Professor Arthur T. Benjamin, popularly known as the Mathemagician, is an American mathematician specialising in combinatorics. He occupies the chair of the Smallwood Family Professor of Mathematics at Harvey Mudd College. His adept techniques explore and simplify mathematics’ fun, quirky side. Often regarded as the Bob Ross of Mathematics, learn more about Professor Benjamin’s’s conversation with our team.

Professor Benjamin poses with some members of the Post Team.

As one of the most renowned “mathemagicians”, spectators are in awe of what you do. Do you think of it as “just math”, or is it somehow magical to you too?

I guess I approach it as a skill. I think of it as performing a magic show. Maybe similar to someone who has practised playing the piano and performing in front of a large audience. They are not composing music on the spot; they are just performing something that they have gotten to do very well over the years. So for me, mental math is like my instrument that I am playing for the audience.

What inspired your interest in the domain of combinatorics?

Mathematics has many different facets, including those that have nothing to do with numbers, like Geometry, Topology, but the math that I love is very number oriented. Combinatorics is the mathematics of counting. In how many different ways can we seat 20 different people? How many ways can we seat them if there are certain restrictions? Questions like those. I find questions like those very fun and very number oriented. It allows you to think about problems very creatively. I guess it was the mathematics that tickled my brain the most; hence I continue to study it because I like to be tickled, mentally, not physically.

When it comes to mental maths, how do you think one can train their cognitive faculties to achieve a desired level of speed and accuracy?

Accuracy comes from understanding the process, and speed comes from lots and lots and lots of practice. Accuracy comes from the technique of squaring a number. You do this, and as you practice more, for example, if someone said what’s 300 times 300, the first time you say that it’s, oh, is it nine thousand? Is it ninety thousand? But after a bit of practice, you know that’s around 90 thousand. But in the beginning, you’re trying to figure out what the sizes of things are; after a while, that’s not a problem; you know the size of the things, and now you have got to get to the exact answer.

You’ve also been a vocal proponent of creative visualisation as a means to understanding mathematics. To what extent do you think that’s applicable, especially when one moves on to higher studies, for instance, if we take higher-order matrices?

I think one of the best things about mathematics is that it can be done in a very creative way. There are often many, many different ways to solve them. Whether we’re talking about an arithmetic problem, algebraic problems, or real-life problems, often there are many promising approaches to a problem, and what’s fun about mathematics is that if you can do a problem in different ways, you’ll get the same answer. That’s true for arithmetic as well as for a lot of real-life problems as well. I found that consistency of mathematics to be absolutely beautiful, which I still do now as a mathematician. Again, I think the ability to look at problems from multiple angles is important; it gives you depth. If you can see from different angles, you’ll see different sides of it. You’ll get the big picture of what you got, and I think that’s true, in all areas of mathematics, from arithmetic to matrices to calculus, and I certainly want to send the message that when people see me, they just see the mental math, they don’t see me doing algebra or calculus. I want to send the message that arithmetic is just the beginning, but it’s the beginning for everybody, and if people get turned off even at that first step, then they probably never going to like mathematics at all. If you give them a good first step, I hope they would take the second and third and fourth and fifth steps.

What would you like to leave as food for thought for the younger generations to ponder upon?

There is a fun and beautiful side to mathematics that you are probably not exposed to in school. It would be as if in school if the only music they played for you was opera, and that’s all you’ve ever heard of music. You might like opera, but you wouldn’t know about the variety of other music out there. Just because you don’t like opera doesn’t mean you dislike music. Just because a lot of math in school doesn’t interest you, there’s a gigantic part of the fun and beautiful mathematics out there that I hope you get to experience.

As students of mathematics, we crack a good number of math jokes. How often do you find yourself indulging in some?

I have certainly heard a lot of math jokes, like, what do you call a hen that counts its egg? A “Mathmachicken”.  You know what I’d like to do? I probably have never said this in an interview; I love the musical Hamilton. What I love about Hamilton, you know, is that my daughters learnt the entire musical, including the cabinet meetings between George Washington and Thomas Jefferson, and I was thinking, wow! These kids learn a slightly fictionalized version of American History and get into it. I mean, Alexander Hamilton, before Lin Manuel Miranda, was just some boring guy on a 10-dollar bill, and no one ever knew anything interesting about this guy unless you were a history major. Because of that musical, a whole generation of kids learnt to love a portion of American History. I would love to do and try something like that for mathematics. When I retire, that is one of the things that is on the back of my mind: can we do something that would be interesting enough, cool enough, or popular enough?

I watch kids who invest thousands of hours in memorising rap lyrics, and cricket statistics, and I wonder if only that energy could be channelled into something like mathematics. Oh my God! How brilliant they could become and how good that would be. If I could create something like that or if I create a musical or a book that a generation of kids knew how to prove that there are infinite prime numbers and found that to be astonishing. There is a beautiful side of mathematics that they are not showing you in school. I think that love of mathematics pays so many dividends for science, technology and for the world! Anyway can’t remember what the original question was, but that is something I would love to do for mathematics, that is, create something that is Hamilton-like.

By the way, I think everyone should learn multiplication tables till 10. Do you really need it? Yes. Especially at a young age, you have that. What is an 8-year-old or 9-year-old going to think about anyway? You can use some of their brain cells to master a skill that will be useful for them for the rest of their lives. But make it fun. Don’t make it monotonous. The worst thing that could happen is for people to take my mental math ideas and say, “Now we are gonna make people learn this every night for hours and hours”, and everyone will hate mathematics.

Given the rise of ChatGPT and Google Bard, do you think that somewhere computational mathematics may find itself somewhat stagnant as human-paced developments would give way to instant artificial intelligence?

I think we should give it time to evolve. I mean, people made fun of the internet and Google Searches in their infancy. With Wikipedia, they used to be like look at what this says about Mathematics. I think I am not worried about ChatGPT putting mathematicians out of work because they cannot think creatively. It just thinks, “What are the most likely words that can appear out of words that are already here?” and it doesn’t understand what it is saying. It is just saying. You can ask some very basic questions, questions that a child would get right, and ChatGPT would just bluff its way very authoritatively. But again, to succeed in mathematics requires you to think differently. Think outside the box, and think from an angle that has not been explored before, whereas ChatGPT is all about doing what seems to flow the best from what has been written before.

I think as far as technology and mathematics are concerned, no, your advances come from thinking in a new direction, not just thinking in the old direction. I think it is a wonderful tool. It is a wonderful starting point. Let’s say I am trying to write a song about the infinity of prime numbers; I may ask ChatGPT to give me some ideas and rhymes. It’s like asking a friend. At least I am not using it as the authoritative, that this is THE answer. It surprised me that ChatGPT is being used for software development. You can ask, “give me a computer program that will do this.” and maybe partly. This is why we see layoffs in software companies. What took software developers months to develop, you get it instantly, and now you can tweak it. Again it won’t put the entire company out of business because you need people to think in new directions, but a lot of the routine work, forget about mental arithmetic, think about writing code; I think in the past, you could have Googled things and found things around the internet but this thing just gives it to you. It is exciting and scary at the same time.

All these big tech companies, we keep hearing- Microsoft is laying off people; Google is laying off people, and Facebook is laying off people. I don’t think I have heard the full reason.

In the same way, this generation grew up with iPhones and the internet as a way of life. What would the next generation who grew up with ChatGPT be like? Whatever the next big thing is, that is based on these models that are at their fingertips since they were born. People are thinking, how is it going to affect education? It can write a college essay that could get a B. You don’t learn from that.

We academics are wrestling over things anyway; I mean, there are enough sites out there where we can buy answers to homework problems which makes professors say, “What is the purpose of homework?” I hope the purpose is that it makes people think and solidify the concepts better, but do you make it required? Do you give it weight? Ultimately you’ll have to be given tests, offline exams showing what you know at your fingertips, even though that is not very realistic.

Professor Benjamin with students and faculty who were present at the show.

Sir, you’re someone who’s been working with patterns, sometimes recognising some which would otherwise go unnoticed. Have you ever contemplated applying it to the share market?

Well, there are certainly people who do and there’s a lot of money paid to people who can discover patterns and correlations. Now, if everybody knows that fact, you can’t make money off of it but if you’re one of the first people to make that connection then yes it can be very rewarding. One of the greatest geniuses in financial math was Edward Thorpe, and he had analysed a card game that was played in the casinos called Black Jack and he figured out how to play the game to have an advantage, and the casinos had to change the rules because he’d figured these things out. He later also applied the same ability to optimize to finding things in the stock market to say certain things are worth this much and if people are selling that much then you can make some good money. I am not trained in finance and macroeconomics but I know some people who are very strong mathematically and who’ve gone on to do very well in the financial sector, and it’s really good for people in that sort of field. I used to say if I hadn’t gone into teaching I might’ve gone into financial mathematics and now I’m saying if I hadn’t gone into teaching I might’ve gotten into data science because it defines a lot of things I like to do.

When one reads about you, one comes across the fact that you’ve been deeply involved with scepticism. With due respect, what do you believe is more true about scepticism, is it a constant state of questioning widely accepted standards, or a temporary suspension of belief?

You know what, I was greatly influenced by another magician by the name of James Randy. He performed as the Amazing Randy. A very successful escape artist and illusionist, but like Houdini, was disappointed in seeing magicians deceive the public using magic tricks represented as legitimate science. Millions believe in communicating with dead people and would spend money on these magicians (or worse). I met him early in my career, as I was starting to perform shows. He got very excited because it allowed him to say that these people are full of it and are not telling the truth, they are making you believe in things that are not true whereas this guy is not cheating. He’s doing amazing things with his mind but he’s not claiming supernatural powers to do it. This is what we should be paying attention to, science is beautiful all by itself and it doesn’t need supernatural mumbo jumbo. If there are things out there that we don’t understand, let’s study and research them.

For instance, in parapsychology, there is not a single repeatable experiment in that field. Does the Extrasensory Perception exist? Probably not, but no one’s been able to measure anything for a little bit of time. As I was transitioning from doing magic onto mentalism, I thought this was magic and I can really pull it off, but after meeting Randy and a few others, I felt guilty that I might be spreading misinformation. After my show, if people thought “Oh my gosh look at that guy he really could read your mind”, I wouldn’t want people to start thinking that was legitimate. I’ve always performed things that for the most part I was willing to explain afterwards. Most magicians would never do that but when it comes to mathematical magic it should be open, there should be no secrets. I think the explanation can be more fascinating than the effect.

Attention has recently become a scarce resource in today’s digital world. This transmogrification has given rise to the study of attention economics. Purported by psychologist and economist Herbert A. Simon,  Attention Economics is a theory that treats attention as a limited commodity when designing and planning marketing schemes and conveying information in general. Diversity and abundance in content together make attention the factor that limits the consumption of information.

Social media companies realise this and use this concept to strategise content preferences when choosing the type of content to push forward to the end user. It is also an important aspect of online advertising, also done primarily through social media. Advertisers use data collected through social media to analyse search trends, past purchases, browser history, etc. of individual users in an attempt to specifically show them content they would be interested in and would subsequently devote their attention to.

Algorithms—The Prime Culprits

Social media platforms often promote their goal of helping people connect with the world. However, such aspirations, start falling flat once we dig deeper into their business models and take a closer look at how computer algorithms are designed. In terms of social media, an algorithm is a function designed to ensure that the order of content is based on relevancy to the user, not chronological timelines. Content is sorted based on popularity, recency, and the record of the past engagement of the user. 

There is a problem, however. Social media platforms often stay opaque about their algorithms. As put forth by Kelly Cotter, assistant professor at Pennsylvania State University, this is known as the “black box problem.” For example, in 2015, Facebook, along with a British firm Cambridge Analytica, collected sensitive data of millions of users to be used for political advertisements. NO consent, however, was taken by them. Considering this scandal and other such dystopian realities portrayed in shows like Black Mirror, this is a matter of concern in today’s digital world. 

The Wealth of Misinformation

Since the onset of the pandemic, misinformation has only heightened, especially on social media. Vaccine debates and WhatsApp forwards of alternate cures were everywhere. Users started relying less on credible news sources. Ofcom’s annual report on news consumption in the UK found that TikTok is the most accelerating platform for news sources, particularly among young adults. The spread of misinformation is facilitated by catchy slogans and vivid images that attract the attention of a vulnerable audience. This is known as popularity bias.

Researchers at Indiana University’s Observatory on Social Media developed Fakey, a game which aims to improve a user’s news literacy by awarding points on fact-checking in a simulated social media environment. The game displays a collection of news articles from a variety of news sources, including newspapers, websites, social media pages, and many more It is up to the user to decide whether to trust a news source or not.

In the book The Filter Bubble, Eli Pariser theorised that due to the algorithmic nature of social media, users are pushed into hyper-partisan isolated circles on the internet, as the algorithm pushes more and more curated content that a user would like to consume. In search engines, the true factual answer is often omitted, but instead, an answer tailored to the user’s past history and preferences. Thus, algorithms are not based on facts—they are based on user perceptions. Consequently, this leads to an ‘echo chamber’ wherein the repeated display of the user’s views leads to increased polarity in his or her mind, thereby limiting nuances in important discussions.

Bombardment of Information

Not only is the misinformation fatal, but there’s also something much worse. When the internet was first introduced, the cardinal spectacle was the availability of information at our fingertips. 30 years later, users are bombarded with information from the second they turn on their devices. It is crucial to know what information to hold onto and what to let go of. A post about the Roe v. Wade can be followed by a cute cat video, thereby reducing the gravity of the news.

While it is important to recognise misinformation, processing available information is just as essential, according to famed author Yuvah Harari. Since social media platforms are often flooded with misinformed opinions, they reduce the scope for critically thinking about a subject before forming an original opinion. It is, therefore, easier now than ever for people to adopt a mob mentality. If that isn’t alarming enough, it gets worse when misinformation bleeds into politics.

Social media posts about political issues started gaining traction during the pandemic [Image Credits: Youtube]

Social Media’s Sway Over Political Spheres

Due to the mob mentality and extreme polarity within social media circles, modern politics has swerved off an ill-fated road and is heading towards a deeper dystopia. Political activism has turned largely performative. Popular movements, for better or for worse, are now largely organised and popularised through social media. Performative activism is given more importance than actual, real-world action. People are more likely to hold an opinion for aesthetic reasons, instead of logical reasons.

A period of ethnic violence mixed in with the widespread dominance of a corporation known for its misinformation is a recipe for disaster. The Rohingya genocide in Myanmar has led to the displacement of 700000 refugees amid mass rapes, killings, and military crackdowns. Hate speech against Rohingya Muslims was commonly propagated, especially via Facebook. Facebook’s algorithms failed to identify it in Burmese posts.

Facebook’s CEO, Mark Zuckerberg, assured the US Congress that they’d bring about changes to the existing hate speech on the platform. However, a report published by Reuters in 2018 clearly indicated the lack of change. Project Honey Badger, outsourced to Accenture, was introduced to detect and investigate hate speech. As of 2022, Rohingya refugees have filed a lawsuit, suing Facebook for $150 billion. A report by Global Witness, a human rights group, showed the approval of eight hate speech ads by Facebook. Meta, on the other hand, says they’re improving the situation. 

Rohingya women protesting against Myanmar crackdown [Image Credits: BBC]

The Goldfish Effect

An interesting observation about the neuroscience of social media usage can be made through the ‘Goldfish Effect’, which is a marketing term used to refer to how short human attention spans can be, to the extent that they can be compared to that of a goldfish. A study by Microsoft in 2015 found that the average adult attention span is eight seconds, which is a significant decline from the average of 12 seconds in 2000.

Social media apps recognise this trend and are constantly shifting their content and algorithmic preferences to promote both the creation and consumption of quick and effective short-form content. The impact of these changes can be felt throughout the social media landscape, marking a sharp shift in their strategies. Consequently, the market has evolved radically in a temerarious bid to exploit this innate human tendency.

The Tides of Changing Trends

The attention economy seems to have adjusted to shortening attention spans, leading to ever-shortening video clips such as Instagram Reels, YouTube shorts, TikToks, etc. Long-form content has taken a backseat, and quick bursts of information seem to be the preferred medium for most people. A great example of this is a recent study showing that the average American teenager now spends more time per day on TikTok than on YouTube, which was earlier the most popular video platform by far. This shift in people’s preferences for content shows a clear future for platforms such as TikTok, with an emphasis on having the strongest impact on the user in the smallest amount of time possible.

This may also be a result of a faster-paced society, where people only give leverage to ideas presented to them quickly and convincingly. People seem to be slowly losing the ability to watch long-form, slow-burns that require effort and time to process and understand. Distortion of the attention economy has had severe consequences for human health and well-being. It has disrupted attention and cognition, leading to loss of memory and focus. Researchers have also found a link between excessive social media usage and the risk of self-harm, especially among young people.

On a fundamental level, the attention economy understands that evolution in technology, attractive interface designs, and clickbait titles allow the control of human attention. Social media activates attraction through emotional experiences. This leads to guaranteed engagement with the platform and a longer consumption time and controls the moments of individual attention of billions of users. This forms the fundamental basis of the attention economy, solidifying the notion of companies perceiving their users not as human beings, but as data sets, with their preferences and emotions amounting to nothing but profit-making opportunities for a corporation. Such an outlook may seem grim, but it highlights the sad reality of today’s dystopian world. 

Impact on well-being, 2017 [Image Credits: Economist.com]

However, all doesn’t seem to be lost. With time, users may gain the maturity required to resist an out-of-control attention economy. By avoiding clickbait and recommended content including promoted advertisements, we can avoid becoming products of this attention economy. This means making conscious, decisions about our content viewing choices, instead of going down whatever rabbit hole the internet decides to send us down that day.

Aldous Huxley’s dystopian sci-fi novel, Brave New World, presents an evanescent world where everybody is distracted all the time. The legal drug in the book, soma, bears a resemblance to antidepressants and anti-anxiety medications. A prescient book written in 1932 is not so different from where the world is currently heading.

Only the vigilant maintain their freedom, and pleasure is seen as the most effective form of control. Users’ minds are tied to an algorithm that keeps multibillion-dollar corporations running, with an impending climate crisis and political changes challenging human rights. The biggest threat is that it is easier than ever to express a free radical thought, but also more difficult than ever to have one. Indeed, it is outlandish to maintain a free and untainted mind, especially when you’re currently holding the thing that chains you to a dark future. 

Featured Image Credits: Unsplash

The doors of the MCH hall swung wide open to welcome the seekers and pioneers of wisdom attending the sixth edition of TEDxMAHE – Journey to Eureka on 3rd April 2022.

The Pro-Chancellor of MAHE, Dr HS Ballal, was the chief guest of the event. The very first speaker was the director of Manipal Institute of Nephrology and Urology. The spearhead of nephrology in Manipal, Dr H Sudarshan Ballal, drew stark contrasts between Archimedes and his own life. He recalled the experience of the pulsating hospital room after the first kidney transplant in Manipal and compared it to those that he had performed in the USA. He concluded by saying that his journey to eureka is not encapsulated in a single moment, but in each nephrologist added to the field.

The following speaker, Chef Sneha Singhi Upadhaya, an alumnus of Le Cordon Bleu, believed in paving one’s own path. She appeared on her mother’s cooking show at the age of 8, and today, she’s BBC India’s pastry chef of the year. She emphasised the importance of following one’s passion, and always knowing the crux of one’s pursuits. Above all, according to her, gratitude is the best ingredient for success.

Zealous and vibrant, Nikkiey Chawla, India’s first transgender model had a showstopping entrance thanks to her acting skills. She talked of the problems that trans-youth face pertaining to acceptance and reverence. Her parents’ support was a major motivator, and her perseverance has led to new avenues for the LGBTQ community in the beauty and entertainment industry. Miss Chawla believes in good deeds and karma as driving forces in life.

The fourth speaker, Mr. Vijay Varada, CEO and founder of Fractal Works, started off his talk with a picture of a capuchin monkey. It led to some insightful details of an experiment about opportunism and gambling amongst humans. He recounted the story of his office burning down and how that proved to be a turning point for his company, which was formerly a student project, now manufacturing factory equipment. This incident made him robust in his work ethic and reminded him of the irrationality of his fears.

All the distinguished speakers enraptured the audience with their interesting stories. [Image Credits: The MIT Post]

What followed was a segment called “social spaces’ wherein refreshments were served, and fun activities were arranged for the audience. It also gave the audience and the speakers a chance to interact with each other.

Performer and Ph.D. scholar at the Manipal Centre of Humanities, Srijan Deshpande, was the fifth speaker of the event. He believes in not restricting oneself to a particular niche. He enjoys familiarising Hindustani music at universities and completely engaged the audience during his talk by making the audience clap to the beat and sing. He used this as an example to show unexplored potential and comfort in uncertainty and drew lots of parallels between music and humanity.

The final speaker, IIT Kharagpur, and Harvard Business School graduate Sneha Biswas, stressed the importance of confidence and education beyond books, with the mantra “Confidence cannot be taught in a classroom.” She further expressed gratitude towards her mother’s encouragement when it came to learning new things and sending her to competitions at a young age. This was also the founding principle of Early Steps Academy, of which Sneha is the CEO. Her business savvy and bold personality engaged the audience and are testaments to her success.

The event was a huge success, as attested by the terrific atmosphere and amazing audience participation.

      Featured Image Credits: The MIT Post