Home / Opinion / Columns /  Opinion | Al-Khwarizmi’s algorithms and the Brahmagupta connection

The present-day province of Khwãrezm sits along the borders of modern-day Turkmenistan and Uzbekistan, bordered by the shrinking Aral Sea, and fed by the plentiful waters of the Amu Dariya river. A thousand years ago, this land had a very famous resident, Abu Abdullah Muhammad ibn Musa Al-Khwarizmi, a scholar, mathematician and an astronomer of repute. His first seminal contribution was to the science of “al jabr", or the “reunion of broken parts", which became algebra. While that itself was enough to make him immortal, it was the Latinization of his name Al-Khwarizmi, or “the native of Khwãrezm", which gave us the 18th century “algoritmi", which eventually became the word “algorithm".

If I were to pick one word, which people use routinely and nod knowledgeably when used, but do not have the faintest idea of what it means, it will be this one. Everything around us—traffic, maps, information, news, social networks, weather forecasting, shopping—seems to be governed by the all-powerful yet mysterious algorithms. An algorithm is nothing but “a set of instructions designed to perform a specific task, based on conducting a sequence of specific actions".

Algorithms have been around for even longer than Al-Khwarizmi. In 300 BCE, Euclid created the famous Euclid Algorithm, which provides a set of instructions to find the greatest common divisor of two numbers. Eratosthenes developed his Sieve of Eratosthenes in 200 BCE; Lui Hui in China developed one for Gaussian eliminations around the same time, and three centuries later Brahmagupta started building Chakravala, a cyclic algorithm to solve indeterminate quadratic equations.

But it is with computing and their massive processing power that algorithms came into their own. They continue to have interesting names—the Gift-wrapping Algorithm, the Shoelace Formula, the Mersene Twister, even Pollard’s Kangaroo Algorithm—and do very interesting things. Perhaps the best known and most powerful algorithm today is PageRank, named after Google co-founder Larry Page, which ranks search results and, thus, decides the fate of millions of companies. Google tweaks its algorithm around 500 times a year. Earlier, it used to make drastic changes; it was called the Google Dance, and sent marketers into a tizzy. The highly accurate Google Maps algorithm, which tells you the level of traffic on your route, is very interesting; not only does it crunch massive time series and hyper-local data, it also takes into account the number and density of Android phones on the road, which communicate their presence and speed of progress to Google Cloud. Now you know why Apple’s maps are not as effective here; they do not have as many phones on the road.

Algorithms are used for myriad tasks and are replacing human beings in many activities. Machine learning (ML) and Artificial Intelligence (AI) are composed of algorithms and data. Using Natural Language Processing (NLP), they are now reading millions of resumes, and reportedly taking unbiased, rational decisions on which candidates to shortlist or hire. They are “manning" retail cash registers, using spreadsheets far more efficiently, predicting weather more accurately, helping us harvest grapes at the right time to make the best wine, and driving our self-driving cars.

However, it is this very efficient black-box nature of algorithms that is setting off alarm bells. If a candidate is rejected by an algorithm, for instance, how do you explain to her why she was rejected? In her 2016 cautionary best-seller, Weapons Of Math Destruction, Cathy O’Neil tells the story of Sarah Wysocki, a brilliant successful teacher whose entire career was undone by biases in algorithms that tested students. Therefore, one of the biggest challenges confronting algorithms and AI is to make them “explainable" and “unbiased". So, how do we ensure that the failings of creators do not creep into their creations?

In the light of recent religious and political events, it is instructive to go back to Al-Khwarizmi. He lived and flourished in currently war-torn Baghdad, the world’s centre of learning then. His first and most famous book gave rise to algebra, but one of his other book’s title was translated in Latin as Algoritmi De Numero Indorum, which would roughly translate into Al-Khwarizmi On The Hindu Art Of Reckoning. He did not create his greatest creations alone. In a lot of his work, he built on the work of Brahmagupta, the great Indian mathematician, and gave us what runs the world today—algorithms.

Jaspreet Bindra is a digital transformation and technology expert, and the author of the book ‘The Tech Whisperer’

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