Category Archives: Mathematics

Toronto’s ArtSci Salon is hosting a couple more October 2025 events

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I have two art/science events and one art/science conference/festival (IRL [in real life or in person] and Zoom) taking place in Toronto, Ontario.

October 16, 2025

There is a closing event for the “I don’t do Math” series mentioned in my September 8, 2025 posting,

…

ABOUT
“I don’t do math” is a photographic series referencing dyscalculia, a learning difference affecting a person’s ability to understand and manipulate number-based information.

This initiative seeks to raise awareness about the challenges posed by dyscalculia with educators, fellow mathematicians, and parents, and to normalize its existence, leading to early detection and augmented support. In addition, it seeks to reflect on and question broader issues and assumptions about the role and significance of Mathematics and Math education in today’s changing socio-cultural and economic contexts. 

The exhibition will contain pedagogical information and activities for visitors and students. The artist will also address the extensive research that led to the exhibition. The exhibition will feature two panel discussions following the opening and to conclude the exhibition.

…

I have some information from an October 12, 2025 ArtSci Salon announcement (received via email) about the “I don’t do math” closing event,

in us for 

Closing Exhibition Panel Discussion
Thursday, October 16 2025
10:00 am -12:00 pm room 309
The Fields Institute for Research in Mathematical Sciences (or online)

Artist Ann Piché will be in conversation with
Andrew Fiss, Jacqueline Wernimont, Amenda Chow, Ellen Abrams, Michael Barany and JP Ascher

RSVP here

…

October 21, 2025

The second event mentioned in the October 12, 2025 ArtSci Salon announcement, Note 1: A link has been removed, Note 2: This event is part of a larger series,

…

Marco Donnarumma 
Monsters of Grace: bodies, sounds, and machines

Tuesday, October 21, 2025
3:30-4:30 PM
Sensorium Research Loft 
4th floor
Goldfarb Centre for Fine Arts
York University

About the talk
What is sound to those who do not hear it? How does one listen to something that cannot be heard? What kind of sensory gaps are created by aiding technologies such as prostheses and artificial intelligence (AI)? As a matter of fact, the majority of non-deaf people hear only partially due to age and personal experience. Still, sound is most often considered through the normalizing viewpoint of the non-deaf. If I become your body, what does sound become for me? Join us to welcome Marco Donnarumma  ahead of his new installation/performance at Paul Cadario Conference Room (Oct 22, 8-10 PM University College [University of Toronto] – 15 King’s College Circle). His talk will focus on this latest work in the context of a largest body of work titled “I Am Your Body,” an ongoing project investigating how normative power is enforced through the technological mediation of the senses.

About the artist:
Marco Donnarumma is an artist, inventor and theorist. His oeuvre confronts normative body politics with uncompromising counter-narratives, where bodies are in tension between control and agency, presence and absence, grace and monstrosity. He is best known for using sound, AI, biosensors, and robotics to turn the body into a site of resistance and transformation. He has presented his work in thirty-seven countries across Asia, Europe, North and South America and is the recipient of numerous accolades, most notably the German Federal Ministry of Research and Education’s Artist of the Science Year 2018, and the Prix Ars Electronica’s Award of Distinction in Sound Art 2017. Donnarumma received a ZER01NE Creator grant in 2024 and was named a pioneer of performing arts with advanced technologies by the major national newspaper Der Standard, Austria. His writings are published in Frontiers in Computer Science, Computer Music Journal and Performance Research, among others, and his newest book chapter, co-authored with Elizabeth Jochum, will appear in Robot Theaters by Routledge. Together with Margherita Pevere he runs the performance group Fronte Vacuo.

…

I wonder if Donnarumma’s “Monsters of Grace: bodies, sounds, and machines’ received any inspiration from “Monsters of Grace” (Wikipedia entry) or if it’s just happenstance, Note: Links have been removed,

Monsters of Grace is a multimedia chamber opera in 13 short acts directed by Robert Wilson, with music by Philip Glass and libretto from the works of 13th-century Sufi mystic Jalaluddin Rumi. The title is said to be a reference to Wilson’s corruption of a line from Hamlet: “Angels and ministers of grace defend us!” (1.4.39).

So, the October 21, 2025 event is a talk at York University taking place before the “Who’s afraid of AI? Arts, Sciences, and the Futures of Intelligence” (more below).

“Who’s afraid of AI? Arts, Sciences, and the Futures of Intelligence,” a conference and arts festival at the University of Toronto

The conference (October 23 – 24, 2025) is concurrent with the arts festival (October 19 – 25, 2025) at the University of Toronto. Here’s more from the event homepage on the https://bmolab.artsci.utoronto.ca/ website, Note: BMO stands for Bank of Montreal, Note: No mention of Edward Albee and “Who’s afraid of Virginia Woolf?,”

2025 marks an inflection point in our technological landscape, driven by seismic shifts in AI innovation.

Who’s Afraid of AI? Arts, Science, and the Futures of Intelligence is a week-long inquiry into the implications and future directions of AI for our creative and collective imaginings, and the many possible futures of intelligence. The complexity of these immediate future calls for interdisciplinary dialogue, bringing together artists, AI researchers, and humanities scholars.

In this volatile domain, the question of who envisions our futures is vital. Artists explore with complexity and humanity, while the humanities reveal the histories of intelligence and the often-overlooked ways knowledge and decision-making have been shaped. By placing these voices in dialogue with AI researchers and technologists, Who’s Afraid of AI? examines the social dimensions of technology, questions tech solutionism from a social-impact perspective, and challenges profit-driven AI with innovation guided by public values.

The two-day conference at the University of Toronto’s University College anchors the week and features panels and debates with leading figures in these disciplines, including a keynote by 2025 Nobel Laureate in Physics Geoffrey Hinton, the “Godfather of AI” and 2025 Neil Graham Lecturer in Science, Fei-Fei Li, an AI pioneer.

Throughout the week, the conversation continues across the city with:

  • AI-themed and AI powered art shows and exhibitions
  • Film screenings
  • Innovative theatre
  • Experimental music

Who’s Afraid of AI? demonstrates that Toronto has not only shaped the history of AI but continues to prepare its future.Step into this changing landscape and be part of this transformative dialogue — register today!

Organizing Committee:

Pia Kleber, Professor-Emerita, Comparative Literature, and Drama, U of T
Dirk Bernhardt-Walther, Department of Psychology, Program Director, Cognitive Science, U of T
David Rokeby, Director, BMO Lab, Centre for Drama, Theatre and Performance Studies, U of T
Rayyan Dabbous, PhD candidate, Centre for Comparative Literature, U of T

…

This looks like a pretty interesting programme (if you’re mainly focused on AI and the creative arts), from the event homepage on the https://bmolab.artsci.utoronto.ca/ website, Note 1: All times are ET, Note 2: I have not included speakers’ photos,

The conference will explore core questions about AI such as its capabilities, possibilities and challenges, bringing their unique research, creative practice, scholarship and experience to the discussion. Speakers will also engage in an interdisciplinary conversation on topics including AI’s implications for theories of mind and embodiment, its influence on creation, innovation, and discovery, its recognition of diverse perspectives, and its transformation of artistic, cultural, political and everyday practices.

Thursday, October 23, 2025

Mind the World

9 AM | Clark Reading Room, University College – 15 King’s College Circle

What are the merits and limits of artificial intelligence within the larger debate on embodiment? This session brings together an artist who has given AI a physical dimension, a neuroscientist who reckons with the biological neural networks inspiring AI, and a humanist knowledgeable of the longer history in which the human has tried to decouple itself from its bodily needs and wants.

Suzanne Kite
Director, The Wihanble S’a Center for Indigenous AI

James DiCarlo
Director, MIT Quest for Intelligence

N. Katherine Hayles
James B. Duke Distinguished Professor Emerita of Literature

Staging AI

11 AM | Clark Reading Room, University College – 15 King’s College Circle

How is AI changing the arts? To answer this question, we bring together theatre directors and artists who have made AI the main driving plot of their stories and those who opted to keep technology secondary in their productions.

Kay Voges
Artistic Director, Schauspiel Köln

Roland Schimmelpfennig
Playwright and Director, Berlin

Hito Steyerl
Artist, Filmmaker and Writer, Berlin

Recognizing ‘Noise’

2 PM | Clark Reading Room, University College – 15 King’s College Circle

How can we design a more inclusive AI? This session brings together an artist who has worked with AI and has been sensitive to groups who may be excluded by its practice, an inclusive design scholar who has grappled with AI’s potential for personalized accessibility, and a humanist who understands the longer history on pattern and recognition from which emerged AI.

Marco Donnarumma
Artist, Inventor, Theorist, Berlin

Jutta Treviranus
Director, OCADU [Ontario College of Art & Design University],
Inclusive Design Research Centre

Eryk Salvaggio
Media Artist and Tech Policy Press Fellow, Rochester

Art, Design, and Application are the Solution to AI’s Charlie Chaplain Problem

4 PM | Hart House Theatre – 7 Hart House Circle

Daniel Wigdor
CoFounder and Chief Executive Officer, AXL

Keynote and Neil Graham Lecture in Science

4:15 PM | Hart House Theatre – 7 Hart House Circle

Fei-Fei Li
Sequoia Professor in Computer Science, Stanford Institute for Human-Centered AI

Geoffrey Hinton
2024 Nobel Laureate in Physics, Professor Emeritus in Computer Science

…

Friday, October 24, 2025

Life with AI

9 AM | Clark Reading Room, University College – 15 King’s College Circle

How do machine minds relate to human minds? What can we learn from one about the other? In this session we interrogate the impact of AI on our understanding of human knowledge and tool-making, from the perspective of philosophy, computer science, as well as the arts.

Jeanette Winterson
Author, Fellow of the Royal Society of Literature, Great Britain

Leif Weatherby
Professor of German and Director of Digital Theory Lab at
New York University

Jennifer Nagel
Professor, Philosophy, University of Toronto Mississauga

Discovery & In/Sight

11 AM | Clark Reading Room, University College – 15 King’s College Circle

This session explores creative practice through the lens of innovation and cultural/scientific advancement. An artist who creates with critical inspiration from AI joins forces with an innovation scholar who investigates the effects of AI on our decision making, as well as a philosopher of science who understands scientific discovery and inference as well as their limits.

Vladan Joler
Visual Artist and Professor of
New Media, University of Novi Sad [Serbia]

Alán Aspuru-Guzik
Professor of Chemistry and Computer Science, University of Toronto

Brian Baigrie
Professor, Institute for the History and Philosophy of Science & Technology, University of Toronto

Social history & Possible Futures

2 PM | Clark Reading Room, University College – 15 King’s College Circle

How does AI ownership and its private uses coexist within a framework of public good? It brings together an artist who has created AI tools to be used by others, an AI ethics researcher who has turned algorithmic bias into collective insight, and a philosopher who understands the connection between AI and the longer history of automation and work from which AI emerged.

Memo Akten
Artist working with Code, Data and AI, UC San Diego

Beth Coleman
Professor, Institute of Communication, Culture, Information and Technology, University of Toronto

Matteo Pasquinelli
Professor, Philosophy and Cultural Heritage Università Ca’ Foscari Venezia [Italy]

A Theory of Latent Spaces | Conclusion: Where do we go from here?

4 PM | Clark Reading Room, University College – 15 King’s College Circle

Antonio Somaini, curator of the remarkable ‘World through AI’ exhibition at the Museé du Jeu de Paume in Paris, will discuss the way in which ‘latent spaces’, a core characteristic of current AI models as “meta-archives” that shape profoundly our relation with the past.

Following this, we will engage in a larger discussion amongst the various conference speakers and attendees on how we can, as artists, humanities scholars, scientists and the general public, collectively imagine and cultivate a future where AI serves the public good and enhances our individual and collective lives.”

Antonio Somaini
Curator and Professor, Sorbonne Nouvelle [Université Sorbonne Nouvelle]

…

You can register here for this free conference, although, there’s now a waitlist for in person attendance. Do not despair, there’s access by Zoom,

In case you can’t make it in person, join us by Zoom:

Link: https://utoronto.zoom.us/j/82603012955

Webinar ID: 826 0301 2955

Passcode: 512183

I have not forgotten the festival, from the event homepage on the https://bmolab.artsci.utoronto.ca/ website,

Events Also Happening

October 22 | 2 PM | Student Forum and AI Commentary Contest Award | Paul Cadario Conference Room, University College – 15 King’s College Circle

October 22 | 8 – 10 PM | Marco Donnarumma, world première of a new performance installation | Paul Cadario Conference Room, University College – 15 King’s College Circle

October 23 | 2 PM | Jeanette Winterson: Arts & AI Talk | Paul Cadario Conference Room, University College – 15 King’s College Circle

October 24 | 7 PM | The Kiss by Roland Schimmelpfennig | The BMO Lab, University College – 15 King’s College Circle (Note: we are scheduling more performances. Check back for more info soon!)

October 25 | 8 PM | AI Cabaret featuring Jason Sherman, Rick Miller, Cole Lewis, BMO Lab projects and more| Crow’s Theatre, Nada Ristich Studio-Gallery – 345 Carlaw Avenue..

Get tickets for the AI Cabaret

(Use promo code AICAB for 100% discount)

Enjoy!

Today (09.16.25) is Pythagorean Triple Square Day—a once in a century event!

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[from Pythagorean Theorem Formula For Kids ar.inspiredpencil.com; Note: I cannot read the Arabic and am not able to credit the artist]

September 16, 2025 is a mathematically significant date as Andrew Paul notes in a September 15, 2025 Popular Science article, Note: Links have been removed,

Pi Day (March 14) is a day of global mathematical celebration, but it’s not the only numerically significant calendar date. It’s far from the rarest, either. In fact, today marks a special occasion that only occurs once this century. Not only is each number in today’s date (9/16/25) a perfect square—their consecutive square roots are also an example of a Pythagorean triple. While an official name has yet to be assigned, “Pythagorean Triple Square Day” encapsulates the moment pretty perfectly.

Here’s the specific math to add it all up: 3 multiplied by itself is 9, 4 squared is 16, and 5 squared is 2025. On top of that, the sum of the first two square roots adds up to 25.

“This date is hiding one of the most beautiful coincidences we will ever encounter,” Terrence Blackman, head of mathematics at Medgar Evers College in the City University of New York, told NPR. “Those numbers, they tell a story that goes back to ancient Greece.”

To be fair, the story actually goes even further back than that. Pythagoras (c. 570—c. 495 BCE) is most famously credited as the first mathematician to discover his namesake theorem. To jog those scary memories of high school math, the Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two other sides. 

However, both ancient Babylonian and Indian theorists had known the same information for centuries. …

Happy Pythagorean Triple Square Day and if you have a chance do read Paul’s September 15, 2025 Popular Science article in its entirety.

Toronto’s ArtSci Salon offers “i don’t do math” and more

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A September 5, 2025 announcement (received via email) from Toronto’s ArtSci Salon highlights three upcoming events. In date order, from the online version of the September 5, 2025 announcement, Note: The online version is on mailchi.mp and is time limited,

Book Launch
To Place a Rabbit
by
Madhur Anand
in conversation with Shyam Selvadurai

Tuesday, Sept. 9 2025
7:00 pm [ 7 – 8:30 pm ET]
Another Story Bookstore
315 Roncesvalles avenue
Toronto

RSVP here

I found more information about the book launch on its eventbrite RSVP page, Note: Links have been removed,

ABOUT THE BOOK

This delightfully clever, artfully layered novel begins when a scientist who has written a popular book of non-fiction attends a literary festival, where she strikes up a friendship with a charismatic novelist. The novelist reveals that her new work is an experiment: a novella she wrote in English only to have it translated and published solely in French—a language the novelist cannot read. Moreover, she has lost her original English manuscript of this work. Hearing this, the scientist, who is fluent in French, impulsively offers to retranslate the novella back into English for the novelist.As she embarks on this task, the scientist finds herself haunted by vivid memories and distracting questions—particularly about a passionate affair from her own life with a French lover. These insert themselves into her translation process, troubling it, then disrupting it entirely. She desperately tries to complete her task before losing control of both the work and her well-organized existence—but soon the novelist and the French lover reappear in the present, further complicating both life and art.Here is sparkling, irresistible debut fiction from one of our most consistently inventive voices, the award-winning and multi-talented Madhur Anand.

ABOUT THE AUTHOR

Madhur Anand’s debut book of creative non-fiction This Red Line Goes Straight to Your Heart (2020) won the Governor General’s Literary Award for Nonfiction. Her debut collection of poems A New Index for Predicting Catastrophes (2015) was a finalist for the Trillium Book Award for Poetry and named one of 10 all-time “trailblazing” poetry collections by the Canadian Broadcasting Corporation. Her second collection of poems Parasitic Oscillations (2022) was also a finalist for the Trillium Book Award for Poetry and named a Globe and Mail Top 100 Book. To Place a Rabbit is her first novel. Anand is a professor and the director of the Global Ecological Change and Sustainability Laboratory at the University of Guelph, Ontario.

ABOUT THE MODERATOR

Shyam Selvadurai was born in Colombo, Sri Lanka. Funny Boy, his first novel, won the W.H. Smith/ Books in Canada First Novel Award and the Lambda Literary Award in the US. He is the author of Cinnamon Gardens and Swimming in the Monsoon Sea, and the editor of an anthology, Story-wallah! A Celebration of South Asian Fiction. His books have been published in the US, the UK and India, and published in translation in France, Germany, Italy, Spain, Sweden, Denmark, Turkey and Israel. His latest novel, The Hungry Ghosts, was published April 2, 2013 in Canada, India and Sri Lanka. Shyam co- wrote the screenplay for his first novel Funny Boy, for which he won the Canadian Screen Award and the New York Cinema Independent Award for Best Adapted Screenplay. Shyam’s new novel Mansions of the Moon is a historical novel about the Buddha’s wife, Yasodhara. In 2016, Shyam had the interesting honour of having a spider named after him: Brignolia shyami, a small goblin spider.

This notice concerns the revival of an event and a call for proposals, the online version of the September 5, 2025 announcement,

Call for Proposals:
RE:SciComm
February 19-20, 2026
Oakham House,
Toronto Metropolitan University,
55 Gould Street, Toronto

RE:SciComm (formerly SciCommTO) — a dynamic, in-person conference exploring the art, science, and strategy of science communication in Canada. The conference will attract science communicators, researchers, journalists, graduate students, and outreach professionals from across the GTHA [Greater Toronto and Hamilton Area] and beyond.

Call for proposals now open until September 15, 2025

conference themes

The RE:ScieComm conference website offers a clue as to why it was mentioned in ArtSci Salon announcements,

Join us for a dynamic conference exploring the art, science, and strategy of science communication in Canada.

Whether you’re behind the mic, in front of a classroom, or crafting stories for the screen, RE:SciComm is the place to build your skills, grow your network, and join the national conversation on science engagement and communication.

In an era shaped by climate change, public health crises, and rapid advances in AI, the need for effective science communication has never been clearer. Science impacts all of us — but how we talk about it, and who gets heard, matters more than ever. RE:SciComm will dive into the challenges and opportunities of today’s engagement landscape, from tackling misinformation to reaching communities historically excluded from science conversations.

Why RE:SciComm?

Formerly known as SciCommTO, the original 2020 conference drew wide praise for its collaborative spirit and practical focus. Now we’re rebooting with fresh energy, a broader scope, and a renewed commitment to advancing inclusive and effective science communication.

…

Call for Proposals Now Open ◐

We’re looking for bold, practical, and thought-provoking session proposals that explore the future of science communication. Workshops, panel discussions, interactive sessions, debates, or something unexpected — if you’ve got an idea that could inspire or empower fellow communicators, we want to hear from you.

*Speakers and Conference Program will be released in October 2025. Registration will open October 2025.

Apply Now

DEADLINE Monday, September 15, 2025 at 11:59 PM ET

Conference Themes

Re:framing

What does inclusive, community-first science communication look like? This theme is about democratizing science and shifting perspectives—getting research out of the lab, beyond academic journals and conferences, and into public spaces where it can be shared, shaped, and understood by all. It’s about centering equity, decolonization, and Indigenous ways of knowing in how we communicate science. Whether it’s through co-creation, storytelling, art, language, or lived experience, we’re looking for sessions that challenge the status quo and open up new possibilities. Let’s explore fresh frameworks, participatory approaches, and best practices that make STEMM [science, technology, engineering, mathematics, and medicine] more accessible, responsive, and representative of the world we live in.

Re:building

As we navigate a rapidly changing world, how do we rebuild public trust in STEMM, and reimagine science communication for today’s reality in Canada? This theme explores emerging challenges and opportunities—from misinformation and AI to science policy and education. We invite sessions that tackle the unique contexts of science engagement in Canada, offering insight into how science communicators can meet the moment with integrity, creativity, and care. Let’s reshape the narrative and design strategies that help STEMM thrive across diverse communities.

Re:igniting

Let’s get inspired. This theme is all about renewal—of relationships, collaborations, ideas, and purpose. What fuels your passion for science communication, and how can we grow the field together? We’re looking for sessions that celebrate creativity, connection, and momentum—whether through innovative formats, bold new projects, or reflections on what keeps us going. Together, we’ll build a more vibrant, interconnected, and future-focused science communication community across Canada.

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Conference Co-Hosts

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The Royal Canadian Institute for Science (RCIScience) is Canada’s oldest scientific society, celebrating its 175th year of science engagement. Through award-winning events and programs, RCIScience sparks curiosity and builds a stronger science culture across Canada.

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SciXchange at Toronto Metropolitan University is dedicated to making science accessible, engaging, and inclusive for all. From hands-on outreach to science communication training, SciXchange brings science to life for communities across the GTHA.

I very much appreciate the visual puns used to illustrate and ‘illuminate’ the conference themes.

This next and last event is more typical of the ArtSci Salon’s offerings, although the more accessible (IMO) description for the event and the artist was on this University of Toronto Jackman Humanities Institute event page,

Description

Join us for a series of events running through September 25 to October 16 that include an opening reception, additional tour and two panel discussions. Together, these events aim to raise awareness about the challenges posed by dyscalculia with educators, fellow mathematicians, and parents while normalizing its existence, leading to early detection and augmented support. It will also explore more broadly on the role and significance of mathematics and math education in today’s shifting socio-cultural and economic contexts.

“i don’t do math” is a photographic series exploring dyscalculia, a learning difference that affects a person’s ability to understand and work with number-based information. While dyslexia (difficulty with language) has become widely recognized thanks to years of advocacy and early detection, dyscalculia remains largely unknown. Research estimates that 3–7% of children, adolescents, and adults are affected (Haberstroh & Schulte-Körne 2019), though the actual numbers may be higher, as only a small fraction of those who struggle with math are ever screened (Sparks 2023).

Despite its prevalence, dyscalculia is often misunderstood—dismissed as a lack of education or mistaken for a personality trait. Left unrecognized, it can impact many aspects of daily life. It is also frequently confused with math anxiety, a sense of apprehension that interferes with math performance and while the two are not the same, dyscalculia can contribute to the development of math anxiety.

Photographer Ann Piché approaches this project both as an artist and an advocate, documenting the experiences of people affected by dyscalculia while engaging educators, learners, and parents in conversations about its effects and possible supports. Her exhibition presents abstract images paired with mathematical formulae, visually translating unfamiliar equations into recognizable photographic forms. The pairing of images and formulas conveys the frustration many with dyscalculia feel when navigating a number-centric world, while accompanying text-based panels guide viewers through the assumptions and challenges that shape these experiences.

The series consists of 15 photographs and 5 text-based panels, including works created during fieldwork visits in courses taught by University of Toronto, Department of Math, Professors Amenda Chow and Sarah Mayes-Tang of Calculus and Symmetry and Professor Pam Sargent of Business Calculus, Professor Ada Chan of Pre-Calculus at York University, and Dr. Pamela Brittain of K–12 Curriculum Education from the Fields Institute.

More information about the events and the participants.

To RSVP please visit https://uoft.me/nc-i-dont-do-math-exhibition. 

About the Artist

Ann Piché is a photo-based artist in Ottawa, Canada. Working in technology since the early 1990’s, Ann was the first female electronic technician hired by the Royal Canadian Mounted Police (RCMP). Experiencing the disconnect that can exist between science and the arts she constructs visual links to build those connections, creating accessible entry points for conversations about the less familiar.

A graduate of the School of the Photographic Arts: Ottawa (SPAO), Ann’s work has been presented in solo exhibitions in Canada and in group exhibitions internationally. Her collaborations include the Department of Mathematics at the University of Toronto and the Fields Institute for Research in Mathematical Sciences. A recipient of grants from the Jackman Humanities Institute at the University of Toronto, the City of Ottawa and the Ontario Arts Council, Ann has been published in North American magazines such as SHOTS and PhotoED.

Ann’s images are not software generated. Working primarily in digital photography, she stages her images using real and constructed landscapes with custom-built sets. Her work explores photographic abstraction and experimental camera techniques, a visual acknowledgement of the anxiety we can feel when facing the unfamiliar.

This initiative is supported by JHI Program for the Arts, the ArtSci Salon & the Fields Institute, and New College. Many thanks to the Departments of Mathematics at the University of Toronto and York University for their collaboration.

…

The ArtSci Salon provided this, from the online version of the September 5, 2025 announcement

ABOUT
“I don’t do math” is a photographic series referencing dyscalculia, a learning difference affecting a person’s ability to understand and manipulate number-based information.

This initiative seeks to raise awareness about the challenges posed by dyscalculia with educators, fellow mathematicians, and parents, and to normalize its existence, leading to early detection and augmented support. In addition, it seeks to reflect on and question broader issues and assumptions about the role and significance of Mathematics and Math education in today’s changing socio-cultural and economic contexts. 

The exhibition will contain pedagogical information and activities for visitors and students. The artist will also address the extensive research that led to the exhibition. The exhibition will feature two panel discussions following the opening and to conclude the exhibition.

Photographer Ann Piché is using her artistic practice both to document the struggles experienced by people affected by dyscalculia, and to educate math educators, students, and parents about its effects and potential support strategies.The series consists of 15 photographs and 5 text-based panels, including work produced during fieldwork visits in Prof. Amenda Chow and Prof. Sarah Mayes-Tang’s Calculus and Symmetry classes; Prof. Pam Sargent’s business calculus class (all three professors are from the dept. of Math.); Prof. Ada Chan’s pre-calculus class (dept. of Math., York University); and Dr.Pamela Brittain’s K-12 and curriculum education program (Fields Institute).

Opening: Thursday September 25, 5:00 pm [ET]
Tour: Saturday September 27, [2025] 2:00 pm [ET] (meet us at the Fields Institute, Atrium 2nd floor)
—-
Panel Discussion: Monday, September 29, 4:00 pm [ET]
Ann Piché (independent artist)
Daniel Ansari (Department of Psychology and Education, Western University)
Darja Barr (Department of Mathematics, University of Winnipeg)
room 230, the Fields Institute for Research in Mathematical Sciences
222 College Street, Toronto
—-
Stay tuned for the Final Panel Discussion on October 16, 10:00 am with Andrew Fiss (Professional & Technical Communication, Michigan Technological University Humanities Department) and other panelists

All panels will be recorded and posted on our Youtube channel

RSVP here

Copernicus’ cosmological model strongly influenced by ancient Muslim astronomer Ibn al-Shatir?

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Caption: Ibn-al-shatir’s lunar model from which Copernicus is reported to have borrowed in composing his cosmological model. Credit: This work is in the public domain in the United States. Credit: https://en.wikipedia.org/wiki/Ibn_al-Shatir#/media/File:Ibn-al-shatir2.gif

An April 14, 2025 University of Sharjah press release on EurekAlert puts forth a fascinating conjecture backed up by research, Note 1: Links have been removed; Note 2: “Did Copernicus Draw on a Medieval Arab Astronomer? New Study Highlights Striking Parallels” on medievalists.net sums up the researcher’s findings,,

New research has revealed that the cosmological model developed by Nicolaus Copernicus, the renowned European Renaissance polymath, bears striking resemblance to the one designed by an Arab astronomer nearly two centuries earlier.

Copernicus, a Polish astronomer who lived in the 16th century, is believed to be one of [sic] early European scientists to have put forward the theoretical model that the Sun was the center of the solar system, defying the church and the accepted wisdom that the Earth was the center of the universe.

Copernicus’s model is called sun-centered or heliocentric. In it, he challenges centuries-old science based on the teachings of Aristotle and Ptolemy, who thought the Earth was at rest at the center of the universe with other planets, including the sun, in its orbit.

The research conducted at the University of Sharjah is a comparative and analytical study which examines in parallel the writings of Copernicus in correlation with the works of the 14th century Muslim astronomer Ibn al-Shatir.

A recently completed Ph.D. thesis posted to the Sharjah University Library website, the research textually and critically analyzes the contributions of the two scientists to see where they concur or diverge in presenting their theories despite a historical gap of more than 200 years between them.

Dr. Salama Al-Mansouri, the research’s author, places Ibn al-Shatir’s cosmological model at the forefront of astronomical achievements in the Islamic scientific tradition. “Ibn al-Shatir was the first astronomer to have successfully challenged the Ptolemaic cosmological system of planets revolving around Earth and corrected the theory’s inaccuracies about two centuries before Copernicus,” says Dr. Al-Mansouri.

The fact that Copernicus borrows from works of scientists and astronomers who preceded him is not new. However, the study highlights the significant similarities between Copernicus and Ibn al-Shatir, an engineer, mathematician and astronomer who was the timekeeper for the Umayyad Mosque in Damascus, Syria.

Correlating the two cosmological models, the study suggests Copernicus was heavily influenced by Ibn al-Shatir’s astronomy and his ideas that the Earth and other solar planets orbit the Sun.

“Ibn al-Shatir’s astronomical manuscripts, particularly his work in Nihāyat al-Sul, demonstrate planetary models that predate and closely mirror those later proposed by Copernicus, indicating a shared mathematical lineage,” says Mesut Idriz, University of Sharjah’s professor of history and Islamic civilization and one of the study’s supervisors.

Nihayat al-sul fi tashih al-usul or “The Final Quest Concerning the Rectification of Principles” is Ibn al-Shatir’s most influential and important astronomical treatise in which, according to the study, the Muslim scientist corrects and refines many of the Ptolemaic models of the Sun, Moon, and planets.

Prof. Idriz acknowledges the complexity of studies based on “historical astronomical manuscripts” as they need to combine a “unique intersection of expertise—astronomy, manuscript studies, and historiography. Muslim manuscript-based research is an intricate process that requires fluency in Arabic and Persian, the medium of writing for Muslim scientists.”

Interpreting medieval astronomical manuscripts is not an easy job as it demands methodological precision, tracing textual transmission, comparing mathematical formulations, and evaluating observational data. To surmount such a sophisticated multidisciplinary approach, Dr. Salama sought advice and assistance from the community of academics at the Sharjah Academy for Astronomy, Space Sciences and Technology (SAASST), which has become a hub for renowned Arab and Muslim astronomers and scientists.

Dr. Salama conducts a critical textual analysis between Copernicus’s most famous work De revolutionibus orbium coelestium or On the Revolutions of the Celestial Spheres – a landmark in the history of science, which triggered the so-called Copernican Revolution – and the astronomical manuscripts of Ibn al-Shatir, particularly his Nihayat al-sul fi tashih al-usul.

The study reveals compelling correlations, underscoring the pivotal role of manuscript translation and transmission in the evolution of heliocentric theory and the assessment of the role the unraveling of Muslim manuscripts can play in rectifying historical inaccuracies about the history of science.

On the importance of the correlations between the work of Copernicus and that of Ibn al-Shatir, Mashhoor Al-Wardat, professor of astrophysics at SAASST, says, “The striking similarity between the planetary models developed by Ibn al-Shatir and Copernicus, particularly those concerning the orbits of Mercury and the Moon, provides clear evidence of Copernicus’s reliance on Ibn al-Shatir’s work …This raises profound questions about the transmission of knowledge from Islamic civilization to Europe and about the roots of modern astronomy.”

Dr. Salama provides an overview of Arabic manuscripts and their Latin translations in European archives in Kraków in Poland, and the Vatican, where Copernicus made his most outstanding contribution to astronomy. She finds that Ibn al-Shatir’s treatise Nihayat al-sul fi tashih al-usul was among the archives. She goes on, “Though in its original Arabic version, the manuscript could not have escaped the attention of a scholar like Copernicus.”

The study provides no definitive proof that Copernicus had read Iban al-Shatir’s works as there were no Latin translations of Ibn al-Shatir’s writings accessible to the researcher. However, the research posits that the Polish astronomer most probably had access to Ibn al-Shatir’s ideas through “intermediary channels” given the strong resemblance between their interpretations and mathematical calculations of planets orbiting the Sun.

The textual parallels between the two astronomers, according to the study, are most noticeable in “the identical calculations and results … imply(ing) that Copernicus may have adapted Ibn al-Shatir’s techniques” in developing “his philosophical shift to heliocentrism” a model which the study admits was Copernicus’s own invention.

However, the study sheds light on areas where Copernicus’s theory draws directly on Ibn al-Shatir. It mentions the lunar model in which the Muslim astronomer uses epicycles to correct Ptolemy’s exaggerated lunar distance variations.

“This is nearly identical to Copernicus’s lunar model in De Revolutionibus,” the study notes. “Both reduced the lunar distance fluctuation from Ptolemy’s factor of two to a more accurate range, relying on similar geometric constructions.

“For Mercury and the inner planets, Copernicus’s use of secondary epicycles and the Tusi-couple-like mechanism echoes Ibn al-Shatir’s approach. Ibn al-Shatir’s Mercury model, with its multiplication of epicycles to eliminate eccentrics, reappears in Copernicus’s work.”

Ibn al-Shatir is also celebrated for his Tusi-couple, a mathematical technique and an innovative mathematical device in which he employs additional epicycles to eliminate the equant—a problematic feature of Ptolemy’s system.

The Tusi-couple derives its name from Nasir al-Din al-Tusi, a 13th century Muslim polymath whose writings show the most accurate tables in antiquity of planetary motions, an updated planetary model, as well as penetrating critiques of Ptolemaic astronomy.

Ibn al-Shatir’s use of the Tusi-couple to simulate linear motion influenced Copernicus who produced similar adjustments, though Copernicus applied them within a heliocentric framework, the study notes.

Writes the study’s author, “Both astronomers (Copernicus and Ibn al-Shatir) replaced Ptolemy’s equant with additional circular motions, achieving uniform motion without an artificial reference point.

“Ibn al-Shatir’s solar model, with a new eccentricity and epicycles yielding a maximum solar equation of 2;2,6°, parallels Copernicus’s solar calculations. This suggests Copernicus may have adopted Ibn al-Shatir’s numerical tables or methods, adapting them to his Sun-centered system.”

Asked whether she thinks Copernicus loaned [sic] at least parts of his theory from Ibn al-Shatir, Dr. Salama adds, “Our analysis reveals that Ibn al-Shatir’s treatise, though geocentric in intent, produced results so aligned with heliocentrism that Copernicus’s debt to him is undeniable—two centuries of separation could not erase this intellectual kinship.”

The research findings apparently seek to rectify what the author perceives as a historical oversight by Western scholars, who are frequently alleged in current Arab and Muslim science literature to have mostly Eurocentric tendencies, marginalizing contributions of Muslim astronomers like Ibn al-Shatir in favor of European figures like Copernicus.

The study is of significant implications to the history of science in the Middle Ages and the European Renaissance. By demonstrating parallels between Ibn al-Shatir’s and Copernicus’s work, the study challenges this Eurocentric narrative that the heliocentric revolution was a solely European achievement.

In the meantime, it underscores the Islamic Golden Age’s role in laying mathematical and observational foundations, prompting historians to reconsider the global flow of scientific knowledge.

The research goes as far as highlighting the need to update science curricula to reflect a more inclusive history, acknowledging contributions from non-Western scholars.

Of the significance of the study, Prof. Hamid al-Naimiy, a renowned astronomer and the research’s main supervisor, said, “This study is a clarion call to rewrite the history of astronomy, ensuring that the brilliance of Muslim scholars like Ibn al-Shatir stands alongside Copernicus in our collective narrative of scientific progress.”

Asked about his opinion of Ibn al-Shatir’s cosmological model, Prof al-Naimiy, who is also Sharjah University’s Chancellor and SAASST’s director, said the Muslim astronomer was a pioneer in Islamic scientific tradition and his treatise “shows that he dismantled the Ptolemaic model and corrected its flaws two centuries before Copernicus. This work emphasizes the significant contributions of our heritage to global astronomy.”

Says Dr. Salama, “Ibn al-Shatir’s empirical refinements within a geocentric framework, paralleled by Copernicus’s adaptation, illustrate how incremental improvements can precede paradigm shifts,” adding that her research “offers a model for modern science, where foundational work in one context can catalyze breakthroughs in another.”

Dr. Salama makes a compelling case for reassessing Copernicus’ work. She also raised a few more questions. Perhaps it’s due to my ignorance but I wonder about using the descriptors ‘Arab’ and ‘Muslim’ synonymously’. At a guess, during Ibn al-Shatir’s lifetime the two may well have been synonymous although you don’t see religion and national group (for want of a better term) used synonymously with European scientists of any period. It suggests additional interesting questions (to me anyway) about religion and about other identifications and the relationship between them with science.

The study “The Latest on the heliocentric theory as explained by Ibn al-Shater and Copernicus: a comparative analytical study” is available here but you do need Arabic language skills to access it.

Trees, mathematics, and art (from Piet Mondrian to Leonardo da Vinci)

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Apparently, trees are ‘roughly’ fractal. As for fractals themselves, there’s this from the Fractal Foundation’s What are Fractals? webpage,

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[downloaded from https://fractalfoundation.org/resources/what-are-fractals/]

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.

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Caption: Piet Mondrian painted the same tree in “The gray tree” (left) and “Blooming apple tree” (right). Viewers can readily discern the tree in “The gray tree” with a branch diameter scaling exponent of 2.8. In “Blooming apple tree,” all the brush strokes have roughly the same thickness and viewers report seeing fish, water and other non-tree things. Credit: Kunstmuseum Den Haag

I have two news releases for a new study about mathematics (fractals) and art. First, there’s the February 11, 2025 University of Michigan news release (also on EurekAlert), Note: A link has been removed,

While artistic beauty may be a matter of taste, our ability to identify trees in works of art may be connected to objective—and relatively simple—mathematics, according to a new study.

Led by researchers from the University of Michigan and the University of New Mexico, the study investigated how the relative thickness of a tree’s branching boughs affected its tree-like appearance.

This idea has been studied for centuries by artists, including Leonardo DaVinci [Leonardo da Vinci], but the researchers brought a newer branch of math into the equation to reveal deeper insights. 

“There are some characteristics of the art that feel like they’re aesthetic or subjective, but we can use math to describe it,” said Jingyi Gao, lead author of the study. “I think that’s pretty cool.”

Gao performed the research as an undergraduate in the U-M Department of Mathematics, working with Mitchell Newberry, now a research assistant professor at UNM and an affiliate of the U-M Center for the Study of Complex Systems. Gao is now a doctoral student at the University of Wisconsin.

In particular, the researchers revealed one quantity related to the complexity and proportions of a tree’s branches that artists have preserved and played with to affect if and how viewers perceive a tree.

“We’ve come up with something universal here that kind of applies to all trees in art and in nature,” said Newberry, senior author of the study. “It’s at the core of a lot of different depictions of trees, even if they’re in different styles and different cultures or centuries.”

The work is published in the journal PNAS [Proceedings of the National Academy of Sciences] Nexus.

As a matter of fractals

The math the duo used to approach their question of proportions is rooted in fractals. Geometrically speaking, fractals are structures that repeat the same motifs across different scales.

Fractals are name-dropped in the Oscar-winning smash hit “Let it Go” from Disney’s “Frozen,” making it hard to argue there’s a more popular physical example than the self-repeating crystal geometries of snowflakes. But biology is also full of important fractals, including the branching structures of lungs, blood vessels and, of course, trees.

“Fractals are just figures that repeat themselves,” Gao said. “If you look at a tree, its branches are branching. Then the child branches repeat the figure of the parent branch.”

In the latter half of the 20th century, mathematicians introduced a number that is referred to as a fractal dimension to quantify the complexity of a fractal. In their study, Gao and Newberry analyzed an analogous number for tree branches, which they called the branch diameter scaling exponent. Branch diameter scaling describes the variation in branch diameter in terms of how many smaller branches there are per larger branch.

“We measure branch diameter scaling in trees and it plays the same role as fractal dimension,” Newberry said. “It shows how many more tiny branches there are as you zoom in.”

While bridging art and mathematics, Gao and Newberry worked to keep their study as accessible as possible to folks from both realms and beyond. Its mathematical complexity maxes out with the famous—or infamous, depending on how you felt about middle school geometry—Pythagorean theorem: a2 + b2 = c2.

Roughly speaking, a and b can be thought of as the diameter of smaller branches stemming from a larger branch with diameter c. The exponent 2 corresponds to the branch diameter scaling exponent, but for real trees its value can be between about 1.5 and 3.

The researchers found that, in works of art that preserved that factor, viewers were able to easily recognize trees—even if they had been stripped of other distinguishing features.

Artistic experimentation

For their study, Gao and Newberry analyzed artwork from around the world, including 16th century stone window carvings from the Sidi Saiyyed Mosque in India, an 18th century painting called “Cherry Blossoms” by Japanese artist Matsumuara Goshun and two early 20th century works by Dutch painter Piet Mondrian.

It was the mosque carvings in India that initially inspired the study. Despite their highly stylized curvy, almost serpentine branches, these trees have a beautiful, natural sense of proportion to them, Newberry said. That got him wondering if there might be a more universal factor in how we recognize trees. The researchers took a clue from DaVinci’s [sic] analysis of trees to understand that branch thickness was important. 

Looking at the branch diameter scaling factor, Gao and Newberry found that some of the carvings had values closer to real trees than the tree in “Cherry Blossoms,” which appears more natural.

“That was actually quite surprising for me because Goshun’s painting is more realistic,” Gao said. 

Newberry shared that sentiment and hypothesized that having a more realistic branch diameter scaling factor enables artists to take trees in more creative directions and have them still appear as trees.

“As you abstract away details and still want viewers to recognize this as a beautiful tree, then you may have to be closer to reality in some other aspects,” Newberry said.

Mondrian’s work provided a serendipitous experiment to test this thinking. He painted a series of pieces depicting the same tree, but in different, increasingly abstract ways. For his 1911 work “De grijze boom” (“The gray tree”), Mondrian had reached a point in the series where he was representing the tree with just a series of black lines against a gray background.

“If you show this painting to anyone, it’s obviously a tree,” Newberry said. “But there’s no color, no leaves and not even branching, really.”

The researchers found that Mondrian’s branch scaling exponent fell in the real tree range at 2.8. For Mondrian’s 1912 “Bloeiende appelboom” (“Blooming apple tree”), however, that scaling is gone, as is the consensus that the object is a tree.

“People see dancers, fish scales, water, boats, all kinds of things,” Newberry said. “The only difference between these two paintings—they’re both black strokes on a basically gray background—is whether there is branch diameter scaling.”

Gao designed the study and measured the first trees as part of her U-M Math Research Experience for Undergraduates project supported by the James Van Loo Applied Mathematics and Physics Undergraduate Support Fund. Newberry undertook the project as a junior fellow of the Michigan Society of Fellows. Both researchers acknowledged how important interdisciplinary spaces at Michigan were to the study.

“We could not have done this research without interaction between the Center for the Study of Complex Systems and the math department. This center is a very special thing about U of M, where math flourishes as a common language to talk across disciplinary divides,” Newberry said. “And I have been really inspired by conversations that put mathematicians and art historians at the same table as part of the Society of Fellows.”

Caption: Leonardo da Vinci’s sketch of a tree illustrates the principle that combined thickness is preserved at different stages of ramification. Credit: Institut de France Manuscript M, p. 78v.

Second, there’s the February 11, 2025 PNAS [Proceedings of the National Academy of Sciences] Nexus news release on EurekAlert, which takes a purely mathematical approach to the work,

The math that describes the branching pattern of trees in nature also holds for trees depicted in art—and may even underlie our ability to recognize artworks as depictions of trees.

Trees are loosely fractal, branching forms that repeat the same patterns at smaller and smaller scales from trunk to branch tip. Jingyi Gao and Mitchell Newberry examine scaling of branch thickness in depictions of trees and derive mathematical rules for proportions among branch diameters and for the approximate number of branches of different diameters. The authors begin with Leonardo da Vinci’s observation that trees limbs preserve their thickness as they branch. The parameter α, known as the radius scaling exponent in self-similar branching, determines the relationships between the diameters of the various branches. If the thickness of a branch is always the same as the summed thickness of the two smaller branches, as da Vinci asserts, then the parameter α would be 2. The authors surveyed trees in art, selected to cover a broad geographical range and also for their subjective beauty, and found values from 1.5 to 2.8, which correspond to the range of natural trees. Even abstract works of art that don’t visually show branch junctions or treelike colors, such as Piet Mondrian’s cubist Gray Tree, can be visually identified as trees if a realistic value for α is used. By contrast, Mondrian’s later painting, Blooming Apple Tree, which sets aside scaling in branch diameter, is not recognizable as a tree. According to the authors, art and science provide complementary lenses on the natural and human worlds.

Here’s a link to and a citation for the paper,

Scaling in branch thickness and the fractal aesthetic of trees by Jingyi Gao, Mitchell G Newberry. PNAS Nexus, Volume 4, Issue 2, February 2025, pgaf003, DOI: https://doi.org/10.1093/pnasnexus/pgaf003 Published: 11 February 2025

This paper is open access.

Arabic manuscript containing lost works of Apollonius discussed in new book about Middle Eastern science (etc.) scholarship

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This February 4, 2025 news item is essentially a book announcement but what makes it exceptionally interesting is how one of history’s great mathematicians had some of his work preserved in an Arabic manuscript, Note: Links have been removed,

Scientists say that the two lost, but extremely important books by Apollonius, the Greek mathematician known to the ancient world as “The Great Geometer,” have survived in an Arabic manuscript kept under lock and key as part of the prized possessions of the Leiden University Libraries in Holland.

The revelation is made in a new volume of 50 chapters titled “Prophets, Poets and Scholars” and published recently by Leiden University Press.

Apollonius (262 BC–190 BC) is believed to be one of Greece’s greatest mathematicians and is renowned for his hugely influential book, “The Conics of Apollonius” in which he introduces the terms hyperbola, ellipse, and parabola.

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A February 4, 2025 University of Sharjah press release on EurekAlert delves more deeply into the topic,

According to the volume, “The Conics of Apollonius (c. 2.00 BCE) was one of the most profound works of ancient Greek mathematics. The work deals with the theory of ellipses, parabolas, and hyperbolas – the curves which you can see if you shine a flashlight on a wall.” Apollonius’s work comprises eight books, but only the first four were available to European scholars during the Renaissance.

The lost books – 5 and 7 – were brought to the Leiden University by the famous Dutch orientalist and mathematician Jacob Golius who had bought them for the university as part of a collection of nearly 200 manuscripts during his various voyages to the Middle East.

The 50 chapters in the book touch on the history of the Netherlands’ relationships with the orient, particularly the Middle East and North Africa, emphasizing that the first encounters with Arabic manuscripts occurred in the early 17th century.

The 17th century saw the first Dutchman, Thomas Erpenius, gaining pre-eminence in oriental studies. “He concentrated on Arabic text editions, primers for students and most importantly an Arabic grammar that would remain in use as a standard work for more than two centuries,” the volume’s editors write in their introductory chapter.

But the first Dutch “to have ever set foot in the Middle east or North Africa was … Jacobus Golius (1596-1667).  On his travels he bought more than 200 Middle Eastern manuscripts for Leiden University,” say the editors. However, “Golius’s fame rests mainly on his lexicon Arabian-Latinum, a large folio volume printed by the then firm of Elzevier in 1653.  The work is based on the Arabic lexicographical manuscripts that he had acquired on his travels.”

It is the manuscripts which Golius purchased for the Leiden University Libraries that attract the attention of numerous scholars who have contributed to the volume. For instance, a chapter focuses on an 11th century Arabic manuscript, which is a translation of the lost mathematical works attributed to Apollonius. In the meantime, the essay dwells on four other Arabic manuscripts bought by Golius to present some aspects of the scientific traditions prevalent in the heyday of Arab and Muslims civilization.

The Arabic translation of Apollonius is fascinating, Dutch mathematician and historian of science, Jan Pieter Hogendijk, says in an email interview, adding that besides its exact science, it is adorned with colored images and written in skillful Arabic calligraphy. “The calligraphy in some of these manuscripts is wonderful and also the geometrical figures were written with extreme care.

“They (manuscripts) are a witness of the mental abilities, discipline, power of concentration, will power and so on which the scientists and also the scribes possessed, and which modern people, spoiled by their gadgets, mobile phones, and so on, do not possess anymore.”

The volume, according to the editors, “serves as an introduction to more than fifty contributions of scholars and librarians who are intimately familiar with diverse aspects of the collections (of Leiden University Libraries), both ancient and modern.”

The volume is a nice read as it is written for the public. It is luxuriously illustrated with ancient maps, images, and extracts from Arabic, Turkish and Persian manuscripts. Besides accounts and analyses of scientific traditions prevalent among Arabs and Muslims in the Middle Ages, the volume narrates some fantasy tales from Arabic travel literature, which still captivate the mind.

In their studies and analyses, the scientists find that their authors would often add an entertaining touch mingled with fantasy to their narrative. “They (the texts) were often mixed with legendary accounts, especially in reports about the outer edges of the known world, where the laws of nature were no longer fixed and strange things might occur.

“There women might grow on trees, people might have arms where we have our ears, and might come across islands exclusively inhabited either by women or by men. All this has left its traces in the Middle Eastern written heritage, and also in the accompanying pictorial tradition.”

In the section dedicated to Arabic manuscripts and titled “The Great Arabic Heritage,” there is emphasis on cosmography besides astronomy, mathematics, zoology, botany, planetology, among other sciences.

There is emphasis on a renowned Muslim cosmographer Ibn Muhammad al-Qazwini’s “Ajaib al-Makhluqat wa Khraib al-Mawjudat (Wonders of Creations and Rarities of Extant Beings), an encyclopedic work which, according to the volume tackles “the humble creatures such as fleas, worms and lice to exotic animals surrounded by mystery and legends.”

Some creatures can be merely fantasy beings like the turtle which “sailors moored their ship on it, taking the motionless animal that had become overgrown with vegetation for an island” – reminiscent of the creatures one comes across in the famous Travels of Sindbad the Sailor.

However, as one of the fascinating chapters in the volume underscores, “sometimes one has to rid oneself of preconceived ideas to understand the descriptions. Such a case is a sea creature described by Qazwini, … its face is like that of man, it has a white beard, its body looks like that of a frog, its hair is like a cow’s and its size like that of a calf. It takes us a moment to see that this is a perfectly adequate description of some kind of seal.”

Mostafa Zahri, University of Sharjah Professor of numerical analysis and mathematical modeling, says the prized possessions of “Arabic manuscripts in Western libraries like Leiden University Libraries serve as invaluable records of Islamic civilization’s intellectual achievements, especially in mathematics and geometry.

“Western institutions, besides Leiden University, namely the British Library, and the Bibliothèque Nationale de France, house thousands of Arabic, Persian, and Ottoman manuscripts containing rare geometric treatises. These collections bridge historical and modern scholarships.”

However, and despite the wealth of knowledge they hold, many manuscripts remain understudied and only greater collaboration, digitization, and accessibility between Western and Arab scholars could unlock their full historical and mathematical value, says Prof. Zahri.

In an email interview, Wilfred de Graaf, Education Coordinator at Utrecht University concurs, emphasizing that only a small portion of collections of Arabic and Islamic manuscript texts have been studied. He attributes the scarcity of studies in this sphere to the lack of scholars in the West who are fluent in oriental language like Arabic, Persian and Turkish, in which most Islamic manuscripts are written.

Nonetheless, he adds that more and more ancient texts are unraveled assisting scholars to obtain “a general view of the development of science in the Islamic tradition. “In the West, there is an interest in the Islamic scientific tradition, not only because of it being crucial for the development of science in Europe between the 11th and 14th century, but also because of the intrinsic nature of its contributions.”

Mesut Idriz, Sharjah University’s Professor of Islamic civilization, says bringing Arabic and Islamic manuscripts to life is among the hardest labors social science researchers face. “Islamic manuscript studies require a nuanced understanding of both the textual and scientific traditions they encapsulate.

“The study of Islamic manuscripts demands specialized knowledge, encompassing paleography, historical context, linguistic expertise, and scientific specialization—areas that are often underdeveloped among contemporary researchers and academics.”

Drawing on Leiden University Libraries’ Arabic manuscripts, a team of Western scientists held a workshop at the University of Sharjah in the United Arab Emirates in January 2025 to teach participants the method by which Arab and Muslim scientists wrote numbers in a numeral system called abjad, in reference to the Arabic alphabet, a right-to-left script.

The abjad is a numeral system in which the first of the 28-letter Arabic alphabet ‘alif’ represents 1, and the second letter ‘baa’ is 2 up to 9. The other letters stand for nine intervals of 10s and then those of 100s ending with 1000.

“The scientists in the Islamic tradition used abjad in combination with the sexagesimal system which is still used today for time (hours, minutes and seconds) and angles (degrees, arc minutes and arc seconds),” Wilfred, who organized the workshop, said.

This is the second workshop in nearly two months Western scientists hold [sic] at the University of Sharjah to present Arabic manuscripts to the Arab academic community and demonstrate the uses Arab and Muslim scientific instruments were put to in the Middle Ages. In them, the participants were made to read in detail the abjad numbers on an early astrolabe, an Arabic astronomical instrument.

Besides the Arabic manuscript in which the two lost works of Apollonius were found, there are extracts and studies in the volume tackling a variety of scientific traditions prevalent among the Arabs in the Middle Ages.

One chapter analyzes a figure from an 11th century manuscript attributed to al-Mu’taman ibn Hud, King of Saragossa between 1081 and 1085. The chapter shows how Muslim scientists managed to solve an ancient Greek geometry puzzle nearly half a millennium before a solution to the same problem was found in Europe. Muslim scientists’ solution of the puzzle, according to the chapter, “is part of a huge mathematical encyclopedia called the Book of Perfections of which a small fragment has been preserved.”

Quoting from yet another 14th century Arabic manuscript, the chapter shows how Muslim scientists could determine the geographical coordinates of no less than 160 cities with a high degree of accuracy and minimum error margin.

“The names of the cities appear in black and the numbers in red are the longitudes in degrees and minutes, and the latitude in degrees and minutes,” says Prof. Hogendijk. “The numbers are written in the alphabetical abjad system used by most astronomers, in which a numerical value is attributed to each letter. The first column begins with localities in the two provinces of Western and Eastern Azerbaijan in modern Iran.”

The book, “Prophets, Poets and Scholars; The Collections of the Middle Eastern Library of Leiden University” Editor: Arnoud Vrolijk, Kasper van Ommen, Karin Scheper & Tijmen Baarda, can be found on its Leiden University Press publication order page.

Say ain’t so! van Gogh’s ‘The Starry Night’ is not a masterpiece when it comes to flow physics according to researchers

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Researchers at Virginia Commonwealth University (VCU; US) have challenged the findings in recent research that was highlighted here in a December 16, 2024 posting “van Gogh’s sky is alive with real-world physics.”

An April 1, 2025 news item (not an April Fool’s joke) on phys.org announces a conclusion that contradicts the original findings,

The Dutch master Vincent van Gogh may have painted one of Western history’s most enduring works, but “The Starry Night” is not a masterpiece of flow physics—despite recent attention to its captivating swirls, according to researchers from Virginia Commonwealth University and the University of Washington [state not district].

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Credit: Pixabay/CC0 Public Domain [downloaded from https://phys.org/news/2025-04-vincent-van-gogh-starry-night.html].

An April 1, 2025 Virginia Commonwealth University (VCU) news release (also on EurekAlert) by Leila Ugincius, which originated the news item, goes on to further refute the claim about Starry Night and flow physics, Note: Links have been removed,

The post-Impressionist artist painted the work (often referred to simply as “Starry Night”) in June 1889, and its depiction of a pre-sunrise sky and village was inspired in part by the view from van Gogh’s asylum room in southern France. The painting is part of the permanent collection of the Museum of Modern Art in New York City.

Last year, a paper published in the September issue of Physics of Fluids – “Hidden Turbulence in van Gogh’s ‘The Starry Night’” – received considerable notice by positing that the eddies, or swirls, painted by van Gogh adhere to Kolmogorov’s theory of turbulent flow, which explains how air and water swirls move in a somewhat chaotic pattern. “[van Gogh] was able to reproduce not only the size of whirls/eddies, but also their relative distance and intensity in his painting,” the paper read.

However, those conclusions are unfounded, according to Mohamed Gad-el-Hak, Ph.D., the Inez Caudill Eminent Professor in VCU’s Department of Mechanical and Nuclear Engineering, and James J. Riley, Ph.D., the inaugural Paccar Professor of Mechanical Engineering at the University of Washington. Their report –  “Is There Hidden Turbulence in Vincent van Gogh’s ‘The Starry Night’?” – appears in the latest issue of Journal of Turbulence.

Here’s a link to and a citation for the paper,

Is there hidden turbulence in Vincent van Gogh’s The Starry Night? by James J. Riley
& Mohamed Gad-el-Hak. Journal of Turbulence Pages 1–2. DOI: https://doi.org/10.1080/14685248.2025.2477244 Published online: 18 Mar 2025

This paper is behind a paywall.

Drat! ARPICO (Society of Italian Researchers and Professionals in Western Canada) Celebrates Women in STEM: Voices of Innovation on Wednesday, February 26, 2025

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(Missed the boat on this one.) I received (via email) a January 18, 2025 notice about an upcoming Society of Italian Researchers and Professionals in Western Canada (ARPICO) event, Note 1: Tickets are free, Note 2: the Eventbrite registration page for the event includes a map showing where the venue is located,

ARPICO is excited to invite you to our first event of 2025, “ARPICO Celebrates Women in STEM [science, technology, engineering, and mathematics]: Voices of Innovation” which will be held on Wednesday, February 26th, 2025 at 7:00 PM at the Museum of Vancouver, History Room, 1100 Chestnut Street, Vancouver, BC.

February 11th marks the celebration of Women and Girls in Science, Technology, Engineering, and Mathematics (STEM), established by the United Nations in 2015 to honor the achievements of women and girls in these fields.

Women’s access to STEM education and careers became a reality in the late 19th and early 20th centuries, with milestones like, for example, Marie Curie breaking barriers in science and Ada Lovelace becoming the first computer programmer. While progress has been made, women are still underrepresented in STEM. Currently, In Canada, women represent approximately 23% of STEM professionals (about 28% in the United States).

At ARPICO, we are proud to celebrate the progress of women in STEM, acknowledging both their contributions and the challenges they continue to face by hosting a special event you won’t want to miss!

This event aims to inspire and empower the next generation of women, as well as people from all walks of life, to take their place at the forefront of innovation, ensuring STEM is an inclusive space for all. Through its initiatives, ARPICO aims to foster an environment where everyone can thrive, share their experiences, and inspire others.

ARPICO is therefore excited to host an event featuring five distinguished women in STEM. These panelists will engage in a dynamic discussion, sharing their journeys, successes, challenges, and sources of inspiration. The event will include a lively Q&A session, encouraging audience participation, reflection on the importance of supporting women in STEM and exploring how diverse talent strengthens STEM fields and society as a whole.

Whether you’re already involved in STEM, want to guide family and friends into these fields, or simply wish to be inspired by the panelists’ stories, this event will be informative, uplifting, and empowering. Reserve your spot!

To read more and to register for FREE admission, please visit EventBrite at https://womenstem.eventbrite.ca

Evening Program

  • 6:30 PM – Doors open for registration
  • 7:00 PM – Event begins. Welcome & Introductions by Nicola Fameli
  • 7:05 PM – Message from Italian Consul General Paolo Miraglia Del Giudice
  • 7:10 PM – ARPICO President’s Address & Moderated Panel Discussion
    • Presentation by Valentina Marchetti, President of ARPICO
    • Panel Discussion: “ARPICO Celebrates Women in STEM: Voices of Innovation”
  • 8:00 PM – Q & A Period
  • 8:15 PM – Refreshments, networking and socializing

We look forward to seeing everyone there.

RSVP: Tickets for this event are required, but FREE; all wishing to attend are requested to obtain “free-admission” tickets on EventBrite

Further details are also available at arpico.ca, arpico facebook, and EventBrite.

If participants wish to donate to ARPICO, this can be done within EventBrite or in person at the event; this would be greatly appreciated in order to help us continue our public lecture program and to build upon our scholarship fund.

Main Event Details

ARPICO Celebrates Women in STEM: Voices of Innovation

February 11th marks the celebration of Women and Girls in Science, Technology, Engineering, and Mathematics (STEM), established by the United Nations in 2015 to honor the achievements of women and girls in these fields.

Women’s access to STEM education and careers became a reality in the late 19th and early 20th centuries, with milestones like, for example, Marie Curie breaking barriers in science and Ada Lovelace becoming the first computer programmer.

At ARPICO, we are proud to celebrate the progress of women in STEM, acknowledging both their contributions and the challenges they continue to face, by hosting this special event featuring five distinguished women in STEM. These panelists will engage in a dynamic discussion, sharing their journeys, successes, challenges, and sources of inspiration.

Their messages hope to inspire and empower the next generation of women to take their place at the forefront of innovation, ensuring STEM is an inclusive space for all.

The event will include a lively Q&A session, encouraging audience participation, reflection on the importance of supporting women in STEM and exploring how diverse talent strengthens STEM fields and society as a whole.

Whether you’re already involved in STEM, want to guide family and friends into these fields, or simply wish to be inspired by the panelists’ stories, this event will be informative, uplifting, and empowering.

ATTRACTING & CELEBRATING THE BEST MINDS

It is essential for nations, universities, and employers to recruit and nurture top talent in STEM fields to ensure continued innovation and progress. However, women remain underrepresented in STEM careers, making up only 23% of STEM professionals in Canada and 28% in the United States.

Promoting gender equity in STEM is about more than fairness—it’s about unlocking a broader talent pool and fostering richer, more innovative solutions. Research shows that when women and men contribute equally, STEM outcomes are more effective and transformative. Empowering women in STEM benefits not only individuals but also entire industries and societies.

THE IMPORTANCE OF STEM FOR THE WORLD, NATIONS & INDIVIDUALS

Science, technology, engineering, and mathematics (STEM) drive the innovations that shape every aspect of modern life. Careers in STEM offer opportunities to collaborate internationally, solve global challenges like climate change and health crises, and make groundbreaking contributions to society.

Nations that invest in STEM not only foster critical research and innovation but also position themselves as global leaders, driving sustained economic growth and securing a competitive edge.

For individuals, STEM careers are highly sought after, often well-compensated, and provide unparalleled flexibility. Beyond technical expertise, STEM education cultivates critical thinking, creativity, and problem-solving skills—qualities essential for navigating and excelling in today’s interdisciplinary and ever-evolving job market. With these skills, STEM professionals can pivot and thrive in diverse career paths, creating limitless opportunities for personal and professional growth.

About The Panelists and Moderators

Dr. Lori Brotto is a leading expert in women’s sexual health, serving as a Professor in UBC’s [University of British Columbia] Department of Obstetrics and Gynaecology and holding a Canada Research Chair. Her research focuses on developing accessible treatments for common sexual concerns in women, with a strong emphasis on equity and digital health technologies. As Executive Director of the Women’s Health Research Institute, she leads nearly 600 members in advancing women’s health research across BCDr. Brotto is a frequent media presence, appearing in documentaries like Netflix’s The Principles of Pleasure and CBC Gem’s The Big Sex Talk. She authored Better Sex Through Mindfulness (2018) and The Better Sex Through Mindfulness Workbook (2022), and her work earned her a UBC Public Education Through Media award in 2023. As a Registered Psychologist in BC, Dr. Brotto works directly with individuals to improve sexual well-being and encourages young women to pursue STEM careers. She engages with the public through social media, empowering women and advancing research in sexual health.

Dr. Cristina Conati is a Professor of Computer Science at the University of British Columbia, Vancouver, Canada. She received an M.Sc. in Computer Science at the University of Milan, as well as a Ph.D. in Intelligent Systems at the University of Pittsburgh. She has been a Faculty Member at UBC since November 1999. Cristina’s research is at the intersection of Artificial Intelligence, Human-Computer Interaction and Cognitive Science, focusing on Human-Centred AI with contributions in the areas of Intelligent Tutoring Systems, User Modeling, Affective Computing, Information Visualization, and Explainable AI. Cristina’s research has received 10 Best Paper Awards from a variety of venues and in 2022 she received a UBC Killam Research Price. She is a Fellow of AAAI (Association for the Advancement of Artificial Intelligence) and of AAIA (Asia-Pacific Artificial Intelligence Association). She is the co-Editor in Chief of the Journal of AI in Education. She served as President of AAAC (Association for the Advancement of Affective Computing), as well as Program or Conference Chair for several international conferences.

Dr. Jaraquemada, Lupe, is a Radiochemist at Alpha9 Oncology in Vancouver, where she develops new radiopharmaceuticals to enhance cancer diagnosis and treatment. She studied in Canada in 2015 during her PhD and later returned to UBC Chemistry for postdoctoral and research associate work with Dr. Chris Orvig. Before joining Alpha9, Lupe worked as a Staff Scientist at BC Cancer’s Molecular Oncology department under Dr. François Bénard. She holds a PhD in Chemical Sciences and Technologies from the University of Cagliari, Italy, and a BSc in Chemistry from the University of Extremadura, Spain. In her free time, Lupe enjoys skiing with family and friends, watching Whitecaps games, and cheering on her two boys at soccer matches at the Italian Cultural Centre.

Camilla Moioli is a Ph.D. candidate at UBC’s ERDE (Energy Resources, Development, and Environment) and Forest Action Labs, focusing on the intersection of land use policy, energy transitions, and climate justice. With a background in Economics and Social Sciences, she uses both micro and macroeconomic methods to explore sustainable development. Camilla has worked with grassroots organizations in Ecuador on local restoration policies and collaborated with research centers in Europe, including EIEE in Milan, IIASA in Vienna, and SDSN in Paris, to incorporate global perspectives. She also teaches Forest and Conservation Economics at UBC and contributes to courses in carbon and energy economics. Camilla holds a BSc in Business from the University of Milano-Bicocca and an MSc in Economics from the Catholic University of Milan.

Dr. Adele Ruosi‘s journey in physics began in Italy, where she earned her Ph.D. and delved into experimental superconductivity while teaching at the University of Naples. Her curiosity then led her to the US, where she conducted research at the University of Illinois at Urbana-Champaign and the University of Wisconsin-Madison. She also taught physics at Temple University and served as the Scientific Administrator of an Energy Frontier Research Center. Since 2019, Adele has been a Science Education Specialist in Physics and Astronomy at the University of British Columbia. When she’s not advancing science education, Adele enjoys exploring the great outdoors of British Columbia

Desiree Fiaccabrino is a BSc Chemistry graduate with First Class Honours from King’s College London, is pursuing a PhD in Chemistry at UBC under Dr. Chris Orvig and Dr. Paul Schaffer at TRIUMF. Her research focuses on developing novel molecules to bind radioactive metals for cancer therapeutics and diagnostics. As President of UBC’s Chemistry Graduate Student Society, Desiree organized professional development initiatives, including career panels with industry and academic leaders. She has mentored undergraduate and MSc students in research and scientific communication. Desiree is passionate about creating tools to bridge scientific discovery with practical applications in nuclear medicine to improve patient care.

Dr. Valentina Marchetti is an expert in endothelial cell dysfunction and progenitor cells in cardiovascular diseases. After completing her PhD at the University of Rome, Italy, she worked as a postdoctoral fellow at The Scripps Research Institute, focusing on stem cells for treating diabetic retinopathies and eye diseases. In 2013, she joined STEMCELL Technologies in Vancouver, where she led the endothelial and eye group and developed products for stem cell research. Currently an Adjunct Professor at Simon Fraser University, Valentina collaborates with the Department of Molecular Biology and Biochemistry. As President of ARPICO, she advances collaboration and public awareness of key research, while promoting Italian-Canadian scientific and cultural exchanges.

FAQ

  • Where can I contact the organizer with any questions?
  • info@arpico.ca
  • Can I update my registration information?
  • Yes. If you have any questions, contact us at info@arpico.ca
  • I am having trouble using EventBrite and cannot reserve my ticket(s). Can someone at ARPICO help me with my ticket reservation?
  • Of course, simply send your ticket request to us at info@arpico.ca so we can help you.

As always, the organizers have been thoughtful about including detailed information.

Merry 2024 Christmas (1 of 2) High school students discovered a new way to prove Pythagoras’ theorem

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I was very thankful to stumble across this story: Calcea Johnson and Ne’Kiya Jackson who are now in university, have found more ways to solve the theorem but this October 28, 2024 news item in ScienceDaily starts with their first breakthrough,.

In 2022, U.S. high school students Calcea Johnson and Ne’Kiya Jackson astonished teachers when they discovered a new way to prove Pythagoras’ theorem [Pythatgoran Theorem] using trigonometry after entering a competition at their local high school. As a result, both students were awarded keys to the city of New Orleans, and even received personal praise from Michelle Obama.

Today [October 28, 2024?] they become published authors of a new peer-reviewed paper detailing their discoveries, published in the journal American Mathematical Monthly.

…

Caption: Ne’Kiya Jackson (left) and Calcea Johnson (right). Photo credit: Calcea Johnson

An October ?, 2024 Taylor & Francis Group press release (also on EurekAlert and published October 28, 2024), which originated the news item, discusses how Jackson and Johnson independently of each other solved the theorem and then worked together to develop more solutions to the theorem,

…

Pythagoras’ famous 2,000-year-old theorem, summarized neatly as a2+ b2= c2, means that you can work out the length of any side of a right-angled triangle as long as you know the length of the other two sides. Essentially, the square of the longest side (the hypotenuse) is equal to the squares of the two shorter sides added together.

Many mathematicians over the years have proved the theorem using algebra and geometry. Yet proving it using trigonometry was long thought impossible, as the fundamental formulae of trigonometry are based upon the assumption that the Pythagorean Theorem is true – an example of circular reasoning.

Nevertheless, both Johnson and Jackson managed to solve the math problem independently of each other and prove Pythagoras’ theory without resorting to circular reasoning — a feat that has only been managed twice previously by professional mathematicians.

Johnson and Jackson then collaborated to share their work at a regional meeting of the American Mathematical Society in Atlanta in March 2023. Encouraged by their reception, Jackson and Johnson then decided to submit their discoveries for final peer review and publication. Their study outlines five new ways of proving the theorem using trigonometry, and a method that reveals five more proofs, totaling ten proofs altogether. Only one of these proofs was previously presented at the conference, meaning that nine are totally new.

“I was pretty surprised to be published” says Ne’Kiya Jackson. “I didn’t think it would go this far”.

“To have a paper published at such a young age — it’s really mind blowing,” agrees Calcea Johnson.

“It’s very exciting for me, because I know when I was growing up, STEM [science, technology, engineering, and math] wasn’t really a cool thing. So the fact that all these people actually are interested in STEM and mathematics really warms my heart and makes me really excited for how far STEM has come.”

In the paper, the authors argue that one of the reasons that trigonometry causes such confusion and anxiety for high school students is that two completely different versions of trigonometry exist and are defined using the same terms. This means that trying to make sense of trigonometry can be like trying to make sense of a picture where two different images have been printed on top of each other.

Jackson and Johnson argue that by separating the two versions, and focusing on just one of them, a large collection of new proofs of the Pythagorean Theorem can be found.

Jackson currently studies at Xavier University of Louisiana and is pursuing a doctoral degree in pharmacy, while Johnson is studying environmental engineering at Louisiana State University’s Roger Hadfield Ogden Honors College.

“I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things, and to let other young women know that they are able to do whatever they want to do. So that makes me very proud to be able to be in that position,” says Johnson.

Commenting on Johnson and Jackson’s achievements, Della Dumbaugh, editor-in-chief of American Mathematical Monthly, says, “The Monthly is honored and delighted to publish the work of these two students on its pages.

“Their results call attention to the promise of the fresh perspective of students on the field. They also highlight the important role of teachers and schools in advancing the next generation of mathematicians.

“Even more, this work echoes the spirit of Benjamin Finkel when he founded the Monthly in 1894 to feature mathematics within reach of teachers and students of mathematics.”

Here’s a link to and a citation for the paper,

Five or Ten New Proofs of the Pythagorean Theorem by Ne’Kiya Jackson & Calcea Johnson. The American Mathematical Monthly Volume 131, 2024 – Issue 9 Pages 739-752 DOI: https://doi.org/10.1080/00029890.2024.2370240 Published online: 27 Oct 2024

This paper is open access.

van Gogh’s sky is alive with real-world physics

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Caption: The authors measured the relative scale and spacing of the whirling brush strokes in van Gogh’s “The Starry Night,” along with variances in luminance of the paint, to see if the laws that apply in the physics of real skies apply in the artist’s depiction. The results suggest van Gogh had an innate understanding of atmospheric dynamics. He captured multiple dimensions of atmospheric physics with surprising accuracy. Credit: Yinxiang Ma

A September 17, 2024 American Institute of Physics news release (also on EurekAlert) reveals how researchers in the fields of marine sciences and fluid dynamics have revealed the ‘hidden turbulence’ in van Gogh’s The Starry Night,

Vincent van Gogh’s painting “The Starry Night” depicts a swirling blue sky with yellow moon and stars. The sky is an explosion of colors and shapes, each star encapsulated in ripples of yellow, gleaming with light like reflections on water. 

Van Gogh’s brushstrokes create an illusion of sky movement so convincing it led atmospheric scientists to wonder how closely it aligns with the physics of real skies. While the atmospheric motion in the painting cannot be measured, the brushstrokes can.

In an article published this week in Physics of Fluids, by AIP Publishing, researchers specializing in marine sciences and fluid dynamics in China and France analyzed van Gogh’s painting to uncover what they call the hidden turbulence in the painter’s depiction of the sky.

“The scale of the paint strokes played a crucial role,” author Yongxiang Huang said. “With a high-resolution digital picture, we were able to measure precisely the typical size of the brushstrokes and compare these to the scales expected from turbulence theories.”

To reveal hidden turbulence, the authors used brushstrokes in the painting like leaves swirling in a funnel of wind to examine the shape, energy, and scaling of atmospheric characteristics of the otherwise invisible atmosphere. They used the relative brightness, or luminance, of the varying paint colors as a stand-in for the kinetic energy of physical movement.

“It reveals a deep and intuitive understanding of natural phenomena,” Huang said. “Van Gogh’s precise representation of turbulence might be from studying the movement of clouds and the atmosphere or an innate sense of how to capture the dynamism of the sky.”

Their study examined the spatial scale of the painting’s 14 main whirling shapes to find out if they align with the cascading energy theory that describes the kinetic energy transfer from large- to small-scale turbulent flows in the atmosphere.

They discovered the overall picture aligns with Kolmogorov’s law, which predicts atmospheric movement and scale according to measured inertial energy. Drilling down to the microcosm within the paint strokes themselves, where relative brightness is diffused throughout the canvas, the researchers discovered an alignment with Batchelor’s scaling, which describes energy laws in small-scale, passive scalar turbulence following atmospheric movement.

Finding both scalings in one atmospheric system is rare, and it was a big driver for their research.

“Turbulence is believed to be one of the intrinsic properties of high Reynolds flows dominated by inertia, but recently, turbulence-like phenomena have been reported for different types of flow systems at a wide range of spatial scales, with low Reynolds numbers where viscosity is more dominant,” Huang said.

“It seems it is time to propose a new definition of turbulence to embrace more situations.”

Matthew Rozsa provides a more accessible description of the research in a September 20, 2024 article for Salon.com, Note: Links have been removed,

… one can look at “The Starry Night” and see a scientifically accurate representation of turbulent, cascading waters — a visual that may have directly inspired van Gogh before he transposed those dynamics into his iconic starry sky while painting in his mental asylum room in the French town of Saint-Rémy-de-Provence.

“Imagine you are standing on a bridge, and you watch the river flow. You will see swirls on the surface, and these swirls are not random.” Yongxiang Huang, lead author of the study, told CNN. “They arrange themselves in specific patterns, and these kinds of patterns can be predicted by physical laws.”

Scientists fascinated by van Gogh’s art are not limited to physicists. When researchers discovered a gecko that reminded them of the paintings of van Gogh, they gave it the scientific name Cnemaspis vangoghi. As a common terms, the authors suggested “van Gogh’s starry dwarf gecko.”

Here’s a link to and a citation for the paper,

Hidden turbulence in van Gogh’s The Starry Night by Yinxiang Ma (马寅翔), Wanting Cheng (程婉婷), Shidi Huang (黄仕迪), François G. Schmitt, Xin Lin (林昕), Yongxiang Huang (黄永祥). Physics of Fluids Volume 36, Issue 9 September 2024 DOI: https://doi.org/10.1063/5.0213627

This article is behind a paywall.