#The Unexpected Math behind van Gogh's ‘Starry Night’

[catsmom]

The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair

[thedalatribune]

© Paolo Dala

Illustration by Paolo Dala (2019)

Turbulence X Vincent Van Gogh

One of the most remarkable aspects of the human brain is its ability to recognize patters and describe them. Among the hardest patterns we’ve tried to understand is the concept of turbulent flow in fluid dynamics. The German Physicist Werner Heisenberg said:

“When I meet God I’m going to ask him two questions: Why relativity and why turbulence? I really believe he will have an answer for the first.”

As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks.

In June 1889, Vincent van Gogh painted the view just before sunrise from the window of his room at the St. Paul de Mausole Asylum in Saint Rémy de Provence (where he admitted himself after mutilating his own ear in a psychotic episode). In the ‘Starry Night’, his circular brushstrokes crate a night sky filled whit swirling clouds and eddies of stars. 

Van Gogh and other impressionists represented light in a different way than their predecessors, seeming to capture its motion... The effect is caused by luminance, the intensity of the light in the colors of the canvas. The more primitive part of our visual cortex, which sees light contrast, and motion, but not color, will ben two differently colored areas together if they have the same luminance; but out brains’ primate subdivision will the contrasting colors without blending. With these two interpretations happening at once, the light in many Impressionist works seems to pulse, flicker and radiate oddly...

Sixty (60) years later, Russian Mathematician Andrey Kolmogrov furthered our mathematical understanding of turbulence when he proposed that energy in a turbulent fluid at length R varies in proportion to the five-thirds (5/3) power of R. Experimental measurements show Kolmogorov was remarkably close to the way turbulent flow works, although a complete description of turbulence remains one of the unsolved problems  in physics. A turbulent flow is self-similar if there is an energy cascade. In other words, big eddies transfer their energy to smaller eddies, which do likewise at other scales. Examples of this includes Jupiter’s ‘Great Red Spot’, cloud formations, and interstellar dust particles. 

In 2004 using the Hubble Space Telescope, scientists saw the eddies of dust and gas around a star, and it reminded them of van Gogh’s ‘Starry Night’. This motivated scientists from Mexico, Spain, and England to study the luminance in van Gogh’s paintings in detail. They discovered that there is a distinct patter of turbulent fluid structures close to Kolmogorov’s Equation hidden in may of van Gogh’s paintings. The researchers digitized the paintings, and measured how brightness varies between any two pixels. From the curves measured for pixel separations, they concluded that paintings from van Gogh’s period of psychotic agitation behave remarkably similar to fluid turbulence. His ‘Self-portrait with a Pipe’, from a calmer period in van Gogh’s life, showed no sign of this correspondence. And neither did other artists’ work that seemed equally turbulent at first glance, like Munch’s ‘The Scream’. 

While it’s too easy to say van Gogh’s turbulent genius enabled him to depict turbulence, it’s also far too difficult to accurately express the rousing beauty of the fact that in a period of intense suffering, van Gogh was somehow able to perceive and represent one of the most supremely difficult concepts nature has ever brought before mankind, and to unite his unique mind’s eye with the deepest mysteries of movement, fluid and, light.

Natalya St. Clair The Unexpected Math behind van Gogh's ‘Starry Night’

[khaelisfics]

Short Soumate AU - the concept was “your soulmark is a reference to what your soulmate likes the most”, and I rather liked it!

Tagging @doctorroseprompts, in case this can fit into a prompt!

I hope you’ll like it! :-)

He had scoured every modern art museum, every ephemeral exhibition throughout the country, combed through thousands of websites about painting, drawing, sculpting, bought hundreds of magazines and books about the subject. No name, no face he had encountered had caused that spark he was desperately looking for.

He tossed his ticket in a nearby bin, annoyed and disappointed he hadn’t found her in that tedious expo in a dark corner of London. Listening to wrinkled man on the verge of falling asleep each time he stopped talking in that monotonous crow had put his patience to the test. Looking at depressing paintings about death and phantasmagorical creatures made by an artist who obviously didn’t know black and grey weren’t the only colours that existed hadn’t helped. Maybe it wasn’t a bad thing he hadn’t found her there, actually. He didn’t know what he would feel if his soulmate happened to be a deranged woman fascinated by necromancia and festering cadavers.

A liquid shiver rolled down his spine at the thought, and he hurried to take out his list of current exhibitions he needed to go to.

“Nope to Nighthorses 66, then,” he mumbled under his breath, crossing the name of the exhibition with the pencil he always kept in his pocket. “Next is… S.C.M. Just hope this doesn’t stand for super creepy monsters."

He shoved his quickly shortening list back into his pocket and headed for the nearest underground station. It was already quite late in the afternoon, and he knew he should call it a day, head back home and get a full night of sleep if he didn’t want to doze off over his desk the morning later. But he also knew the disappointment and frustration of not making any progress, the longing he felt to finally find her growing into some kind of unhealthy obsession only predicted long hours spent tossing and turning in his sheets without finding Morpheus’ comforting embrace.

He took a quick look at his watch, ignoring the soulmark on his arm as if it’d just been a cheap tattoo he would forever regret, and made his decision. He hopped out of the train a few stations later, didn’t look twice at the large mural on the wall he had learnt a few years back had been painted by a foreign young artist, and made his way up the stairs. He was getting tired to try and see her where she wasn’t. A sticker on lamp post with a cartoonish drawing. Crass tags in back alleys, elaborated frescos on iron curtains. Street traders who sold ridiculously expensive prints of artworks stolen on the Internet. Everywhere he looked, he was tempted to believe it was her, and every time, he was a tad more disillusioned when he found out it wasn’t.

His worn chucks squished on the wet pavement as he made his way to one of his favorite places. It was a cramped bookshop in the corner of an ever-deserted street he had discovered the first time he had moved in this part of the city, rather by accident than real intention, and he came back to it every week, some weeks every day. It wasn’t as much the books as the owner that always brought his steps back to that small shop that smelled of yellowed paper and dust. Rose, was her name. A young woman with honey-eyes and wheat-hair, full lips and round nose. He knew she was just his friend, but sometimes, he wished his soulmark could be a small pile of books, or a meaningful quote from her favorite author - not that odd-shaped moon that belonged in a Van Gogh painting. His soulmate was an artist, not a bookworm. Not the woman he had dreamt of so often he believed he must have broken a hundred rules and, though unwillingly, cheated on his real soulmate on several occasions. Not Rose. Never Rose.

The small bell chimed when he pushed the ancient door open and the sound of his steps died on the heavy carpet. She was nowhere in sight - probably in the cellar she called a storage room, or in the broom cupboard she called an office. She would eventually pop out, like she usually did whenever the bell rang. His feet took him to the only alley he was interested in, and he picked up an old encyclopedia that had lost a bit of its varnish. He had always wanted to buy this book, but it almost was a relic, and not only did it look like it, it was also worth it. He sifted through random pages, smiling at the centuries-old mathematical formulas and theorems that had long been replaced by more precise, and especially more valid ones.

“You should buy it before it’s gone.”

He hurried to slide the heavy book back in its space at the sound of her smiling voice and twirled on his feet to greet her with a smile of his own.

“Rose, hi, how…” he started before his mouth gaped open and his voice died in his throat.

He first noticed the dark blue apron she was wearing over her eternal oversized jumper. Then he spotted the pencil she had stuck behind an ear. And he finally understood the multicoloured stains dotting and streaking the apron were paint. That wasn’t right. Rose loved books. She was a bookseller. Not an artist. He would know if she were, after so much time spent sharing coffees and pointless conversations. So much time spent wishing she could be the one.

“Fine, if your question was how are you,” she giggled, wiping her hands on her apron so she could give his shoulder a friendly slap without harming his pinstriped jacket. “How are you?”

“I, uh, yeah, good, I suppose,” he nodded - he found his voice again when he managed to ame his heart hammering against his ribs. “What are you doing with all that equipment?”

“What does it look like I’m doing, John?” she taunted as she motioned for him to follow her through the maze of crammed corridors. “I was about to close, I didn’t think anyone would come so I just started working on a little something. D’you wanna sneak a peek?”

“You never told me you liked painting,” he said, almost reproachful.

“You never asked.”

She led him to the door that was plastered with a large sticker that read storage, offered him a shy smile and pushed the door open with a finger.

He couldn’t move. Instead of a dark, small room filled to the brim with rows of old books, he saw a bright, large space void of anything. Anything but paintings, hanging on the walls, haphazardly propped up against the walls. Colours bursting out of the canvas like fireworks, fiery landscapes and smooth still-lives, abstract shapes that made him feel so many things at once his heart flew to his throat, meticulous portraits of people she probably knew given the depth and the familiariaty that oozed from the faces. She was painter. A very talented painter. An artist. Rose was an artist.

“I wanted to show you the one I’m working on,” she said as she strutted towards her easel that was directed towards the window, unaware he was staring a her as if she’d just turned into one of the monsters he’d seen at the weird exhibition. “I think… You’re the expert, maybe you can tell me if I did it right?”

He could only nod even though he barely heard her words and watched, speechless and on the verge of collapsing under the weight of the unexpected revelation. Rose was an artist. She turned her easel towards him, and what he saw made his stomach twist into tight and uncomfortable knots.

“That’s a golden spiral,” he said, running a feverish hand through his spikes of hair. “Logarithmic spiral, it’s… Maths.”

“Yeah, I know,” she smiled, a quivering smile that lacked its usual enthusiasm. “Does it look… Dunno, accurate?”

“Accurate isn’t the first word that came to my mind,” he said softly, taking a few steps towards the painting to let his fingers hover over the snake of yellow and soft orange. “This looks beautiful, Rose.  Why did you paint this?”

“‘Cause I found out…’ she started, sheepishly rocking on the ball of her feet. “What my soulmark is. I didn’t want to know, because I’ve always thought I would meet my soulmate whether I knew or not. But then… I mean, you came along and you made it really hard to resist the temptation.”

“What’s your soulmark, Rose? Please, show me.”

He held his breath as she slowly rolled her sleeve up her arm, stared at her pale skin covered with lines and lines of tiny numbers from her wrist to the crook of her elbow. He wanted to scream his joy, cry his relief, he wanted to hug her and kiss her and let his whole body and soul finally love her. But he simply blinked and swallowed it all down. She had never told him about her mark. She had never wanted him to know, and she probably had a hundred good reasons not to tell him.

“That’s the Fibonacci sequence,” he told her, unconsciously tugging on his own sleeve to make sure she wouldn’t see his mark. “It’s… My favorite sequence, actually.”

“I know,” she shrugged with an embarrassed twist of her lips. “I mean, I figured. You’ve bought several books about that sequence from me, you know. Doctor Smith, clever scientist and mathematician and all.”

He noticed the dejection in her voice, the way she gently kicked the foot of her easel and lowered her eyes to the carpet. He was hurt, deep and violent, that she didn’t seem to want any of what he had to offer, but that didn’t make him any less indifferent to her own pain. He slipped a finger under her chin to catch her eyes and give her a gentle look she didn’t want.

“Talk to me, Rose,” he said softly, fully cupping her cheek when she started to bow her head again. “Tell me what’s wrong.”

“I know you’ve got a bit of Starry Night on your arm,” she answered with a sharp nibble on her lip. “I know that… You would have found out I like painting, sooner or later.”

“Why wait until now, then?” he asked, befuddled by the tears that started to roll down her cheeks. “Rose, I don’t understand, what’s wrong?”

“Look at me, John,” she sighed, swatting his hand away from her face. “Look at me and tell me I’m the soulmate you’ve always wanted. Tell me I was made for you. Tell me you can ever love me. I don’t want you to think I’m the one is all. There has to be someone else for you, John.”

They matched. He didn’t understand why she refused to see it, refused to believe it, refused to accept she could be his soulmate. They matched. That’s all he understood. Her mark was a mathematical sequence. His mark was actually borrowed from a Van Gogh painting. They matched. And he had fallen for that woman so long ago, To know he had already learnt everything he loved about her, to know she was the one. That left no room for tears or unhappiness.

Despite her protests, he cupped bot her cheeks again and hurried to press a soft, lingering on her lips before she could draw back. Rose was an artist. Rose was the one.

“You’re the one I’ve always wanted,” he whispered, catching her lips between his again to steal her answer. “You were made for me, like I was made for you.”

“John…” she tried to complain, though she was slowly melting into his arms, little by little, a little more each time his hot breath caressed her chin and his lips danced against her own. “I’m not…”

“There’s no one else for me. You, just you. God, why did you have to wait so long, Rose, we’ve lost so much time. All that time spent looking for you when I had already found you. All that time spent pretending I didn’t love you when I could have shown you how much I do. “

“You do?” she breathed out, pulling away to see that truth in his eyes.

He only sat on her stool and pulled her sitting over his lap, his mouth hungrily looking for those lips he wanted to devour, his chest pressing hard against that body he wanted to touch, his heart reaching out for that shared loved he wanted to drown into. Rose wasn’t just an artist. She was his soulmate.

[icodesouthlake]

iCode Southlake is now offering 💯 🔣 online classes, with live instructors 👩‍🏫👨‍🏫👩‍💼👨‍💼!

iCode-Southlake 👩‍💻👨‍💻Available Schedule: 📰https://icodeschool.com/southlake-online-kids-coding-progr…/

Call Now 📲@ 817-527-5270

For a Virtual Visit 🗺@ https://icodeschool.com/southlake108/

[hooking]

A list of cool TED-ed lessons for when you’re bored

Biology & Chemistry

Why are some people left-handed?

The science of spiciness 

Poison vs venom: What’s the difference?

The power of the placebo effect

What’s the big deal with gluten?

How sugar affects the brain

How do vitamins work?

What are those floaty things in your eye?

The Benefits of a Bilingual Brain

Math, Tech & Physics

Schrödinger's cat: A thought experiment in quantum mechanics 

What is the Heisenberg Uncertainty Principle?

Why is glass transparent?

Why is ketchup so hard to pour?

The Infinite Hotel Paradox 

Is there a limit to technological progress? 

How big is infinity? 

One is one... or is it? 

What’s an algorithm?

Logarithms, Explained

How computers translate human language

Solid, liquid, gas and... plasma?

Space 

The basics of the Higgs boson

Questions no one knows the answer to

Dark matter: The matter that we can’t see

The death of the universe

Is space trying to kill us?

Art & Lit/Writing

Why is Vermeer's "Girl with the Pearl Earring" considered a masterpiece?

The unexpected math behind Van Gogh's "Starry Night

What makes something “Kafkaesque”?

What “Orwellian” really means

Beware of nominalizations (AKA zombie nouns)

Comma story

Buffalo buffalo buffalo: one word sentences and how they work

Life & Knowledge

Mary’s Room: A philosophical thought experiment

Are ghosts ships real?

What’s the difference between accuracy and precision?

How exposing anonymous companies could cut down on crime

[talltalestogo]

The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair

[mathematicianadda]

IntMath Newsletter: CSS matrix, Humble Pi, van Gogh

29 Aug 2019

In this Newsletter:

1. New on IntMath: CSS matrix math 2. Resources: Humble Pi, AnswerThePublic 3. Math in the news: Proof 4. Math movies: Parker, van Gogh 5. Math puzzle: Mystery object 6. Final thought: Dry leaves

1. New on IntMath: CSS matrix math

I recently gave a talk to a local meetup group on the mathematics behind CSS matrix. CSS stands for "cascading style sheets", and is the system where Web designers can set font sizes, colors, and also set sizes and vary shapes for objects like images and videos.

Matrices are used to transform geometric objects (scale, skew, rotate, translate and so on.) Computer games make extensive use of matrices to simulate depth, 3D objects and so on.

Here is the content of the talk. It explores how CSS transform is the result of matrix multiplication. Even if you're not interested in Web design, it's interesting to see another real-life application of matrices.

See CSS Matrix - a mathematical explanation

I also developed the following interactive graph applet that demonstrates the concepts in the talk.

This is an interactive graph where you can vary sliders to see how CSS matrix changes the size, shape and location of an object.

See CSS matrix interactive applet

2. Resources

(a) Humble Pi: A Comedy of Maths Errors

When I was teaching a group of engineering students some years ago, I went to my boss with an idea. I suggested we incorporate examples of cases where things went wrong, so students would learn the importance of accuracy and the safety issues that can arise out of sloppy and inaccurate mathematics.

He wasn't enthusiastic and squashed the idea, saying it would scare off students from choosing the degree. I felt it was a lost opportunity.

So I was interested when I came across the book "Humble Pi - A Comedy of Maths Errors" by Matt Parker.

Matt Parker's Humble Pi

This readable book was exactly what I had in mind when I approached my boss. Let's learn from cases where people made math errors, and see what the consequences were – not to apportion blame, but to learn what can go wrong.

We all make math errors, but usually the worst outcome is a drop in grade, or momentary embarrassment. The people working in science and engineering fields should be aware of why their math teachers insisted on accuracy.

So I suggested the book for the local library, and was pleasantly surprised how long I had to wait before I could read it (it turned out to be quite popular).

I recommend this book for any math student or teacher.

One of the videos below features Parker, covering some of the same errors detailed in the book.

Disclaimer: I have no connection with Matt Parker (other than through Twitter) and receive no commission.

(b) Teachers: Address the questions students are really asking

Some teachers see their job as simply giving out information, but there is no "value add" in that approach, especially since students can easily access such information in abundance.

One thing we can do better while teaching a topic is to actually address the questions students really have about that topic. One approach is to simply ask students what their questions are, and there are a lot of apps and sites that facilitate this process (e.g. Google Forms and Survey Monkey are both easy to use).

Another thing to consider is to look at the questions students are likely to ask, before you even start planning the lessons. AnswerThePublic is a good resource for this.

AnswerThePublic is a database of common questions that people ask about topics. It provides a rich source of ideas on how we might go about introducing a topic, and pre-empting the stumbling blocks.

See Answer the Public

Topics to try are:

Algebra (you'll see e.g. "How is algebra used in real life?", "Who invented algebra?", etc)

Calculus (e.g. "When does a limit exist?", "Where to start?", "How is it used in computer science?", etc)

Matrix (e.g. "When is a matrix orthogonal?", "Matrix when a^2 = a?", etc)

You can choose the "Data" tab at the top of each visualization to get easier-to-read lists of questions, and download the lot as a CSV (for Excel).

Sometimes in this resource you see questions that may seem quite odd, like "Does calculus cause kidney stones?", but "calculus" means "stone" and in medicine, it refers to a build-up of hard substances in the body. I get it on my teeth.

3. Math in the news

Story of the Gaussian correlation inequality proof

The title "Gaussian correlation inequality" sounds scary, but it goes something like this.

I have a dart board sitting on a rectangular shape, and assume I'm a good dart player. When I throw a lot of darts at it, I expect the accuracy of my throws to form a somewhat bell-shaped curve distribution. That is, most of the darts land somewhere close to the middle, and there are less dart holes as I go out from the middle.

The greater the circle overlaps the rectangle, the probability of striking both goes up.

The probability that a dart lands on both the circle and the rectangle is greater than or equal to the product of the individual probabilities.

At first, they didn't believe a German retiree had actually proved it.

See A Long-Sought Proof, Found and Almost Lost

4. Math Movies

(a) What Happens When Maths Goes Wrong?

This is a one-hour presentation by Matt Parker at the Royal Institution, London. It covers some interesting examples that are worth considering.

See What Happens When Maths Goes Wrong?

Parker is the Public Engagement in Mathematics Fellow at Queen Mary University of London.

(b) The unexpected math behind Van Gogh's "Starry Night"

Turbulence is one of the most tricky phenomena to model using mathematics. It is complicated and chaotic.

This video by Natalya St. Clair explores how Van Gogh incorporated turbulence in his art to give the impression of movement.

See: The unexpected math behind Van Gogh's "Starry Night"

5. Math puzzles

The puzzle in the last IntMath Newsletter asked about radii of mutually tangent circles. In fact, it turned out to be a 3x3 system of equations - it wasn't really a geometry question.

Correct answers with sufficient reasons were submitted by Russell, Nicola, Tomas and Thomas.

New math puzzle: Mystery object

This time, some investigation may be involved.

Mystery object

The above object was used to achieve a particular mathematical outcome – one that is still vitally important to this day. What is the object, where was it used, and what was the mathematical outcome?

(If you can't actually find it or figure it out, your speculation will prove interesting!)

You can leave your response here.

6. Final thought - what it could be like

Equatorial Singapore, where I live, is normally lush and green, and doesn't experience leaf falls as is normally the case for most places in Autumn.

However, this year we've had the driest and second hottest July on record, and practically no rain so far in August causing my local park to look like this:

Dry leaves and dead grass in Singapore.

Such dry and hot conditions are caused by a positive Indian Ocean dipole, the situation where the Western Indian Ocean is hotter than the Eastern part, causing hot droughts over Australia and most SE Asian countries.

These make ideal conditions for farmers in Indonesia to set off forest fires in order to plant more palm oil, so there's been many fire hot spots reported there.

Meanwhile, the dry season in the Amazon has been the excuse, along with President Bolsanaro's encouragement, for farmers there to burn vast amounts of the Earth's lungs for ever-expanding methane-producing cattle farms.

In the Arctic, fires across the tundra continue to burn, spewing even more carbon into the atmosphere.

These events are giving us an insight into how things will be if governments, companies and all of us fail to address our land use, our consumption, and our "economic growth at all costs" mentality.

We can stop it, but will we?

Until next time, enjoy whatever you learn.

Related posts:

Updated matrix interactive Here's an applet where you can investigate how matrix...

IntMath Newsletter: Resources, primes, matrix app and role models In this Newsletter: 1. Resources for the new school year...

Is a 1×1 matrix a scalar? A 1×1 matrix is often regarded as a scalar...

IntMath Newsletter: Piano trig applet, continued fractions In this Newsletter: 1. New applet: Piano note frequencies interactive...

from SquareCirclez https://ift.tt/2L6diKb via IFTTT from Blogger https://ift.tt/2Uf55q0

[cleverkittentimetravel-blog]

The Unexpected Math Behind Van Gogh’s Starry Night

TED-Ed (https://ed.ted.com/lessons/the-unexpected-math-behind-van-gogh-s-starry-night-natalya-st-clair)

One of the hardest patterns we’ve tried to understand is the concept of turbulent flow in fluid dynamics. Art can be used to depict how turbulent flow looks. 

In June 1889, Vincent van Gogh painted the view just before sunrise of his room at the Saint-Paul Asylum in Saint-Rémy-de-Provence where he’d admitted himself after mutilating his own ear. 

In Starry Night, his circular brushstrokes create a night sky filled with swirling clouds and eddies of stars. Van Gogh and other Impressionists represented light in a different way than their predecessors - seeing to capture its motion, for instance, across sun-dappled waters. 

The effect is caused by luminance - the intensity of light in the colours on the canvas. The more primitive part of our visual cortex, which sees light contrast and motion (but not colour), will blend two differently coloured areas together if they have the same luminance. But our brain’s primate subdivision sees the contrasting colours without blending. With these two interpretations happening at once, the light in many Impressionist works seems to pulse, flicker and radiate oddly. That’s how this and other Impressionist works use quickly executed and prominent brushstrokes to capture something strikingly real about how light moves. 

60 years later, Russian mathematician Andrey Kolmogorov furthered our mathematical understanding of turbulence when he proposed that energy in a turbulent fluid at length r, varies in proportion to the 5/3 power of r. Experiments in turbulence show Kolmogorov was remarkably close to the way turbulent flow works - although a complete description of turbulence remains one of the unsolved problems in physics. 

A turbulent flow is self-similar if there is an energy cascade. In other words, big eddies transfer their energy to smaller eddies, which do likewise at other scales. Examples of this include Jupiter’s Great Red Spot, cloud formations and interstellar dust particles. In 2004, using the Hubble Space Telescope, scientists saw the eddies of a distant cloud of dust and gas around a star and it reminded them of Van Gogh’s Starry Night. This motivated scientists from Mexico, Spain and England to study the luminance in Van Gogh’s paintings in detail. They discovered there is a distinct pattern of turbulent fluid structures, close to Kolmogorov’s equation, hidden in many of Van Gogh’s paintings. 

The researchers digitized the paintings and measured how brightness varies between any two pixels. From the curves measured for pixel separations, they concluded that paintings from Van Gogh’s period of psychotic agitation, behave remarkably similar to fluid turbulence. His Self Portrait with a Pipe, from a calmer period in Van Gogh’s life, showed no sign of this correspondence and neither did other artists’ work that seemed equally turbulent at first glance like Mvnch’s The Scream. 

[icodesouthlake]

Van Gogh’s art, math and technology all in one

[blog-art-man-world-blog]

The unexpected math behind Van Gogh's "Starry Night"

[yukishakura]

Two Words, “This moment”

I stumbled upon this episode after watching TedEd’s video about “The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair” , saw a comment in the video talking about this episode. I searched about him right away on wiki, learning a summary of his life, and then watched this episode out of curiosity, and oh my ;-;

It does feel like it’s not fair for him to live his life like that, but then I read one comment in youtube, “And now he lives on in his paintings for as long as humanity appreciates art. So essentially for being pushed aside during his life, he has been granted immortality in death.“ - ProblmSolvd Not many people have the privilege , and perhaps he knows and watches from the next life.