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What do plants know about numbers? A certain spiral pattern commonly seen in sunflowers, pinecones, and many species of cacti contains some surprising numerical properties. In this brisk talk, Paul Dancstep investigates this pattern through several kinetic sculptures by artist John Edmark. These mesmerizing artworks provide a number of insights into the mathematical lives of plants.

As someone who failed Algebra 1 three times and to this day cannot figure out the tip on a lunch check, this was the most mesmerizing, brilliant explanation of a basic mathematical principle I have ever seen. Oh, how I wish I could "do" math! And what a terrifically enthusiastic, awe-inspiring talk! Thank you!

I too had difficulty with Algebra (and still do), yet managed to become a Mechanical Engineer. Yet, I easily understand anything geometric and breezed through Calculus and other maths. This was a mystery to me until it became clear than I'm dyslexic, a fact confirmed by a neighbor who happened to be the Director of the Dept of Neurology at Stanford University after we had an exchange with several weird questions I answered; he told me that dyslexic people make the best Mechanical Engineers! I believe the theory about evolution 'side-stepping' common adaptation for using symbols to convey logic that allowed a genetic legacy for some people to think differently and have difficulty with the abstractions of symbols like letters and words on paper, i.e., being dyslexic. I suggest you look into that for your own difficulty, noting that you were fascinated by this video.

Just goes to show, it really *is* all down to the teacher.

Yup. Failed pre algebra three times and then dropped out of 10th grade. Took a bunch of pure LSD and discovered that absolutely *EVERYTHING* is "spirally". A must read: The Curves Of Life by Theodore Andrea Cook. Its a real gem guys. You should get a copy and pass it on to the next generation. Good luck finding one.

@SIMKINETICS Absolutely fantastic story! Im just about certain im dyslexic. Yet I build houses. All the way from concrete to fine finish trim. Math has never been my strong suit and I blame a bit of it on the system of educating our youth. If a student cant pass pre-algebra he ist allowed the privilege to learn the higher courses. Doesnt seem right. I would have absolutely crushed a geometry course. Thanks for sharing man.

The true failure is when you stop trying ;) Math is hard, it's no biggie

One of the best presentations I have ever been honored to witness. I only wish I had been there in person to praise the presenter and the artist, both of whom are outstanding in their respective fields.

this is all equally fascinating as it is inspiring. i just fell in love with phyllotactic spyrals. math and art and nature coming together

8/5 stars for this one!!! Just finishing my first Abstract Algebra class, and this video just brings about so many thoughts relating to the topics we've covered this semester. ❤️♾️

What an inspiring talk! This is the sort of knowledge that I absolutely adore - beautiful and worthy just to behold, but with the potential to become useful in unexpected ways.

simply putting things between other things ends up giving you some incredible patterns. the spirals and patterns you see in nature come from new cells just going to where there is the most space. some times you do see plants that create perfect 90 degree symmetry though, with 4 leaves that are evenly spaced around the stalk. generally this only happens when the stock is extremely long such that the leaves can't cast shadows on the ones below them

I'm giving this video presentation a standing ovation! This was visually stunning, beautiful, and engaging. Thank you!

Wow - What an amazing talk and what fantastic art. Thank you for sharing.

Love this. Thanks for posting it. Just awesome models of some of the complex beauty nature evolves into.

In visual, as well as audio, there are resonant patterns or tones as it were, where the origin pattern passes one of those patterns you described as a "Checkered pattern", back at 5:12 mins into the video. I believe what the eye is perceiving here is the resonant visual frequency of the overall 3D object. It is quite amazing.

I love this connection indeed. Very well said, and inspires me to look more into this analogy

That is an incredibly interesting way to think about it!

John Edmark is such an inspiring artist , working with nature ,math ,and art is just genius , they all elaborate on each other + I have never thought a microwave would lead to creating cool patterns

This is amazing, these patterns are related to phi, the golden ratio - and how it is the irrational number that is the least able to be approximated by a fraction of rational numbers. It's the most efficient way to stack things around a point - as if it used a rational angle, things would meet up in cycles and inefficiently stack, and if it used an irrational number that was well approximated, eg pi being close to 22/7, it would *almost* meet and nearly clash. Numberphile has a great video on this.

This is mind blowing! Thank you so much for this great talk

Damnit. As someone who has gone through many phases of being enamored with the fibonacci spirals and how they relate to nature, this just gave me a whole new invigoration in that fascination.

Many times great ideas come to people on this sort of stand by mode, watching the plate rotating, thinking about a fallen apple, watching the water rising while the body deeps in... It's like the mind needs space to run at the maximun capacity. Amazing video! Gratitude!

Wonderful, Wonderful movie. Although the "blooming" animations make me dizzy and a little sick, the magic and beauty together with those little math secrets hiding in every such pattern - are worth a million looks (and likes) One of the best "math" videos I've seen a long time Thanks

Seems like tiny imperfections sort of strobe around and do more damage than expected, and the 3D printing process is a bit grainy and comes with tiny imperfections. Different manufacturing processes or a better, more polished finish could resolve it. I think making it more precise and more smooth could help a lot.

The double pine cone looking thing when spun freely transforms into the typically known shape of DNA. and each piece of the jigsaw is same in shape and just the size increases. Gives a deep insight about the pattern in human evolution (physically and spiritually) With each new generation a new piece is added that's the same in shape but it expands the overall picture

I wonder what the actual angle is on dna?

I’m not a scientist, I’ve never been good in science. I started this video not expecting to understand what’s going on but man you did a great job.

this isnt related to my field at all as a chem phd but i love the way this dude builds up on concepts when hes explaining -- i really wanna emulate his style of presenting

I can't handle how interesting this is :-) I want to see in person! But thanks for posting this presentation! ~Trav

As soon as you mentioned needing to rotate multiple levels at proportional amounts, I immediately thought of something like the Lazy Susan (didn't know it was called that lol). I wonder what the spirals look like for 2:3, 1:2, and even 1:1 - or if those spirals are even possible.

Great talk. And your explanatory visuals were great too.

fascinating lecture, I thought I understood Fibonacci patterns but as always, the more you learn the more you realize how little you know. Great Talk Thank you.

Yes, especially scientists.... they actually "know" the least !

Really cool and very fascinating presentation!!! But was actually surprised he didn't touch on the fact that the 137.5 degrees rotation is the same as the golden angle which is derived from the golden ratio.

You missed the fact that it is the Sommerfield fine structure constant! Plays a part in electron orbitals!

Beautiful presentation. Also, the ratio of neighboring Fibonacci numbers approximates the Golden Ratio; a pattern seen throughout nature. For example, 21/13 ~ 1.62, the Golden Ratio.

Very beautiful ! BTW, I think the lazy suzan thing refers to the Aristotle paradox.

The shape of those 4-sided polygons the spirals are made of look very similar to the kite shape in the infinite kite-and-dart version of the Penrose tiling. Feels like that is not at random, since they are both connected to Fibonacci numbers, but I am not knowledgeable enough to tell you exactly how or why. I love like this kind of exploratory art though, that finds new ways to explore something about our universe and finds interesting ways to show that.

Brillante y hermoso! Muchas gracias por compartirlo

absolutely brilliant video. Only gripe, I feel there must be an obvious connection between the patterns shown in transtower and the patterns we get with pendulums of increasing length. When the cutouts line up with a specific number of other cutouts each time, it reminds me of the balls of a pendulum lining up in the same way, anyone see the connection?

interference patterns

What a great presentation. No superfluous talk and great visualizations. This guy should teach how to make presentations and talks. Kudos.

Just had one of those very rare "wow" moments. Need to see more of this!!!

Understanding or learning at childhood and becoming in awe in sixties is life. Thanks KZbin AI.

You can make bulbs with the fibonacci sequence, start winding a line around a sphere at a constant angle and put dots at 1, 2, 3, 5, 8, 13 etc and you'll end up with dots covering the sphere in the right places that happen to all be pretty much equidistant! :D

Good to know that curiosity is still leading to amazing discoveries provided you know how to look.

Few things I confirmed in this lovely video - Fibonacci was a genius beyond measure, nature is always even more amazing, and this guy stares at his food while he waits for it in the microwave...Great Video!

I love the fact that mathematicians change the rules so that their idea continues to work.

thanks... really interesting to have this explained properly.

beautiful and witty, every frame is a piece of art

this was really fascinating, thanks for sharing

Hi I'm a industrial designer and I'm very interested in John Edmark's work and nature's geometry patterns, and parametric arquitecture, I saw in a video that he modeled the blooms in rhinoceros, so I want to know if you know what plugin of grasshopper he occupy for do this ?, thank you

I don't use Grasshopper, just Python scripting language for Rhino.

@John Edmark hi, did you use a laser cutter to make your breathtaking pieces? And maybe a 3 D laser cutter as well? I'm totally mesmerized and if I could, I'd spend my remaining life doing what you do. Not going to get any sleep tonight. You're the best!

@Ekaterina Thank you for your kind words about my work. I use a standard 2D laser cutter. I've never heard of a 3D laser cutter. I use a 3D printer for the blooms.

@John Edmark oh, I'm so sorry, I meant to say 3D laser printer! Your work is so time consuming but I know you don't mind that. Working out the sizes of the pieces and programming them to the laser cutter is such an incredibly skilled task. You're so brilliant ! I keep watching your work again and again and don't need to see anything more in my life. Sorry to take you away from your work to answer my questions. Thank you so much! Best wishes.

This actually spooks me, like how deep does math go? We think we know most of it but how sure are we? Like it just takes one dude to paint by number and it just **works** so neatly (not knocking his art at all, i feel like paint by number is a very accurate way of putting it) I’m completely sober btw

Another reason - as if any more was needed - to absolutely be entranced by math. Amazing, amazing, amazing. But I repeat myself.👏🏻👏🏻👏🏻

Frankly you deserve as much credit as John

That's frankly not true

7:58 that has to be the best jigsaw puzzle ever (in some sense of "best"). You can have it be a single solid color, and still it would be possible to solve it, merely by sorting the pieces by size.

This is how i think the real shape of the fabric of the universe(s) works, but in every direction possible at the same time 🖤

24:07 This must be the millionth time I rewatched it. So visually and acoustically pleasing.

Wonderful, many thanks for this presentation. Jacob Yatsko does similar explorations, and i'm currently embarking on applying them to music. Personally, I believe that God Himself invented mathematics, and has put them into nature for us to discover. Here's an exploration of the Mandelbrot set by Dr Jason Lisle.

5:10 phyllotactic spiral can only be checkered if both spirals are odd 7:00 chromataxis 10:00 helicone 13:50 lazy susan

As a math teacher, I say thank you. Live long and prosper.

12:06 - Imagine applying this design to the construction of future residential skyscrapers; The 'Stair-Stepping' elements that appear with each 137.5 ° angular change (of floor) could be a series of indoor/outdoor organic garden terraces. In other words, when the structure is in 'Tower Mode', the gardens would be inside the structure and angled slightly (for efficient irrigation,like in vertical farming). I could see it as being something akin to an ultra-modern and efficient transforming indoor/outdoor terraced transformer of a building)... The future is going to be beautiful.

There's plans for another Skyscraper in Dubai that will be taller than the BUurj khalifa and will have a step-like design with 3 spokes and over hanging gardens

Not if socialists have anything to say about it.

Gotta love yooooootoooobe's new shadow banning practices. I can only see half of the comments, *AND(!)* I can't engage in discourse with people on this thread simply because I don't care for socialism. What a joke! This used to be a platform that encouraged humanity. It's a dried out husk of what it once was. I'm on my 15th account now for just talking as I would with a stranger at the bar.

imagine going into architekture with these insights

Amazingly beautiful. Math is in everything. Math, music and art. We must not forget nature. I perceive patterns in everything.

THAT, - was absolutely phenomenal!!! THANK YOU!!!

The trans tower mechanism is also a technique of mechanical analogue computers. There are some good ex US forces training videos on YT which explain these methods

Simply Amazing and Mesmerizing! Thanks for sharing.

there is a way of creating this illusion without the need for camera's or frame rates ,i wonder does the artist know this and has he ever considered adding a clockwork type kinetic motion to it .in my mind i see a waterfall that can be seen to run backwards without the need for camera trickery i think ill build it

How can I recreate this in a CAD program? I've done a lot of searching, but not finding good results (most is about golden rectangle). It looks like they all use 137.5 (I was able to use phi, inverse it, multiply by 2pi and subtract from 2pi to get the ~137.5), but I am especially interested in making a checkered (13:21) in either Autocad or rhino/grasshopper. Once rotated what do I scale by? Should I rotate the tile (if so, how do I make the tile, and place it based on it's size), or should I rotate the points, then connect them the make the tile? I'm good at traditional origami, but I find fractals difficult. Any help or links to other resources would be helpful. Thanks in advance!

Hey Scott. While watching this great talk, I started asking myself similar questions. I will explore more. If you have reached any conclusions that you can share, I appreciate sharing them to same me some time. I intend to draw them on GeoGebra. It has both 2D and 3D drawing capabilities.

@Scott Macri im going to try it in lightwave 3d i got the 137.5 easy enough but what would the size increase ratio from iteration to iteration be. lets say first piece 1 inch on a side what would that measurement be for piece 2 at 137.5 degrees away. not being a mathematician i still assume it would be a constant ratio . in lightwave there are ways to fake it with only making 1 piece using instances with a spline curve path and varying size attributes so if you do a tesseract the inside would obviously be the smallest and the outer ring would be the largest. but id rather be able to try this naturally im sure i could write a script to insert the sequence numbers to autogenerate. but even manually in Lightwave it wouldnt be too hard as the variables are all right there to insert.

@Q5Grafx Here is what I did: ibb.co/pykkBsv I think even if you haven't used grasshopper, you should be able to tell what is going on. For a long time I got stuck when I thought about it in terms of copying quadrilaterals. But when I just rotated a point by 137.5, and move it in slightly by some scalar (like you said), then that ratio will continue all the way around. Eventually, the points will spin around until I have a grouping of 4 close enough to make my first quadrilateral. In this case, 33 iterations. The amount I moved it in didn't really have any magic. I found 0.01 to work. So each rotation, my point gets 1% closer. After 33 passes, the fourth point of my quadrilateral is a good distance away to make something somewhat square like. You can tweak this number too; if you increase to 1.2% or 1.5%, your spiral will get steeper. Go too steep, and your brains ability to recognize spirals within dots will shift from a 13:21 to something lower. Decrease it too much, and the spirals will get shallower, making it higher than a 13:21. Did all that make sense? These are just my findings so far and I am not a mathematician either, so, I may not be explaining well. LMK if you have any questions.

I have no fucking idea but godspeed man

"Big whorls have little whorls which feed on their velocity. Lesser whorls have smaller whorls, and so on to viscosity." - Romilly Allen Check out the wonderful book titled *THE CURVES OF LIFE* by Theodore Andrea Cook Its over a hundred years old, but poignant as ever. You wont be disappointed. Promise.

I'll never look at my microwave the same way. Grateful for minds, the likes, of John Edmark and Paul Dancstep.

Fascinating. Thank you.

super talk, I'm just surprised that you didn't talk about the golden number (1+V5/2)...

Gorgeously beautiful designs, well presented in both image and word.

Finally, people who think in a similarity to me! It's almost like coming home.

A M A Z I N G!!! Thank you for sharing one of the God's secret of creating nature. Blessings.

19:02 That is amazing What a payoff of a whole lot of thought and a eureka moment

this video is evidence that any time someone mentions the fibonacci sequence, you are done with math and thinking, and its time to roll a doobie and wait until he starts telling us his theories of ancient alien astronauts

Amazing stuff thanks.

We find beauty in all things organic. When we play around with organic things, we find more beauty.

blowing vesels in my brain already love this stuff brother

I've tried the deep sleep meditation videos.....this one works the BEST! Thanks man.😀

bruh

Watching this on psilocybin or DMT makes everything a lot more logical.

This talk was so interesting.

Thanks. That's astounding and beautiful, with deep insights into the nature of life. tavi.

Phyllotactic spirals are amazing

Absolutely fascinating !

No, thank *you*. A beautiful, entertaining, and instructive video.

Incredibly beautiful!

I just couldn't stop watching this video until it ended.

I'm confused about 11:12. This appears to be a demonstration of an addition of AREA to the shape (by adding the new piece) and then rotating it backwards to reveal that the area is the same was it was before the addition. That's not possible. What am I missing?

Oh, I think John Edmark answered my question in another video. It’s not the same area, because it’s bigger. But if you rotate it backwards 137.5 degrees, AND scale it down slightly, it’s exactly the same shape.

Wish i could study this focused for 27 minutes

The configuration of lazy susans at 17:00 can be used to trisect an angle. I wonder if this can be translated to two dimensions so that this could be done using only a compass and straightedge, long held to be impossible?

math art is very surreal, like the universe showing off for you

Checkered is definitely the type of word that sounds alien when it's said too many times.

Yeah there's a relationship between nature and the musical scale. Golden ratio is in the musical scale too not just nature.

Absolutely fascinating.

0:47 can it be also used to Form a city based on this Look and what would be the benefits?

15:26 Engineered to being your cup or vessel back in its original orientation if synched up with typical 1-minute increments.

Anyone know if and what 3D modeling program they used for the blooms?

They are mostly created in code using Python scripting language and then displayed and tweaked in Rhino

🤯 Amazing! No words.

TIL I learned that if a you cross a mathematician with an engineer and they're inclined to make art, at some point you get an artichoke in a lathe.

mind blown!

They should use that pattern at 11:42 for making a pack of nested cookie cutters for gingerbread trees.

this is like word association math. idk why hes talking about this but its cool

the way the patterns overlap feels so 4D

Amazinng!!!

wow! wow... don't even understand how to find correct words!!! so great! going to check my favorite pine cone...

I'd like to see what causes Fibbonachi...what are the proteins doubg?

Made my day.

Excellent presentation.

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