The Mathematical Code Hidden In Nature
Summary
TLDRThis script explores the mathematical underpinnings of nature's patterns, focusing on Alan Turing's 'reaction-diffusion' theory. It reveals how simple equations can explain complex biological phenomena like zebra stripes and leopard spots. Despite initial skepticism, Turing's work has been validated by recent biological discoveries of actual 'morphogens'. The narrative also poignantly touches on Turing's tragic life and his profound contributions to both computing and biology, emphasizing the beauty and power of mathematics in understanding our world.
Takeaways
- š§¬ The diversity of life's patterns can be explained by simple mathematical equations, challenging the notion that biology is too complex and unpredictable for such simplicity.
- š¦ The mystery of zebra stripes is not just about camouflage but also serves to confuse biting flies, highlighting the multifaceted purposes of biological patterns.
- š¢ Alan Turing's mathematical model, known as 'Turing patterns', provides a framework for understanding how complex biological patterns emerge from simple chemical interactions.
- š Turing's work in mathematical biology was initially overlooked, possibly due to the overshadowing of DNA's discovery and the skepticism towards a mathematician's contribution to the field.
- š§Ŗ The concept of 'morphogens', as introduced by Turing, refers to chemicals that spread and react differently to create various biological patterns, a key to understanding morphogenesis.
- š The reaction-diffusion equations describe how two chemicals interact and spread, leading to the formation of patterns like those seen on animals' skins.
- š By adjusting variables in Turing's equations, such as the rate of chemical production and diffusion, different patterns like spots or stripes can be generated.
- š± The rediscovery of Turing patterns in the 1970s by Gierer and Meinhardt spurred further interest in applying mathematics to understand biological development.
- š¬ Recent biological findings have identified actual morphogens, supporting Turing's theories and demonstrating the practical application of his mathematical models in nature.
- š” Turing's legacy extends beyond his mathematical and computational contributions, as his work in biology has inspired new avenues of research and deepened our understanding of life's complexity.
Q & A
What is the mystery underlying the variety of patterns in the living world?
-The mystery is how such a variety of patterns, like spots and stripes, can arise from the same simple biological building blocks: cells and their chemical instructions.
What is a Turing pattern and who discovered it?
-A Turing pattern is a set of patterns in nature, such as spots, stripes, and waves, that can be explained by a set of mathematical equations. They were discovered by mathematician Alan Turing in 1952.
Why were Turing's ideas initially ignored when he published his work on biological patterns?
-Turing's ideas were largely ignored at the time of publication possibly because they were overshadowed by other significant discoveries in biology, such as the double helix structure of DNA, or because the scientific community was not yet ready to accept mathematical explanations for biological phenomena.
What is 'morphogenesis' and how does it relate to Turing's work?
-Morphogenesis is the biological process that causes an organism to develop its shape. Turing's work is related to this process as he published a paper called 'The Chemical Basis of Morphogenesis' which included equations describing how complex shapes can arise spontaneously from simple initial conditions.
What is a reaction-diffusion system and how does it create patterns?
-A reaction-diffusion system is a model that involves two or more chemicals moving around and reacting with each other. It creates patterns by having one chemical (the activator) that promotes its own production and the production of an inhibitor, while the second chemical (the inhibitor) suppresses the activator. The interaction and diffusion of these chemicals can lead to the formation of various patterns.
How do the concepts of activator and inhibitor chemicals relate to the formation of biological patterns?
-In the context of biological pattern formation, the activator chemical promotes its own production and that of an inhibitor, while the inhibitor chemical suppresses the activator. This interplay, along with the differential rates of diffusion of these chemicals, can lead to the formation of various patterns such as spots or stripes.
How did Turing's mathematical models predict the patterns on a cheetah's fur?
-Turing's models predicted patterns by simulating a reaction-diffusion system where an activator (like a fire) and an inhibitor (like firefighters) interact. The activator promotes its own production, while the inhibitor suppresses it. The key to getting spots, as opposed to a uniform color, is that the inhibitor diffuses faster than the activator.
What role did Alan Turing play in World War II and the development of computer science?
-Alan Turing was a famous wartime codebreaker who played a significant role in decoding the Enigma machine, which is estimated to have shortened World War II in Europe by more than two years. After the war, he was instrumental in developing the core logical programming that forms the basis of modern computers.
What challenges did Turing face in his lifetime, and how were they related to his work?
-Alan Turing faced significant personal challenges, including criminal charges for being in a homosexual relationship at a time when it was illegal in the UK. He chose chemical castration treatment over prison, but tragically died from cyanide poisoning two years after his treatment began, likely a suicide. These challenges were unrelated to his scientific work but tragically cut short a brilliant career.
How have biologists verified Turing's mathematical models in the context of actual biological systems?
-Biologists have verified Turing's models by finding actual morphogensāchemicals or proteins inside cellsāthat behave as his model predicts. Examples include patterns on a mouse's mouth, bird feathers, human arm hair, and shark denticle scales, all of which are sculpted by the diffusion and reaction of molecular morphogens.
What is the significance of Turing's work in the field of biology and mathematics?
-Turing's work is significant because it demonstrated that mathematics could be used to explain complex biological patterns, leading to a new field of study called mathematical biology. His work has inspired new questions and approaches in understanding the underlying processes of biological development and pattern formation.
Outlines
š§¬ The Mystery of Biological Patterns
This paragraph introduces the complexity and beauty of biological patterns, questioning how such diversity arises from basic cellular components. It highlights the role of mathematics in explaining these patterns, referencing Alan Turing's work on 'Turing patterns' that can account for various natural designs. The paragraph also touches on Turing's lesser-known contributions to biology, emphasizing the interdisciplinary nature of his pursuits.
š The Power of Reaction-Diffusion Systems
The second paragraph delves into the concept of 'reaction-diffusion systems' as explained by Turing. It describes how the interaction between two chemicals, an activator and an inhibitor, can lead to the formation of complex patterns, such as those seen on a cheetah's fur. The paragraph uses an analogy of a forest fire and firefighters to illustrate this process, emphasizing how different rates of diffusion can result in various biological patterns. It also discusses how these mathematical models can be adapted to irregular shapes, reflecting the natural world's diversity.
šµļøāāļø Turing's Legacy and the Future of Mathematical Biology
The final paragraph reflects on Turing's legacy, noting the initial lack of recognition for his work in biological patterns due to overshadowing scientific discoveries and societal attitudes. It discusses the rediscovery of Turing patterns and the subsequent validation of his theories through the identification of actual morphogens in nature. The paragraph also touches on the complexity of biological systems, such as the patterning in mammalian limbs, and Turing's pioneering role in computer science and codebreaking. It concludes with a tribute to Turing's multifaceted genius and the enduring impact of his work across disciplines.
Mindmap
Keywords
š”Morphogenesis
š”Turing Patterns
š”Reaction-Diffusion
š”Activator and Inhibitor
š”Diffusion
š”Morphogens
š”Binary Pattern
š”Homosexual Relationship
š”Chemical Castration
š”Pardon
š”Binary Code
Highlights
The mystery of biological diversity arises from simple ingredients like cells and chemical instructions.
Mathematics, not DNA, can explain many of biology's varied patterns.
Alan Turing's mathematical rules, known as 'Turing patterns', explain patterns in nature like stripes and spots.
Mathematical biology helps describe and predict complex biological systems.
Turing's work on 'morphogenesis', the generation of form, introduced a series of equations for complex shapes.
Reaction-diffusion equations describe how chemicals move and react, leading to pattern formation.
Diffusion and reaction combined can explain biological patterns, contrary to previous beliefs.
Biological patterns like cheetah spots are formed by the interaction of activator and inhibitor chemicals.
Turing's equations can create a variety of patterns by adjusting variables like chemical diffusion rates.
The shape of the surface on which patterns form can influence the final biological pattern.
Turing's 1952 article on biological patterns was initially ignored, later gaining recognition.
Biologists have recently found molecular morphogens that fit Turing's mathematical model.
Turing's work has inspired new questions in biology and the use of mathematics to understand nature's beauty.
Alan Turing's legacy includes contributions to codebreaking, computer science, and mathematical biology.
Turing's notes contained a unique binary code, showcasing his advanced thinking even without modern computers.
The world may have missed out on further groundbreaking work had Alan Turing not passed away prematurely.
Turing's multifaceted genius is celebrated for his work in codebreaking, computer logic, and biological pattern formation.
Transcripts
The living world is a universe ofĀ shapes and patterns. Beautiful, complex,Ā Ā
and sometimes strange. And beneath all ofĀ them is a mystery: How does so much varietyĀ Ā
arise from the same simple ingredients:Ā cells and their chemical instructions?
There is one elegant idea that describesĀ many of biologyās varied patterns,Ā Ā
from spots to stripes and in between. Itās a codeĀ written not in the language of DNA, but in math.
Can simple equations really explain somethingĀ as messy and un-predictable as the living world?Ā Ā
How accurately can mathematicsĀ truly predict reality?Ā Ā
Could there really be one universalĀ code that explains all of this?
[OPEN]
Hey smart people, Joe here.
What color is a zebra? Black with whiteĀ stripes? Orā¦ white with black stripes?Ā Ā
This is not a trick question.Ā The answer? Is black with whiteĀ Ā
stripes. And we know that because someĀ zebras are born without their stripes.
It might make you wonder, why do zebras haveĀ stripes to begin with? A biologist might answerĀ Ā
that question like this: the stripes aid inĀ camouflage from predators. And that wouldĀ Ā
be wrong. The stripes actual purpose? Is mostĀ likely to confuse bloodthirsty biting flies. Yep.
But that answer really justĀ tells us what the stripes do.Ā Ā
Not where the stripes come from, or whyĀ patterns like this are even possible.
Our best answer to those questionsĀ doesnāt come from a biologist at all.
In 1952, mathematician Alan Turing published aĀ set of surprisingly simple mathematical rulesĀ Ā
that can explain many of the patterns that weĀ see in nature, ranging from stripes to spotsĀ Ā
to labyrinth-like waves and even geometricĀ mosaics. All now known as āTuring patternsā
Most people know Alan Turing as a famous wartimeĀ codebreaker, and the father of modern computing.Ā Ā
You might not know that many of the problems thatĀ most fascinated him throughout his life were,Ā Ā
well, about life: About biology.
But why would a mathematician beĀ interested in biology in the first place?
That's a really good question!
I'm Dr. Natasha Ellison, and I'm from theĀ University of Sheffield, which is in the UK.
I think so many mathematicians are interested inĀ biology because it's so complicated and there'sĀ Ā
so much we don't know about it. If you thinkĀ about a living system, like a human being,Ā Ā
there's just so many different things goingĀ on. And really, we don't know everything.
The movements of animals, populationĀ trends, evolutionary relationships,Ā Ā
interactions between genes, or howĀ diseases spread. All of these areĀ Ā
biological problems where mathematical modelsĀ can help describe and predict what we see inĀ Ā
real life. But mathematical biology is alsoĀ useful for describing things we canāt see.
Joe (05:44) What do you say when people ask,Ā Ā
why should we care about math in biology?
Natasha (05:54): Why should we careĀ Ā
about what mathematics describes in biology?Ā Ā
The reason is because there's thingsĀ about biology that we can't observe.
We canāt follow every animal all the timeĀ in the wild, or observe their every moment.Ā Ā
Itās impossible to measure every gene andĀ chemical in a living thing at every instant.Ā Ā
Mathematical models can help make sense ofĀ these unobservable things. And one of theĀ Ā
most difficult things to observe in biology isĀ the delicate process of how living things growĀ Ā
and get their shape. Alan Turing called thisĀ āmorphogenesisā, the āgeneration of formā.
In 1952, Turing published a paper calledĀ āThe Chemical Basis of Morphogenesisā.Ā Ā
In it was a series of equationsĀ describing how complex shapes like theseĀ Ā
can arise spontaneously fromĀ simple initial conditions.
According to Turingās model, all it takes to formĀ these patterns is two chemicals, spreading out theĀ Ā
same way atoms of a gas will fill a box, andĀ reacting with one another. Turing called theseĀ Ā
chemicals āmorphogens.ā But there was one crucialĀ difference: Instead of spreading out evenly,Ā Ā
these chemicals spread out at different rates. Natasha (15:49):Ā
So the way that we create a Turing pattern isĀ with some equations called reaction-diffusionĀ Ā
equations. And usually they describe how twoĀ or possibly more chemicals are moving aroundĀ Ā
and reacting with each other. So diffusionĀ is the process of sort of spreading out.Ā Ā
So if you can imagine, I don't know,Ā if you had a dish with two chemicalsĀ Ā
in (GFX). They're both spreading out across theĀ dish, they're both reacting with each other.Ā Ā
This is what reaction-diffusionĀ equations are describing.
This was Turingās first bit ofĀ genius. To combine these twoĀ Ā
ideasādiffusion and reactionāto explain patterns.
Because diffusion on its own doesnāt createĀ patterns. Just think of ink in water.Ā
Simple reactions donāt create patterns either.Ā Reactants become products andā¦ thatās that.
Natasha (20:48): Everybody thought backĀ Ā
then that if you introduce diffusionĀ into systems, it would stabilize it.Ā Ā
And that would basically make it boring. What IĀ mean by that is you wouldn't see a lovely pattern.Ā Ā
You'd have an animal, just one color, but actuallyĀ Turing showed that when you introduce diffusionĀ Ā
into these reacting chemical systems, it canĀ destabilize and form these amazing patterns.
A āreaction-diffusion systemā may soundĀ intimidating, but itās actually pretty simple:Ā Ā
There are two chemicals. An activator & anĀ inhibitor. The activator makes more of itselfĀ Ā
and makes inhibitor, while theĀ inhibitor turns off the activator.
How can this be translated to actual biologicalĀ patterns? Imagine a cheetah with no spots. WeĀ Ā
can think of its fur as a dry forest. In thisĀ really dry forest, little fires break out.Ā Ā
But firefighters are also stationed throughoutĀ our forest, and they can travel faster than theĀ Ā
fire. The fires canāt be put out from the middle,Ā so they outrun the fire and spray it back from theĀ Ā
edges. Weāre left with blackened spots surroundedĀ by unburned trees in our cheetah forest.
Fire is like the activator chemical: ItĀ makes more of itself. The firefightersĀ Ā
are the inhibitor chemical, reactingĀ to the fire and extinguishing it. FireĀ Ā
and firefighters both spread, or diffuse,Ā throughout the forest. The key to gettingĀ Ā
spots (and not an all-black cheetah) is thatĀ the firefighters spread faster than the fire.
And by adjusting a few simple variables like that,Ā Ā
Turingās simple set of mathematical rulesĀ can create a staggering variety of patterns.
Natasha (34:18): These equations thatĀ Ā
produce spotted patterns like cheetahs, the exactĀ same equations can also produce stripy patternsĀ Ā
or even a combination of the two. And that dependsĀ on different numbers inside the equations. ForĀ Ā
example, there's a number that describes howĀ fast the fire chemical will produce itself.Ā Ā
There's a number that describes how fastĀ the fire chemical would diffuse and how fastĀ Ā
the water chemical would diffuse as well. And allĀ of these different numbers inside the equationsĀ Ā
can be altered very slightly. And then we'd seeĀ instead of a spotted pattern, a stripy pattern.
And one other thing that affects the patternĀ is the shape youāre creating the pattern on.Ā Ā
A circle or a square is one thing, but animalsāĀ skins arenāt simple geometric shapes. WhenĀ Ā
Turingās mathematical rules play out on irregularĀ surfaces, different patterns can form on differentĀ Ā
parts. And often, when we look at nature,Ā this predicted mix of patterns is what we see.
We think of stripes and spots as veryĀ different shapes, but they might beĀ Ā
two versions of the same thing, identicalĀ rules playing out on different surfaces.
Turingās 1952 article wasā¦Ā largely ignored at the time.Ā Ā
Perhaps because it was overshadowed byĀ other groundbreaking discoveries in biology,Ā Ā
like Watson & Crickās 1953 paper describingĀ the double helix structure of DNA. Or perhapsĀ Ā
because the world simply wasnāt ready to hear theĀ ideas of a mathematician when it came to biology.
But after the 1970s, when scientistsĀ Alfred Gierer and Hans MeinhardtĀ Ā
rediscovered Turing patterns in a paper ofĀ their own, biologists began to take notice.Ā Ā
And they started to wonder: Creating biologicalĀ patterns using mathematics may work on paper,Ā Ā
or inside of computers. But how are theseĀ patterns *actually* created in nature?
Itās been a surprisingly sticky questionĀ to untangle. Turingās mathematics simplyĀ Ā
and elegantly model reality, but to trulyĀ prove Turing right, biologists needed toĀ Ā
find actual morphogens: chemicals or proteinsĀ inside cells that do what Turingās model predicts.
And just recently, after decades of searching,Ā biologists have finally begun to find moleculesĀ Ā
that fit the math. The ridges on the roof ofĀ a mouseās mouth, the spacing of bird feathersĀ Ā
or the hair on your arms, even theĀ toothlike denticle scales of sharks:Ā Ā
All of these patterns are sculpted inĀ developing organisms by the diffusionĀ Ā
and reaction of molecular morphogens,Ā just as Turingās math predicted.
But as simple and elegant as Turingās mathĀ is, some living systems have proven to beĀ Ā
a bit more complex. In the developingĀ limbs of mammals, for example, threeĀ Ā
different activator/inhibitor signals interact inĀ elaborate ways to create the pattern of fingers:Ā Ā
Stripe-like signals, alternating on and off.Ā Like 1s and 0s. A binary pattern ofā¦ digits.
Sadly, Alan Turing never lived to seeĀ his genius recognized. The same year heĀ Ā
published his paper on biological patterns, heĀ admitted to being in a homosexual relationship,Ā Ā
which at the time was a criminal offense inĀ the United Kingdom. Rather than go to prison,Ā Ā
he submitted to chemical castration treatmentĀ with synthetic hormones. Two years later, inĀ Ā
June of 1954, at the age of 41, he was found deadĀ from cyanide poisoning, likely a suicide. In 2013,Ā Ā
Turing was finally pardoned by Queen Elizabeth,Ā nearly 60 years after his tragic death.
Now I donāt like to make scientists sound likeĀ mythical heroes. Even the greatest discoveriesĀ Ā
are the result of failure after failure and areĀ almost always built on the work of many others,Ā Ā
theyāre never plucked out of the aether andĀ put in someoneās head by some angel of genius.Ā
But that being said, Alan Turingās work decodingĀ Ā
zebra stripes and leopard spots leaves noĀ doubt that he truly was a singular mind
Natasha (37:55): The equations that produce these patterns,Ā Ā
we can't easily solve them with pen andĀ paper. And in most cases we can't at all,Ā Ā
and we need computers to help us. So what's reallyĀ amazing is that when Alan Turing was writingĀ Ā
these theories and studying these equations, heĀ didn't have the computers that we have today.
Natasha (39:01):Ā
So this here is some of Alan's Turing's notesĀ that were found in his house when he died.Ā Ā
If you can see that, you'll noticeĀ that they're not actually numbers.
Joe (39:17): It's like a secret code!
Natasha (39:20): Yeah. It's like a secretĀ Ā
code. Itās his secret code. It's in binaryĀ actually, but instead of writing binary out,Ā Ā
because you've got the five digits, he had thisĀ other code that kind of coded out the binary. SoĀ Ā
Alan Turing could describe the equationsĀ in this way that required millions ofĀ Ā
calculations by a computer, butĀ you didn't really have, you know,Ā Ā
really didn't have a fast computer to do it.Ā So it would have taken him absolutely ages.
Joe (40:15) What hasĀ Ā
the world missed out on by theĀ fact that we lost Alan Turing?
Natasha (40:25): Itās extremely hardĀ Ā
to describe what the world's missed out onĀ with losing Alan Turing. Because so often heĀ Ā
couldn't communicate his thoughts to other peopleĀ because they were so far ahead of other peopleĀ Ā
and they were so complicated. TheyĀ seemed to come out of nowhere sometimes.Ā
Natasha (25:52) When you read accountsĀ Ā
of people who knew him, they were saying the sameĀ thing. We don't know where we got this idea from,Ā
Natasha (40:42) So what, what he could have achieved.Ā Ā
I don't think anyone could possibly say. Natasha (42:14)Ā
I have no idea where we would have gotĀ to, but it would have been brilliant.
One war historian estimated that the work ofĀ Turing and his fellow codebreakers shortenedĀ Ā
World War II in Europe by more than two years,Ā saving perhaps 14 million lives in the process.
And after the war, Turing was instrumental inĀ developing the core logical programming at theĀ Ā
heart of every computer on Earth today,Ā including the one youāre watching this video on.
And decades later, his lifelong fascinationĀ with the mathematics underlying natureās beautyĀ Ā
has inspired completely new questions in biology.
Doing any one of these things would be worthĀ celebrating. To do all of them is the markĀ Ā
of a rare and special mind. One that couldĀ see that the true beauty of mathematics isĀ Ā
not just its ability to describe reality,Ā it is to deepen our understanding of it.
Stay curious.
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