Where arts meets mathematics

‘I am attracted to curves that I find in the mountains of my country, in the sinuousness of its rivers, in the waves of the ocean, and on the body of the beloved woman’

Einstein had remarked that to appreciate the universe one would need to understand curves. Not sure if he was seduced by curves, but it is clear that straight lines and square corners do not determine what we make of the universe. Like human body, the universe is beautiful because of its magical patterns and exquisite shapes. Be it the human cell, the lowly creatures or the distant galaxies, the remarkable theory of curve is at work everywhere. Such is the magic of this theory that the entire universe manifests itself in curves, from the fold to a wigwam.

Reproductive biologist may consider curve as a work of evolution but for a structural engineer curve is what connects mathematics with art. And, within this connection may lie insights on understanding why things are shaped the way they are. While we often take shapes for granted but deep within each must be a cause for the object to take a particular form. University of Cambridge structural engineer Allan McRobie, who previously designed boringly rectilinear bridges and towers, found that the stability of engineering structures is essentially governed by their smoothly curved energy surfaces. This is how an unexpected link between the world of careful engineering calculation and a freer graphical expression emerged, leading to a beautiful language of folds, cusps and swallowtails.

Nothing comes closer than ‘human nude’ to draw a connection between art and mathematics, as a large part of our fascination for curves originates there. Need it be said that evolutionary biology rests on curves, our genes guide us to like the body shapes of our mates. The pervasiveness of these curves is striking because human body is a one-stop object for viewing different type of curves, a perfect justification for a book connecting mathematics with art to have a seductive curve on the cover. The curve resembles a swallowtail, the essence of beauty depicted by two back-to-back cusps connected by folds. Beautiful though it may be, a swallowtail on the waist of a human body is nowhere near as profound as the immense organization required to create all the components of that living, breathing, thinking human. The question worth exploring is how biological shapes emerge to be the shapes they finally become.

In some ways, the beauty in the swallowtail curve is indeed a precarious point of stability which engineers use to explain the catastrophe theory, the sudden change that induces abrupt outputs, developed by noted mathematician Rene Thom. However, the final shape of an object is on account of the energy of a protein that folds itself into any one of a number of possible configurations, indicating which stable pathway will eventually be followed. That is how some cells arrange to become bones and others into hair follicles.

The Swallow's Tail

The Seduction of Curves is a colorful and richly illustrated book in which human bodies are described through geometry, and connected to structural engineering, optical physics and more. The beauty of the book is that it pulls curves out from the confines of subjectivity, and situates them in the objectivity of mathematics. It is a book of mathematics nonetheless, which can be simply seen as a work of fine arts. By giving special attention to outrageous Spanish surrealist Salvador Dali’s iconic painting The Swallow’s Tail, McRobie brings together the theme of the catastrophe theory in understanding curves. Having met Thom towards later part of his life, much of Dali’s work then on was reflective of their intense association ‘everything I do from now on will be devoted to the phenomenon of catastrophes’.

Spread across nineteen profusely illustrated chapters, the book is about seven curves, four from cuspoid (fold, cusp, swallowtail and butterfly) and three of umbilic family (elliptic, hyperbolic and parabolic), which are the basic building blocks, the fundamental components of curved form. These curves also represent a way by which something can suddenly change. This is the essence of the catastrophe theory, which studies how smooth and subtle changes in a system can result in sudden and abrupt outputs. Collapse of elevated roads or oil rigs are classic examples of such drastic end results. Given the significance of curves, one wonders if as children we should have been taught alphabets of curved geometry beginning with fold, cusp, swallowtail and butterfly in place of straight-line Euclidean geometry sequence of terms like triangle, square, pentagon and so on. Will it begin to change anytime soon?

In many ways this is a remarkable book which has more visuals than text, and it will be a pity if it goes unread. Interestingly, the illustrations and pictures are a study in themselves providing depth, dimension and relevance of curves in our lives, making one wonder if there were no curves in our universe. At some point in reading through the book one begins to view straight lines and angles with disdain, much like well known Brazilian architect Oscar Niemeyer, who was influenced by Le Corbusier but had developed an aversion for straight lines. Niemeyer was attracted to free-flowing, sensual curves, and had remarked ‘I am attracted to curves that I find in the mountains of my country, in the sinuousness of its rivers, in the waves of the ocean, and on the body of the beloved woman’. Several of the famous architectural structures standing today bear testimony to the power of the curved form. The future seems to be in triggering sensuous resonances in the minds of observers.  

The book is a bold attempt at evoking multiple feelings towards curves. Allan McRobie deserves praise for sensually drawing parallels between natural and the constructed world.

The Seduction of Curves
by Allan McRobie
Princeton University Press, Oxford
Extent: 159, Price: $35

First published in Current Science, dated Aug 25, 2018.

Not that desires didn't exist!

Far from what the laws state and what the state feels, Indian women have come of age in exploring their sexiness.

Rich in the forbidden content, Cyber Sexy tracks the search for satiating desire from those mythical days in the elusive garden to the brave new world of virtual flesh. Howsoever the individuals may shun it publicly for being politically and morally incorrect, desire runs deep through various facets of our individual and collective lives. Demand meets supply as countless categories of desire dotted across the internet help people in their daily swim across the fleshy landscape. If we were to look within ourselves without judgement or shame, as Richa Kaul Padte echoes, there is a high chance that we will find ourselves faced with variations of the same desires that we condemn others for. Variants may range from sheer pleasure to dreadful perversion. 
 
Taking readers on a cyber tour of online pleasure, the author provides a nuanced understanding on why our foregone conclusions on the topics of sex, identity, and desire are gender-biased and flawed. Why is it that sexual desire, and not sexual pleasure, a moral problem? Why is there an undue emphasis on male desire for seeking sexual pleasure? Why does society make women feel ashamed of expressing their desires?  And, why is there an almost default assumption that online sex (read porn) is worse for women? 

David Leeming, author of upcoming Sex in the World of Myth, lends a helping hand by arguing that sex is as important in myths as it is in our lives. Despite ancient sculptures and medieval paintings bearing testimony to desire being eternal to humans, the irony is that reality manifests itself between the sheets or behind the closets. Further, the colonial idea that anything related to sex is immoral and dirty persists under regressive laws, holding forth the obligatory need for the state to protect women from its purported impact, both moral and physical.

The book blows the lid off such assumptions. Far from what the laws state and what the state feels, Indian women have come of age in exploring their sexiness. They are as adventurous as their counterparts, or even more if the case stories are any indication, as 30 per cent of all visitors on the porn websites were women in 2017. This does indicate that women have agency and autonomy to explore their hidden desires, caveat being that their conversation on the subject can refresh the narrative on the harms of obscenity or objectification. Not many will agree though! 

Cyber Sexy is a provocative undertaking on a subject that is pregnant with hitherto unnoticed categories of desire. Not that these desires did not exist, internet only enabled people who desired differently to feel a little less alone by giving shape and support to the thing that lives inside them. And, it proliferates because it stirs the universal set of emotions that lie buried underneath. But not for the conservatives who frown at such notion being outrageous and insane as it ends up corrupting unsuspecting minds. Little is realized, and the book offers enough evidence, that people are exploring each other’s bodies, sexting one another, and uploading their unmet desires on the internet. To pretend that these aren’t happening does not make them any less true.

Taking a deep dive into the kinky treasure of online porn, Richa comes out holding a mirror on society’s totally subjective moral judgement. As the country runs through its millennial churn, the question worth probing is why women’s bodies are often the battleground on which the fight for morality takes place? Why cyber technology is held dangerous for women only? Reading through this intrepid narrative, it is tough not to agree that the solo aim of pushing desire into morality’s deepest trench is to monopolize the power for defining gender roles in a man’s world

Cyber Sexy provides an equalizing narrative on how the artificial binaries have begun to blur. Although concerns regarding seeking consent, avoiding objectification and curbing coercion are not entirely misplaced, the need to redefine our approach towards fleshy fruits freely hanging on the internet is critical for the society to begin acknowledging desire as an integral part of human rights to sexuality. While there is no denying the need to fix the parts that are going wrong, there is an equally compelling reason to prioritize peoples’ rights to bodily autonomy and agency. 

Radical and uncompromising, Cyber Sexy is a book on woman’s perspective on cyber porn by a woman. This is a timely study as the impact of internet outreach has yet to be felt by two-third of the country’s population. But it puts to rest the fallacy that by valuing desire one compromise on family values, societal norms, and inner spirituality. It is an engaging and must read book on a subject on which only male giggles been heard in the past. Richa Kaul Padte invites the other half to join in serious conversations, but cautions upfront that women are not coy anymore – we have agency and autonomy, and have desires and fears too.  

Cyber Sexy
by Richa Kaul Padte
Penguin, New Delhi
Extent: 255, Price: Rs. 399

First published in Outlook on July 19, 2018.

The coming of conscious machines?

The development of thinking machines evokes as much hope in the future as fearful dystopia.

Mankind has gone through three distinct turning points in its evolutionary history - discovered fire 100,000 years ago; developed language 10,000 years, and invented wheel 5.000 years ago – which triggered multitudes of other advances that have revolutionized human existence. Since then, within the overall arc of human history, not much seems to have changed. Else, we wouldn’t be living like those who lived five millennia ago, with parents and pals in cities with markets and governments. And, we wouldn’t fear life, share gossip, build relationships and celebrate birthdays like those in the past. Isn’t it a trivia that lot has changed without much remaining the same?

With a deep understanding of human history, tech entrepreneur and futurist Byron Reese offers a nuanced understanding of the change that is at our doorsteps, in the form of what he terms ‘the Fourth age’. This age will unleash the power of artificial intelligence and conscious computers in our daily existence, seemingly intelligent non-humans who will act autonomously to perform tasks that will ease our lives. There is every reason to believe that automation will bring efficient and healthy living within the reach of everybody on the planet. The prevailing technological turbulence will bring about dramatic breakthroughs in artificial intelligence and robotics in the next fifty years compared to what has been witnessed during the last five thousand years. 

The next generation artificial intelligent machines will outsmart its predecessors – from self-driven car to the talking robot – by being as smart as you and me. These will do more than what it would have been programmed to do, by figuring out what the new task expects it to perform. Within the emerging world of artificial general intelligence (AGI), the development of thinking machines evoke as much hope in future as fearful dystopia. Will machines make human redundant? Will smart automation gobble up all the jobs? Will it usher permanent Great Depression? 

Since it is about the change we haven’t seen yet, any discussions on the subject leads to confusion and misconception. The confusion is further compounded when the likes of Elon Musk, Stephen Hawking, and Bill Gates propound that artificial intelligence is a fundamental risk to the existence of human civilization, while their illustrious compatriots Mark Zuckerberg, Andrew Ng, and Pedro Domingos lend weight to the argument that human future is safe in the hands of intelligent machines. Despite such polarized positions, the foremost fear concerning AGI is about its impact on jobs. Fears of a permanent Great Depression are beginning to cast its impact on people in the streets. Everyone seems to be asking: Will I lose my job? Will smart robots eliminate more jobs than the economy will create?  What should I do to protect my job? 

Reese takes the question head on, although it is devilishly complex because it isn’t known what all jobs robots can replace; to what level business will invest in developing artificial intelligence; and how will cost of labor impact the adoption of technology? Therefore, it is not a back-of-the-envelope calculation to determine the net effect of technology on jobs. What is perhaps easy is to realize that there are just three possible scenarios i.e., robot will take all jobs; robots will take some of the jobs; and robots will take none of the jobs, to make some sense of it.

Without doubt, introduction of technology does reduce the need for workers in particular sectors. Although the transition is often difficult, those eliminated from low-skilled jobs graduate into improving their skills to take on different jobs. However, the question is whether these numbers add.  The Bank ATMs and online trading websites are two interesting examples. It did rattle the bank tellers and the stockbrokers but over time technology has not only helped employ more people in building ATMs but the stockbrokers have exhibited their cognitive abilities too. The erstwhile low-skilled jobs have gained value through the use of computing technology. 

Although understanding the ever-expanding job market is mindboggling, no visible relationship between the use of robots and loss of job has yet been established. Despite the installation of far more robots between 1993 and 2007, Germany lost just 19 per cent of its manufacturing jobs compared to a 33 per cent in the US. Same has been true in other countries such as Italy, South Korea, and France that deployed more robots, lending credence to the widely held view that technology mostly augments workers, not replaces them. On top, people have always been able to create new jobs, more in the changing time now than ever in the past.   

The Fourth Age is about comprehending the accelerating change, and about understanding the universals of technology that drive progress. Understanding those universals will give us new insights on humanity’s unmistakable journey toward social justice and personal empowerment aimed at liberating humans, in the words of Charles Dickens, from the clutches of dehumanizing jobs. The need is to gain clarity on duality of co-existence with machines.

For robots to replace humans at home and in the workplace, AGI would need to exhibit the entire range of the various types of intelligence that humans have, such as social and emotional intelligence, the ability to ponder the past and the future, as well as creativity and true originality. To overcome the hurdles of attaining consciousness in computers, Elon Musk is proposing commingling computers with human brain to take directions. To make the best of both, the challenge lies in decoding the billions of synapses between a hundred billion neurons.  

While the cost of building robots is coming down, the challenge to build an AGI on the structure of the human brain has yet to show any tangible results. After spending a billion of dollars, the Human Brain Project is in total disarray. Reese provides a detailed account of the current competing societal perspectives on the relation between humans and our machines, on accelerating technological change, and on the future of mankind in a world of robots and humanoids. 

The core of the argument, however, is draw distinction between monism and dualism as two dominant beliefs about the nature of reality. While for monists creating a machine with human attributes is a serious possibility, dualists fervently disagree that a silicon-based computer will ever grasp the intricacies of a carbon-based human. Science is nowhere close to describing something like consciousness yet, but our relentless move forward and upward characteristic will reduce us from being Homo sapiens to Homo dissatisfactus. Byron Reese takes the reader into the rapidly unfolding world of artificial intelligence and robots, the one that is sure to revolutionize our physical being but our mental domain as well. Without doubt, The Fourth Age, is upon us. 

The Fourth Age
by Byron Reese
Simon & Schuster, New Delhi
Extent: 320, Price: Rs 399.

First published in the Hindu BusinessLine, dated July 9, 2018.