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Vector

A Surprising Story of Space, Time, and Mathematical Transformation

A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions—sparking both controversy and discovery. 

The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word “vector” might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough—and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn’t have such a deep understanding of our world.

Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it’s not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional “spaces,” and why you’re likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone.

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Vector Reviews

Everyone understands what it means to move at some particular speed in some particular direction. But it took a long time to start thinking of such behavior in terms of a single clarifying concept, the vector. Arianrhod’s lively and detailed chronicle explains why vectors and tensors are at the heart of our best ways to think about the universe.

There have been lots of books about the evolution of modern physics: from Newton to Maxwell to Einstein and on to quantum theory. But seldom does an author pay attention to the mathematical revolutions that made those physical theories possible. Only as the mathematical toolkit expanded from simple scalars to include such tools and ideas as quaternions and vectors and tensors could physicists and mathematicians find the language to describe an increasingly bewildering universe. Arianrhod does a remarkable job telling the story of the mathematical revolution under the hood, the engine that drove the physics revolutions of the nineteenth and twentieth centuries; the result is a book well worth your time.

With a flair for exposition that makes the complex simple, and a gift for storytelling, Arianrhod is without peer in conveying the beauty, and power, of mathematics. William Rowan Hamilton, James Clerk Maxwell, and Albert Einstein come alive in this dramatic tale of a simple idea that changed our world.

Arianrhod’s Vector, a masterpiece of science exposition, reads as a welcoming cognitive cliffhanger tour of vectors, their generalizations, and their accompanying symbolic tools of mathematical physics, all dovetailing through germane history vignette accounts of astonishing connections and applications.

‘If all mathematics disappeared,’ physicist Richard Feynman opined, ‘it would set physics back precisely one week.’ To which mathematician Mark Kac retorted, ‘Precisely the week in which God created the world.’ Arianrhod persuades us that vectors and tensors are among those creations. Students and teachers should read this excellent book together.

Einstein's Heroes by Robyn Arianrhod

Einstein’s Heroes: Imagining the world through the language of mathematics

 The Age non-fiction book of the year, shortlisted

 The Victorian Premier’s Literary Awards (history), shortlisted.

 Translations: French, Japanese, Korean, Turkish

Imagine you are fluent in a language so powerful that when you write it down, it mysteriously takes on a life of its own, beyond your thoughts or control. A magical language of prophecy, with which you can accurately describe things you cannot yet see or even imagine.

Einstein’s Heroes blends science, history and biography to take you on a journey of discovery about the phenomenon of mathematics – humanity’s universal language and one of our most amazing accomplishments.

It takes as its axis the lives and work of the brilliant scientists who inspired Einstein, particularly James Clerk Maxwell, Michael Faraday and Isaac Newton. Together Maxwell and Faraday settled a centuries-old physical dispute, which Newton had left in his majestic wake, and established mathematics as the ultimate arbiter of physical reality.

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Untapped signifies the Australian Literary Heritage Project, which digitises culturally significant out-of-print Australian books. I was dismayed when UQP let my Einstein’s Heroes go out of print in Australia, so I’m delighted that Untapped has rescued it digitally, and Brio Books has published a new print edition, available here.

Einstein’s Heroes Reviews

Arianrhod’s achievement is to so masterfully combine history, biography, and mathematics as to absorb and enlighten even the mathematically maladroit. 

A thrilling story…. Arianrhod is an easy author to like, and not simply for the clarity of her narrative. She brings out the human side of the scientists. She also is a student of imaginative prose: Her explication of a novel by the Australian David Malouf helps introduce ideas about mathematics, and she quotes the poet William Blake to crystallize a thought about Maxwell…. Scientists’ quest for knowledge is exhilarating to Arianrhod, and she conveys that to the reader.

On one level, Robyn Arianrhod’s Einstein’s Heroes is about the crowning achievement of classical physics – James Clerk Maxwell’s understanding of electricity, magnetism, and light. But on another level, Arianrhod adeptly examines a much deeper idea: why is mathematics the language of nature and how do physicists tap the hidden power of numbers to understand the physical world? Einstein’s Heroes does an admirable job of explaining the strange allure that mathematics holds over the scientists who so dramatically altered the way we look at the universe. 

The overarching theme of Einstein’s Heroes is that mathematics is a universal human language — complete with its own rules of grammar, structure, and form — that has come to serve as the primary means by which scientists describe the physical universe. Arianrhod admirably sustains this note …  [she] has a knack for explaining things simply, as opposed to simplistically.

With exceptional skill, Arianrhod makes her subject clearly understood through metaphor, example, and story. She has given us a treasure – a combination of history, biography, and essay that clearly shows how and why the language of mathematics is essential to imagination in modern physics. Her unique book deserves high praise and should be read by anyone who enjoys science writing at its best.  

In her brilliant new book, Dr Robyn Arianrhod tells the story of the three scientists whose pioneering work paved the way to 20th-century physics… The depth and breadth of Arianrhod’s reach is impressive. She moves easily from Maxwell’s life to discuss ancient Greek, Indian, Islamic and Chinese mathematics, as well as the work of modern scientists such as Newton, Faraday, Einstein and others. Her lucid prose is as comfortable with the details of Maxwell’s personal life as it is with the intricacies of his physics. But, as its subtitle “Imagining the World through the Language of Mathematics” suggests, Einstein’s Heroes is ultimately a book about mathematics, a language Arianrhod sees as “a celebration of the human spirit”. In Maxwell’s work, she has found the perfect medium for exploring its beauty.

Offers readers an engaging intellectual exercise combining physics, language, mathematics, and biography.

Arianrhod is an infectiously enthusiastic writer, keen for her audience both to admire Einstein’s heroes and to understand their contributions to fundamental mathematical physics.

An intriguing blend of science, history, and biography…. Arianrhod’s well-written, fascinating discussion of intertwined topics not usually presented in one book aimed at general readers is highly recommended.

Seduced by Logic: Émilie du Châtelet, Mary Somerville and the Newtonian Revolution

The Queensland Literary Awards (science), shortlisted

The Queensland Literary Awards (history), shortlisted

National Biography Award, longlisted

Isaac Newton’s Principia changed forever humanity’s understanding of its place in the universe – not with the traditional tools of theology or philosophy but with the seductive logic of mathematics.

But it was the spirited French aristocrat Émilie du Châtelet who played a key role in bringing Newton’s revolutionary opus to a Continental audience. Together with her lover Voltaire, Émilie – a largely self-taught scholar – personified the exciting mix of science, literature, politics and philosophy that defined the Enlightenment.

A century later, in Scotland, Mary Somerville taught herself mathematics and rose from genteel poverty to become a world authority on Newtonian physics. Mary’s many books, and her charm, made her a legend in her own lifetime.

Connected by their passion for mathematics, Somerville and Du Châtelet bring to life a defining period in science and politics, revealing the intimate links between the unfolding Newtonian revolution and the origins of intellectual and political liberty.

Seduced by Logic is a thrilling foray in the lives of these extraordinary women – and the fascinating ideas that seduced them both.

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Seduced by Logic Book by Robyn Arianrhod

Seduced by Logic Reviews

[I]mpressively far-reaching … Arianrhod takes the wide scope of her book as an opportunity to discuss Newtonian mathematics, the history of the Enlightenment, and women’s education, to name just a few of her subjects. And no matter what the topic, her prose is natural, graceful and lucid. 

It is impossible not to be caught up in Arianrhod’s enthusiasm for her subject and I was gripped from the first page. 

An elegant and inspiring history of how scientific revolutions make their way. 

Seduced by Logic is far more than an account of the lives of Emilie du Châtelet and Mary Somerville. This book exposes the nature of scientific revolutions, and in the process, outlines the progression of fundamental scientific debates. […It is] both captivating and comprehensive, an interdisciplinary work with wide appeal. In telling her story, the author transcends traditional academic disciplines – history, philosophy, and physical science – and creates something richer in the process.

[For those who want] to understand du Châtelet’s achievement with Principia, Arianrhod is excellent.

Seduced by Logic offers the lay reader an easy and agreeable introduction to some crucial scientific debates… [Arianrhod’s] biographical perspective makes the narrative especially lively and engaging… [and ] one cannot help but be captivated by her intellectual honesty and enthusiasm.

Anyone who enjoys the history of science, especially from the underrepresented feminist perspective, should appreciate this well-crafted narrative.

Young Einstein by Robyn Arianrhod

Young Einstein and the story of  E=mc^2

Originally a bestselling Kindle Single; now published by Ligature.

Everyone recognises the famous physicist with the wild, white hair. But what sort of person was the young Albert Einstein, before he became universally acclaimed as the archetypal genius? And how did his genius unfold?

In this, compact, brilliant work – originally a Kindle Single – scientist Robyn Arianrhod blends biography with popular science to tell the story of how young Albert developed a theory that–unknown to him at first–contained the seeds of his extraordinary equation E = mc2.

Arianrhod, who wrote her PhD on Einstein’s general theory of relativity, makes the ideas behind the equation accessible to the lay reader and sets young Einstein’s exploration of these ideas against the backdrop of his first loves, his family and marriage and, above all, his childlike wonder at the nature of the universe.

She introduces his heroes and scientific inspirations and the friends who believed in him when no one else did. In personalising Einstein she brings to life both the man and his science in a short, easy-to-read narrative. In showing how he discovered his famous equation and what it means, she draws a compelling portrait of this prodigious intellect whose unfathomable grasp of the building blocks of physics would change our world forever.

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Thomas Harriot: A Life in Science

He was one of the greatest scientific minds of all time – the contemporary and equal of Galileo Galilei and Johannes Kepler, and a worthy precursor to his fellow Englishman Isaac Newton. Yet after his death in 1621, Thomas Harriot all but disappeared from history. His accomplishments were forgotten, his contributions eclipsed by others. The papers containing his unpublished experiments, calculations, theories, and notes, reflecting a lifetime of work, were lost for over 150 years, until they were eventually discovered in a trunk in an old castle.

With brilliant clarity, keen sympathy, and a deep appreciation of his scientific contributions, Robyn Arianrhod offers a rich account of Harriot’s life and achievements. Arianrhod’s immersive biography restores him to his rightful place in the scientific pantheon in the only way possible: through his scientific papers. The man who emerges from these pages is one whose mind was in constant motion – observing, recording, calculating, calibrating, seeking answers to questions that have absorbed humankind for millennia.

Thomas Harriot puts a human face to scientific inquiry in the Elizabethan and Jacobean ages, with all their creative ferment and perilous turmoil, and at long last gives proper due to one of history’s most remarkable figures.

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Thomas Harriot A Life in Science by Robyn Arianrhod

Thomas Harriot: A Life in Science Reviews

Thomas Harriot is one of the most unique personalities in the history of science. [… Robyn] Arianrhod knows the primary sources very well and skillfully manages to make the complex themes developed by Harriot—from astronomy to algebra—accessible. The book, conceived for a wide-ranging public, does not fail in scientific rigor. It rests on a strong foundation of primary and secondary literature, listed in a rich, up-to-date bibliography, that makes an excellent introduction to Harriot’s corpus. Visual aides also heighten the book’s accessibility… accompanied by an analytical index that lists personal names, topics, and themes, including current historiographic debates like Harriot’s comparison with Galileo, Descartes, and Kepler.

Arianrhod’s seamless blend of storytelling and science puts Harriot into full historical context. Though he inhabited a world of court intrigues, plague, and political upheavals, Harriot’s unflagging intellectual curiosity set him apart then, and makes him more than worthy of respect now, as this fascinating biography amply proves.

I learned much from the many enjoyable hours I spent reading this captivating book. In embarking on this well-crafted literary work you will soon develop a confident sense that either Harriot is with you in the room, or you are with him on the high seas on Sir Walter Raleigh’s Tiger. The elegant writing gracefully guides us past mathematical and scientific hurdles in a joyful time-traveling page-turner that never slows down.

In a largely harmonious meld of biography and science writing, Arianrhod furthers the drive to resurrect the reputation of English mathematician Thomas Harriot (1560-1621)…. A significant achievement that builds on previous works and takes the next step in establishing Harriot’s genius.

Now the lay reader has a chance to become acquainted with Harriot thanks to the elegant, vivid prose of mathematician and physicist, Robyn Arianrhod. […] Maths lovers will rejoice in Arianrhod’s scholarly explication of Harriot’s achievements. But those who are not maths geeks will still find this book an intellectual feast [… for] Arianrhod’s book reveals the full intellectual tapestry of the times.

At long last a first-rate biography of Thomas Harriot. Though unknown to many, Harriot’s scientific work casts a long shadow, and for ‘Harrioteers,’ as his fans are known, Robyn Arianrhod’s beautifully written and deeply researched book is the one we’ve been waiting for. A triumph and a must read!
With beautiful prose, astute historical understanding, and impeccable mastery of a near-inexhaustible array of fields, Robyn Arianrhod resurrects the life and works of this enigmatic Renaissance man. The world of an Elizabethan sage who was an intimate of the greatest soliders, scholars, and poets of the age springs to life in Arianrhod’s pulsating narrative.
Robyn Arianrhod restores Harriot to his rightful place alongside Galileo and Kepler in the pantheon of pioneering early modern scientists and shows how, as one friend put it, he was ‘robbed of glory.’ Thomas Harriot: A Life in Science is a wonderful combination of biography, history, and popular science that pulses with the spirit of its time.

[… Robyn] Arianrhod’s book is well constructed and written, which results in a well-paced read, an entertaining combination of biography, history, and popular science suitable for academics and, indeed, for anyone interested in these areas. The book is packed with fascinating historical detail, and the importance of the context in which [Harriot’s] scientific contributions were formulated and the life that he led is very much to the fore. […] Arianrhod challenges the neglect of Harriot, and forces us to consider him and his contributions more carefully. I will certainly increase Harriot’s visibility in my teaching, and I will recommend this book to my students.

The story of Thomas Harriot’s life and works, were it not so well documented by such a respected scholar as Dr. Arianrhod, could easily be thought a work of pure fiction – and extravagant, scarcely believable fiction at that. Yet it is all true. That Dr. Arianrhod has devoted the time and effort in bringing [Harriot] back to us through this absolutely captivating biography is something for which we should all be deeply grateful, and in similar gratitude, we owe it to the memory, indeed, the unrelentingly curious and inquiring spirit, of Thomas Harriot himself, to read it. 

In 1585, Harriot himself joined an expedition to establish an English outpost on Roanoke Island, off present-day North Carolina. Ms. Arianrhod’s vivid account applies a modern moral lens to the rapacious actions of his fellow proto-colonists… Throughout the latter half of the book, the Damoclean threat looming over Harriot is palpable, as the nodes of power shift around him.

Robyn Arianrhod […] adds the latest cornerstone to the edifice of Harriot’s resurrected reputation. Hers is an authoritative, often engrossing marriage of history and science … By studying his life and career, Harriot helps us understand how modern mathematics and science began to emerge. Arianrhod’s is a significant achievement.

BOOK CHAPTERS:

 2023: ‘On Writing Harriot’s Biography,’ Thomas Harriot: Science and Discovery in the English Renaissance, Robert Fox (ed.), Routledge

1992: ‘Physics and Mathematics, Language and Reality: Dilemmas for Feminists,’ The Knowledge Explosion, Cheris Kramarae and Dale Spender (eds), Teachers College Press