Secretly Incredibly Fascinating - The Fibonacci Sequence

Episode Date: July 1, 2024

Alex Schmidt and Katie Goldin explore why the Fibonacci sequence is secretly incredibly fascinating.Visit http://sifpod.fun/ for research sources and for this week's bonus episode.Visit https://maximumfun.org/boco to get your digital art for Episode 200! There are also posters in the vault for Episodes 50, 100, and 150.Come hang out with us on the SIF Discord: https://discord.gg/wbR96nsGg5Get tickets to see us LIVE at the London Podcast Festival this September: https://www.kingsplace.co.uk/whats-on/comedy/secretly-incredibly-fascinating/

Hey folks, I have a fast heads up about my audio on this episode. It still sounds good. We only put out episodes where the audio sounds good. We did need to use my backup system instead of my usual system because one of my mic cables turned out to be frayed. So I like to give a heads up for people with amazing ears or with amazing headphones or speakers. You might notice I sound slightly different.

I sound good. And I hope you enjoy this episode about the Fibonacci sequence. The Fibonacci sequence, known for being numbers, famous for being numbers in math class some way. Nobody thinks much about it, so let's have some fun. Let's find out why the Fibonacci sequence is secretly incredibly fascinating. Hey there, folks. Welcome to a whole new podcast episode. A podcast all about why being alive is more interesting than people think it is. My name is Alex Schmidt, and I'm not alone because I'm joined by my co-host, Katie Golden. Katie! Yes! What is your relationship to or opinion of the Fibonacci sequence? I have a vague recollection of learning it in middle school. That's it?

of learning it in middle school. That's it. Yeah. That was pretty much me too. I've only had two like surprises about it lately. One is that some of my sources pronounced it Fibonacci, not Fibonacci. No, come on. Fibonacci? Yeah. Fibonacci. Fibonacci. Fibonacci. No, I've always heard it Fibonacci. Yeah. And so either way, I think it's fine. And we'll also talk about that name being kind of made up later. And then also there's just a modern artist I'll link about named Mario Mertz, who makes neon signs of the Fibonacci sequence in a lot of his art. And that's like in the main museum here in Beacon, New York. So I've seen it a lot. That seems neat. It's really cool. Yeah,

it's good. But thank you to Joka Strength on the Discord for suggesting this because it's truly Zipf. Never think about it. Yeah. It turns out it's all around us, but you don't get it brought up to you outside of one time in math class. Yeah. Right. Like I remember stuff like, hey, look at this curled up fern. That's Fibonacci for you. And I couldn't really grasp it. I couldn't grasp the significance of a fern. I'm just trying to look at a fern, man. Buzz off. Yeah. All right. You want me to do math while looking at this fern? Folks, most episodes, our first fascinating thing about the topic is a set of fascinating numbers and statistics.

This week, like every number is just part of a bigger takeaway and story. So for the Fibonacci sequence episode, there's no numbers and stats segment. It's kind of the whole thing, you know? It's just all of it. It's all numbers. It's all numbers. But the one numbers to say, just to establish what this is in case folks don't remember that one day of math class in seventh grade, the Fibonacci sequence is a sequence where each number is the sum of the previous two numbers. You just add the two numbers in front to get the next number. And so the first

set of these is 0, 1, 1, 2, 3, 5, 8. You can leave the zero off or not. It doesn't really matter. But starting with zero and then 1, 1, 2, 3, 5, 8. It's a good starting place because like the first number being 1, the sum of 1 and 0 is 1. Then the sum of 1 and 1 is 2. The sum of 1 and 2 is 3.

If you want a visual version, just rapidly Google the sequence. You won't get the rest of our show, but you'll see it. It'll make it easy. Yeah. Adding, adding the last two numbers, forming a pattern. And then it starts escalating pretty quickly because you get bigger sums, goes to 13, 21, 34, 55, 89. Oh, my social security number. Weird. That's you, Katie Fibonacci. If this was people's last name,

they'd just give them all that same number. That'd be a good bit over at the Social Security Administration. Yeah. You want to chop it up over at that bureaucracy, you know? The name sounds Italian, but I've never actually known any Italians with the surname Fibonacci. It is both made up and based on the name of an Italian person who really lived. Yeah. Okay.

That tracks. Yeah. And the closest actual last name is Bonacci. Okay. Which is a name that's around. Yeah, yeah, yeah. That sounds a little more accurate. But the fib, I have not heard of a fib Bonacci.

Yeah. Yeah, and it always just felt like kind of a random thing to me, having heard of it in math class, because why bother? Like, sure, you can do this, but why bother? Right, exactly. And then it turns out it's amazing because takeaway number one, the Fibonacci sequence contains other sequences of Fibonacci sequences

as well as a golden ratio. Hmm. There's Fibonacci sequences inside of the Fibonacci sequence. The golden family ratio. Wow. How did I forget that the golden ratio is like the next thing in my little doc? I should start a podcast called The Golden Ratio.

And I just talk about times I've been ratioed on Twitter. Honestly, a pretty good idea. I like it. Like horrible tweets and why they're horrible. Right, exactly. Yeah, it's really good. Let's make it happen. And the key sources for this part include a book called The Magic of Math.

It's by Harvey Mudd College professor Arthur Benjamin. And a book called A Brief History of Mathematical Thought by Oxford PhD graduate Luke Heaton. And he's also a science communicator rather than a professor. We'll have sources links of all sorts because seeing this is kind of helpful. Relatively quickly, this seemingly simple sequence is also full of other Fibonacci sequences, which is part of why people find this interesting and not just like a curiosity you can do. Explain to me how a Fibonacci sequence can contain another Fibonacci sequence. Like you have a series of numbers. How does that contain another sequence? There's multiple different ways. And one of them is that you get a sequence

if you square the numbers. If you square the numbers, then the resulting squares also add up to Fibonacci numbers. One simple version is if you start at the very beginning, right? We have one and one are just ones. So nothing happens when you square them. But then the next numbers are two and three. And so if you square two, you get four. If you square three, you get nine. And then the sum of those squares, four and nine,

the sum of that is 13. And 13 is one of the next Fibonacci numbers in the regular sequence. Oh, that's wild. Yeah. And then this repeats itself forever. If you do all the squares, then when you add adjacent squares, you get every other regular Fibonacci number. And I know that might be word salad and number salad in a listener's head without visual aids. And it is a thing. And we'll link about it if you want to like, see that in fine grain detail. No, I kind of get it. So it's like,

you have two numbers, you square them, then you add them, then that would be not the next number, but the number after that in the Fibonacci sequence. Yeah. In the regular Fibonacci sequence, it brings you down the sequence. Like the, I keep bringing up one, one, two, three, five, eight, because I think that's the easiest to digest start of the sequence. And so we did the squares of two and three, adding up to a Fibonacci number. The next pair, if you square three and square five, you get three squared is nine, five squared is 25. And when you add nine and 25, you get 34, which is in the regular Fibonacci sequence too. And this happens forever.

Right. Okay. So you get the numbers in the Fibonacci sequence that, Right. Okay. So you get the numbers in the Fibonacci sequence that, is there like a pattern to, at what point they occur after those numbers that have been squared? Like, so you have, you've squared those numbers. Now you get that number that is in the regular Fibonacci sequence, but like how many seems like it's a bit advanced in the sequence. Exactly. Yeah. So it's just every alternating regular Fibonacci number. You get 13 by doing this, and then you skip 21, you get 34. You skip 55, you get 89. You skip 144, you get 233. Because we haven't listed deep in the Fibonacci sequence, but they get a lot bigger really fast and in a way that feels kind of random

because you're adding up much bigger numbers all of a sudden. It's weird when you look at math and it kind of does things that seem like kind of random patterns. It's odd that this is a pattern in math, and it's a little spooky. Yeah, you'd think it would just be nothing, the Fibonacci numbers. Like, oh, okay, you made this list, I guess. But no, it has other features. It's amazing. Right. And another feature there is those squared Fibonacci numbers, if you just add them up continuously, you continue to get multiples of regular Fibonacci numbers.

I know that was confusing, but the squared numbers, like the first two are one and one, they just square to one. And then the next number is two, which squares to four. And then the next number is 2, which squares to 4. So if you add up 1 and 1 and 4, the sum of that is 6. And 6 is 2 times 3. 2 times 3 are the next regular Fibonacci numbers after 1 and 1. And this just keeps happening as you go. So if you add up the squares 1, 1, 4, and 9, you get 15, which is 3 times 5.

3 times 5 are the next regular Fibonacci numbers. This one is even harder to keep in your head if you're doing laundry, but it's another thing. Yes. I'm a person who struggles with auditory math. Does that make sense? Math when it's done out loud. I am too. So I kind of get it though. So you're adding up the numbers and then that sum of those numbers is a multiple of like one of the next numbers in the sequence. Yeah. Yeah. The sums of the squares equal sets of multiplied regular Fibonacci numbers. Okay. Okay.

And the other exciting thing about our sources here is the author of the book, The Magic of Math, Professor Arthur Benjamin. He also did like a five minute TED talk. And it's one of the rare TED talks I'd really recommend because it's really concise and the visuals help. And it's these two things we just described. Yeah. Slides.

Give me slides. If you don't trust us or just want to see it, you can see it. Alex is just lying about math just for the thrill of it. Just my own arcane grifts. Step two, question mark, step three, profit. It's's great it's going good and then the other sequence within the fibonacci sequence involves the golden ratio hey coined by katie golden yeah it's fun to have a last name that also means another thing makes it really easy for people to spell it oh well uh yeah this is spelled different and the golden thing is just referring to like the metal gold and people thinking this is magical uh it's also known by a greek letter uh it gets called the irrational number phi so not pi right but it's that same kind of thing. Those are the two most famous examples of Greek mathematicians being some of the first people to find an irrational number that is an interesting ratio.

Pi is more famous. It's 3.14 and so on. And it's a ratio with circles. Phi is a ratio that it works with many other shapes. And it came up on our pentagrams episode, on our triangles episode. It's a ratio between basically larger versions of the same shape and smaller versions of the same shape. Right. Like rectangles within a rectangle. Exactly. Yeah. And if folks have ever seen- Or curves within a curve. Like, yeah, like I've heard of the golden ratio being discussed a lot when it comes to Greek architecture. So columns within say like a larger building or like a cross section of Nautilus or something that, but yeah, that's all I remember.

of a nautilus or something that, but yeah, that's all I remember. I'm glad. Cause I had heard that too. And some of that is made up. It turns out. I was lied to. I knew it. And I was led to, to, this was really revelatory. And if folks have ever seen like a picture online where there's sort of a spiral, like a nautilus inside of rectangles that expands out. That is a diagram of the golden ratio in rectangles and in a logarithmic spiral. But it turns out a lot of people online have just like Photoshop that onto stuff where it's not actually quite this thing. I see. I want to know if Donald Duck lied to me because when I was a kid, I watched this like Donald Duck thing on math and there is a whole thing on like the golden

ratio. It was supposed to like make Donald Duck excited about math because Donald Duck was not excited about math. He kept swearing. Sound off in the Discord if you've seen the Donald Duck math thing. I think it was made in the 60s or something. I'm not from the 60s, but I watched it. I had the video, the VHS. Also, I really like the idea of Eddie Explainer that stars Donald Duck, who almost can't talk. Yeah. His role in this was mostly to make disparaging comments about math and then be proven to be the fool. The narrator was saying all the math stuff and Donald Duck was, you know, like getting thrust around.

Yeah, exactly. In various math scenarios. Yeah, what a guy. Yeah. And yeah, and this ratio is a real thing, especially in geometry and also parts of nature. The numbers of it, the beginning of it is 1.61. And you don't really need to know the rest of the digits,

but it's like pi where it goes on forever. Then I won't. But this ratio around 1.61, it turns out you can either multiply or divide Fibonacci numbers to get early on an approximate version of the ratio and then endlessly closer and closer to it in a way that is mathematically meaningful. I, hmm. No, say that sentence again. It didn't sink in. So like when you multiply or divide adjacent Fibonacci numbers with each other, you get versions of this ratio. So like the division version, if you have the list, if you divide

a Fibonacci number by the previous one, like the smaller one before it, you get something close to this ratio. Easy samples are like Fibonacci number eight. The previous one is five. So if you divide eight by five, you get 1.6. Exactly. Okay. And this ratio was around 1.61, blah, blah, blah. Going upward, 13 divided by 8 is 1.625.

21 divided by 13 is 1.615. 34 divided by 21 is 1.619. 55 divided by 34 is 1.6176. And so this seemingly just kind of chucked together a little math experiment of the Fibonacci sequence, it contains one of the two most amazing to Greeks and others mathematical ratios the whole way. That's weird too, because it's like, it's not the exact ratio, but it's close. Yeah. but it's close yeah that's even weirder that it's like not you know it doesn't it's like close to being a perfect pattern but it's not this first takeaway is very mathy and probably the most mathy part of the show the rest of this is just really weird expressions of this sequence

like i really wanted to establish that it has any interesting math in it at all, because then that explains how it is a thing in the world. Like, like you would, if somebody just came up to you and said, I invented a little game of adding all the numbers together, you would be like, stop bothering me, but it's more than a game. That's actually a thing. Yeah. And I want to emphasize, I'm not speaking bad about math here. I don't dislike math and I actually found it really interesting. I'm not like, I don't use math in my day-to-day life in terms of my career much. So, you know, I'm not like well-practiced in it these days, but for me, math is for some reason, very visual. I struggle so much just talking about it. And I

know people who, who for them math, they can like, I mean, my brother, for one, like they can sort of just in their head, visualize it while talking about it. And that's, that's wild to me. Boy, do I struggle. And you're like, picture two numbers. And, and I, I almost pass out because I'm like, picture two numbers with my brain. I'm the same way. And I think the other one like that is chess. Like there's those people who can do a chess match in their head and just hold all the pieces.

And one move in, I don't remember the board. I'm done. I'm out. My husband is good at chess and he'll try to teach me, well, these are the moves you want. And it's like, okay, I get all of that. And it's like, all right, but then why did you move that piece there? It's like, because I don't actually see anything right now. I'm looking at a bunch of little horses and a checker pattern and I'm going cross-eyed here.

Yeah. I'm going cross-eyed here. And I think part of all of us just wanting to see math so often and use our eyes to help, it is also part of a myth about the sequence and the golden ratio. Because takeaway number two, the Fibonacci sequence does happen in nature, but not nearly as often as the internet will tell you it does. Did they lie to me about the ferns? Are the ferns like nothing special? Especially like a fiddlehead fern where it's a little coil.

Yeah. That's more of just a coil. It turns out there's a bunch of things in nature and also art and architecture that are broadly kind of around 1.6 or related to Fibonacci or the golden ratio. But there's only a few still amazing cases of we think this actually iterating itself and happening. I see. Key source here is an amazing PBS show. It's called It's Okay to Be Smart. It's hosted by Joe Hanson. Other key source is the math book from Pythagoras to the 57th Dimension.

That's by science writer Clifford A. Pickover. Because when the human mind considers geometry, it can imagine lots of amazing perfect ratios and interlockings of things. But, you know, like life is a lot messier, squishier, asymmetrical. Perfect geometry doesn't always happen in the world. It does turn out that several plant species have evolved to grow their petals or leaves in shapes or numbers that do fit the Fibonacci sequence. That's a real way this has happened and it's amazing. sequence. Yeah. Like that's a real way this has happened and it's amazing. It's very cool because even though, like you said, like nature's not necessarily perfect in terms of geometry, there's still a lot of really uncanny geometry. Like nature loves symmetry. Like when you look

at animals, a lot of them are bilaterally symmetrical. A lot of them are, you know, can be even more symmetrical like a starfish, right? And like you said, like all of these ratios happen and you look at sort of the, it's interesting because a lot of it is just functionally the easiest way in which that plant or animal can form and develop. Like when you're thinking of like the cellular development, like in the embryo or a young plant or something where it's like, you know, these, these cells are dividing and, and, you know, growing these things. It just turns out that that is the most efficient way for growth to happen. And, or, or in terms of structural integrity, like this is the most structurally sound. So an example that I think is easy to visualize,

easier than visualizing embryonic development, because that's tough is, um, is beehives. Like, you know how like beehives have those perfect little, uh, what are they like little hexagons? Yeah. The honeycomb or whatever. Yeah. Yeah. The honeycomb, what are they, like little hexagons? Yeah, the honeycomb or whatever. Yeah. Yeah, the honeycomb. It looks really, really perfect. And it's like, well, why do bees make, machine this like really, really nice, perfect, I don't know that this has anything to do with the golden ratio.

It's just an example of like why there are certain structures in nature. And it's like, well, they would make, basically they make little holes, right? But then as they squish more little holes together of the same size, then it squishes them into these hexagon shapes. So, and then that's how you fit that mini within this area, right? So it's like, that's, it's just a structural way in which to fit a bunch of holes together of the same size. I didn't know that's how the shape happens. That's awesome. Yeah. So again, I don't know that that has anything to do with the golden ratio.

It probably does not. But that is... It does not, yeah. Don't feel bad, bees. We still love you, even if you're not Fibonacci. You don't got to be Fibonacci or Gucci or any-chee. And the ways it has been F fibonacci numbered has tended to be like spirals of plant stuff right so maybe the pine cone right yeah apparently the pine cone is

one oh okay okay and a similar one is the overly similarly named pineapple pineapples have scales on the outside and yeah oh i'm just understanding why it's called a pineapple jesus seriously yeah because because i think they're pretty genetically different but humans no they're pine cones are from conifers pineapples i thought were from sort of a bush they're not even from a tree yeah it's all's all lies. Yeah, yeah. Right. Oh my God. I can't believe pineapple. I get it because they look like pine cones, but they have flesh like an apple. My God. Okay. Yeah. And I'm reeling. This one's hard to describe with words, but we'll have pictures, especially for pineapples of but we'll have pictures, especially for pineapples, of the scaly parts of a pineapple or those nubs of a pine cone. If you count the spirals of that, the spirals are a Fibonacci number usually. If you go in one direction on the outside of a pineapple, you get eight parallel

rows of scales. Another direction, it's 13 rows, like kind of a basically vertical direction. There's 21 rows and 8, 13, 21. Those are all Fibonacci numbers. There's also a lot of flowers with an amount of petals that is a Fibonacci number. Like there'll be five petals or eight petals or 13 petals. And then also a lot of the leaves on stems of some plants will be arranged at angles that fit the Fibonacci numbers and the golden ratio. It turns out you can turn the ratio into a golden angle, like a protractor angle, which is about 137.5 degrees. That's my new hard-hitting talk show, the golden angle, where I try to get the angle on recent news events. And Fox News is like she has totally different politics from us, but the name's so good. We just have to air it.

We have to air it. I'm stuck. Right. Nuts. And the geometric golden angle. stuck. Right. Ah, nuts. And the geometric golden angle, it turns out if you just kind of go around a stem, like it's an axis and go leaf, leaf, leaf, leaf at that obtuse angle of 137.5 degrees, it matches a lot of plant growth. We think those plants might have growth hormones that keep the new parts spread out from each other. We don't exactly know really.

And at the same time, any of this plant growth fitting Fibonacci stuff, you know, nature is squishy and inexact. And if a plant is squishy or inexact from the sequence, it still lives. Like this is just kind of the shape that they've happened to do, sort of like bees have happened to do the non-Fibonacci honeycomb. Yes. And Johansson points out that there's tons of other plants that don't do this kind of thing, like maize, aka corn. It's just kind of squares. It's not anything to do with this, and that is also good in nature too. Right. It's sort of like water. When it moves and encounters wind resistance,

it forms a teardrop shape because it is conforming to that wind resistance. So like plants, a lot of plants probably have these patterns. They don't have to have them, but they do because they are conforming to some resistance in some kind of way, like either structural resistance or structural pressures. or structural pressures. There's a concept in evolutionary biology called spandrels, where it's like you'll have some kind of, when you're in architecture, you have like an arc, like an archway, and then you have within a rectangular sort of door,

like you have the arch or the archway, and then like between the arc and the square, the rectangle, there's that like little corner. That's like one part of it is like a curve and then, and then basically a right angle. And sometimes, and that's like a spandrel. You don't actually need that structurally. It's, it doesn't actually serve like a structural architectural purpose. And sometimes they would like decorate it and stuff, but still there's no like architectural purpose to have it. It's just because that's what occurs there when you have an archway and then a rectangle. And so that I feel like that explains a lot in terms of evolutionary biology, where you

have like certain structures where it's like, oh, why does it have to be this way? It's like, well, because just that's how, as you're constructing, say, a bunch of nubs that have to interlock in this way. That's just how they have to, like, go. That's such a perfect term for this. Yeah. Yeah. It's exactly why some plants do some Fibonacci in some species. And some of them don't.

And others completely don't. And it's all just what they found. And apparently with leaf arrangement in particular, it's probably for catching the most sun with the fewest gaps. And so sometimes that's golden ratio angle stuff. And sometimes it's not totally different. It is some form of a pattern, right? Like it's kind of like symmetry, like symmetry is a type of pattern where you have a one-to-one ratio, like on either side of this line of symmetry. Yeah.

Like in an interesting pattern, but one that's just born out of necessity and also the ease in which something can develop during the embryonic phase. And so, you know, you can kind of look at the Fibonacci sequence as something similar to that, right? It's not a magical number, but it's something that maybe is just more likely to happen when you have to cram a bunch of leaves on a plant. And it seems like a bunch of people just have run with this in a magical direction. And so the other part of this takeaway is folks should be relatively skeptical of claims that the golden ratio is all over nature. And it seems like part of the myth comes from people deciding that either the name golden ratio or the real geometric diagram of spirals creating more rectangles is just cool. Like it's such a cool name or shape.

It must be everywhere. It turns out nautiluses, they have a logarithmic function for their shell shape, but it's not quite golden ratio stuff. It's just super similar. And we just are not aware that a separate cool mathematical thing is happening. Right. And I thought that until I researched this, like I thought it was, oh, the golden ratio, like that nautilus thing. But no, it's just different.

Yeah. Yeah. I mean, I think also like a lot of times the golden ratio is used in terms of art and architecture as like, this is something a lot of artists do because for some reason, like we really like this look, but it's like the Nautilus, like, yeah, that's pleasing. And maybe there's sort of a math behind it, but also ultimately like the reason we look at a pineapple and go like, that's cool, isn't because it's a Fibonacci sequence. But the reason we like Fibonacci sequence type things is

because it's so often found in nature and we like stuff from nature because we have to like stuff from nature so that we can go out and eat it and collect it. Yeah, that's right. Yeah. With art and architecture, apparently a few relatively modern artists have consciously used it, but just because they heard it's beautiful. Salvador Dali used it some in art and Le Corbusier used it in architecture somewhat, but like some earlier examples, people pull like the Egyptian pyramids, nothing to do with it. The Da Vinci drawing of the Vitruvian man, apparently that man is in like a circle and a square. Apparently the circle and the square would be laid out differently if they actually fit the golden ratio and Fibonacci sequences. It's just that Da Vinci read the work of Vitruvius, a Roman doctor,

and then drew something he liked and put some shapes around it. But people just figure any shapes like that, it's probably golden because that name is cool, you know? Yeah, it is a cool name. It is for really cool people. Only cool people have that name. But also, hello, wake up, Da Vinci. People don't have four arms and four legs.

It's basic biology. Yeah, pull it together, man. Yeah. Yeah, come on. You've seen a person. People have really run with this in a creepy way with human bodies in general. Uh-oh. They've been like, two is a Fibonacci number and we have

two eyes or five is a Fibonacci number and we have five fingers and all that's just made up. Yeah. And they've also put the spiral over like the faces of celebrities and been like, see the proportions are like the rectangle. And no, it's just that they have a relatively symmetrical face or something. And it's, there's nothing there. The wildest claim is that apparently the internet started saying that if you measure a DNA strand, the, in like the incredibly tiny units, it's called an angstrom is the unit of length for that size. But they claim that the height and width of a single spiral of human DNA matches a golden rectangle and it actually doesn't. Okay. They went and checked and it's like close, but it's not that

ratio and it's not what's going on. Literally the writer Dan Brown of the Da Vinci code books is one of the kinds of people pushing the idea that everything is golden ratio in the world. Oh, I was going to say I was. That's really funny. It's like nature Illuminati stuff. That's really funny because I was going to earlier I was going to say, is this this is coming from Dan Brown? Because like he would do that.

Yeah, it's Dan Brown stuff. It's Dan Brown stuff. Dan Brown, by the way, Dan Brown's sort of depiction of what it's like to be an academic professor is so unhinged and funny where it's like, yeah, I'm just like, students are, you know, swarming around me saying how smart I am and like, like just having their minds blown and lecture every day. And it's like, it's really not, it's really not like that. He pushes that harder than fully the Indiana Jones movies.

Like they get him out of the classroom pretty fast because it's not that believable. The one time you see him and they're being ogled. It's like, OK, come on. Like, yeah, it's creepy, man. That's weird. That's that's weird. And you're wrong. We're so, I guess, like answer oriented as a species, we really want there to be like one master equation,

one simple master equation that describes everything. Because, you know, I'm actually, I occasionally do a podcast with Daniel Whiteson called Daniel and Jorge Explain the Universe. It's an astrophysics, particle physics podcast where we talk about stuff. And it's really interesting to me how, I mean, like if you're looking for like an equation to solve issues of the universe, it's just it's such complex math. It's such complex sort of theory and stuff. It's, you know, it's not like you can have some really simple equation that just explains everything. It really, truly does not work that way. Yeah. And it's the more interesting thing that several different equations explain everything. Right. But none of them covers everything, everything on its own. And you have to like learn a lot of equations and then, you know.

Yeah. And even once you have equations that explain stuff, then like there's this huge problem in, in physics where they try to make quantum mechanics and general relativity, the two big sort of things in physics that describe really small things and really big things. And they try to make it like the math for those two things work together and it doesn't. So it's like, uh, which is cool. It's very cool. It's cool. It doesn't make sense. Very frustrating,

but very cool. Cause it means there's still so much room for discovery, but yeah, we, it's like, we so much want that magic number, right? Like ultimately that's so unsatisfying because it doesn't make any sense to have just one little math equation or one pattern or sequence or something describe everything. We want that, but at the same time, do we? Because that would be kind of boring, wouldn't it? Right. It would be boring if everything is that spiral of rectangles. Yeah. Because I'm part of the universe. I don't want to just be a spiral of rectangles. Yeah. Because I'm part of the universe. I don't want to just be a spiral of rectangles. Yeah. I mean, it depends, I guess. I'd be okay being a spiral of rectangles if I could still like have ice cream and stuff. Oh, now I'm tempted. Oh boy. Oh, well. It's soft serve Fibonacci.

And yeah, so that's how much or little this is around you. And it's cool how much or little it's around you. And we're going to take a quick break and then return with why any of us have heard of it at all. In particular, exploring the guy and also how anybody heard of this sequence. Okay. I don't think there's a guy named Fibonacci that has to be made up. It kind of is. Great. But there was a guy named Fibonacci that has to be made up. It kind of is. Great.

But there was a guy. All right. Lied to you again. Folks, as you know, direct listener support is the entire reason that this podcast exists from the very first episode all the way to episode 200 and now beyond. That's the only way this show is a thing. So please go to MaximumFun.org slash join. If you are not yet someone who does that support, you get to have the warm feeling of knowing that you make this show a thing and also a bunch of amazing stuff, too, like tangibly. So it's a wonderful thing. Please check that out, MaximumFun.org slash join.

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And we are back and we are going to both really celebrate Fibonacci and also shine light on why there's a bunch of mythical stuff about Fibonacci. Right. Was his real name just like Al Johnson and he wanted a cooler name? So he's like, no, no, no. I'm Alfonso Fibonacci. Yeah, let's explain his name first with takeaway number three. Fibonacci was never named or called Fibonacci. I knew it. Liar.

Also, he lived long enough ago that names were kind of different than at least the standard American and English-speaking world names of a first name that's your given name and a surname that's your family name. I see. Okay. What time period was this? He lived in the 1100s AD and the early 1200s AD. Okay. So that's a bit ago. Yeah. Like less than a thousand years ago, but not a lot less. And he was an Italian man. Okay. Most people would have called him something like Leonardo of Pisa. Okay. And one obstacle to him being famous as a Leonardo is that Leonardo da Vinci came later. So that's maybe a little bit why we call him something else.

But there are so many Leonardos. So, you know, you can't just like corner the market on the name Leonardo. Yeah, I agree. Also, da Vinci is just from from Vinci. True. It's basically theci is just from Vinci. That's true. It's basically the same kind of name. Right. So he was never called Fibonacci in his life.

Centuries later, people invent that name. And if people have heard our episode long ago about surnames, they know that that was not totally standardized in Europe in the 1100s. That existed, and also the ancient Romans did a bunch of surnames, but this guy would have called himself maybe Leonardo of Pisa because that's his Christian given name in his home city. And his most famous book was a book called Liber Abaci written in Latin. But in that book, he called himself something else.

He called himself a Latin phrase of Filius Bonacci. Filius Bonacci. Okay. What does Filius Bonacci mean in Latin? Yeah. A key source here is Stanford professor Keith Devlin. He says that the most literal meaning of Filius Bonacci is son of Bonacci. Okay. And then the way he was using it is the similar but distinct meaning of family of Bonacci. Okay, interesting. Yeah, in modern Italian, figlio is son, and figlia is daughter, and figli are, you know, offspring, children's. are, you know, offspring, children's. Yeah. And it's pretty much because Italian is so influenced by Latin, it's pretty much that meaning. And this name gets coined in 1877 by a guy who made a contraction of Phileas Bonacci. I see. And called him Fibonacci.

Okay. That's, you know, actually that feels more legitimate than I thought. Like someone just trying to rebrand this to make it sound cooler than it was, right? Like it's not completely made up. Yeah. It's his real name and he was a real person. And also if you shouted Fibonacci in his house, he wouldn't look up. Right. It's not his name or how he thought of himself or anything. His made up name is famous to us and got coined much later for a few reasons. One of them is takeaway number four. The person we call Fibonacci revolutionized European mathematics by gathering other people's ideas. Okay. Well, you know, a curator of other ideas. Yeah. And it's like pretty positive for what it is. It turns out Fibonacci advanced European math

and by extension science and society in a huge way while not inventing or coming up with much of anything. But he was also like very open about this is where I got these ideas and here they are. So that's pretty good. Then that seems, yeah, that seems extremely legitimate. It sounds like he's just collecting everything that has been done right up till that point that's relevant and then trying to spread it around that that you know it sounds like he's pioneering the sci-com community yeah pretty much yeah like like a mathcom sci-com guy and yeah and in a time when that was harder because it was very hard to print books or travel or anything so you know it's cool i'm saying we're as cool as fibonacci

is what i'm saying, Alex. Yeah. I mean, you have your own ratio named after you. I do. I've got, it was named after me in 1989. Yeah. And, and again, this guy we call Fibonacci, he was really named Leonardo and from the Fibonacci family. His key book was a book called Liber Abaci, and he wrote this in 1202

AD. Here's the first line of the book, translated to English. Quote, these are the nine figures of the Indians. Nine, eight, seven, six, five, four, three, two, one. With these nine figures and with this sign zero, which in Arabic is called Zafiram, any number can be represented as will be demonstrated. End quote. It turns out as late as 1202 AD, Europeans were using Roman numerals, like to do math.

Oh, Jesus. They didn't have, since this is a verbal show and stuff, we've just been using numbers in a way that they did not. They didn't have the probably most accurately called Hindu-Arabic numerals that we all use today. Arabic numerals are so superior to Roman numerals. They're so much better. God, Roman numerals suck so bad.

Yeah, and like other cultures in particular, East Asian character scripts have their own numbers that are also far superior to Roman numerals that are still used today. Like people like the Mayans had zeros and had base systems that are better than Roman numerals and Incan people tied knots in a way that was better than Roman. Everybody had something better than Europe until relatively recently. But did they come up with the light and refreshing Caesar salad? They did not. So take that. There you go.

Everyone, including ancient Rome. Yeah. They wouldn't have even had Caesar salad, right? Because it seems like half of the ingredients of Caesar salad, they were probably post-Columbian exchange. Yeah, yeah. Caesar salads would be a good show. I know the basic story of a hotel guy named Caesar Cardini, but anyway, yes. Yeah, it was just so bad doing math in Europe. And that also helps explain the origin of calling that circle ratio pi and calling the golden ratio phi is that the numbers they had to work with were Roman numerals and then some Greek letters that they assigned to a couple important irrational ratios. That was all they had. Europe was a mess at this point.

Just they're drinking doo doo water, using Roman numerals, kissing rats on the mouth. Yeah. Yeah. Like the Western Roman Empire ended in like the 400s or so. And then 800 years later, they were using Roman numerals still. No one was making them. They just didn't have better systems. It's so bad to live there. And it turns out that it took until as late as the 1400s for these numerals that Fibonacci helped introduce to really get going in Europe. Still, there was a lot of resistance to it. There were also people who claimed that those numerals, and in particular, using them to make decimals, would be used by scammy businessmen to trick people out of their money. So we should

stick to Roman numerals and whole numbers. How would that scam people? Like, what was the logic there? Simply that the math was more advanced and new. Oh, I see. I see. And like decimals, you can do, I guess, the kind of true thing of like shaving parts of cents off transactions. And I guess most internet businesses do that. Yeah, no, that's yeah. They were kind of right. They were kind of right. Right. Like like one ninety nine ninety nine. You know, like you put you make it ninety nine cents and it feels less than two dollars. I love it because the anti-Arabic numeral people were both correct about business scams and ultimately wrong because modern math makes life better. Like they were right and wrong in a very profound way.

It's worth it to like be slightly scammed into getting something for $199.99. Yeah, exactly. And so those were the two subjects of Fibonacci's main book. And he became humongously famous in his own lifetime for this and was celebrated just for writing a book about Arabic numerals and decimals. Have you guys seen these numbers? Look at them. Like, look what you can do. It doesn't take forever to write out 28. Very quick. God.

And Fibonacci could do math and stuff, but he didn't invent any of this. His contribution was that his father was a wealthy merchant. Both of them did business in places like. Nepo baby. Yeah. And like both of them did business in places like Muslim North Africa, in particular, what's now Algeria. And then he saw what Muslim traders

were doing with numbers and decimals and wrote a Latin language book about it. So like he just let people know. You got to see what these guys are doing with numbers and decimals, you guys. You got to see it. Their hands aren't cramping from all the Roman numerals. Yeah. And he should be famous because he made everybody's lives better in Europe. And also it's for stuff that is not the Fibonacci sequence and was not his idea at the same time. And we also call him a different name than he really was. It's a really complex actual reason he should be famous. Right.

Yeah. One could argue a more important reason, I guess. I don't know. I guess you could argue against that. But who did actually do we know who actually came up with the Fibonacci sequence or is it just not very clear? Not him. And it's not clear. that was parallel invented a lot, especially once you have sort of Arabic numerals or any kind of symbolic numbering system. It probably was something, you know, a few mathematicians realized. Yeah, and that's part of our final takeaway number five.

Fibonacci did not create the sequence and only talked about it once in a really weird way. Like pervy way? Was he perverted about it? Sort of, yeah. Oh, okay. That was a joke, but all right. It turns out that in his super famous book that did the huge achievement of spreading good numbers and decimals in Europe. One page had one thought experiment about rabbit reproduction that expressed the Fibonacci sequence of numbers.

Okay. All right. And he didn't come up with it. And he just like threw one thought experiment in about rabbits having sex with each other forever. Okay. And then making more bunnies. And I guess the more bunnies are the later numbers in the Fibonacci sequence. Exactly. Yeah.

Like you said, a few people came up with this sequence of numbers independently. We're not sure who got there first. independently. We're not sure who got there first. We know one example is in the year 1150 AD, a poet in India named Hemachandra, he was trying to figure out poetic rhythms in the Sanskrit language and different ways you can do that. And he stumbled upon Fibonacci sequences when he was counting out rhythms and syllables. Oh, wow. That's really cool. Sanskrit poetry. Whoa. As much as there was complicated math at the beginning of the show, there's an easy way to generate this sequence. You just add up the numbers in front of each other. You can get there. And so we don't know who, but somebody besides Fibonacci got there first. Hema Chandra did it in 1150.

Yeah. I think, again, there there is something interesting that like music or poetry and rhythm and stuff that we really enjoy may also be reflected in the fact that there are certain patterns and stuff found in nature that we also enjoy. Yeah. Poetry and music have a lot of math to them. And yeah, it's just legitimately cool. People don't need to draw goofy golden spirals on stuff that doesn't have it. Just find the actual cool stuff, please. And so Fibonacci just heard about this sequence of numbers, and he also didn't think of it as important to him or a main thing for him. On one page of this big book, Liberabaci, he wrote a

thought experiment, which is really gross. Here's the thought experiment. Imagine you have one pair of baby rabbits, and this is all about pairs of rabbits. You're thinking of, I have one pair. If they need one month to mature to sexual maturity, and then each time they mate, it takes a month and produces another pair of baby rabbits. And your rabbits never die from that one pair of rabbits. How many rabbits can you get forever? I see. I see. So that's kind of like a, it's like exponential rabbit growth with a lot of incest, but you know, they're rabbits.

Yeah. The two biggest like problems, if you ever tried to make that real, is the massive incest. And then also just actual rabbits produce more babies per litter. And so none of it really makes sense in nature. But his thought experiment, if you're not counting total rabbits, if you're counting total pairs of rabbits, the parameters of a pair needing one month to mature and it taking one month per new pair of rabbits from an existing pair. There's diagrams online, you can find them of just, it makes a family tree of rabbits where it's a Fibonacci sequence of numbers of pairs. And that is the only time he ever talked about it. Okay. Even though that seems like the incest part, it seems kind of pervy.

Rabbits are not above that, though. I don't think that would be preferred given the incredible genetic bottleneck that you would have. Yeah. But I also like that it's an even less appealing way of teaching Fibonacci numbers than just the regular way. Yeah, it just seems overly complicated. Stop. Yeah. Why are we talking about rabbits now?

I'm confused. Why are the rabbits immortal? Everyone's middle school math teacher did a better job of teaching it than Fibonacci's book. Just tell me to add the numbers in front of each other. I don't need to think about this weird rabbit prison where we're like forcing them to bait. Right. Just show me a pine cone and say like, look, Fibonacci. And I'll be like, I'll take your word for it. Yeah. Okay. Great. Cool. I believe you. I believe you. Let's go back inside. I don't know. Sir, put the pine cone away. I believe you. So that one page of a much more important book is ultimately how later people name this after this guy and make a new name for him.

Because apparently the book and the impact of Leonardo of Pisa kind of get forgotten for some centuries. Also, people discover the true importance and amazingness of the math of the number sequence. And so wrap around to 1877 AD, relatively recent, 1877, a French mathematician named Edouard Lucas decides that, hey, we should just like honor this guy, hey, we should just like honor this guy, this Italian Leonardo of Pisa for his mathematical achievements. And no one's put a name on this number sequence yet. OK. And so since he mentioned it one time ever, and since it's kind of too late to name like Arabic numbers after him or something, not that we need to. Yeah, you can't like we're calling math Fibonacci now. need to. Yeah, you can't like we're calling math Fibonacci now. Right. Like like we can't just name all of math that or like name Europe getting better that. Yeah. Although if you renamed math

to Fibonacci, that might make it seem cool. Right. Like, man, this this feels cool, like a like a fancy purse or like a pasta or something. So it might make it more appealing. Yeah, it has like a perfume commercial vibe, I guess. We could do it. Yeah. Like math by Fibonacci. And that's what they say to the camera. I did a little head move too.

He did. You guys all missed it, but it was very good. But so this guy says, hey, why don't we name the sequence? Because it's mentioned one time in a weird way in the book. This is a way to honor the guy if we name the sequence after him, because it's not like claimed yet. And then this guy coins a contraction of Phileas Bonacci. I see. I see. OK. And then the actual guy, Leonardo da Pisa, comes crawling out of his grave going like, really? Like the rabbits thing? Man, that was one of the pervious things I wrote. What about the cool Arabic numerals? That's the absolute low point of my work, guys.

Right. Guys, I just did that when I, honestly, I was like a little bit too far into the mead. I was like, man, rabbits, right? What if you had a rabbit sex pit? Man, we were we're just like really deep into that mead, man. Yeah, they almost kicked me out of pizza for that one. I was almost Leonardo outside of the friggin city. Am I right? Nowhere. outside of the friggin' city. Am I right? Da nowhere!

Folks, that is the main episode for this week. Welcome to the outro with fun features for you, such as help remembering this episode, with a run back through the big takeaways. Takeaway number one, the Fibonacci sequence contains other sequences of Fibonacci numbers and a golden ratio. Takeaway number two, the Fibonacci sequence happens in nature, but not nearly as often as the internet will tell you it does. Takeaway number three, Fibonacci was never named or called Fibonacci. Takeaway number four, the person we call Fibonacci revolutionized European mathematics and life

by gathering other people's ideas and printing them in Latin. And takeaway number five, Fibonacci barely has anything to do with the Fibonacci sequence other than one thought experiment about rabbits. Those are the takeaways. Also, I said that's the main episode because there is more secretly incredibly fascinating stuff available to you right now. If you support this show at MaximumFun.org. Members are the reason this podcast exists. So members get a bonus show every week where we explore one obviously incredibly fascinating story related to the main episode. This week's bonus topic is two quick stories about Fibonacci poems and Fibonacci stock market stuff, maybe. Visit SIFPod.fun for that bonus show, for a library of

more than 16 dozen other secretly incredibly fascinating bonus show, for a library of more than 16 dozen other secretly incredibly fascinating bonus shows, and a catalog of all sorts of MaxFun bonus shows. It's special audio. It's just for members. Thank you to everybody who backs this podcast operation. Additional fun things, check out our research sources on this episode's page at MaximumFun.org. Key sources this week include a miniature library about math, the book The Magic of Math by Harvey Mudd College professor Arthur Benjamin, the book A Brief History of Mathematical Thought by Oxford PhD graduate and science communicator Luke Heaton, the book The Grapes of Math by math communicator and lead math writer for The Guardian

Alex Beos, And lots of digital resources too, in particular an amazing episode of the PBS show It's Okay to Be Smart, hosted by Joe Hanson. That page also features resources such as native-land.ca. I'm using those to acknowledge that I recorded this in Lenapehoking, the traditional land of the Munsee Lenape people and the Wappinger people, as well as the Mohican people, Skadigook people, and others. Also, Katie taped this in the country of Italy, and I want to acknowledge that in my location, in many other locations in the Americas and elsewhere, Native people are very much still here. That feels worth doing on each episode, and join the free SIF Discord, where we're sharing stories and resources about Native people and life. There is a link in this episode's description to join the Discord.

We're also talking about this episode on the Discord. And hey, would you like a tip on another episode? Because each week I'm finding you something randomly incredibly fascinating by running all the past episode numbers through a random number generator. This week's pick is extraordinarily recent. It is episode 200. That is about the topic of helium. Fun fact, we use super cooled helium for basically every high tech and advanced and awesome process in modern life, just all the time. So I recommend that episode. I also

recommend my co-host Katie Golden's weekly podcast Creature Feature about animals, science, and more. Our theme music is Unbroken Unshaven by the Budos Band. Our show logo is by artist Burton Durand. Special thanks to Chris Souza for audio mastering on this episode. Special thanks to the Beacon Music Factory for taping support. Extra, extra special thanks go to our members. And thank you to all our listeners. I'm thrilled to say we will be back next week with more secretly incredibly fascinating. So how about that? Talk to you then. Maximum Fun A worker-owned network

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