Introducing Creative Squares

Transcript

Welcome to the Art Against Mental Illness podcast. My name is Alex Loveless and this is my podcast about the healing powers of art. For artists, art lovers, the art curious and anyone with an interest in mental health and well-being. Hi everybody, I’ve got something a little bit different for you this week. Some of you might remember episode 27 back in December where I interviewed my friend Mark Burden. It was a great conversation, we touched on all sorts of issues, but one of the things we kept coming back to was the intersection between art, science, technology and mathematics and we enjoyed that conversation so much we got together and decided that we would start our own podcast that focused on exactly that, the intersection between art, science, technology and mathematics. And so we’ve done that and our first episode has just been published. The podcast is called Creative Squares and it can be found wherever you find your podcast. So this week I’m going to share episode one of Creative Squares for your delectation. If you like it go and follow it, rate it, review it and share it on all your usual places and more episodes will come. I’m not sure what sort of schedule this is going to go on. We’re still finding our feed, it’s still early days, but if you subscribe to it the next episode will just pop into your feed when it comes out. So without further ado here’s the first episode. It’s called The Golden Ratio, Aesthetic Alchemy or Creative Conformity and we discuss the golden ratio, what it means, what it is, how it’s derived, how it’s used and we take a slightly critical view on its place in culture, the arts and mathematics. I’m really pleased with this and I really hope you enjoy it and I’ll be back soon with a normal episode. Thank you. Welcome to Creative Squares where we discuss the intersection between art, science, maths and technology. I’m Alex Loveless. I’m Mark Burden. To kick off this podcast we’re getting to cover one of the most well-known art maths crossovers, the golden ratio aka the golden section aka phi aka 1.6180339877 etc. The reason this is such a great starting point for this podcast is it turns up not only in maths and art but in biology, engineering, architecture, computing, music and points towards Renaissance, Da Vinci, Dali, Dan Brown and presumably some other folks with names that don’t start with DA. But are the golden ratio and other compositional paradigms merely a tyranny of conformity and an illusion of familiarity? That’s what we’re going to discuss today. But before we do let’s refamiliarize ourselves with what the golden ratio actually is. To understand the golden ratio you first need to understand something called the Fibonacci sequence. Mark, do you want to take us through what that is and why it’s important? When I think about Fibonacci I think about the natural forms in life and kind of like growth formations in nature, specifically plants. And Fibonacci is a number sequence that is defined by a series of numbers and I’ll just reel them out 1 1 2 3 5 8 13 21. And you get the next number in the sequence by summing up the previous two. So in this case we get the first two numbers in the sequence 1 plus 1 and then we sum them up to get the third number which equals 2. And then to get the next number in the sequence we sum up 2 plus 1 to give us 3. And then we get 3 plus 2 equals 5 and so on. So we get an infinite number series based around integers and it just carries on like that. And when we think about how that could be reflected in nature you know if we look at simple things like the formation of a tree going from its main trunk to all of the little twigs and branches right at the end it follows more or less a kind of like Fibonacci sequence where the main trunks get broken into two and then into three and so forth and you end up with loads of little twiglets and bits at the end that you know in springtime transform into leaves. Yeah absolutely and we see it on the petals of flowers tend to be one of one or other of the Fibonacci numbers and it turns up in all sorts of weird places. I think people see it almost everywhere. It’s one of those numbers that mathematicians get quite excitable about a bit like pi and prime numbers and want to know as much about as possible. But how does that the Fibonacci sequence relate to the golden ratio? A good question and in fact it’s to do with the the way in which the proportions are built out. So if you think about a rectangle there’s a particular proportion between the shorter side and the longer side that is harmonious and that relates to the the number phi. So if you take one side and divide it by the other side you’ll get the number phi which is different from pi and very easy to confuse the two if you’re not used to phi and pi but phi is that number the 1.618 dot dot dot which is a regular number and is as long as as pi but yeah it’s that ratio. So it creates a kind of like harmonious balance when you’re looking at those two aspects on a rectangle. So shorter side versus longer side and it’s the proportion of which when you’re looking at the two that creates this level of harmony that we see in nature. So we have this rectangular shape with a spiral inside there that has been used most notably by people like Leonardo da Vinci but many many others to aid composition of pictures and paintings. And I guess the theory here is that since the Fibonacci sequence is seen so frequently in sort of nature and in the real world that it has some sense of aesthetic beauty that is inherent within nature i.e. we find nature beautiful the Fibonacci sequence to stroke the golden ratio turns up in nature a lot and therefore if you have your painting composition aligned with the golden ratio then you draw a line between a comparison between your picture and the natural compositions in nature and behind all of that we have this mathematical construct the sequence called the Fibonacci sequence. Yeah you’re spot on there Alex and again you know when we think about the way in which the rectangle for the golden ratio that we’re used to seeing in fine art and in compositional devices for fine art it’s made up of those series of squares you know so you get the one plus one and creates another square of two plus two and that creates another square of three plus three and five plus five and then we get the the square of eight plus eight so you’ve got within this proportion rectangle a number of focal points which is different from what we potentially get with just a standard square and I know that we both compose our art a lot of the time in terms of standard square and the the thing about the square is there’s really only one center of focus which tends to be the central point but with the the spiral shape which is inherent in the Fibonacci series and the golden ratio you get different points of interest and typically this is where Leonardo and those early Renaissance paintings they were using one point perspective plus the golden ratio to define their compositions to give it a feeling of naturalism but also of purity and symbolic power and harmony by using this mathematical device so I think it’s it’s kind of it’s interesting that it was rediscovered by Fibonacci from other sources and then it was it was used in in the Renaissance to kind of create a different type of aesthetic that was supposedly more harmonious but we can see that the proportions were used in a lot of temple building and important buildings of power you know these defined proportions that create a kind of a sense of harmony and a sense of power yeah absolutely and so I think Fibonacci didn’t discover this sequence it’s been known about in various parts of the world for millennia he was simply the person who popularized it in Europe and it was instrumental in kicking off the Renaissance he popularized quite a lot of other concepts at that time as well and a lot of this thinking came from the East, Asia, Islamic science and mathematics it supposedly turns up in architecture and it’s been theorized that you know it was used in the construction of the great pyramids for example in Giza which is a somewhat tenuous assertion as far as I understand we’re getting to ancient alien territory here but it turns up all over the place and it tends to be a way to make things feel harmonious and to fit in with a natural sense of proportion and construction and I think it’s not dramatically different in some senses from like some of the other compositional rules like the rule of thirds and the sort of the classic art school or even just school, art class at school, diktats around if you’re painting someone or drawing a picture of someone as a portrait don’t have them dead center staring out at you right if you’ve got a vase of flowers and some other bits and you want to create a composition where the vase of flowers is slightly offset to the side and these compositionally make a certain amount of sense although you can find exceptions absolutely everywhere for these. I immediately thought as soon as I said the vase of flowers well thank off the sunflowers are dead center as far as I remember but I broadly sort of agree with it but the whole mystique that goes with the golden ratio is sort of something that transcends simple compositional rules and at not least the likes of Dan Brown and his Da Vinci Code and all the conspiracy theory stuff that happens around that that you know that people when they see the golden ratio or they think they see the golden ratio in use then there’s something more deeply symbolic going on than simply oh don’t place things dead center for example the Mona Lisa right has the has that composition yeah that’s right the Mona Lisa is completely dominated by the Fibonacci sequence or the golden section so it’s amazing when you when you place on the Fibonacci grid to the Mona Lisa you just find that almost every single aspect of the composition is based around an underlying mathematical you know sacred geometry is that a case is that the case of so if you’ve got the the Fibonacci square with the spiral with the the down point of a spiral downward so you’re looking at it from a um a portrait perspective would Mona Lisa’s face be where the middle of the spiral is is that what we’re saying here it’s pretty much like that if I remember correctly yes and so I’m actually looking at the the portrait behind my head there that’s one of my it’s not really a portrait it’s just a painting one of my paintings actually I don’t think that’s a an appropriately proportioned rectangle rectangular painting but I suspect that that is almost Fibonacci ish where I’ve put her face there right um which is which is not in fact there’s two of them look the other side of my head they’re both sort of in that same place and so most for historically when people have been doing portraits that they tend to sit like Mona Lisa does right so I don’t see a massive I mean yeah you can you can put the Fibonacci spiral on that and and have it roughly at her in the middle of the face but what else is there is there more going on there than that I think I think that’s interesting I mean I think there was you know especially when you look at the early Renaissance a lot of the paintings are based around the underlying mathematical principle of composition so Benini or any of the the North European artists were kind of like contemporaries of Leonardo and Michelangelo and Raphael were also using that as a compositional device and so then it was it’s more than just how we frame a portrait it’s it’s to do with the fact that it was an idea of let’s make this a harmonious experience even if we’re depicting something that is more difficult to digest which in some ways you know some of the Christian iconography you know was some of the Renaissance paintings that relate to Christian iconography the shooting of Saint Sebastian shot to pieces with arrows and stuff like that there’s a there’s a level of violence in the image and yet at the same time there’s a harmonious composition that allows you to contemplate that level of violence or level of martyrdom if you want to look at it from that perspective so I think there’s a kind of intuitive way in which the audience engages in the art that gives them a kind of like a harmonious high but it’s also because of the harmony because of our association with that harmony it’s something that gives a level of attraction that can be manipulated I guess and that that’s kind of interesting in one sense but also as you kind of like hinted at there’s a level of tyranny to that particular aesthetic if you’ve seen it too much you just you may get a little bit bored with it you know may just all be a little bit too harmonious and you don’t think the world is quite like that so it’s not a reflection of our everyday reality in that sense well or not there at all right and so there’s no there’s no hard and fast rules that the number of petals on on flowers tends to be they tend to be Fibonacci numbers although there’s some various theories about the fact why that what why if it really is a pattern why that might be because apparently the Fibonacci sequence is quite a good way quite an efficient way of packing things in so seeds within within flowers often follow roughly some sort of Fibonacci like rule and you can see that from the way that the the golden ratio rectangle is divided up it’s an extremely efficient way of packing things so it’s not beyond the realms of credulity that the the over billions of years nature found certain ways of maximizing for for space and efficiency because that’s simply what natural selection does so I can get for one point where yeah okay maybe that there’s a rule a general rule around you know flower petals and Fibonacci and maybe Fibonacci turns up more often than would be represented by pure chance but to jump from that to the Mona Lisa to the the pyramids you start to get a little bit of waft of confirmation bias because you can you can just take any you know any house because houses certainly in this country are generally rectangular and and start to you know let’s take this measurement to this measurement oh no that’s not you know that’s not the golden ratio but if I take this measurement to this measurement it is well hold on you know that’s not exactly a rigorous scientific process and and so I you know I’m I’m not massively convinced that the golden section is different from the the rule of thirds in any dramatic way and I’m I’m not massively convinced it it it’s it’s actually there where people say it is now the flip side to that is that we know it’s in DaVinci’s paintings because he told us right we know apparently it’s in Bach some of Bach’s compositions American prog metal band tool recorded the whole album Lateralis that sent us around the Fibonacci sequence in the beat and and the structure of the songs in the album so it definitely is there but you know Lateralis is a hard listen like it’s a hard album to listen to and it’s really long and complicated and almost nothing repeats right and and from that sense you know aesthetics or harmony I’m not sure most people would say theming in a whole album Fibonacci led to a more harmonious album I think most people will argue the exact opposite unless of course you’re a tool fan so I mean that’s my question is it really improving things you know I mean or is it just a convention that that has has has emerged and has attached to it a slightly high degree of emphasis yeah I mean I think it’s one of those things that people get interested in and then they push it back and say oh it’s a bit old-fashioned we’ll do something else but within the history of art it’s one of those themes that people seem to keep going back to you know it’s a source of interest and curiosity and you use it and then you maybe put it in the bin for a while or it goes out of fashion and you end up having a different focus but I think you mentioned when we were chatting before about you know the the abstract compositions of Mondrian and again you know if you look at those compositions you think well they’re just abstract they’re they’re quite pleasant but when you do the analysis you find out that they’re based around you know a lot of golden section proportions within the canvas so whether that’s something that happened intuitively or whether that’s something that was kind of like pre-programmed and pre-designed and pre-composed just different question I was very interested in looking at Marcel Duchamp’s large glass was kind of like techno image of intelligent emotional machines interacting with each other and again you know I I wasn’t aware that he would ever use something like the golden ratio but in all of the drawings he did which are the precursor to the large glass he was using the golden ratio and so that whole composition not usually mentioned in a lot of the art historical literature around the large glass is completely based around the the golden section and I mean he he said it was kind of like a mechanical approach to doing art but it’s interesting that that was a kind of like a level of aesthetic that he was using crops up every crops up everywhere and then you think oh no this is there’s just too much bias and no I don’t want my stuff to look like everyone else’s. Well and precisely right and so if we take this sort of idea of the composition of the Mona Lisa which is also just a fairly sensible and pleasing composition for any waist up portrait for your your average school photo right and and that’s cool right and and I’m I don’t really think that that paradigm needs to be massively disrupted but then you get this idea that well why is it like that well this person did it before who copied this person did it before did who copied this person who did it before and some of them may have been aware of of the compositional imposition of the of the golden ratio but most people were just sort of going well when I see portraits this is what they look like I based my work on X on Mondrian and therefore when you look at it you’ll find that there’s some golden ratio in there and we get a certain convergence because this is the paradigm or the the standard way of of composing pictures within a rectangle and and so we get this self-fulfilling thing that keeps going and going and going and to the point where when someone violates the rule either the the third the rule of thirds or the golden ratio or one of the others people look at that and go oh that makes me uncomfortable that’s a bit weird that’s a bit off but what’s going on there you know there’s this this idea that oh no we have these compositions because we see them naturally in nature but I don’t think that’s at all clear I don’t think that’s at all a done deal and and therefore are they only uncomfortable simply because they’re used to seeing things in that composition right the artificial things in that composition and the actually had da Vinci decided to use some other method of composition that everyone at this point would be going oh look there’s Mona Lisa as we always see us you know doing a headstand or something no I mean I think I think you’re right I mean a lot of art is um it’s based around uh this this idea of repetition we’re told what art is we’re told what it looks like and um in some ways it’s a kind of a meme that um it’s kind of like manipulated through time and therefore if if something looks a bit like art and smells a bit like art then we we make a connection to say I think it’s probably is art and then you’ve always always got artists throughout the history of uh art since the Renaissance anyway you know the one to just do something different oh I don’t like that I can make it a bit more naturalistic I can put a bit more shadow to this I can make it a bit more exciting I can give a different subject matter blah blah blah so they’re always artists always change the rules and they hate rules really they like some of them some of the time and but if they get in the way they want to get rid of them and I think it’s a bit the same with um you know the harmonies of the the golden section the harmonies of Fibonacci and the fact that there’s a level of tyranny to it as well it makes you ask the question can you have something beautiful or can you have something visually interesting and stimulating that is not the golden section and of course the the answer is yes but as we move into this area of AI generated work and mathematical patterns supporting um you know a lot of the artificial intelligence and machine intelligence then we we we have different philosophical questions about you know what’s the nature of aesthetics are we creating a closed loop via the algorithms that machine intelligence is using to uh to continually generate like-minded art so you know something that has got the same DNA as its precursors I don’t I don’t think it needs to be like that but I think there may be algorithms in the background that uh make these things that look like art and kind of smell like art use these patterns to to uh to make them more convincing and more appealing to human human vision and eyes and intellect there’s quite a lot to unpack there and we’re not going to do it all today there’s definitely some more um we may need another conversation might need another few hundred but some points that jump out one is that um the the flip side to the conformity is that if there are no rules to break then you can’t break any rules and and as you point out artists like breaking rules and and uh making art isn’t always about aesthetics and making things look pleasing uh when you subvert the the standards on on composition and it makes people uncomfortable well then then you probably meant them to feel uncomfortable right and the and and if that’s what you wanted then that’s that’s a piece of art fit for the purpose for which it was designed and of course there are always going to be uh just a few pure brute force statistics um a center ground right a more popular way of doing things and so that happens to be the Fibonacci sequencer golden section the rule of thirds and these things and um could it have been different is an open question does it matter at this point probably not because people that’s where people have coalesced anyway right now when you touch on the whole AI thing um that’s where things start to get mega thorny because obviously you take something like Dali or mid-journey one of these uh generative AI algorithms and models that uh produce uh images based on um text instructions i.e. uh give me a picture of a Volkswagen Beetle in the style of Van Gogh right which it would probably do a decent enough job of and you probably weren’t looking for a great master work there anyway maybe just needed a graphic for your blog or something now um that those models have learned uh rightly or wrongly um that has learned from everything that is found on the internet which includes probably a billion photo snaps but a lot of um images of of the great masters of uh you know painters uh the the all through history many of which will have used um very standard uh compositional practices uh which which the machine is learning it’s not learning in the sense that it knows what it’s doing it’s simply saying well when i see pictures they usually look like this so if you want to portrait it’s probably going to be roughly golden ratioed and and then it all gets compounded and and everything starts to feel more and more homogeneous because um these models can’t be creative it’s simply they’re not intelligence the artificial intelligence moniker is a massive misnomer and that they’re simply regurgitating and vomiting out stuff that they’ve seen before and they’re going to vomit out in roughly the way they’ve seen it before and therefore the more ai art that gets out there the more homogeneity there’s going to be around things like composition and structure and and and it’s sort of it you get to this point where you know are we ever going to see anything that looks different ever again um and and it’s quite depressing in that sense yeah i know it’s going to be interesting to see where it goes i mean the um ai generated art i mean it’s a word a word prompt versus a visual prompt or a material prompt and that means that the work is generated it doesn’t have a level of materiality until it’s printed out or it forms into some form of uh 3d printing i guess you know you can imagine that something like that may happen in the not too distant future unless it you know probably happened already because you know jewelry design is now being created by 3d printers and stuff like that so you know this whole mishmash of um hybrid compositions by machines and humans is is already it’s already happening i’ve been using large language models much more than i’ve used the image-based ones and i use them for either writing text as a bit of a shortcut you know i get them sometimes to do coding for me in python and and what i’ve found is that they i have a way i want to do things it’s fairly specific to how i work and and just how i learned those languages and so on or how i write how i write my blog um my blog posts or or podcast episodes and things like that and then so you get it so can you write some code to do this and it writes it in a certain way and i’m like no i don’t want it done that way right so you go into it and you say well no no okay can you do it again but write it this way and it doesn’t want to right it’s simply like no i can’t do it that way can only do it this way right and and if you’ve ever done any programming but it’s the same with creative writing it’s there’s an infinite way number of ways to do anything and and but it only wants to do it in the prevalent way now whether i’m right or wrong to want it be done differently um it’s kind of beside the point just shut up and do what i told you but it doesn’t it’s not being belligerent it’s just saying i’m sorry i just don’t understand uh you’re gonna have to have it done this way because it’s the only way right and and i and i can see that with art right and and so by using ai to do things like design uh or even composition or anything like that for uh artists using it for um ref creating references for figure drawing or something right you you can’t get it to to compose it differently it just is too much effort and and therefore like it is going to have that impact everywhere all over the place of driving this homogeneity of of of composition and appearance of of art i just it just seems very likely to me and that’s quite sad um but also if you want to stand out then don’t do it that way have square artworks for example mark i think that could be very interesting yeah i mean i think the the challenge with square artworks is that you have to work harder at the compositions well i do i i love squares um and i can see one there on on my shoulder and i love uh my other favorite aspect ratio is two by one um whichever way that is the the the portrait version of two by one another one that forces you to do interesting stuff with compositions and and not something that you can easily apply um fibonacci to although i’m all i’m very likely doing some version of the rule of thirds it tends to be my go-to but mostly i just do this intuitively anyway right and so how do you compose a how do you compose a painting uh well i i move things around until it looks good to me right do you you know stick a grid across the canvas or something no i don’t right you know sometimes i’ll use them because if i’m playing around with uh compositions within like i photo or something it automatically imposes a grid it’s sometimes quite helpful especially if i want to get things centered oh which you’re not supposed to do which i do all the time and um it’s a bit of a case of it’s always been intuitive to me now someone will come in this house and you know mathematically analyze all my paintings and and tell me that oh no they’re all fibonacci you know i mean they’re all absolutely you must be some sort of genius because they’re all absolutely perfect golden ratio but i certainly have never used it have you uh no i i’ve always found it too difficult it’s never worked for me so i’m i’m very intuitive in terms of the way that i construct compositions but if i’m looking at historical paintings i’m amazed by how much of the underlying composition can be based around the golden section so that that for me has been an interesting insight um certainly over the course of the last few years just to to look at the compositions and notice how much of them are based around these mathematical proportions and the question that you you hint at there alex is you know are we going with this new machine intelligence world that we’re creating or the machines are creating themselves you know are we going to see more of those mathematical patterns in terms of um output or a processing power to that that overall composition and i think artists can then decide whether they want to use that or whether they just rely on their intuition and their visual their visual skills to be able to balance things out whether it’s a center sense defined composition or whether it’s not but i think there’s a lot of things that humans do intuitively that machines find incredibly difficult to do but there’s certainly something in there in terms of um watch this space you know how is it going to involve what’s our relationship to that involvement you know are we going to be doing more stuff that’s hybrid are we going to do more stuff that’s um completely intuitive and doesn’t look anything naturally like fibonacci but may still have that fibonacci um element to it when someone comes along and analyzes it later well that’s it right so you’ve got a pattern within a pattern within a pattern you’ve got turtles all the way down there’s something specifically um recursive about this conversation and and and you know the fibonacci is a recursive function and and so is it there well we know that pi is there right pi is there because every time you see a circle that’s pi right that there’s not there’s no ambiguity about this the fibonacci sequence definitely exists because you can do it and it can be extrapolated to it you know at pretty extreme lengths but is it there in nature it’s it’s less clear right um but but we assume that it is and uh as you sort of zoom out in a in a sort of fractal sense um yes maybe you do see it in a lot more places and maybe uh it depends on your your lens and your zoom level on on sort of human culture and and which particular features you zoom in on maybe it’s it’s much more present and um cynics like me uh can just shut the hell up but um i’m i’m being a bit of devil’s advocate here because i because it’s an interesting conversation right and i tend to be uh quite skeptical by nature um and i tend to quite like pushing against uh people with things that to me resemble uh conspiracy theories or or just generally finding patterns where they probably don’t exist um but but also large because i just don’t care right i i think it’s an interesting subject but i i i just don’t have any use for it and and so i can sort of take any stance i want on this one um but i’ll probably keep being somewhat cynical um about the whole thing until someone proves to me more um more concretely but on the math side uh well there’s whole um there’s whole journals written on the fibonacci sequence um so i suspect there’s much more to be found there and i do wonder whether there’s certain ways you can line up the fibonacci numbers and uh create something aesthetically pleasing that way but uh i’m sure someone’s tried it probably have i mean and again you know we may find with uh the images rather than the portraits that you do the images that you use the head um you probably find that there’s a level of fibonacci just in terms of the proportions of different aspects of the head you know relationship the eyes to the nose to the mouth and chin and forehead and so forth you know there’s there’s probably something there but you know i don’t think that’s the meaning of uh the work you’re doing it’s just inherent in the fact that you’re using a a representational image of a head so i think yes you know we need to be a little bit careful about how pervasive uh fibonacci in the golden section is in the natural world and uh cautious in terms of its interpretation and um you know a level of bias in in in our history whether that’s traditional or um you know this kind of new stuff that’s coming out of machines well chicken and egg right and now you’re going to tell me that the egg is somehow in the shape of a fibonacci or something um i’m sure it is i’m sure it is i’m a believer today so i don’t i don’t buy any of your criticism uh right i think probably uh we’ll wrap this one up um i i know we could have gone deeper on any number of aspects on this uh and i and the reason we’re not doing that is simply because we know we’re going to have to come back to it whether we do more episodes on the fibonacci and the golden section or whether it just turns up you know i’ll be astounded if we don’t do something on the renaissance um and delve down on more of da Vinci stuff um and you know we’ve got to talk about the last supper and all that type of thing um this stuff is going to come back up again so um we will definitely revisit but probably won’t be for a little while um but i think i think we’re done so uh thank you for joining us today and we’ll see you again soon bye yeah thanks thanks for your time and thanks for listening and being engaged if you have any questions let us know