Sunday, March 22, 2026

The Math Behind Van Gogh's "Starry Night"


Physicist Werner Heisenberg said, “When I meet God, I am 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. Natalya St. Clair illustrates how Van Gogh captured this deep mystery of movement, fluid and light in his work.


Lead in


Draw some flowing water. How can you represent something fluid, with static lines?


Lead in: What do you think makes this picture so well loved?

Look at the title:

“The unexpected math behind Van Gogh’s ‘Starry Night’ by Natalya St. Clair:

What do you think the article will say about the picture?

 

Read the article and find out:

One of the most remarkable aspects of the human brain is its ability to recognize patterns 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 Saint-Paul-de-Mausole asylum in Saint-Rémy-de-Provence, where he’d admitted himself after mutilating his own ear in a psychotic episode.

In “The 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, seeming to capture its motion, for instance, across sun-dappled waters, or here in starlight that twinkles and melts through milky waves of blue night sky.

The effect is caused by luminance, the intensity of the light in the colors on the canvas.

The more primitive part of our visual cortex, which sees light contrast and motion but not color, will blend two differently colored areas together if they have the same luminance.

But our brain’s primate subdivision will see 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.

That’s how this and other Impressionist works use quickly executed, prominent brushstrokes to capture something strikingly real about how light moves.

Sixty 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 five-thirds 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 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 that 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 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.

 


Go to Ted Lesson:

The math behind Van Gogh's "Starry Night"


1. Who admitted van Gogh to a mental asylum?
2. What is an energy cascade?
3. What is turbulence?
4. What is relativity?
5. What is the Hubble telescope?
6. What is amazing about van Gogh's 1889 Starry Night painting?


Discuss

1. Is it important that Van Gogh seems to have accidentally represented turbulence? Why?
2. If we can just take photographs or films of fluid things, why bother trying to represent them through painting or drawing? 





Descension


  1. One key ability of the human brain is recognizing _________ and being able to describe them.
  2. Among the most difficult patterns scientists study is ________ in ________ dynamics.
  3. The physicist _________ once said he would ask God about _________ and _________.
  4. In June 1889, _________ created a painting based on the view from his room in an asylum in _________.
  5. In The Starry Night, _________ brushstrokes form a sky full of swirling _________ and starry eddies.
  6. Impressionist artists showed _________ in a new way, capturing its _________ in scenes like water or the night sky.
  7. This visual effect comes from _________, meaning the intensity of _________ in the colors used.
  8. In 1941, _________ suggested that energy in turbulent flow depends on the _________ power of length.
  9. In turbulent flow, an _________ cascade occurs, where larger eddies pass energy to _________ ones.
  10. Researchers later found that the luminance patterns in Van Gogh’s paintings resemble _________, especially during times of _________ agitation.

Hannah Gadsby: Nanette | The Sunflowers

lead in:


Who painted this?

If I give you "unsolicited" advice, does it mean the advice is...
A) poorly researched?
B) unasked for?
C) not from a lawyer?
D) not advice that I follow myself?

Discuss

1. Should people who suffer from mental illness take medication or try to cope without it?

2. Is there a connection between artistic talent and mental instability?

3. How might the medication van Gogh was taking have actually been partly responsible for the Sunflowers?


Guide questions

1. According to the man, why should artists not take medication for mental health problems?


Kahoot Quiz

The Math of Starry Night

Verb patterns

I like studying verb patterns. - OK.

I like to study verb patterns. - OK, but I prefer the other one (sounds more 'modern'?)


I enjoy studying verb patterns. - OK.

I enjoy to study verb patterns. - NOT OK.


Can we sort this out?

It's a question of the order of the actions.

Verb + to-inf

First action (looks towards) second action.

Verb + gerund

Later action (reflects upon, looks back to) preceding action.

So, you...

remember to do it (in the future)

and

remember doing it (in the past)


But...


then there are other things that complicate things further, like:

  • verb + to--infinitive / -ing form
  • verb + object + (to-) infinitive "tell her to do it"
  • verb + object + -ing form "watch them doing it"
  • verb + that clause "suggest that she does it"


Verb patterns practice (Random Idea)

Verb patterns practice (Perfect English)


Speaking practice - verb + gerund

Speaking practice - verb + infinitive


More practice here (Quizlet)


I Will Survive





At first I was afraid, I was petrified (1)

Kept   THINK    I could never live without you by my side

But then I spent so many nights   THINK   how you did me wrong

And I grew strong (2)

And I learned how  GET   along

And so you're back

From outer space (3)

I just walked in   FIND   you here with that sad look upon your face

I should have changed that stupid lock, I should have made you leave your key

If I'd known for just one second you'd be back  BOTHER   me

Go on now, go, walk out the door

Just turn around now

'Cause you're not welcome anymore

Weren't you the one who tried    HURT  me with goodbye?

You think I'd crumble (4)?

You think I'd lay down and die?

 

Oh no, not I, I will survive

Oh, as long as I know how   LOVE  , I know I'll stay alive

I've got all my life  LIVE

And I've got all my love  GIVE  and I'll survive

I will survive, hey, hey

 

It took all the strength I had not   FALL   apart

Kept trying hard   MEND   the pieces of my broken heart

And I spent oh-so (5) many nights just   FEEL   sorry for myself

I used   CRY

But now I hold my head up high and you see me

Somebody new

I'm not that chained-up (6) little person still in love with you

And so you felt like    DROP   in and just expect me   BE  free

Well, now I'm saving all my lovin' for someone who's loving me

 

Oh no, not I, I will survive

Oh, as long as I know how   LOVE  , I know I'll stay alive

I've got all my life  LIVE

And I've got all my love  GIVE  and I'll survive

I will survive, hey, hey



 

Discuss

  • Who is the singer talking to?
  • How did she feel at the beginning of the song?
  • What changed her feelings?
  • What message does the song give?
  • Is the song more sad or more positive? Why?
  • What does the song say about being strong?

  • What new words or phrases did you hear?
  • Can you find a line that shows confidence?
  • Tell a short story about a time you “survived” something difficult.

 

1.      What does this word mean?

2.      Grow (become) + adjective  - to grow strong, to grow weak – what else can we grow?

He grew…anx____, la___, more confi_____, he grew more at ease

Also… I grew to love languages, I grew to love broccoli, They grew to love one ano____

Discuss: What’s something you have grown to love? Is there anything you’ve grown to hate?

3.   What does “outer space” mean here?

4.      What does ‘crumble’ mean?

5.      Oh-so means “very” – what is the difference between “so tired” and “very tired”

6.      A chained-up person is unable to escape a bad relationship

Wednesday, March 18, 2026

The McGurk Effect





Which sense do you think is more dominant....

taste or smell?
seeing or hearing?
touch or taste?



Watch:

The McGurk Effect


The McGurk Effect

 

Watch video

 

1.     What do you think this video is mainly about?

2.     What surprised you the most while watching?

3.     What is one key idea you took away from it?

 

 

 

Watch again, fill the gaps:


At any ___ moment we are being ____________ by sensory information.

 

Our brains do a ____________ job of making sense of it ___.

 

It seems easy _________ to separate the sounds we hear from the ______ we see, but there is one illusion that reveals this ____ always the _____.

 

In the illusion, _____ we see ___________ what we hear.

 

If we close our eyes we actually hear the sound ___ it ___.

 

If we open our eyes, we actually see how the mouth movements can influence _____ we’re hearing.

 

What’s remarkable about this illusion ___ even knowing how it’s _______ doesn’t seem to ____ a difference.

 

The speech brain just takes in that information. It doesn't care what _______ knowledge you bring to _____.

 

 

 

 

 

 

 

 

Language Comprehension

1. What does “bombarded by sensory information” suggest about how much we see and hear?
A. We receive a large amount of sensory input all the time
B. We experience very little at once
C. Only one sense works at a time

2. What does it mean that the brain “makes sense of it all”?
A. The brain organises and interprets sensory input
B. The brain ignores most information
C. The brain only focuses on sound

3. In this illusion, what does “overrides” mean?
A. One sense dominates or replaces another
B. All senses work equally
C. One sense stops working

4. Why is the effect described as “bizarre”?
A. It is confusing and unexpected
B. It is normal and easy to understand
C. It only affects some people

5. What do “conflicting information” and “salient information” mean here?
A. Information that disagrees / the most noticeable sense
B. Information that matches / the weakest sense
C. Information that repeats / the quietest sense

 

Reflection

6.     Do you notice times in daily life when your senses compete? Give an example.

7.     Does this illusion make you trust your brain more or less? Why?

8.     How does “what we see overrides what we hear” change how you think about your senses?

9.     Why do you think the illusion still works even when you understand it?

  1. Would you rather your brain be ‘truthful’ or ‘efficient’? Why?

_______________
Check

 
At any one moment we are being bombarded by sensory information.

Our brains do a remarkable job of making sense of it all.

It seems easy enough to separate the sounds we hear from the sights we see, but there is one illusion that reveals this isn't always the case.

In the illusion, what we see overrides what we hear.

If we close our eyes we actually hear the sound as it is.

If we open our eyes, we actually see how the mouth movements can influence what we’re hearing.

What’s remarkable about this illusion is even knowing how it’s done doesn’t seem to make a difference.

The speech brain just takes in that information. It doesn't care what outside knowledge you bring to bear.

Kahoot quiz

Seeing is Believing

Pitching a product

 

Product Ideas

Give them a mark out of 5 

Remember - the idea should be exciting, but also make sense as a business idea (i.e. it will make money and stay afloat)

 

1. Portable solar charger for phones and laptops   ___

2. Peer-to-peer tutoring platform for students ___

3. DIY bubble tea making kit ___

4. Screen-time lock box for phones during study ___

5. Edible spoons and forks made from grains ___

6. Smart study planner that creates schedules automatically ___

7. Posture-correcting backpack with alerts ___

8. Uniform recycling and resale service ___

9. Lost-item tracking tags for essential items ___

10. Customisable healthy lunchbox delivery service ___

11. Exam stress relief kit for students, (contains a mystery prize) ___

12. Pet “translator” app that interprets animal sounds ___

 

Match to their category

A) Tech & Innovation

B) Sustainability & Environment

C) Food & Lifestyle

D) Education & School Life

E) Health & Wellbeing

F) Fun & Creative

 

 

 

Now talk about one or two of the products you graded higher using these 5 points.

1. Problem – What’s the issue?

2. Solution – Their product/service

3. Target Market – Who will buy it?

4. Why It’s Better – What makes it unique?

5. Money – Price + how it makes profit

 


5 more ideas 

Air bnb for storage

A surpise a month

Virtual travel experiences

AI meal planner

Mobile EV charging service 


Talk about these in relation to these business ideas

Problem

Customer

Marketing strategy

Outlay

Risks

Further business opportunities that might arise from this basic business idea

 

 

 

 

 

 

 

  1. Why / people / your / would / choose / product / over / others?

  1. What / the / biggest / is / risk / your / to / business?

  1. How / before / long / you / break / even?

  1. What / your / makes / product / different / from / competitors?

  1. How / you / would / make / or / deliver / this / product?

  1. Who / your / exactly / is / target / customer?

  1. If / you / I / gave / $10,000, / how / you / would / spend / it?

  1. Why / you / are / the / right / people / to / run / this / business?

  1. What / go / could / wrong / with / your / idea?

  1. How / much / it / does / cost / to / make / one / unit?

  1. How / you / will / reach / your / customers?

  1. Could / a / company / bigger / easily / copy / your / idea?

  1. How / this / could / business / grow / in / the / future?

  1. What / does / role / each / team / member / play?


Tuesday, March 17, 2026

The Senses



Think of a taste. Any taste. What taste comes into your mind?

Think of a sound. Any sound. What sound is it?

Think of a sight. Any sight. What is it?

Think of a smell. Any smell. What is it?

Think of a texture or surface you are touching. What is it?

Now discuss with others.

 

 

I’m going to read out a list of things. For each thing decide which sense it most strongly connects to for you. Write the thing after each sense:

Sight:

Sound:

Touch:

Taste:

Smell:

Discuss your responses together. Are you similar or different? Explain your responses and try to understand the differences.


1. flowers

Sight
Sound
Smell
Taste
Touch


Think of a taste. Any taste. What taste comes into your mind?

Think of a sound. Any sound. What sound is it?

Think of a sight. Any sight. What is it?

Think of a smell. Any smell. What is it?

Think of a texture or surface you are touching. What is it?

Now discuss with others.

 

1.      1. Associations

I’m going to read out a list of things. For each thing decide which sense it most strongly connects to for you. Write the thing after each sense:

Sight:

Sound:

Touch:

Taste:

Smell:

Discuss your responses together. Are you similar or different? Explain your responses and try to understand the differences.

2. Coins

  1. What do coins taste like?

3. Garden

  1. Do you have a garden back at home?
  2. Does it have walls, a fountain, a pond, birds, tall trees, grapes, flowers, a barbeque, statues, bricks, a vine, bushes, grass, insects, a compost bin, or outdoor chairs?

4. Cheese

  1. Is cheese popular in your country?
  2. What do you eat cheese with?

5. Snakes

  1. Have you ever seen a real snake in the wild (not at the zoo)?
  2. Have you ever touched a living snake? What did it feel like?

6. Fire

  1. Do you know how to light a campfire?
  2. What can you cook in or on a fire?
  3. What does hair smell like when it catches fire?

7. Rain

  1. How often does it rain in your country?
  2. Do you like rain?
  3. Have you ever had to walk home in the rain with no raincoat or umbrella? Where? When?

8. Keys

  1. How often do you lose your keys?
  2. How many hours of your life have you wasted looking for keys?

9. Cigarette

  1. Do you smoke?
  2. Do or did your parents smoke?

10. Xmas Tree

  1. Does your family ever have a real Xmas tree for Xmas?
  2. Do you give gifts at Xmas in your family?
  3. What did you get last Xmas?

11. Storm

  1. Do you enjoy storms?

12. Sand

  1. What does sand taste like?
  2. Can sand be annoying?
  3. What can sand be used for?

13. Bread

  1. What is your favourite kind of bread?
  2. Could you live without bread?

14. Shower

  1. How long are your showers?
  2. Is there a nice shower where you're currently living?

15. Dogs

  1. What animal is most similar to a dog?
  2. What’s a good name for a dog?
  3. What kind of dog is your personality like?

16. Coffee

  1. How do you like to have your coffee?
  2. Is coffee bad for you?

 



What is the most beautiful flower?



















2. coins


Sight
Sound
Smell
Taste
Touch


What do coins taste like?












3. garden


Sight
Sound
Smell
Taste
Touch


Do you have a garden back at home?
does it have...
walls    a fountain   a pond    birds   tall trees     grapes    flowers    a barbeque   statues
bricks    a vine     bushes     grass     insects    a compost bin       outdoor chairs



 











4. cheese


Sight
Sound
Smell
Taste
Touch


Is cheese popular in your country? What do you eat cheese with?












5. snakes


Sight
Sound
Smell
Taste
Touch



Have you ever see a real snake in the wild? (not at the zoo)
Have you ever touched a living snake? What did it feel like?










6. fire


Sight
Sound
Smell
Taste
Touch


Do you know how to light a campfire?
What can you cook in / on a fire?
What does hair smell like when it catches fire?













7. rain


Sight
Sound
Smell
Taste
Touch



How often does it rain in your country?
Do you like rain?
Have you ever had to walk home in the rain with no raincoat or umbrella? Where? When?









8. keys


Sight
Sound
Smell
Taste
Touch


How often do you lose your keys? 
How many hours of your life have you wasted looking for keys?








9. cigarette


Sight
Sound
Smell
Taste
Touch


Do you smoke?
Do / did your parents smoke?








10. Xmas tree


Sight
Sound
Smell
Taste
Touch


Does you family ever have a real Xmas tree for Xmas?
Do you give gifts at Xmas in your family?
What did you get last Xmas?










11. storm



Sight
Sound
Smell
Taste
Touch


Do you enjoy storms?










12. sand



Sight
Sound
Smell
Taste
Touch


What does sand taste like?
Can sand can be annoying?
What can sand be used for?






13. bread



Sight
Sound
Smell
Taste
Touch


What is your favourite kind of bread?
Could you live without bread?

bagels, baguette, naan, roti, hamburger buns, dark bread, other?



14. shower



Sight
Sound
Smell
Taste
Touch


How long are your showers?
Is there a nice shower where you're currently living?





15. dogs



Sight
Sound
Smell
Taste
Touch

What animal is most similar to a dog?
What's a good name for a dog?
What kind of dog is your personality like?



16. coffee


Sight
Sound
Smell
Taste
Touch


How do you like to have your coffee?
Is coffee bad for you?





Image result for nose







Do you have a good sense of smell?















What are some of your favourite smells?












Think of three natural smells and three artificial smells.








Outside exercise


Outside exercise

 

 

Go out for a walk outside and find 10 different smells. Write them down.

 

  Smell source       adjectives / description   comparison       mark out of 5

1.

2,

3.

4.

5.

6.

7.

8.

9.

10.





Alternatively, divide into groups each concentrating on a different sense.

group1 
smells

group2
sights

group3
sounds

group4
touch









How many words are there for "sweet" in your first  language?
Can you think of any synonyms for "sweet" in English?











What is "umami"?





Dictionary
Definitions from Oxford LanguagesLearn more
umami
noun
  1. a category of taste in food (besides sweet, sour, salt, and bitter), corresponding to the flavour of glutamates, especially monosodium glutamate.




basic taste/smell vocab

sweet 
sour
fragrant
acidic
fumy
smoky
salty
spicy
musty
earthy
metalic
woody
grassy
off
rancid
soapy



In English we also might describe sweet smells and tastes with these words:

try putting appropriate nouns with these

E.g. Tangy + orange juice

Fruity
Caramel
Nutty
Gingery
Floral
Chocolate-y
syrupy
Buttery
Butterscotch
citrus-y
Banana-ry
Aniseed
Liquorish
Malty
Vanilla
Berry
Rich
Biscuity
Minty
Tangy
Tropical
Zingy
Sugary
Cinnamon-y
Honeyish
Milky


We use these adjectives to describe colours...

cool
warm
hot
bright
pale
florescent
dark
deep
light
fiery
mellow
pure
vivid

How do our adjectives for smell differ from our adjectives for colours in English?


We tend to describe tastes and smells by comparing them to similar tastes and smells, whereas with colour we can focus on their degree of intensity. 


But we also compare colours with other things

ocean
forest
lemon
royal
emerald
sapphire
sky
pitch
dirt
fire-engine
battleship
eggshell
snowy