Angels in the Sky, Microbes on Earth

Some Remarks on the Natural Sciences in al-Manār

Rainer Brunner (CNRS) One of the main topics throughout Muḥammad Rashīd Riḍā's long career as a religious and social reformer was the issue of educational reform as a necessary precondition for all other kinds of renewal. Apart from general articles on the importance of knowledge and education which he penned for his journal al-Manār, he made two more concrete and specific efforts in this regard: First, Rashīd Riḍā himself founded an institution of higher learning (Dār al-daʿwa wa-l-irshād) which was intended to train graduates according to his vision of a combination of religious and worldly subjects. And secondly, the discussion of the relevance of natural sciences also took place in al-Manār, mainly in contributions by Muḥammad Tawfīq Ṣidqī, a trained physician whose articles illustrate the balancing act religious reformers had to do in order to reconcile their religious convictions with scientific findings.

In the first part of Najīb Maḥfūẓ' famous trilogy, Kamāl, the youngest child of the family and a bright pupil, makes it a point to report regularly to his mother, Amīna, what he has learnt at school. Although she is glad to discover that what the boy is taught in religious classes did not differ much from her own traditional knowledge of religion, she is very unhappy about non-religious subjects. The natural sciences, in particular, prove to be hard to swallow for her, such as the question "whether the earth rotates on its own axis in space or stands on the head of an ox". Kamāl's brother Fahmī, whom she secretly asks about the truth of the matter, finds an elegant solution by answering that "the earth is held up by the power and wisdom of God", which leaves the ox unhurt in her imagination. 1 The plot is set in Cairo at the end of the First World War, and it is safe to assume that there were many Kamāls and Amīnas at the time. After all, conflicts brought about by traditional certainties being shaken by new concepts, discoveries, or inventions were ubiquitous at the onset of modernity, not the 1 Mahfouz, Palace walk 65. A condensed summary of the classical cosmological worldview in Islam, based on Muṭahhar b. Ṭāhir al-Maqdisī's al-Badʾ wa-l-taʾrīkh, is given by Radtke, least and to no small a degree in Muslim societies from the early 19 th century onward. Kamāl later on, as a grown-up, loses his faith.

What this little scene also shows is the fact that one of the main venues of these clashes were schools and other places of education, and it therefore comes as no surprise that many reform thinkers of the Islamic world focused their attention on the perceived need to adapt traditional reasoning to the new requirements. Muḥammad ʿAbduh (d. 1905) may have been the most famous religious scholar who called for a modernization of the traditional educational institutions, above all Azhar University, and the introduction of non-religious subjects and methods into their curricula. 2 But he was far from being the first or only one to become aware of the problem. As is wellknown, under Muḥammad ʿAlī's long rule (1805-1848), many new schools, aiming at the technical and administrative reform of the country, were established, which not only undermined the ʿulamāʾ's long-standing monopoly on all educational matters, but also set in motion a process of knowledge transfer and appropriation in the field of the natural sciences. 3 The foundation, from the 1870s onward, of a considerable number of journals, both in Egypt and beyond, also contributed to the circulation of information about technical and scientific achievements among a broad readership. Mention may primarily be made of the two Cairo-based journals al- Muqtaṭaf (established in 1876) and al-Hilāl (1892) which devoted much space to matters of modern science. The case of the former is especially illuminating, as the two Syrian Christians Yaʿqūb Ṣarrūf and Fāris Nimr who had originally founded al-Muqtaṭaf in Beirut moved to Egypt in 1884 in the wake of the first big scandal about science in the Arab world sparked off by the debate on Darwin's Theory of Evolution. 4 When Muḥammad Rashīd Riḍā (1865-1935) started his journal al-Manār in 1898, shortly after his arrival in Cairo and the beginning of his collaboration with Muḥammad ʿAbduh, the question of education played an important role from the outset. 5 Hardly any issue appeared during its early Weltgeschichte 80-81.

2 Gesink, Islamic reform 165-196. 3 For a detailed analysis of these developments, see Crozet, Les sciences modernes en Égypte passim.

years without Rashīd Riḍā's editorials calling for thorough reforms on all fronts and all levels, his social concerns always being firmly grounded in a decidedly religious worldview, in contrast to those of many of his Christian or secular colleagues from other journals. Thus, for instance, he vehemently supported female education by rejecting "wrong" traditions according to which women should be prevented from learning to write. 6 As it would clearly go beyond the scope of this article to give an overview of all calls for reforms in al-Manār, one particular subject will be singled out here that reveals this interdependency of social problems and their religious background in a characteristic way, namely the significance of the natural sciences.

After all, Rashīd Riḍā reminded his readers several times that he had made it clear to the rector of al-Azhar early on that preserving the Islamic religion and the dignity of the believers as well as returning Islam to its former supremacy needed, among other things, the natural sciences (al-ʿulūm al-kawniyya) and that this was precisely what al-Manār was calling for. 7 The topic as such is not entirely new, but it has previously been studied mainly in regard to the fatwās that Rashīd Riḍā issued on a regular basis, and the running commentary of the Quran (Tafsīr al-Manār) that he started in collaboration with ʿAbduh and continued, after the latter's death in 1905, on his own. 8

What is more, the focus of these studies is predominantly on Darwinism, the related (and more vehemently debated) problem of materialism in a broader sense, as well as the theological conclusions that might be drawn therefrom as far as the fate of the human soul is concerned. Surprisingly little attention, however, has been paid to those articles in his journal that focus on the natural sciences proper, and this from a (seemingly) scientific point of view. For reasons which will, I hope, become clear in the following, they also merit our interest. But before we turn to these items that were penned by a close friend and collaborator of his, a few words on Rashīd Riḍā's background and his own efforts towards institutional reform are necessary.

Islamic reformism 2-9; for more details on his early career and the founding of al-Manār, see Ryad, A printed Muslim 'lighthouse'. (1845-1909) in January 1879. Although the school was forced to close merely three years later, this turned out to be his decisive educational awakening experience. Al-Jisr was one of the first religious-minded reform thinkers to acknowledge the necessity of adding new scientific knowledge as well as foreign languages to the traditional curriculum of religious studies in order to enable his students to meet the needs of the time, and, not least, to combat the advance of the Christian missionaries and their schools. 10 It was al-Jisr, Rashīd Riḍā recalls in his memoirs, who made him understand that reform and progress were only possible for the umma if religious and secular branches of knowledge were brought together, and if the religious scholars were familiar with the modern era in order to defend the Islamic faith. 11 This is not to say that they necessarily agreed with all aspects of modern science; al-Jisr himself was rather sceptical about the theory of evolution (knowing Darwin, however, only second-hand, through the writings of the German materialist Ludwig Büchner and his Arab supporters as well as opponents), 12 and Rashīd Riḍā once complained to him about having answered the question of the spherical form of the earth and its orbiting the sun only in a hypothetical manner, thus insinuating doubts about it. When al-Jisr reminded him of the fanaticism of all those in the country who had no clue of these sciences and whom he did not want to provide cause for gossip, this did not really satisfy his disciple: "If someone like you in whose religion and knowledge the umma has confidence does not encourage us to speak out the truth, 9 Rashīd Riḍā, al-Manār wa-l-Azhar 139. from whom else should we hope for it?" 13 It is in the nature of things that the religious reformer Rashīd Riḍā, as soon as he arrived in Egypt and following ʿAbduh's example, immediately showed deep concern for the Azhar. His first visits there left a devastating impression on him, when he watched, for instance, the ritual sweeping (kansa) at al-Shāfiʿī's grave, after which the dust would be distributed among the believers because of its blessing, or when he heard of that noble lady from Russia who converted to Islam, came to Egypt in order to visit the Azhar, and who -upon seeing all the students from abroad (mujāwirūn) sitting around and eating radishes, onions, and broad beans -turned away weeping and sobbing. 14 Yet he deemed the time-honoured institution reformable, and the first years of al-Manār are replete with proposals, demands, and recommendations that aimed, above all, at introducing new subjects, such as mathematics, geography, sociology, hygiene, and the principles of natural history. He was all the more persistent as, at least according to his own judgment, many Azhar scholars sent their own children to governmental schools in order to have them study the very same secular subjects which they refused publicly for the Azhar. 15 At some point, perhaps after ʿAbduh's death in July 1905, 16 Rashīd Riḍā must have understood, however, that he could not overcome the opposition from within the Azhar, his aforementioned ostentatious agreement with its rector notwithstanding. 17 This was, then, when the plan to establish an educational institution of his own, as his teacher al-Jisr had done nearly thirty years previously, started to form in his mind. Its purpose was not to compete with the Azhar as a fullyfledged university, but rather to set up a cadre training unit in order to counter the growing influence of Christian missionaries, both in Egypt and elsewhere, whose schools were also attended by many Muslim pupils -which, it turns out, he considered the Azhar as no longer being capable of achieving. 18 After unsuccessful initial steps in 1909-10 to realize his project in Istanbul, he decided to pursue it in Cairo, where, after much networking and fundraising, and in spite of polemical articles in the daily press, the House of Propagation and Guidance (Dār al-daʿwa wa-l-irshād), a boarding school situated on the Nile island of al-Rawḍa, was finally inaugurated on 2 March 1912. 19 Since the main idea of the school was to train future missionaries (duʿāt) to be sent to faraway Muslim communities to prevent them from falling into Christian missionaries' hands, the curriculum consisted quite naturally to a large degree of the usual religious subjects. There were two noteworthy extensions into the "modern" subjects: first, students at the Dār al-daʿwa were obliged to learn a European language, and could add other foreign languages as well. This reveals a distinct sense of pragmatism on the part of Rashīd Riḍā, who -although he considered himself without doubt to be the representative of modern Islamic daʿwa par excellence -apparently did not understand, let alone speak, any foreign language, a fact that he sometimes noted with a certain regret, but never to the degree that he felt the need to remedy this problem during his life. 20 And secondly, more importantly in our context, the natural sciences were also an integral part of the classes and were made up of elementary courses in biology, physics, chemistry, and physiology, if possible even supported by practical experiments; astronomy was taught in connection with general mathematics. 21 This was not only complemented by the additional subject healthcare (ḥifẓ al-ṣiḥḥa), but also by the general prescription for the students to pay attention to their physical hygiene and to lead a moderate and safe life -the latter being a constant cause for concern to Rashīd Riḍā throughout his own life. In the same vein, he found no fault in repeatedly allowing the use of telephones or telegraphs in order to transmit the news of the sighting of the new moon at the beginning or end of Ramaḍān from anywhere in the country to the authorities in the capital. 24 But his enthusiasm had strict limits, as is also shown in his Ramaḍān statements: a phone call to communicate that the moon had been sighted, was alright, astronomical calculation to determine when it would be visible, or when it could be taken for granted under a cloudy sky, was not. Throughout his career, Rashīd Riḍā attached great importance to the necessity of seeing the moon with the naked eye, and the reason for this is fairly simple: while communication channels are not mentioned in the Quran, the sighting of the moon is, in Q 2:185 (fa-man shahida minkum al-shahr fa-l-yaṣumhu). Therefore, it was a matter of religious authority, which, in Rashīd Riḍā's conviction, could inconceivably be left to "every Tom, Dick and Harry who have nothing to say in religious matters, even if they did not contradict the Qurʾān and stipulated that corporal punishment was categorically forbidden. For some admiring remarks on the British devotion to bodily exercise and sport as well as their cleanliness, see his aforementioned (note 20) travelogue to India, Rashīd Ryad, Islamic reformism 54-56, 137-139, 243-276; on [369], Ryad reproduces what is likely to be the only existing photograph of Ṣidqī.

generation." 30 Even his most natural enemies, the missionaries themselves, did not deny him their respect for the shrewdness of his writings. 31 As far as his articles on the natural sciences are concerned, these did not go entirely unnoticed by his contemporaries either: it was none other than Ignaz Goldziher who, in his last book on the history of Quranic exegesis, devoted a few lines to him in the context of the interpretation of the Quran in the light of modern science. 32 Ṣidqī got in touch with Rashīd Riḍā for the first time in 1903, when he sent him an article on "the prohibition of the pig and the impurity of the dog". The author was identified only by his initials M.T.Ṣ. and introduced as "a student of medicine in Egypt". 33 At first sight, this comes across as yet another apologia for Islamic dietary law and purity concepts, the more so as Ṣidqī states in this introduction that he offered the article for publication so that the readers might understand the wisdom of the Islamic sharīʿa inherent in these stipulations. Yet it immediately turns out to be a rather thorough biological and medical explanation of tapeworms, their provenance, characteristics, mode of operation, and dangerous effects both on the animals and, through food or bodily contact, on humans. In particular, he details the structural differences to other worms, such as the beef tapeworm, which result in beef or mutton being considerably less problematic for the human body than pork. 34 In order to drive his message home with greater emphasis, he did not make do with biology proper, but also included a reference to Islam, which cared not only for spiritual reform, but also for the reform of the body, and which, by prohibiting the consumption of pork (and alcohol), anticipated the retardation of human cognitive faculties and thus preserved 30 Jeffery, A collection of anti-Christian books 34. 31 The British missionary George Swan called Ṣidqī's book ʿAqīdat al-ṣalb wa-l-fidāʾ (1913) "a remarkably clever book, the strongest, perhaps, that has yet appeared in favour of Islamic Modernism". Swan, The Matbuli incident 177. 32 34 Ṣidqī used the common Arabic word for worms (dīdān, sg. dūda), but also introduced the veterinary terminology, identifying the pig tapeworm as tīnīyā sūlīm (i.e., taenia solium), the beef tapeworm as tīnīyā sajanītā (sic!, i.e., taenia saginata), and the dog tapeworm as tīnīyā īkīnūkūkus (i.e., taenia echinococcus); Taḥrīm 303, 304, 307.

them from harm. 35 By this nexus of science and religion, and by concluding with a Quranic verse (Q 41:53), Ṣidqī apparently struck the right chord in Rashīd Riḍā, for in the following years, he became one of the most regular and productive authors in al-Manār, besides the patron himself. In several of his contributions, he touched upon natural phenomena only in passing, mainly using them as a launching pad for exegetical reflections or polemical attacks against Christianity, although he constantly emphasized his rational approach and his inspection of religion from a marked common-sense perspective.

This was the case, for instance, in a series of six articles with the programmatic title "Religion from the perspective of a sound mind" which consisted of theological reflections on the necessities and axioms of matter, the conditions of prophecy, the general character of Islam as a strictly egalitarian religion, and the refutation of alleged Christian distortions of the correct meaning of the Quran. The closest he came to science here was in a short passage in the fifth part of the series, when he made some remarks about Darwinism and the usual suspects: setting things straight against the (unnamed) materialists, Ṣidqī called Darwin's theory the ultimate point that human intellect had reached so far in trying to explain the enigma of creation. Geological traces, fossils, the similarities between animals, especially their foeti -all this could not be explained in a better way. But this was not to say, he immediately qualified, that it was an absolute truth or that one could not also draw other conclusions, since many theories that had vigorously been defended in the past had then be disproved: the tenets of the four elements, the geocentric model of the world, the four temperaments and their effects on many illnesses. As far as the materialists' criticism of the Quran was concerned, this was simply baseless in Ṣidqī's eyes, for the holy book did not claim that Adam was created directly from clay, and it only stated (Q 4:1) that many men and women were descended from Adam, not all; while Adam and Eve could thus be the Arabs' ancestors, other peoples might just as well have other forefathers. 36 Although this was not particularly new or innovative, it was a remarkable step in al-Manār -and it promptly aroused criticism by some readers for whom this modest concession went too far and who demanded that Rashīd Riḍā intervene, which he, however, refused to do. 37 For Ṣidqī, however, this was apparently reason enough to return to this issue some years later, in an article that explicitly asked the question "how was mankind created?" 38 Again, he begins by paying lip service to Darwinism, calling it the best theory available for explaining nature. But in order to emphasize that it remained a theory only, he then sets out to present a number of fundamental objections to it, and he does so from a seemingly strictly scientific point of view. How should we, for example, explain the changing or completely vanishing function of organs that had once existed in some species but then passed out of use, such as the pineal gland which, according to some, had once been a third eye, as is still observable in the parietal eye of some lizards? Why should the disappearance of some teeth from the upper jaw of whales or mammals count as a proof of evolution? We might in fact say, he continues, that God created the foeti of all animals in one and the same way, but then unfolded them into different species. Just as one could not claim that the male derived from the female or vice versa, just because both possess elements of the respective other sex, it is impossible to say that humans had once been a different species, just because some vestigial organs such as the appendix are left. The existence of such traces is therefore not a sign of evolution, but rather a hint at a common origin of all animals. At this point, Ṣidqī has already changed sides, and it is easy for him to make the game end in a draw -albeit with distinct advantages on the part of the nonevolutionists: if Darwin's followers (aṣḥāb Dārwīn) acknowledge that they cannot explain the sense of the thymus, the carotid, or the coccygeal bone, "we, too, acknowledge (iʿtarafnā naḥnu ayḍan) that we do not know the rationale of some ancient organs, so there is no difference between our school and theirs, except that they more daringly claim to know the secrets of being and are more smug about what they know, even if it becomes clear every day that in what they assert they are impotent liars (annahum fīmā yazʿumūn kādhibūn wa-ʿājizūn)." 39 While maintaining

that the definitive answer to the question how mankind was created is known only to God, Ṣidqī then ends his article with a fanciful theory of his own about the human 36 Ṣidqī, al-Dīn fī naẓar al-ʿaql al-ṣaḥīḥ, part 5, 737-740; cf. also Elshakry, Reading Darwin 175-176. 37 Shavit, Scientific and political freedom 76. 38 Ṣidqī, Kayfa khuliqa l-insān?

origins on the basis of parthenogenesis, the way Christ came into existence without a father, i.e., without a male sperm donor. True, he says, this has so far only been observed with small animals, but what constitutes the norm in one species may well happen as an exception in a different one. 40 The next field of science still possessed by their delusions and believed that the earth was flat and carried by an ox -Amīna's scare from the beginning. 43 Around the same time, Rashīd Riḍā was asked by some readers whether there was indeed anything in the noble Quran that supported the view that the earth was spherical and revolved around the sun. In both fatwās, he answered in the affirmative and adduced some appropriate verses -but in neither case did he refer to any of the available textbooks, not even to an article from his colleagues of al-Muqtaṭaf, but rather to two figures who were only remotely in touch with modern astronomy. 44 It seemed clear, therefore, that beyond secular 39 Ṣidqī, Kayfa khuliqa l-insān? 306. 40 This never happened; instead, Muḥammad Tawfīq Ṣidqī stepped in and wrote a long piece on "the orbit (ʿilm al-falak) and the Quran". 47 The slight variation in the title as compared to Shahrastānī's book appears to be programmatic: Although often used interchangeably for "astronomy", falak denotes the celestial sphere in general and is used in this sense also in the Quran (Q 21:33 and 36:40), whereas hayʾa (lit. "shape") is not. 48 Ṣidqī's text consists of two distinct layers which are, however, constantly and deliberately interwoven. On the one hand, he tries to give an accurate picture of the universe, couched in scientific terms: our solar system (majmūʿa) with the eight planets known at the time, 49 plus the existence of dwarf planets, the fact that their orbits are elliptical and that their respective length of a year depends on their orbital period, that they are dark bodies illuminated only by the sun, the different degrees of brightness resulting thereof, the powers of gravitation, fixed stars (which are not really "fixed", as they move constantly, as do all celestial bodies), comets and their characteristics, the existence of other remote galaxies, et cetera -the whole set-up is there, and although there are (unlike in al-Muqtaṭaf) neither diagrams nor other visualizations, Ṣidqī tries to make up for it by adducing some English terms in brackets. 50 Not everything is perfect (Halley, mudhannab Hālī, for instance, is mixed up with other comets), 51 and nothing of it was remotely new even in his days; nevertheless, in view of his anticipated readership, Ṣidqī provided, on a modest level, a fairly reliable summary of the universe. But science proper was not his primary concern, as is already announced in the title, and therefore a second layer stretches through the text, which is entirely exegetical. The Quran is omnipresent, and not a single detail of the universe comes along without the appropriate Quranic support. To single out but a few: the gravitational attraction of fixed stars towards their circulating planets is corroborated by Q 79:27 and 51:7; its cessation would lead straight to Q 82:1 and 84:1; moons orbit planets which are sunlit because of Q 71:16; all stars are in constant motion according to Q 81:15 and 21:33; planet earth's circling round the sun becomes clear from Q 65:12, 21:30 and 27:88; and whatever silly and absurd ideas the ancients may have cherished about the stars, the Quran did away with them in Q 24:43 and 39:21. 52 As to star constellations, they are only illusions, although what is mentioned in Q 53:14 and 16 as sidrat al-muntahā may be of this kind -the more so as the term sidra not only denotes the final destination of all creation after Judgement Day, but could also be derived from the Latin word sideris, i.e., "stars". 53 Imagining the existence of other galaxies (ʿawālim) besides ours, inhabited by other creatures, is no problem, Ṣidqī posits, since the Quran constantly addresses God as rabb al-ʿālamīn, Lord of the worlds in the plural. 54 Distances, however, are gigantic, as is indicated by Q 22:47, 70:4 and 32:5; our neighbouring galaxy is 19 131 030 000 000 miles away, and its light reaches us only after more than three years. 55 This means that our sun along with its planets orbits another sun which thus functions as the sun's central body, and it is absolutely conceivable that all these solar systems (majāmīʿ) 50 Ṣidqī, ʿIlm al-falak wa-l-Qurʾān 578-579, 582, 593, 599; by contrast, al-Muqtaṭaf published already in the very first issues articles on astronomy accompanied by illustrations, see, e.g., al-Muqtaṭaf 1 (1876), 7-9, 29-32, 58-60. Al-Manār did not have any illustrations throughout its existence. 51 Ṣidqī states that it appeared in 1843, 1880 and 1882; to his credit, it has to be said that Halley's appearance in April 1910 (on p. 583, he writes "finally, there appeared one which we observed last year, i.e., 1910") was preceded, some months previously, by another, brighter comet which was later dubbed "1910 I"; see for details Tammann, Halleys Komet 240. Al-Muqtaṭaf was better informed: 36 (1910), 203-204. 52 Ṣidqī, ʿIlm al-falak wa-l-Qurʾān 580, 581, 586, 589, 595, 598, respectively. 53 Ṣidqī, ʿIlm al-falak wa-l-Qurʾān 583-584; on the term see also Rippin, "Sidrat al-Muntahā". 54 Ṣidqī, ʿIlm al-falak wa-l-Qurʾān 593, 597. then gather (qāṭiba) around one single and common centre where some sort of electromagnetic induction is effective. This, Ṣidqī concludes, is what is probably meant by the term ʿarsh in Q 23:86-87 when it talks about "the Lord of the Great Throne". As to the question whether this ʿarsh is fixed or in motion, and what kind of force is active there (after all, it can't be gravitation), Ṣidqī answers that God makes a specific power work here which is called "the carriers of the throne" (ḥamalat al-ʿarsh), and which we do not perceive, just as we do not perceive magnetism, electricity, or other gravitational forces; eight such forces called "angels" (malāʾika) are duly described in the Quran (69:17; also 39:75 and 40:7). 56

Ṣidqī's Lectures at the Dār al-daʿwa

Ṣidqī was involved in Rashīd Riḍā's abovementioned school Dār al-daʿwa wa-lirshād from the very beginning, as one of the ten members of the administrative council (majlis al-idāra). 57 When the school opened, he was, apparently besides his regular job as a prison physician, entrusted with the teaching of science, medicine and, sure enough, Christianity. 58 The articles on the sciences which appeared in the following years were prepared by him clearly in the context of his lectures. The first set, made up of three parts, was a rather curious item, particularly for a journal like al-Manār, for it consisted of a glossary of Arabic terms, often (but far from exclusively) of a scientific nature, and it was intended to refute those critics who maintained that the Arabic language was not able to express scientific facts adequately. In most cases, the English equivalents are given, sometimes accompanied by short explanations in Arabic; but there is no alphabetical or otherwise discernible order, and no criteria are named according to which a word was included. The result is an interesting chaos, with words like athāth al-bayt (furniture) standing next to al-farzaja (pessary), or al- 55 Ṣidqī, ʿIlm al-falak wa-l-Qurʾān 579. 56 Ṣidqī, ʿIlm al-falak wa-l-Qurʾān 590-591. Ṣidqī readily acknowledges here that he got this idea from a talk he once had had with Rashīd Riḍā. In a fatwā issued some time after Ṣidqī's death, Rashīd Riḍā referred to this interpretation himself, when answering the question how Q 36:38 ("And the sun -it runs to a fixed resting place") was to be understood. In his answer, he directed the reader to Ṣidqī's article, but also adduced a ḥadīth via Abū Dharr; Rashīd Riḍā, Ḥarakat al-arḍ, 670-671. Given Ṣidqī's overall reasoning, Stolz's conclusion that "through such arguments, a reader also received a surprisingly thorough introduction to modern astronomical terms" (The lighthouse 201) seems a little over-optimistic to me. 57 Rashīd Riḍā, Jamāʿat al-daʿwa wa-l-irshād 115 (where he was presented as "the author of the book al-Dīn fī naẓar al-ʿaql al-ṣaḥīḥ").

judarī (smallpox) next to istamnā (to masturbate). 59 Apparently, these lists were meant to be teaching material for his courses at the Dār al-daʿwa, and the lecture notes for these courses then resulted in a second set of articles that were published in al-Manār in 19 instalments, between October 1914 and October 1919. Here, the structure is fairly clear, and so is the intention: the students should become familiar with the basics of some natural and medical sciences in general, and sanitary rules in particular. Two important side effects were supposed to be the Arabization of scientific vocabulary and, inevitably, the application of these sciences to Islamic religious texts. 60 In view of these general guidelines, and given

Ṣidqī's own education as physician, the curriculum was as follows: elementary chemistry (part 1); physics, including the atmosphere, electricity, optics (1-3);

anatomy and inner organs, including metabolism and sexuality (3-8); hygiene, including clothes, personal care, household, sleep and dreams (8-9). The by far most detailed part, covering the remaining nine parts, was on bacteriology and pathology, which is certainly also due to the fact that epidemic diseases were a constant threat in the Middle East (and far beyond) in this era, especially in the context of local pilgrimages and the annual ḥajj to Mecca. 61 Ṣidqī accordingly details a great number of infectious diseases caused by parasites, all kinds of bacteria (typhus, plague, cholera, tuberculosis, and many more) or insects (malaria, various fever diseases), and ends his catalogue of dreadful things with a chapter on syphilis (al-ifranjī, probably derived from "French disease"). 62 All in all, this adds up to no small amount of usable and practical knowledge, the more so as Ṣidqī gives the particulars about the causes for every illness, its symptoms, treatment and prophylaxis in a very systematic manner. 63 As it turns out, he is quite up-to-date with regard to medical research, for he even quotes the British medical review The Lancet on the necessity of adopting hygienic measures against the spread of gonorrhoea (which is in his eyes both a 58 Ryad, Islamic reformism 163. 59 Ṣidqī, Kalimāt ʿilmiyya ʿarabiyya part 2, 677-678. 60 Ṣidqī, Durūs sunan al-kāʾināt, part 1, 853. 61 See, e.g., Essner, Cholera der Mekkapilger; Tagliacozzo, Hajj in the time of Cholera. 62 Ṣidqī,part 19,[305][306][307][308][309][310][311][312][313][314] This explains why other scientific issues do not loom large here; Darwinism, for instance, is relegated to a single footnote -in which Ṣidqī calls the theory again "all in all correct without doubt" (fa-l-madhhab fī l-jumla ṣaḥīḥ lā shakk fīhi), not the least because of Q 71:14; Durūs sunan confirmation of the calls for cleanliness in Islamic law and an urgent warning against the lousy conditions in brothels). 64 He knows not only the name and the fame of Louis Pasteur and Robert Koch, whom he calls "one of the greatest scholars of his time" 65 , but also of those who only recently detected the pathogens of whooping cough (Jules Bordet and Octave Gengou) or dysentery (Kiyoshi Shiga and Walter Kruse). 66 And he is aware that there are a few things everybody could do in order to avoid a tuberculosis infection: isolation of and keeping one's distance from the infected, avoiding crowded places such as theatres or cinemas (dūr al-ṣuwar al-mutaḥarrika) -in short, things that sound disturbingly familiar at the time of writing the present article (January 2021). 67 This is not to say, however, that Ṣidqī did not seize the opportunity for exegetical digressions in these lectures either. Already in his list of words, he inserted an entry on sijjīl, which he rendered as "pumice-stone", identified in the Quran as the stones that God made rain on the people of Lot (Q 15:74) and the "people of the elephant" (Q 105:4). While the former, Ṣidqī explains, means a volcanic eruption, in the latter case these stones were probably infected with smallpox germs (mīkrūb al-judarī) which then led to an epidemic among the aṣḥāb al-fīl. Ṣidqī here -knowingly, one may surmise, although he does not mention the name -follows Muḥammad ʿAbduh's footsteps, who had also interpreted this verse as a sign of an outbreak of smallpox or measles. 68 During his lectures, Ṣidqī sometimes comes up with intriguing variations on themes he had already dealt with previously. As we have seen above, the fatherless birth of Jesus could have been, in his eyes, the result of parthenogenesis. 69 Now, in the context of sexual organs, he comes to discuss hermaphrodites, and considers the idea al-kāʾināt, part 5, 207-208. 64 Durūs sunan al-kāʾināt, part 15, 353-354. (The reference is to M.F.H. Gamble, "A contribution to the etiology of epidemic cerebro-spinal meningitis", The Lancet 188.4850 (12 Aug. 1916), 277-279). 65 Ṣidqī, Durūs sunan al-kāʾināt, part 9, 531 and part 13, 225. 66 Ṣidqī, Durūs sunan al-kāʾināt, part 15, 357 and part 16, 426. 67 Ṣidqī, Durūs sunan al-kāʾināt, part 13, 232-233; Ṣidqī adds more pieces of advice: boiling and cooking food well, avoiding bodily, mental, and sexual overexertion, doing sports in fresh air, eating easily digestible things, getting enough sleep, refraining from smoking and from inhaling exhaust fumes. 68 Ṣidqī, Kalimāt ʿilmiyya ʿarabiyya, part 2, 674-675; cf. Vacca, Sidjdjīl and Beeston, al-Fīl; on ʿAbduh's exegesis see Shabana, In pursuit of consonance, 15. Ṣidqī joins here (675-676) another exegetical exercise: talking about volcanos, such an eruption may have been the reason why Dhū l-Qarnayn's wall against Gog and Magog (Q 18:95) no longer exists. See also van Donzel, Ott, Yādjūdj wa-Mādjūdj; Radtke, Weltgeschichte 136.

that Mary might have been such a hermaphrodite, in the sense that she had both female and male sexual characteristics, the female ones being predominant and thus enabling her to give birth and suckle the infant. True, he concedes, this is an utterly rare case, and we do not know of any other example, but it would not contradict the belief that Mary and Jesus were a "sign for the worlds" (āya li-l-ʿālamīn, Q 21:91), for "in your creation, and the crawling things He scatters abroad, there are signs for a people having sure faith" (Q 45:4). 70 Also, the angels, whom we have met earlier on as the central cosmic force that stabilizes God's throne, 71 make a remarkable comeback in microbiology. Lecturing about the general characteristics of microbes and their mode of operation, Ṣidqī makes a point of stressing that whatever is sent by God onto earth, every force of nature, can be called malak, by virtue of Q 13:13, which establishes a connection between thunder and the angels. The microbes which are sent by God can therefore be classified as angels as well, since dead bodies decompose only through the agency of microbes, whereby gases are released. Now if we say that the spirit (rūḥ)

is the ethereal matter linked to a body, we cannot exclude the option that this rūḥ is released when the corpse decomposes because of the microbes in it -which takes us to Q 6:93 where the angels, in the agonies of death (ghamarāt al-mawt), stretch out their hands and say "deliver your souls!" By this, Ṣidqī quickly protests, he is not denying the existence of other heavenly guardians, and Gabriel most certainly is one of a different kind; rather, microbes fall under the category of what is described as angels, without all angels being microbes. Moreover, also Q 35:1 which mentions the angels' wings can be applied to microbes, since some of them, such as the cholera microbes, have fringes in pairs. In this sense, he ends his angelic excursion, the jinns, whose semantic root means "to conceal", may also be a placeholder for microbes which have been sent by God but are hidden from human view. and dogs, by affirming that his intention was to make his readers aware of the foresight of the sharīʿa, this was his lifetime programme: to explain scientific details against the backdrop of religion as a meaningful superstructure. The only reference work that was permitted in this context was the Quran, for there, all scientific findings had already been anticipated, as Ṣidqī never tired of stressing. 80 It goes without saying that his approach to natural science from the religious side was perfectly in line with Rashīd Riḍā's demands on the purpose of his Dār al-daʿwa wa-l-irshād: in the curriculum, it was explicitly stipulated that all sciences of natural laws (ʿulūm sunan al-kāʾināt) had to be taught in an Islamic way (ʿalā ṭarīqa islāmiyya) in which all rules would be expressed with God's law (bi-l-sunna al-ilāhiyya), e.g., by naming them "God's law of gravitation, God's law in the extension of bodies through heat", etc. While the teaching method of mathematics (which characteristically did not play any role at all in the Manār articles) was the same as in public schools, astronomy, like the other natural sciences, would be combined with Quranic verses in order to explain that 5. However, he neither referred to these articles later in the context of the Dār al-daʿwa wa-lirshād, nor with regard to Ṣidqī's contributions. 77 Dallal,Islam,165. 78 So the Quran was ever-present for Ṣidqī. In contrast, completely absent in his texts was the Prophet. This had of course much to do with his general and unyielding rejection of the genre of ḥadīth per se that has already been mentioned above. 82 It paid off for him particularly in his treatment of astronomy, for there was not only the ox carrying the earth on its horns that somehow no longer met scientific criteria. There was, in addition, another famous ḥadīth to the effect that the sun every day, after it has set, prostrates itself before God's throne, whereupon it is granted permission to rise again the following day. While Rashīd Riḍā for many years was at loggerheads with Yūsuf al-Dijwī (d. 1946), a conservative Azhar scholar, over precisely this tradition, and spilled much ink to put things straight, 83 all this was no problem at all for Ṣidqī.

He dismissed these traditions by plainly and simply ignoring them. There was one exceptional case, in his lectures on hygiene and housekeeping, when he came to mention the famous tradition "if a house fly falls in the drink of anyone of you, he should dip it (in the drink) and take it out, for one of its wings has a disease and the other has the cure for the disease." Here, it suited him just fine that the ḥadīth was transmitted by Abū Hurayra, who had a dubious reputation in certain circles anyway, and so he made do with a footnote and a few disparaging remarks on this "glutton who lived off the Prophet and his companions". 84 Ṣidqī ended this passage by reassuring his students that even if the Prophet had said such a thing, it would not be obligatory for Muslims to emulate him in purely worldly issues, because in this realm prophets were allowed to err. This remark is rather characteristic of Ṣidqī's idea of prophets in general and of Muḥammad in particular: he was nothing but a tool in the Lord's hands Reading holy scriptures from a faithful, yet markedly "scientific" perspective and explaining the laws of nature by quoting Quranic (or, for that matter, Biblical) verses often looks like an attempt to have one's cake and eat it, too. 87 As it became increasingly impossible to ignore the radical change of the traditional worldview, it 85 Ṣidqī, al-Dīn fī naẓar al-ʿaql al-ṣaḥīḥ, part 2, passim; part 3, 495-497. On the term ummī and its many interpretations, see Günther, Muḥammad, the illiterate prophet. It is also telling in this context that Ṣidqī is ready to accept as real Muḥammad's so-called "Night Journey" (isrāʾ), which is associated with Q 17:1 and 53:1-21, whereas he rejects the story of Muḥammad's ascension to heaven (miʿrāj) which is based on tradition literature; for Ṣidqī, this was only a dream that was in no connection with the isrāʾ; ʿIlm al-falak wa-l-Qurʾān, 585-586; on the issue of heavenly journeys in Islam in general, see Günther, "Gepriesen sei der, der seinen Diener bei Nacht reisen ließ" (with extensive bibliography). 86 Ṣidqī, Durūs sunan al-kāʾināt, part 7, 370. 87 To give but one, perhaps slightly surprising, example from a different context: in 2014, the professor for applied physics at the Karlsruhe Institute of Technology, Thomas Schimmel, gave a public lecture at the University of Munich on "Der Urknall und die Gottesfrage. Ein Streifzug vom Inneren der Atome bis an die Grenzen des Universums" which ended in an implicit proof of the existence of God and an outright sermon. The lecture is available at https://videoonline.edu.lmu.de/de/node/6459 (last accessed: 10 February 2021. I owe this reference seemed, to some, more promising to take the bull by the horns by asserting that all discoveries and inventions had already been announced in the Quran, which merely had be read accordingly. It is therefore only natural that from the late 19 th century onward, the intensifying debates on issues such as astronomy or Darwinism which by necessity affected the religious worldview also made their way into Quranic exegesis. Muḥammad Tawfīq Ṣidqī's articles fit into this category quite well, although he did not write a Quranic commentary proper. The closest he came in this regard was a fourpart series of articles on "the Quran and science", yet again directed against

Orientalists and missionaries and their (alleged or real) misconceptions of the Quran, in which he singled out a great number of verses in order to show their compatibility with modern science. The Quran, he concluded, may not have been revealed in order to teach the humans natural sciences, but it contained enough exact scientific expressions and details which were known to nobody at the time, and which no Arab could ever have studied, had there not been God's revelation. 90 His seemingly strict focus on rational thinking did not preclude him from occasionally showing some to Ulrich Rebstock). 88 On the genre of tafsīr ʿilmī in general, see Jansen, The interpretation of the Koran 35-54; recent studies are Elshakry, The exegesis of science, and Shabana, In pursuit of consonance (both with comprehensive bibliographies); on Jawharī's commentary in particular, see Daneshgar, Ṭanṭāwī Jawharī. 89 Al-Kawākibī, Kitāb Ṭabāʾiʿ al-istibdād, 208-209; see also Weismann, al-Kawākibī, and the references given there. 90 Ṣidqī, al-Qurʾān wa-l-ʿilm, part 4, 452.

affinity towards supernatural phenomena such as necromancy or telepathy. [START_REF]ʿādāt fī l-islām 122-123[END_REF] And it most certainly did not preclude him from having an utterly conservative and patriarchal understanding of society: he demanded that the legal age for marriage of girls be lowered to fourteen or possibly younger in order to avoid promiscuity, masturbation and lesbianism among them, 92 he defended polygyny as a protection against prostitution, fornication and contagious diseases, still being optimistic that women would understand that the husband is their provider and breadwinner (ʿāʾiluhā wa-kāfiluhā) [START_REF] Ṣidqī | Dīn fī naẓar al-ʿaql al-ṣaḥīḥ[END_REF] . And the strict egalitarianism of Islam as illustrated by Q 2:256 (lā ikrāh fī l-dīn) notwithstanding, if prevented from daʿwa, Muslims were ordered to fight (umirū bi-l-qitāl) in order to ward off temptation (fitna), until the threatener submits to the rule of Islam (Q 2:193) [START_REF] Ṣidqī | fī naẓar al-ʿaql al-ṣaḥīḥ, part 4, 699-700. The reader be reminded here of Ṣidqī's other field of activity, namely[END_REF] -by which last sentence he may be identified as a precursor of 20 th -century Islamist ideologues. 95 After the closure of the Dār al-daʿwa wa-l-irshād and Ṣidqī's death, the natural sciences ceased to be of notable importance in al-Manār, and on the few occasions when Rashīd Riḍā later on referred to cases in point, mostly in the context of fatwās, he did so on strictly exegetical grounds. 96 This also spared him a more thorough attempt at coming to terms with the fashionable "scientific" exegesis of the Quran.

With regard to this approach, he maintained a characteristically ambivalent attitude.

On the one hand, he mildly criticized Jawharī's abovementioned al-Jawāhir, saying that it contained "everything except exegesis" (without, however, denying the author God's reward for his good intentions). 97 On the other hand, he had no qualms about availing himself of it and declaring Darwinism as acceptable because of the support of a number of Quranic verses. [START_REF] Riḍā | [END_REF] While advocating for the inclusion of the natural sciences in the educational curricula, he never wavered between priorities of

  Ḥadīth maʿa Shaykh al-Azhar 158; Rashīd Riḍā returned to this episode later on twice: Jamʿiyyat al-daʿwa wa-l-irshād 59, and al-Manār wa-l-Azhar 240-241. 8 With regard to Rashīd Riḍā's fatwās, see Stolz, By virtue of your knowledge; Shavit, The evolution of Darwin 19-23; Shavit, Scientific and political freedom 75-79; with regard to the treatment of science in the Tafsīr al-Manār, see Jomier, Le commentaire coranique 150-163; Nispen tot Sevenaer, Activité humaine 84-101. 1 Rashīd Riḍā's daʿwa School and the Necessity of the Natural Sciences for Islamic Reform Muḥammad Rashīd Riḍā hailed from a family of notables near Tripoli in what later became Northern Lebanon. After attending the local Quranic school and the national al-Madrasa al-rashīdiyya (which he left after one year because all the classes were conducted in Turkish 9 ), he entered the Arabophone al-Madrasa al-waṭaniyya that had been opened by Ḥusayn al-Jisr

2 Muḥammad Tawfīq Ṣidqī and his Reading of the Natural Sciences

  Sunna."25 As the normative religious texts were Rashīd Riḍā's home ground, he approached problems pertaining to natural science exclusively from this angle, not from the perspective of science proper with which he was not familiar enough. Both in his contributions to the materialism debate and in his treatment of traditions about Prophetic miracles that touched on cosmological issues, his reasoning remained thoroughly theological, and his occasional excursions into the laws of nature never left the frame of natural theology.26 The lighthouse 259-262.26 Stolz, By virtue of your knowledge 234-246 (on the materialism debate); Juynboll, Authenticity 145-147 (on miracles such as the splitting of the moon, or the opening of Muḥammad's breast and the washing of his heart).

Riḍā, ʿUjāla 449-450 23 Rashīd Riḍā, Riḥlat ṣāḥib al-Manār 939-940. 24 Rashīd Riḍā, Bāb al-fiqh 697; Rashīd Riḍā, al-ʿAmal bi-khabar al-tilifūn; Rashīd Riḍā, Ithbāt shahr Ramaḍān 64. This question was not yet unanimously decided at the time; for details on this debate, see Skovgaard-Petersen, Defining Islam 80-99. the Nevertheless, articles about more scientific aspects of nature did have a place in al-Manār for more than a decade. They were all written by one of Rashīd Riḍā's closest collaborators and personal friends, plus his family doctor, Muḥammad Tawfīq Ṣidqī. Born in 1881, he studied medicine, graduated in 1904 and then served as a physician in various prisons in Cairo, before he died of typhus in 1920. 27 Besides his articles on the natural sciences to which we will turn presently, he made a name for himself because of a great number of controversial contributions to two topics that have received their fair share of attention in Western scholarship: his uncompromising rejection of the entire corpus of the Prophetic ḥadīth (and the debate it triggered off) has been analysed by G.H.A. Juynboll, 28 while his various polemics against Christianity have been studied in great depth by Umar Ryad. 29 Some of these attacks against the missionaries in Egypt were so fierce that they brought the Manār close to being banned by the British authorities, but at the same time, Ṣidqī was acknowledged as "easily the most subtle, up-to-date, and best informed controversialist of his 25 Rashīd Riḍā, Ithbāt hilāl Ramaḍān 585; other statements to this effect are: al-Ṣawm wa-l-fiṭr 915-916; Ḥikmat al-ṣiyām 814-815; Iʿtibār ruʾyat al-hilāl 706-707; al-Jawāb ʿan masʾalat al-ṣiyām 436-437; Ithbāt shahr Ramaḍān 64; Masʾalat hilāl Ramaḍān 278; see also Stolz, 27 See the obituary by Rashīd Riḍā, Tarjamat al-ṭabīb Muḥammad Tawfīq Ṣidqī. 28 Juynboll, Authenticity 21-32; cf. also Brown, Rethinking tradition 40-42, 67, 74. The debate was caused by Ṣidqī's articles in 1906/07 (al-Islam huwa al-Qurʾān waḥ dahu) and dragged on until autumn 1909. 29

  Goldziher, Richtungen 349; two more early references are Adams, Islam and modernism 239-242, and GAL S iii, 323-324; they all referred to Ṣidqī's article on astronomy, see below, note 47. The only noteworthy posterior references are Jansen, The interpretation of the Koran 43-44. and, to a rather limited degree, Stolz, The lighthouse 200-201.

33

Ṣidqī, Taḥrīm al-khinzīr wa-najāsat al-kalb 308; on the cultural history of the pig in Islam, see Kruk, The saddest beast?; on dogs, see Mikhail, The animal in Ottoman Egypt 67-87.

  Ṣidqī turned to only a few months later was hardly less controversial. The reception, adoption, and controversial discussion of modern astronomy and heliocentrism had by then been going on in the Ottoman Empire in general and Egypt in particular for over a century. The first modern Arabic textbook on astronomy appeared in 1874, and some journals, like al-Muqtaṭaf, regularly published articles that sought to propagate the heliocentric model among a wider public. 41 Alas, as was the case with Darwinism, reluctance was enormous. Muḥammad al-Aḥmadī al-Ẓawāhirī, who was later to become Shaykh al-Azhar and Rashīd Riḍā's reformist nemesis, 42 complained as late as 1904 about the pitiable students who were

  Ṣidqī, Kayfa khuliqa l-insān? 306-307; Ṣidqī used this argument also in his anti-Christian writings, see Ryad, Islamic reformism 251-252.; Shavit, Scientific and political freedom 76, misses this article and thus portrays Ṣidqī as a more or less unconditional supporter of Darwinism. 41 See Stolz, The lighthouse 145-206; Dallal, Islam, science 162-165; see also above note 13. 42 On al-Ẓawāhirī (1878-1944; rector 1929-1935) and his controversies with Rashīd Riḍā see Brunner, Education 120-131. 43 Al-Ẓawāhirī, al-ʿIlm wa-l-ʿulamāʾ 101. 44 Rashīd Riḍā, Kurawiyyat al-arḍ; Rashīd Riḍā, Ithbāt istidārat al-arḍ; the two references in the latter fatwā are, first, to the Ottoman statesman Ghāzī Mukhtār Pāshā (1839-1919) who served as the powerless Ottoman "Extraordinary Commissioner to Egypt" during the British rule; as an amateur , also in religious circles, one had to look for an answer to this question. The first to do so was the Iraqi Shiʿite scholar (and later Minister of Education), Hibat al-Dīn al-Shahrastānī who, in 1910, published a long treatise on "Astronomy (al-hayʾa) and Islam" in which he declared modern knowledge about the cosmos not only to be compatible with Islamic tenets and Quranic revelations, but in fact even based on them. 45 Rashīd Riḍā, to whom the author had sent a copy, published a very short announcement in al-Manār and promised, in shāʾ allāh, a more detailed review of it. 46

astronomer, he also proposed a comprehensive calendar reform, based on the solar year; on him, see Reinkowski, Uncommunicative communication 409 and passim. The second reference is to Muḥammad Bayram al-Khāmis (1840-1889), a Tunisian reformer and prolific author, and his most important book Ṣafwat al-iʿtibār, which is a world history, local Tunisian historiography, and travelogue; on him, see Tunger-Zanetti, La communication 125-127 and index, s.n. Bayram al-Ḫāmis.

journalists

Trying to Have the Cake and Eat it, too

  72Muḥammad Tawfīq Ṣidqī's lecture series ended in October 1919, half a year before his69 See above, note 40.70 Arberry's translation; seeṢidqī, Durūs sunan al-kāʾināt, part 6, 302-303; the passage is also dealt with by Ryad, Islamic reformism 252; on the importance of hermaphrodites in Islamic law, see Rebstock, Mathematische Quellen (with extensive bibliography). 71 See above, note 56. 72 Ṣidqī, Durūs sunan al-kāʾināt, part 10, 604-607. By this last remark, Ṣidqī is once again back to ʿAbduh (again without mentioning his name) who famously also interpreted the jinns to be microbes; see Berger, Esprits et microbes 557; Elshakry, The exegesis of science 501; Jansen, The death; the third part, on illnesses whose pathogenic agents were not yet known at the time, never appeared in al-Manār. As a separate book, it had already been published in 1915, and Rashīd Riḍā had spoken very highly of it in a short review, particularly underscoring two points: first, it contributed to the Arabicization of scientific When looking at Ṣidqī's articles on the natural sciences in al-Manār as a whole, one notices a few striking characteristics. For one thing, there are no references whatsoever to the long tradition of Arabic or "Islamic" science, neither in the field of astronomy nor in medicine -as if Ibn al-Haytham, Ḥunayn b. Isḥāq or al-Bīrūnī had never lived. 75 This shows in fact two things: on the one hand, Ṣidqī was completely detached from the findings of pre-modern Muslim science, and he did not even use the classical tradition for the apologetic accusation that European scientists had actually only appropriated what had originally been conceived in "the Orient". 76 While this is The interpretation of the Koran 44. Drafts of further lectures did exist, and the facsimile reproduced in Ryad, Islamic reformism, 371, is likely to be such a draft, as it deals with illnesses that had not been treated in the previous lectures (Bee Poison, and its medical use for muscle growth; Bell's Paralysis/Bell's Palsy and its causes). Ṣidqī's intention to continue his lectures even after the closure of the Dār al-daʿwa was thwarted by his premature death; see the short notice (presumably by Rashīd Riḍā) at the very end of the printed book: Ṣidqī, Durūs sunan al-kāʾināt (3 rd edition), 363. 74 Rashīd Riḍā, Madrasat Dār al-daʿwa (1915); al-Baṭal, Faqīd al-islām 197; see also Ryad, Islamic reformism 165. 75 On the classical medical and astronomical tradition in Islam, see in detail GAS, iii (medicine 247-256 on Ḥunayn, d. 873) and vi (astronomy 251-261 on Ibn al-Haytham, d. 1041, and 261-276 on al-Bīrūnī, d. 1048). 76 This does not hold true to the same degree of Rashīd Riḍā, at least not with regard to the initial stages of al-Manār, for in its third volume (1900), he had published a five-part series on classical Islamic civilization and the need to revive it for the sake of Arab unity and renaissance. There, he devoted also a fair share of attention to the discoveries of classical Arab astronomy and to a brief history of Arab mathematics: Madaniyyat al-ʿArab, esp. part 3, 388-391; part 4, 412-414, and part strikingly true also for debates about modern astronomy in other venues, 77 Ṣidqī was no less detached from his own environment. A trained physician, he paid homage to those who detected microbes, but this was the exception, because otherwise, there was no integration of his articles into contemporary academic reasoning. Neither did he refer to Egyptian or Ottoman astronomers and their findings, 78 nor did he, in his statements on Darwinism, mention Ḥusayn al-Jisr, Jamāl al-Dīn al-Afghānī, Muḥammad ʿAbduh, Shiblī Shumayyil, or anyone else who had previously participated in the debate. 79 But this was not the point for him, because what counted for him in the end was not scientific progress and increased knowledge about nature, but religious reinsurance. When he began his very first contribution in 1903, on pigs

	terminology, and secondly, it served as a mediation (tawfīq) between science and
	religion, in the sense that benefiting from science was a religious command, and that it
	did absolutely not contradict the belief in God and the trust in Him (tawakkul) to guard
	against the attacks of microbes. 73 Rashīd Riḍā's school closed at some point
	afterwards, during the war, after a continuoal and ultimately unsuccessful struggle for
	funding. 74
	4 interpretation of the Koran 39. 73 Rashīd Riḍā, Kitāb Durūs sunan al-kāʾināt 719-720.; a second edition came out in 1348/1929-1930
	(328 pp.), a third one in 1354/1935-1936 (370 pp.); cf. Nuṣayr, al-Kutub al-ʿarabiyya 271 (entries
	m/402 and 403); Jansen,

  It is characteristic that his astronomy article appeared in the very same year as Carlo Alfonso Nallino's lectures on the history of Arab astronomy in the Middle Ages which he had given (in Arabic) in 1909/1910 at the Egyptian University: Nallino, ʿIlm al-falak; see Reid, Cairo University and the Orientalists 51. Ṣidqī, al-Dīn fī naẓar al-ʿaql al-ṣaḥīḥ, part 3, 496; ʿIlm al-falak wa-l-Qurʾān 593-594; Durūs sunan modern knowledge corresponded to what God had revealed to the Prophet 1300 years ago. 81

79

This was also in marked contrast to al-Shahrastānī who in his abovementioned book al-Hayʾa wa-l-Islām (see above, note 45) not only knew the history of astronomical studies, but was also well aware of contemporary scholarship:

Al-Shahrastānī, al-Hayʾa wa-l-Islām 37-38, 59

; see also

Bashkin, The Iraqi Afghanis and ʿAbduhs,[144][145][146][147][148][150][151][152]

  Authenticity 147-148. On the classical background, see Radtke, Weltgeschichte 20, 277.84 Ṣidqī, Durūs sunan al-kāʾināt, part 8, 456-457; the portrait Ṣidqī drew of Abū Hurayra was so order to transmit the Quranic revelation, and the only miracle here was that God chose a poor orphan for this task, a nabī ummī, which means "illiterate", full stop.Ṣidqī goes to great lengths to prove historically that Muḥammad grew up in a completely uneducated society and that he was in a state of constant bewilderment and only knew to discern truth from falsehood when God's revelation finally reached him.85 What was primarily directed against the missionaries and intended to counter the allegation that Muḥammad was a "false prophet" who only appropriated what Jesus and others had said before, had indirect repercussions on Muslims, too.Refraining from quoting any ḥadīth on any of his topics meant scaling down Muḥammad, who completely disappears behind the Quran and is more or less cancelled out as a normative model for the believers. When Ṣidqī, in a long sidetreatise, defends marrying off girls at a very young age, he naturally also mentions that Muḥammad married ʿĀʾisha when she was only nine years old (after she had already

	al-kāʾināt, part 15, 354. 81 Rashīd Riḍā, al-ʿUlūm wa-l-funūn 816. 82 See above, note 28. 83 Rashīd Riḍā, al-Manār wa-l-Azhar 20, 68-88; cf. Juynboll,

negative that Rashīd Riḍā felt compelled to insert a slightly attenuating footnote of his own: Ṣidqī, Durūs sunan al-kāʾināt, part 8, 458; on the afterlife of this debate see Juynboll, Authenticity 141-143; on the many polemics in modern times around Abū Hurayra in general Juynboll, Authenticity 62-99. The tradition (via Bukhārī) is very handy at https://sunnah.com/bukhari/59/126 (last accessed: 10 February 2021). Another passage where Ṣidqī criticized in passing traditions on contagion is Durūs sunan al-kāʾināt, part 10, 609-610.

in been engaged to Jubayr b. Muṭʿim b. ʿAdī for two years). But for him, it is not a question of today's Muslims having to emulate the Prophet and marry young girls

because Muḥammad had done so; instead, he concludes that this was customary in a hot country where all girls reached puberty so early in life, so that it was rather Muḥammad who emulated nature by doing what everybody around him did.

86

  Muḥammad Aḥmad al-Iskandarānī (d. 1889), like Ṣidqī an Egyptian physician, is usually credited with the establishment of what came to be called the "scientific exegesis" (tafsīr ʿilmī) of the Quran, and it was Ṭanṭāwī Jawharī (1862-1940) who in the 1920s-30s published the most important work of this genre, his al-Jawāhir fī tafsīr al-Qurʾān al-karīm in 26 volumes. 88 But it was not only in the field of Quranic exegesis proper that this road was taken, as could be seen in the contributions by Ḥusayn al-Jisr or Hibat al-Dīn al-Shahrastānī; even an early precursor of Arab nationalist thought, ʿAbd al-Raḥmān al-Kawākibī (d. 1902), deemed it appropriate to incorporate into his political treatise against Ottoman despotism a number of verses which allegedly anticipated modern scientific discoveries, including microbes. 89

For details, see Glaß, Der Muqtaṭaf und seine Öffentlichkeit ii, 415-434; on the debate about Darwin in general, see Elshakry, Reading Darwin passim. On al-Hilāl and its founder, the Greek orthodox Jurjī Zaydān, see Dupont, Ǧurǧī Zaydān passim.

Handy introductions to Rashīd Riḍā's biography and works are Ende, Rashīd Riḍā, and Ryad,

Rashīd Riḍā, al-Manār wa-l-Azhar

14Rashīd Riḍā, 233. 15 Rashīd Riḍā, 231, 251; a great number of relevant statements were later on assembled by him in this last book of his which came out in 1934, see Rashīd Riḍā, al-Manār wa-l-Azhar 201-252.16 Gesink, Islamic reform 210-211. 17 See above, note 7.18 Rashīd Riḍā, al-Manār wa-l-Azhar 253.

Ṣidqī, Taḥrīm 306.

My sincere thanks go to Werner Ende, Ulrich Rebstock, Umar Ryad, and Monika Winet for their helpful comments.


Arnaud Quillent

Samy Ammari

Émilie Chouzenoux

Víctor Elvira

Nathalie Lassau

MACHINE LEARNING BASED GUIDED DIAGNOSIS OF PAROTID TUMOURS FROM MRI

Diagnosis of parotid gland tumours rely on magnetic resonance examination, fine-needle aspiration biopsy, or in some cases, invasive surgery that can damage facial nerves. In this work, we propose a machine learning model that can discriminate parotid tumours into histopathological subtypes from magnetic resonance imaging (MRI) scans, and further evaluate its impact on the diagnostic decisions of radiologists. We aim at improving the diagnosis of parotid neoplasms while avoiding any physical harm to patients. The radiologists improved their performance after observing the predictions of the algorithm. We conclude that machine-learning-based radiomics classification can assist radiologists.

DATA

The cohort gathers patients that underwent an MRI examination for parotid tumours at Gustave Roussy Cancer Campus (France) between 2012 and 2021. All the patients subsequently underwent surgery, with histopathologic examination performed in the same center. The data includes four MRI sequences (T1w, T1ce, T2w, DWI) of 134 patients, along with histopathological subtypes categorized into pleomorphic adenomas (benign), Warthin's tumour (benign) and carcinomas (malignant) (see Fig. 1(b)).

METHODS

Parotid gland tumours were manually segmented using the software Olea Sphere on the four different MRI sequences (see Fig. 1(a)). Using the same software, 108 radiomic features were extracted from the MRI sequences. Harmonization steps at the image and feature levels compensate the high variability of the data. A feature selection step based on the F-test method sorts out variables that are independent of the target. The classification is perform through random forest algorithm, with a five-fold cross-validation, using an 80:20 ratio between training and test samples.

RESULTS

Radiologists and the proposed machine learning model were exposed to the MRI data to classify the tumors. The machine learning technique reached an accuracy of 0.720 and a mean AUC of 0.838 on test set when considering all classes (see Fig. 1(c)). Senior radiologists displayed worse performance compared to the juniors and to the algorithm. Finally, all radiologists were given the opportunity to change their decision by observing the algorithm prediction. Seniors improved their accuracy in a 5.6% and juniors in a 6.3%. which was sampled after the new 3 T Signa Premier was put into operation, comprised data from the three devices. This was motivated by [13] which uses different MRI devices for training and validation, but keeps the same magnetic field strength for both. Such a set-up allows us to verify the generalisation to new MRI systems of similar power while avoiding significant bias. Class distribution of the whole dataset was preserved in a stratified manner while creating both training and test sets: the frequency of appearance of each histopathological subtype was kept.

Model building Random forests are more robust than other machine learning models when dealing with high-dimensional feature sets, and are also more polyvalent [20,21]. Moreover, this family of algorithms is quite often used to classify radiomics [10,22,23] and tends to be less inclined to overfitting [24], a property that could help the algorithm to generalise to MR images from the new device considered in the test set. Hence, the random forest model was retained in our work. In order to compensate the imbalanced class repartition, classes were given different weights to increase the influence of the least populated ones. different MRI sequences (see section 1.1, MRI protocol). Studied MR images are 3-dimensional, but we chose to segment 2D regions of interest (ROI) using the axial slice with the largest tumour surface area. Within this slice, the entire tumour region was segmented, including its core and eventual necrosis. Figure 2 presents an example of such segmentation. This task was performed using Olea Sphere software from Olea Medical 1 . Output ROIs were double-checked by a radiologist with 10 years of experience (S.A.).

Model training

Features extraction Radiomic features were computed from all four considered sequences using Olea Sphere software with the following settings: 1 mm 3 voxel resampling, 64 gray level bins to compute the histogram. A total of 108 radiomics per sequence were extracted and complied with the IBSI standard [17]. They were sampled as follows: 16 shape-based features, 19 first-order features, 23 gray level co-occurrence matrix (GLCM) features, 16 gray level run length matrix (GLRLM) features, 15 gray level size zone matrix (GLSZM) features, 5 neighbouring gray tone difference matrix (NGTDM) features and 14 gray level dependence matrix (GLDM) features. Appendix A summarises the computed features. Hence, a single tumour was represented by 4 ⇥ 108 = 432 real numbers.

Radiomics are also subject to high heterogeneity. ComBat normalisation [18,19] can be used to reduce variability across devices, but several safety checks performed on our data suggested no significant improvement when applying this method to our problem. Here again, no normalisation technique was used.

From the medical records of the patients, phenotypic variables age and sex were retrieved, as they are often linked to different types of tumours [1,2]. Those two variables were concatenated to the computed radiomic features and used as input to the machine learning system.

Machine learning task

Our goal was to discriminate parotid gland tumours according to their histopathological subtype. This corresponds to a classification task, where each type of tumour is a different class. The goal was to classify images summarised by their radiomics features.

Separation into training and test sets

Figure 2 .

 2 Figure 2. Examples of segmentation on the four acquired sequences: T1w, T1ce, DWI and T2w (clockwise).

Figure 1 .

 1 Figure 1. Flowchart showing how relevant data were chosen. The red box indicates malignant tumours, the green ones correspond to benign tumours.

Figure 3 .

 3 Figure 3. OvR ROC curves calculated from the algorithm predictions for each histopathological subtype class represented in the experiment, along with points corresponding to the metrics of the 9 radiologists. Some points are coinciding, resulting in only 6 of them being distinguishable on the graph (their corresponding overlapping symbols are displayed).

Fig. 1 :

 1 Fig. 1: (a) Segmentation of MRI image. (b) Dataset description. (c) One-Versus-All ROC curves of the algorithm predictions for each tumor class and performance metrics of the radiologists.


Flavio Angeloni
email: angeloni@idmp.uni-hannover.de

Annika M Wille

Christian Hausch

Representation of numbers and variables in Austrian Sign Language

Keywords: Sign language, variables, numbers, representations, classifiers

Sign languages provide various possibilities to sign about elementary algebra. Essential in this context are representations of numbers and variables in the sign language space. The study presented here investigates how sign language space is used in Austrian Sign Language. In particular, it addresses how numbers and variables are located on multiple axes with different signs.

Introduction

The paper presented here is part of a broader project on the topic of sign language and mathematics education. Since language has an essential role in mathematics learning [START_REF] Fleming | Languages of schooling within a European framework for languages of education: Learning, teaching, assessment[END_REF], it is worthwhile to look at how mathematics is signed about in sign language [START_REF] Krause | What you see is what you get? -Sign language in the mathematics classroom[END_REF][START_REF] Wille | Explaining geometrical concepts in sign language and in spoken language -a comparison[END_REF][START_REF] Krause | Sign Language in Light of Mathematics Education: An exploration within semiotic and embodiment theories of learning mathematics[END_REF]. The project focuses on elementary algebra [START_REF] Angeloni | Signing about elementary algebra in Austrian Sign Language: What signs of the notion of variable can represent[END_REF]Angeloni, in press). The part of the study presented here deals specifically with the representation of numbers and variables in the sign language space.

Theoretical framework

There is not only one sign language in the world, but many, which are different from each other. The examples below are in Austrian Sign Language (ÖGS). Sign languages are languages with their own structure, which is different from the structure of spoken languages. They are realized in a fourdimensional space (three spatial dimensions plus time) and consist of several components (called manual and non-manual). There are different types of signs. In particular, three of them are relevant for the study presented here: direct pointing signs, buoys and classifiers. Direct pointing signs are signs that point to something. Their handshape is a raised pointing index finger in the direction of the referred. Buoys are signs (typically of the non-dominant hand) that remain fixed while the dominant hand continues to sign. Classifiers (CL) or depicting signs [START_REF] Lackner | Austrian Sign Language (ÖGS) Corpus Annotation: Annotation des ÖGS-Korpus[END_REF] are often defined in different ways [START_REF] Oviedo | Classifiers in Venezuelan Sign Language[END_REF]. Here, a classifier is understood as a sign that represents entities (of whatever kind) based on their characteristic features. A classifier "classifies" objects or processes based on their common features and represents them with the same hand shape (e.g., the index finger can represent a person or a pencil) [START_REF] Zwitserlood | Classifiers[END_REF]. Classifiers can be signed to refer to a characteristic property, the position, and the movement of the signifier [START_REF] Beecken | Grundkurs Deutsche Gebärdensprache: Stufe I; Arbeitsbuch [Basic course German Sign Language: Level I; Workbook[END_REF][START_REF] Angeloni | Signing about elementary algebra in Austrian Sign Language: What signs of the notion of variable can represent[END_REF].

An important feature of sign languages is their simultaneity. This means that in the (visual) modality of sign language it is possible to articulate meaningful units simultaneously. Simultaneity is preferred in sign languages to the linear arrangement of morphological elements (typical for spoken languages). This depends in particular on the type of relation between the various terms or concepts that occur in a phrase: If they are organized in a syntagmatic relation, then they are signed simultaneously and this is typical for sign languages [START_REF] Grote | Denken Gehörlose anders? Auswirkungen der gestisch-visuellen Gebärdensprache auf die Begriffsbildung. Das Zeichen[END_REF]. In the syntagmatic relation the terms are related to each other as in a sentence. When a term is named, it is connected, for example, with what properties it has, what it does, or where it is. In a paradigmatic relation one associates the term with everything that fits into a category to which this term belongs, or into a subcategory of this noun. In this case, one does not think in terms of sentences, but in terms of single nouns. For mathematics education, this can have implications for the organization of content and how it is addressed or explained. These considerations are also relevant in the analysis of sign language signs, whether already known or not.

Research interest

Our study is concerned with communication about elementary algebra in sign languages. In the paper presented here, we focus on the topic of signing about numbers and variables in the Austrian Sign Language and, specifically, on the following research question:

• RQ: How can numbers and variables be represented in the sign language space of (Austrian)

Sign Language?

Learning environment

The learning environment that was developed for the study is based on the "Knack-die-Box" (crack the box) model [START_REF] Affolter | Das Mathematikbuch 7 [The mathematics book 7[END_REF]. Similar to the learning environment in [START_REF] Angeloni | Signing about elementary algebra in Austrian Sign Language: What signs of the notion of variable can represent[END_REF], the participants have to solve three tasks according to the dialogic principle "think, pair, and share" [START_REF] Green | Kooperatives Lernen im Klassenraum und im Kollegium: Das Trainingsbuch [Cooperative Learning in the Classroom and in the collegium: The Training Book[END_REF]. First, each student deals with the task alone. In this phase, the students do not have to find a solution to the problem. Then, the students (in pairs or very small groups) share with each other their ideas about a possible (way to a) solution. In the last phase, possible solutions are discussed in the class. In such a setting, the participants have the chance to become active in their language ÖGS. The purpose is to sign about variables without signing some artificial signs for the word "variable", which are not naturally signed by native signers. The learning environment includes three tasks with blue and red boxes and matchsticks, which were represented in a stylized form like the two examples in Figure 1. At the beginning, we do not know how many sticks are in the boxes, but we do know that the two arrangements must have the same total number of sticks. The tasks are presented to the participants in ÖGS, i.e., no German language is used. First, they get the information that two boxes that have the same colour contain the same number of sticks. Then the two arrangements of a task are signed (Figure 1a) with the information that the two arrangements must have the same total number of sticks. The participants are asked to find out how many sticks are in the blue and respectively in the red boxes. When they have found and discussed a solution, the next task is given (e.g., Figure 1b).

Methods

The research took place in June 2022 in form of two 60-minutes sessions. The participants were seven deaf adults (age range: 30 to 70) with different mathematical backgrounds divided in two groups (one per session) of three and four persons. Their basic language was ÖGS or regional variants thereof (cf. [START_REF] Angeloni | Signing about elementary algebra in Austrian Sign Language: What signs of the notion of variable can represent[END_REF]. The sessions were moderated in ÖGS by a teacher (first author). He took care of the technical tools and moderated the share-phase. All the sessions were video recorded. For the annotation of sign languages there are different systems. Frames of the videos which are relevant for the research questions were annotated according to a simplified form of the annotation system of Lackner (2019) for ÖGS explained above. The focus of the research question is on the sign language space. A fundamental component of the sign language annotation is the gloss. A gloss names a single sign that does not necessarily correspond to the meaning of the sign. For example, the gloss CONTENT (glosses are written in capital letters) corresponds to a certain sign that does not necessarily mean "content" or something similar. Furthermore, it is not a translation. Glosses are annotated in capital letters. Below you will find the legend of the annotations used here:

• Signs for numbers are annotated with No:GLOSS -e.g., No:THIRTEEN.

• The annotation of the pointing sign is IX:GLOSS with the referred in the referent line -e.g. IX:THIRTEEN. • For classifiers the annotation CL:HANDSHAPE.description-of-action is used -e.g. CL:IX.Itmoves-diagonal-upwards means that one hand with the hand shape of an outstretched index finger (IX) moves diagonally upwards, and this sign is a classifier. • A buoy is annotated with H:GLOSS -e.g. H:CL:B means that the classifier with the hand shape (for the letter) B (CL:B) is fixed.

Other components of sign language, like movements, are annotated on a separate line directly under the gloss to which they refer. The following is the annotation legend for the components (from the examples presented below):

• The direction of the movement is annotated in the line "Mov. direct." (e.g., "downwards").

• A movement has also a quality that is annotated in the line "Mov. quality" (e.g., "slowly").

• The movements of the mouth are annotated in the line "Mov. mouth" (e.g., "blow-strong, long, broad" means that the air comes out of the mount for a (relatively) long time, the mouth is almost closed, so that the lips could also vibrate).

Not every line is reproduced in the transcripts below. If a line is empty, it is omitted (e.g., if there is no movement, the line with the quality of the movement is omitted here). Therefore, not only the annotations, but especially the frames of the videos are used for the analysis of the material. An initial screening of the video frames and transcript identified scenes in which participants were signing about numbers and variables. A first interpretation of these scenes was discussed with a native signer (third author). Based on this preliminary evaluation, one-to-one interviews with the participants were planned. As of today, two of these have been carried out. The others will be implemented in the near future. In the interviews, uncertain interpretations of the first screening were addressed. In addition, other questions were asked, such as: "Why did you sign it like that?", "Do you know how it could have been signed differently?" and "What is the difference between these variants?". The interviews were video recorded and interpreted similarly to the learning sessions.

Findings

Regarding the research question of how numbers and variables can be represented in the sign language space of (Austrian) sign language, we can notice different representations that occur in the learning environment. In general, we observed that signs in relation to numbers and variables were signed on different sign axes. We can distinguish here between representations on a vertical and on a horizontal plane.

The vertical plane

We call the plane in the sign language space parallel to the signer's body vertical plane. If the participants signed about numbers or variables on this plane, then they mostly signed three different types of signs: the classifier in Figure 2b, the (specific) number signs such as in Figure 2c (signed here on the left due to the dominant hand of the signer) or, in some cases, the general sign NUMBER.

Regarding the sign axes, here is what we could observe. The vertical axis in Figure 2a is normally oriented upwards, so that positive numbers are represented by the signers in the upper part of the axis and negative ones in the lower part. (This was confirmed in the interview.) Participants also sometimes set a mark for zero with one hand, while the other hand signed the classifier for the number or for the variable above or below the mark. Similarly, specific numbers are signed in relation to a mark. The mark is thus a buoy. If the mark is not set, then one does not know whether the value of the sign is positive or negative. The participants commonly signed the information "positive" or "negative" in advance (an example appears in Table 1). The negative numbers are deeper and deeper.

In this example there is no mark for zero (or another number), but the sign of the numbers (in this case "minus": MINUS NUMBER) is signed at the beginning. So now one knows that the classifier "CL:IX.It-points-downwoards" represents numbers that become smaller and smaller. In the following example, the participant has signed the mark (H:CL:IX.upwards), but she does not give the information about its value. More specifically, with the classifier in Figure 2b, the numbers or the variables are represented on the vertical axis relative to their value. That means, a classifier that refers to a number or variable near zero is signed approximately, as in Figure 2b. If the referred number or variable is very big, then the arm is stretched upwards and the classifier has a big height. If the value of a variable is unknown, the classifier in Figure 2b is repeatedly moved up and down. Moreover, if the participants have represented a specific number or value of a variable (e.g., of value 13) with the classifier, then they previously signed the specific ÖGS-sign for the referred number (e.g., THIRTEEN). In the case of specific values, the participants also signed only the number with the number signs on the corresponding height. Two examples: four, six and so on.

In the example above (11:33v2), the ÖGS-signs No:TWO, No:FOUR and No:SIX are signed with increasing height. The sign NUMBER is then signed upwards.

Figure 3a shows two diagonal axes. On those axes, the signers have signed only numbers that are fixed and form an ordered sequence (such as Figures 3b to 3d). In the example in Figure 3, the numbers 13, 5 and 1 are signed, with the height of the sign becoming lower. If the numbers in the sequence become greater, then the number signs were signed with increasing height on a diagonal axis. An example from the interview: We could additionally see in the interviews that there is no difference between the two diagonal axes in Figure 3a. The interviewee explained that the diagonal axes and the vertical axis in Figure 2a can be used equivalently. However, if there is an image that is referred to by signing (e.g., numbers are written on the black board or they refer to objects shown on a picture), the image influences which axis is chosen. If a number was not fixed and could become arbitrarily big, this was signed on the diagonal axis as in Figure 3e. The case of an arbitrarily small number did not occur. We call the plane in the sign language space that is in front of the signer's body and parallel to the floor, horizontal plane. When the participants signed about numbers and variables, they also signed on different axes on the horizontal plane. They signed on the axis in Figure 4a with an orientation that does not necessarily correspond to the usual orientation with the positive numbers on the right side with respect to an origin. It also happened that the signers signed according to an orientation with the negative numbers on the right side. On this axis, the classifier from Figure 2b was not signed, but the specific number signs for numbers or the general sign NUMBER. Two additional axes away from the signer's body occurred in the sessions: Figures 4b (diagonally The numbers increase diagonally upwards become arbitrarily big. This representation is realized with a variation of the classifier in Figure 2b: the hand shape is basically the same, but the fingers vibrate as if they were playing the harp (Figure 4c). In addition, the participant in the interview signed that it is possible to set a mark on the axis in Figure 4d for the first number. For example, the mark on the normal axis in Figure 4d is set to 100: The participant himself confirmed that the concrete value does not matter. Analogical to the diagonal axis in Figure 3, the case of an arbitrarily small number did not occur. In single cases, it was signed in the direction behind the signer's body (Figure 4e). For example, if someone signed about negative numbers or numbers that are behind a fixed mark and become arbitrary small.

The horizontal plane

Discussion

Numbers and variables can be represented in various ways in sign language. As discussed above, the sign language space and in particular vertical, diagonal and horizontal planes and axes can be used. Three types of signs could be identified in this study for numbers or variables: Signs for concrete numbers, the general sign for number, and classifiers. Thereby, the classifier acts like a bridge between numbers and variables, since it can be signed for both. For example, in Figure 2b, the classifier represents a number located at a certain height on the vertical axis. This classifier, when moved (up and down), can also represent a variable that stands for an unknown or unspecific number. These observations are consistent with the syntagmatic relations of sign language phrases: A sign that refers to a number or variable is usually signed with the associated property (e.g., "large" or "unknown") or additional information is given about what to do with it. This is possible due to its simultaneity and occurs with syntagmatic relations. The results suggest that when teaching mathematics a simple translation from spoken to sign language of mathematical terms may not be sufficient and that further aspects of these terms should be considered. Additionally, of particular interest, is how numbers and variables are set in relation to each other along the axes. This will be part of our subsequent research.

FigFigure 1 :

 1 Fig. 1a: Task 1 Fig. 1b: Task 2 Figure 1: Pictures for the three tasks (the colour names are not in the original learning environment)

Fig. 2a :Figure 2 :

 2a2 Fig. 2a: The vertical axis Fig. 2b: A classifier for a number Fig. 2c: Sign for the number 1 Figure 2: The vertical axis

Figure 3 :

 3 Figure 3: The diagonal axes

  Fig. 4a Fig. 4b Fig. 4c Fig. 4d Fig. 4e

Figure 4 :

 4 Figure 4: Axes on the horizontal plane

  ) and 4d (normal to the signer's body). On these axes, the signers have represented a number or a variable that is not fixed and can 01:03:15i1 Part. 2: NUMBER ALWAYS CL:IX.It-moves-diagonal-upwards Translation:

Table 1 : Annotation of an excerpt from the video no. 4 of the problem solving event

 1

	00:25v4	Participant 1:	MINUS	NUMBER H:CL:B CL:IX.It-points-downwoards

Table 2 : Annotation of an excerpt from the video no. 4 of the problem-solving event

 2

	01:10v4	Participant 1:	H:CL:IX.upwards	PLUS	NUMBER	MINUS	NUMBER
		Mov. direct.:			upwards		downwards
		Mov. quality:			slowly		slowly
		Translation:	The positive numbers are in the upper part and the negative numbers are in the lower part.

Table 3 : Annotation of an excerpt from the video no. 2 of the problem-solving event

 3

	11:33v2	Particip. 1:	H:IX:RED H:IX:RED	IX	IX	EQUAL
		Referred:	box on the left box on the right box on the left box on the right
		Translation:	The red boxes on the left and on the right, the two boxes have
			COLOR	NOT	NUMBER IT-DOES-NOT-MATTER	No:TWO
		Translation:	the same color. There is any (fixed) number, it does not matter if two,
			No:FOUR		No:SIX		NUMBER	NUMBER
		Mov. direc.:					upwards
		Mov. qual.:					from slowly to fast
		Translation:

Table 4 : Annotation of an excerpt from the video (no. 1) of the interview

 4

	01:03:12i1 Part. 2:	TO-SIGN	ALWAYS	CL:B.It-moves-diagonal-upwards
	Translation:	It is always signed diagonally upwards

Table 5 : Annotation of an excerpt from the video (no. 1) of the interview

 5