Muslim Civilizations Solving for Unknowns
Muhammad Al-Khwarizmi is a scholar renowned for his monumental contributions to the fields of mathematics, geography, and astronomy. This paper will explore the motives that directed Al-Khwarizmi to delve into these scholarly areas and how he contributed to them. The sources used in this paper include the book titled ‘Science and Islam: A History’ by Masood, the book titled ‘A History of Science in World Cultures: Voices of Knowledge’ by Montgomery and Kumar and the book ‘1001 Inventions: The Enduring Legacy of Muslim Civilization’ revised by Salim T.S. Al-Hassani as well as detailed research papers and references found online. This study will employ literary analysis of his publications and examine the contextual period he was a part of. This paper deduces how the demand for the simplification and precision of certain Islamic applications led him to progress the study of algebra, geography, and astronomy. This finding is important to stress as the Western World attempts to water down the motivations of Islamic scholars being partly Islam itself and how these contributions were foundations to countless things we utilize today.
Al-Khwarizmi was among the legendary luminaries of Baghdad’s world-famous academy, ‘the House of Wisdom’, where important works of scholarship throughout the world were collected and developed. He advanced the areas of mathematics primarily due to the compelling issues within the Caliphate, such as inheritance, land ownership, and taxes, by pioneering algebra with his published book titled ‘The Compendious Book on Calculation by Completing and Balancing,’ ‘Al-Jabr wal Muqabala’ in Arabci. Additionally, he was able to calculate the direction of the Qibla, while advancing the area of geography. He also revised Hindu sources to assess the appearances and positions of the heavenly bodies and compute the calculations needed for the Islamic Calendar. Compiled from the Caliphate’s demands and the understanding of Islamic concepts, Al-Khwarizmi pursued these areas with great expertise. Baghdad and its Caliphs, at that golden age, allowed al-Khwarizmi the resources that helped him flourish and fulfil his potential so well.
In the paper that follows, I first introduce the Caliph’s demands for knowledge on Islamic-related notions and Al-Khwarizmi’s religious motivations to successfully complete them to argue that his incentives were religiously-rooted. Next, I outline the relevant Islamic issues, like inheritance and the taxes placed within the Caliphate system, to explain Al-Khwarizmi’s primary motivation towards his eminent contribution to mathematics, specifically the subject of algebra. Thirdly, I illustrate Al-Khwarizmi’s work in computing methods to figure out the direction of the Qibla that aids Muslims in their daily prayers to demonstrate his expansion on geography. Lastly, I discuss the calculations he produced behind the Islamic Calendar and his research regarding the celestial bodies, specifically the Moon, to prove his contribution to the study of astronomy.
Algebra
The Caliph presented Al-Khwarizmi with the pressing climate for rulings regarding land ownership, the calculation of appropriate shares, and the taxes issued within the Caliphate. According to Masood, “he wrote his book on algebra in response to a request from the caliph to come up with a simple method for calculating Islamic rules on inheritance, legacies and so on” (Masood 142). The Quran includes the most common inheritance situations and has derived their calculations, but the variety of situations not mentioned resulted in to the demand for ways to calculate these shares of inheritance. Al-Khwarizmi mentions his driving force for developing algebra in his work by stating, “That fondness for science, … that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala, confining it to what is easiest and most useful in arithmetic.” The Quran encourages people towards conducting research in the sciences in 39:33: “And whoso brings the truth and believes therein such are the dutiful.” There are also multiple hadiths that drive one to seek knowledge, such as “Scholars should endeavor to spread knowledge and provide education to people who have been deprived of it. For, where knowledge is hidden it disappears.” He asserts that God and his fondness of learning prompted him to expand on his work in mathematics, thus relating to religion and the concepts it poses as being incentives for his work (Nick).
He specifies the topics that drove him to complete his pioneering work, which happen to coincide greatly with Islamic concepts, such as inheritance. In his introduction to the book in which he describes algebra, he says that the aim is to work with “what is easiest and most useful in mathematics, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or when measuring lands, digging canals and making geometrical calculations” (Masood 142-143). All the cases mentioned comprise of Islamic notions and the interests in the Caliphate’s development. He premises an entire chapter on the calculations of a range of inheritance problems, such as:
Suppose that a man who is terminally ill allows two of his slaves to buy their freedom. The price of one slave is 300 dirhams. This slave dies, leaving a daughter and two sons. He also leaves property worth 400 dirhams. Then his former master dies, and he leaves three sons and three daughters. How much do each of the children receive in inheritance?” (Masood 143).
Today, we view algebra as an area encompassing the idea of symbols replacing unknown numbers in calculations; however, al-Khwarizmi never used symbols, but rather wrote everything out in words. For the unknown quantity, he would not use ‘x’ or ‘y’ but the word ‘shay,’ the arabic term for ‘thing’. When al-Khwarizmi’s work was being translated by the Spanish, “the Arabic word shay was transcribed as xay, since the letter x was pronounced as ‘sh’ in Spain. In time, this word was abbreviated as x, the universal algebraic symbol for the unknown” (Devlin).
Algebra was a unifying theory that allowed rational numbers, irrational numbers, and geometrical magnitudes all to be treated as algebraic objects. It gave mathematics a whole new dimension and a development path, much broader in concept than before. It also enabled future development. Al-Khwarizmi’s immense algebraic contribution was a revolutionary move away from the Greek concept of mathematics, which was essentially based on geometry.
Al-Khwarizmi worked mainly with linear and quadratic equations in his book “The Compendious Book on Calculation by Completing and Balancing,” where he introduced a simplification method for reducing equations. The method was called al-jabr and al-muqabala. It involved removing negative terms from the equation and reducing positive terms to the simplest form. Rules of al-jabr and al-muqabala can be used to reduce any equation to one of the six simple standard forms given by al-Khwarizmi.
The 6 kinds of quadratics classified by al-Khwarizmi are:
1. Squares equal to roots (x² = square root of 2)
2. Squares equal to numbers (x² = 2)
3. Roots equal to numbers (square root of x = 2)
4. Squares and roots equal to numbers (x² + 3x = 25)
5. Squares and numbers equal to roots (x² + 1 = 9)
6. Roots and numbers equal to squares (3x + 4 = x²)
(Nick)
Any quadratic equation could be reduced into one of these six standard forms. The suite of universal solutions al-Khwarizmi provided with the six quadratic classifications proved to be able to solve all kinds of quadratic equations. For this, later Mathematicians Galileo and Fibonacci held him in very high regard (Masood 144-145).
Qibla Direction
“Where is the Qibla?”, is a common question Muslims ask when it is time to pray one of the five obligatory daily prayers. Muslims around the world pray towards the Kaaba, located in Mecca, Saudi Arabia, the direction of the qibla. Facing towards the qibla, is one of the six conditions or requisites of the prayer for being valid. In other words, if a person does not turn his or her face to the qibla direction within an acceptable declination, his or her prayer is invalid according to scholarly consensus. Thus, the direction of the qibla should be established as accurately as possible. The qibla direction is not only important for prayer, but also for performing various ritual acts like reciting the Qur’an, announcing the call to prayer and the ritual slaughtering of animals for sacrifice. Furthermore, Muslim graves and tombs are laid out so that the body would lie on its right side and face the qibla. The angle of the qibla direction is not fixed and depends on the location in the world and thus, it should be calculated for each mosque very precisely with a proper method (Veli).
In an effort to aid Muslims in finding the qibla, the Caliph al-Mamun instructed al-Khwarizmi to work on this problem. With a team of 69 others, al-Khwarizmi helped create the first correct world map in world history and took part in a project to find the Earth’s circumference, in which he measured the length of a degree of a meridian in the plain of Sinjar, located northern Iraq. His book, Surat al-Ardh (Arabic: كتاب صورة الأرض), which translates to “The Image of the Earth”, is a revised version of Ptolemy’s Geography, consisting of a list of 2402 coordinates of cities and other geographical features. Especially where more local knowledge was available to al-Khwarizmi, such as the regions of Islam, Africa and the Far East then his work is considerably more accurate than Ptolemy’s. A copy of his manuscript is preserved at the Strasbourg University Library. Thanks to al-Khwarizmi’s contributions and others, the Qibla problem was solved by finding the shortest arc of the great circle anywhere on the globe between a person’s location and Mecca.
Astronomy
Another of al-Khwarizmi’s famous contributions, written around 820, was Zij al-Sindhind, “Astronomical Tables Based on Hindu Methods,” also requested by al-Mamun. Some of the material from Hindu sources had been translated half a century earlier by Harun al-Rashid, but al-Khwarizmi’s version proved to be more of an asset for religious purposes. It contains as many as 116 tables on the movements of the Sun, Moon, and planets; star positions; computations of eclipses; and also first appearances of the crescent Moon; calculations for the Islamic calendar; and geographical latitudes and longitudes (helpful for qibla) (Montgomery and Kumar ch7).
Conclusion
Every major contribution proposed by Al-Khwarizmi was rooted deeply in religious curiosity and advocacy for precision. The demands of the Caliphate drew him towards expanding on these scholarly areas. Derived from translated Greek works, a thousand years earlier, to translations of the Arabic texts, western Europe was able to advance in mathematics and the sciences promptly. This was able to pave the way for the Scientific Revolution of the 17th century, thus contributing to the 21st century world we are a part of today. As a sign of service to the Muslim faith, al-Khwarizmi’s developed a method to calculate the time of visibility of the new moon, indicating the beginning of the Muslim month, and compute the calculations for the Islamic Calendar, inheritance, and taxes.
In conclusion, algebra and algorithms are enabling the building of computers, and the creation of encryption. Without the dedication of Islamic scholars like Muhammad Al-Khwarizmi, who contributed immensely to the world of scientific knowledge by preserving and advancing it, it would be unclear whether Europe would lead the scientific realm today and whether the state of the modern technology industry would have remained the same.
References
Al-Hassani, Salim T. S. 1001 Inventions: the Enduring Legacy of Muslim Civilization. National Geographic, 2012.
“Alkhwarizmi.” R P, https://research-paper.essayempire.com/examples/history/al-khwarizmi-research-paper/.
Devlin, Keith. “Devlin’s Angle.” The Mathematical Legacy of Islam, https://www.maa.org/external_archive/devlin/devlin_0708_02.html.
Gamba, Milky. “Arab Algebra and Mathematics.” AlShindagah Online, https://www.alshindagah.com/sepoct2002/arab.html.
Masood, Ehsan. Science and Islam a History. Icon Books Ltd, 2017.
Montgomery, Scott L., and Alok Kumar. A History of Science in World Cultures: Voices of Knowledge. Routledge, Taylor & Francis Group, 2016.Veli, İbrahim, et al. “Investigation on the Accuracy of Existing Qibla Directions of the Mosques from Different Periods: A Case Study in Çorum City, Turkey.” Tehnički Vjesnik, Hrčak, 16 Dec. 2018, https://doi.org/10.17559/TV-20170226111205.
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