An increasing number of our daily activities are assisted by complex mathematical equations that are smarter than we are.
Not that many people – except accountants maybe – would be comfortable solving everyday problems using complex mathematical equations.
Want to know the quickest route to work? There is a complex piece of maths that can tell you. Looking for a good book? Another complex equation can recommend one.
These equations, known as algorithms, were once used almost exclusively by mathematicians and physicists to solve complex problems. Now they reside at the heart of everyday computer-based processes.
“An algorithm is a recipe, like in a cookbook,” says Toby Walsh, a professor in artificial intelligence at The University of New South Wales and data innovation group Data61.
“It is a sequence of instructions that a computer will need to follow to actually compute something interesting, such as how to get from A to B.”
Walsh says as we become more reliant on computers, the internet and technology in general, we will also become more reliant on algorithms.
As companies and consumers generate more and more data, storage is no longer enough to maintain a competitive advantage. It’s the actions derived from the data that generates value.
Here are how some businesses have wielded math to gain the upper hand over their competitors in order to make our everyday lives more convenient and connected.
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Sat-nav route calculation
One of the most ubiquitous algorithms in modern life is the “A* search” pathfinding algorithm. Originally designed to help the earliest robots find their way around, this algorithm now lies at the heart of sat-nav systems.
If you have ever made a wrong turn and heard the “recalculating route” message, that is the A* algorithm very efficiently determining the best route from a large number of variables including distance and speed.
The Luhn algorithm
Ever wondered how websites know you have entered a wrong digit when typing in your credit card details online? That’s the Luhn algorithm in operation.
Every credit card number is arranged using a specific method and when simple mathematical formulas are applied to all but the rightmost digit (called the “checksum”) and the product of these calculations does not match the checksum, the credit card number is deemed invalid.
Amazon’s recommendation engines
It’s spooky how effective some websites are at recommending products you might like to buy. That insight comes from tracking all of your activity on a website, including what you buy and browse, and feeding that into a mathematical engine along with everyone else’s activity to generate possible matches.
This “item-to-item collaborative filtering” is used by Amazon to recommend items under categories such as “frequently bought together”.
Businesses battle for the best math equations
Improved recommendations are big business for online companies, with Netflix awarding a US$1 million prize in 2009 to a team who created an algorithm that improved the accuracy of the company’s recommendations by just 10 per cent.
Algorithms also play a key role in keeping our personal data safe. Cryptographic hashing applies a set of rules to an existing piece of data, such as a password (called the “message”), to turn it into a complex string of data (called the “hash value” or “message digest”).
The rules work in such a way that even changing a single letter in the password returns a significantly different hash value. When used correctly, it should be practically impossible to recalculate the original message from the hash value.
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You might think of Uber as a company that finds you a ride when you need it. But at its heart, Uber is governed by a complex set of algorithms, the most interesting being the one that governs what you pay.
Uber’s so-called “surge pricing model” uses algorithms to raise and lower prices based on market conditions, such as weather or if there is a significant event taking place, such as New Year’s Eve. By raising prices at busy times, more drivers are supposedly encouraged onto the roads, increasing car availability.
But Uber’s secrecy regarding how the algorithm works has raised the ire of many people (particularly those who have paid hundreds of dollars for a lift home on New Year’s Eve).
Ever wondered why some web pages appear higher than others in Google’s search results? That’s the PageRank algorithm at work. It counts the number and quality of links to a page to determine how important it is – the more links, the more important the page and the higher it is ranked.
However, links are not the only determinant of a page’s ranking as Google also takes into account factors such as how quickly the page loads, whether it loads well on mobile devices and use of keywords and other on-page elements.
The good news for business owners who want to take advantage of algorithms is that many are in the public domain and freely available. But according to Walsh, the real challenge is having the brains to develop and apply them – and they don’t come cheap.
“This is not yet push-button technology and there aren't that many PhDs out there capable of making the technology work,” he says.