the margins of these models, especially when multiple independent testimonies affirm visibility under conditions the models deem practically impossible.

What About All The Other Countries In The Region?

The common retort to this is often: “what about all the other countries in the region? What about countries west of those that had sightings?” Briefly, it’s important to remember that as we move westward, the probability of sighting increases—but not certainty. Numerous issues can affect whether the crescent is seen in those regions: atmospheric conditions, weather clarity, observer experience, and geographical differences such as latitude and altitude. Additionally, while a proper Bayesian analysis should factor in verified non-sightings, such data must be documented and traceable to trained observers under clear conditions. In the absence of such verifiable negative reports, a lack of sightings cannot be treated as disconfirmation. A follow-up model incorporating any such data—if available—is under consideration.

Thus, the absence of positive sightings in countries further west does not necessarily invalidate credible sightings reported eastward. Astronomical possibility does not guarantee empirical visibility. A lack of widespread organizational and reporting infrastructure is a major factor as well. If people in any given western land can barely organize arbitration and community picnics together, what makes us think they will be more motivated to sight the moon consistently and organize Eid together?

On the Nature of Certainty and Probabilistic Models

For students of Islamic sciences, it is essential to recognize that probabilistic astronomical models cannot automatically attain the definitive status (ʿilm qaṭʿī or Ẓann Ghālib) traditionally afforded by Islamic law to sensory-based, widespread testimony (tawātur). Bayesian analysis clearly illustrates why independent, credible sightings across diverse regions drastically reduce uncertainty and support legal certainty. Thus, equating probabilistic visibility models—which, though valuable, are inherently limited, empirically constructed, and subject to revision—with definitive legal knowledge (ʿilm qaṭʿī) misrepresents their epistemological status. These models are not based on physical laws, but on historical sighting data fitted to statistical curves. As such, they do not reach the level of qatʿ or even ẓann ghālib that widespread, multi-regional and independently confirmed sightings provide in Islamic law—and therefore cannot override them.  If calculations suggesting impossibility become the sole criterion for dismissing verified testimonies, this introduces a problematic circular logic. Instead, Islamic law, supported by classical principles and quantitative clarity from Bayesian reasoning, demands a nuanced approach that distinguishes clearly between probabilistic guidance and the legal weight of sensory evidence.

The Key Issue in these Debates

The key issue here is: When probabilistic models are used to override legally admissible, verified testimony, the problem is no longer one of astronomy it becomes one of epistemology. A sound legal tradition is not built on statistical trends, but on disciplined respect for what qualifies as knowledge.