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hello and welcome to technically speaking where scientists and Engineers come together to chat about a common interest share knowledge and satisfy some curiosity I'm Antonia and I'm joined by Laura and Emma to talk about Chaos Theory we've heard the term but what does it mean and how can it be used to understand life the universe and everything to start off with Laura what's your interest in this as a scientist slash as a scientist it's life scientists there's Lions this last person that's
interested in random things yes so yeah I think because I'm interested in random things I come across random terms like that quite a lot and it's one of those things you hear about why you don't really know what it is and I've I've looked things up occasionally and I've never really quite understood it and it sounds like it's quite a powerful thing that can help understand lots of things in life so I'm Keen to hear from physicists what it really is well luckily with us today
we've got Emma and Emma you've been studying in physics at University if you come across this on your course please say yes otherwise we won't have an episode today yeah yes don't worry I have um yeah I did a I did a module that was called non-linear Dynamics and um in that we touched about like how chaos comes around and what systems it um can be used in and how we can use it to kind of understand different systems and how unpredictable they are but um more than just physics though I did um
an earth Sciences module um just last semester and um like a focus of that module was understanding how to predict weather and um we touched on chaos a lot there so it's quite nice to see um the mathematical side of it but then also I guess applications to it and what it actually is because I've also heard of it before in um in films and in media but um they're actually kind of studied it so yeah I hopefully should be helpful but um we'll see helpful physicists it's
good to know Laura didn't you study earth science as your original undergraduate subject yeah I came out with a degree in earth science with astronomy having started off as I say to do random things yeah um I definitely didn't study Chaos Theory or any of its applications though I've only really come across it starting off in the media again um the butterfly effect the film from what's that 2004 and yeah just like random pop culture things um so I guess I've heard of it being used for doing
things like understand protein folding and I was just mentioned weather forecasts and I do wonder what else it can be applied to so I mean my background is a bit of molecular simulation as well from my PhD that I came across it then and it seemed like this really big thing like trying to figure out how proteins fold is apparently really weird really difficult to understand so I wonder if that's a good starting point kind of follows on from our um episode about collagen a little bit I
suppose yeah so what is the process of proteins folding I I did very little biology Beyond gcsc so I don't remember anything about that in my studies does anyone want to explain what that covers I I can I mean I think maybe lawyer you might be better but I've done some some biology in my in my biophysics time um and so what I understand from it is obviously when you have a protein folding into a complex structure you you always start off with an amino acid
chain and like a sequence of amino acids and um they will kind of fold into the secondary structure in the tertiary structure um based on like which amino acids are where in the like so how the hydrogen bonds fold except like Etc um but um there's been studies that shown like the temperature at which like that um process happens the folding or the location where they are in the cell can also determine the shape um which then also determines the function so it's highly dependent on the
exact condition that the amino acid sequence is in um and that can change like what peptide you end up with and so um to kind of give a bit of a background to what chaos is um to help understand it in this context is we learned it as um chaos is how a small change in the initial conditions of a system lead to large change in the final outcome and so that's where it applies to peptide folding because um you have um peptide I don't know if I said peptide and protein like
interchangeably but I'm meaning that it's the same thing before I get before I get everyone confused um but yeah so it's the idea that you have like a different temperature with the same amino acid sequence can lead to like a different protein structure um which I think is really interesting and that's inherently chaotic from the definition but you know it also applies to many different systems okay but I don't know if you want to add more to that Laura because I feel like I just kind of
hopped in there no well this is the thing so of molecular simulation it always works on these really well defined principles and we know these principles are only an approximation for what happens in real life because at the end of the day you can only simulate so many things on a computer and this was all about looking at the interaction between atoms and using those principles to try and explain what's happening and you can build in things like the effective temperature say but the
simulations don't necessarily match what happens in real life I guess because there are these little changes as you mentioned that we can't really capture in the simulation that well um so you mentioned the definition of chaos a small change makes a big difference the more formal definition that I read you might hate me for saying this is a stochastic Behavior or deterministic physical systems um leading to a set of differential equations does that sound like something
that's totally made up or misunderstood it definitely you know it sounds like to be fair um all these equations Etc um but I looked into that definition a bit more as well um especially the deterministic versus stochastic um and for the Layman deterministic generally means if you put the same like initial result you're always going to get the same outcome so you have like a system that's very well defined um and so you know what the result is going to be given a given a given input
um but it's just stochastic is kind of more chaotic system where like your end outcome can change uh even if you have the same initial conditions and so I was looking into it it's kind of like uh not argued point but um chaos is supposedly deterministic but the argument is to why we get these different results is because we can't actually Define the initial conditions um to an infinite Precision so they will always be different and so they will always follow even if they're following
the same set of equations so you can get a different outcome um so some people can call them the chaos or deterministic system because it's still following the same set of equations but some people also call it stochastic because um it's the argument that they're different so it's kind of a similar concept um and the differential equations um aspect of that um for what I understand is that whenever I have done Chaos Theory it's always been applied to systems which can
be described by differential equations and I was just speaking to Laura before um and I think it's because when you're solving differential equations or you know an integral you always need to define a moment in space and time you need to define a condition in order to describe the evolution of the system whether it's for any able Mass people like solving the constant of integration you need you need information about where the system is at the start to be able to solve it fully and so I think
that's where those kind of equations start to come into the definition because it's kind of simpler to understand it that way I guess if you know what differential equations are but if you don't then maybe it's maybe it's harder it's been a long time since I've done any differentiation but I do remember it from a level maths as being like a way of finding the gradient of a line on a graph say and that was very well defined and it was just following fairly easy to understand mechanism
that doesn't sound like chaos theory at all because Chaos Theory sounds like in a way it's inherently difficult to Define what happens I guess that comes back to what you said about having those like almost boundary conditions or known starting conditions yeah um because the differential equations that I've like what's like kind of the the Baseline that everyone kind of uses to understand chaos I think initially especially from like a physicist perspective is if you have a pendulum
and then this you do pendulums and stuff in DC GCSE physics um where there's like an equation of motion which describes how the pendulum moves and like its acceleration position velocity and that's the differential equation is describing those aspects of the motion of the pendulum and uh in certain conditions like small angle kind of amplitude oscillations I I've said I know I've said a lot now I've said to solve a lot of words but in the in kind of in that limit that specific limit
um it's been shown that the pendulum is always going to kind of Swing the same way um but if you change it to be like a high amplitude oscillation or like a large angle displacement again oh I feel like I'm keep on saying more things I know any physicist watch listening to this will be totally they'll they'll know exactly what I'm talking about but essentially when you don't have this like constraint on the differential equation uh then you get this more chaotic system and so
um I think it gets introduced into like especially my Physics degree later in my like in my studies because you start to investigate these cases where you don't have the perfect constraints on it so that's why people don't I think get introduced to it early even though it applies to a lot of systems that we do is because it's you start to see it happen more when you take away these constraints I don't know if I've just talked about anything relevant there I feel like I've gone on a bit of a
tangent about yeah so pendulums I think I guess yeah you've covered a lot of ground so we can try and like break break it down a little um maybe maybe starting from the point of pendulums start so so from my because I didn't study this this at all from my understanding of what you've said about pendulums you're saying in if you look at it in a specific a set of conditions you could pretty much predict what it's going to do but once you start going further away I don't know like
a longer drop and wind direction and then the pendulum starts acting a little bit unpredictably and you could get different results is that is that what you're saying or is that how yeah yeah yeah it's yeah yeah exactly what I'm saying especially a good way to think about it and this is what people have done like people attract the motion of this is um let's say you have a pendulum so I could just ball on a string hanging from the ceiling and if you attach another pendulum to that ball and then
if you like this is entirely chaotic like no matter what constraints you put on it if you hold them both up and then drop them the motion of that second pendulum it always tracks through a different point of space every time and that's because it's just entirely chaotic because there's loads of kind of mini School differences in the initial conditions and you're never going to get it to be exactly the same and that's kind of like um not like a the perfect example of chaos
but that's one that people always like show visually because I mean you can probably look at like YouTube videos and there's so many videos of people doing these kind of double pendulum experiments and simulations get ran maybe it's the lowest budget example we can use yeah but yeah people have like even done simulations of double pendulum systems as well and uh try to track you know the paths and how similar they are and you know every single time it's different point in space that gets moved
upon so I thought like the pendulum is I don't know I think I realized my my point initially is what was Laura was talking about she's doing like gradients and understands differentiation in that kind of context um advancing a bit more to differential equations which is essentially differentiation anyway um one of the reasons why it's always like constant and feels like this very secure way of maths I think when you're younger is because you don't get introduced to the fact that there
are constraints on your systems until you go further so I think that's why it kind of feels like hard to make the connection between I guess differentiation and then like the non-linearity of differential equations okay I think that was my point so you mentioned non-linearity I think we covered this in an episode I can't remember the title of the episode now it was a Netflix film you were talking about where someone's life sort of split into and you're following two parallels timelines
oh yeah yeah yeah it was the Multiverse episode yes it was thank you that's what I was trying to think of and I couldn't remember the word yeah but so you mentioned non-linearity there and it being or not being it so non-linearity is where our cause has an effect right that's what you said I think and non-linearity is where you don't necessarily have that link so it's essentially the same thing it's kind of theory yeah yeah I think maybe maybe kale series is one of those things where it's
like if you if you look hard enough everything's chaotic because how do we know all the initial conditions to everything or is it just the limit of maybe that's like the if we had enough computing power or enough understanding do you think we could get to a point where things are no longer Chaos Theory but in fact a very very complex series of non-linear equations I'm trying to do this at work basically I don't know I think because I've run some simulations before which have been
like of non-linear systems and in order to kind of actually initiate the non-linearity you have to use like some kind of random generated seed number because if you use the same initial conditions that you do just get the same and so like in order to explore how chaotic something is we have to like input the like chain in the initial conditions ourselves so I don't know if like we did have the full set of you know everything to describe it all would we even get
that much out of it as scientists I think like people use the differences in the final results to like track errors and understand how you know probable different outcomes are based on how much the final results vary so I feel like we actually kind of understand the chaos theory is also I think a part of it is also understanding the actual final results and how to use them like it's not an inherently bad thing to have a chaotic system I think it's just important to understand it and
we got some examples of you know systems that we do Define as chaotic and maybe how how do we try and make them understandable I can definitely talk about weather prediction I think that's something that it's also it takes away from the physics room for a moment and it's probably a lot more kind of easy to listen to but um when weather gets predicted they use some kind of current data that you have on like how much rainfall is has fall in the past 24 hours or however they measure the rainfall
um and the temperature Etc and then they use like equations that describe those systems uh which is especially easy for like wind temperature they just like some kind of fluid dynamics I don't know I'll stop talking about physics now but like you have these initial conditions that you have the equations and then you get a prediction for the outcome um but it's there's like a known fact that you can't really trust a weather forecast after around five days to a week because
if you leave it long enough then the initial conditions um kind of the system just becomes more chaotic and it starts to stray away from the actual prediction and so a lot of work has been done in weather prediction to try and um improve the accuracy of how well you know those initial conditions to extend how like how long you can trust a weather forecast for and so I think there's like a fact that like every 10 years you can trust the weather forecast for one day longer or something
so who knows like maybe but I think there's a limit to that I don't think in 50 years you'll be able to know exactly what the weather's going to be like in a month's time I think that's just kind of a strange extrapolation would you say that's a non-linear uh predictive model then yeah yeah for sure not like Moore's Law oh yeah yeah yeah yeah yeah yeah so Moore's Law is about the improvements in like computational power isn't it or the size of a computational chip yeah versus its
ability to compute things yeah I'm going to stop saying that word yeah yeah most Boys still going strong though like this was in the 60s I think they theorized it and it still Rings True to this day I don't know if weather forecast has that much in it because I feel like it does it is it doesn't for me make sense that we would ever know what the weather's gonna be like exactly in the next I don't know the next month which makes sense with what we know now but I feel
like if we had infinite computational power still the way we measure the rainfall rate or the temperature is going to have an error associated with it and so that error gets like transferred into the system and Computing you're using and that kind of gets bigger with um with the longer you leave it but that's also the well the interesting points about running this kind of they call it like Ensemble averages with weather prediction is uh the difference in the
final results is used to kind of predict the error so if you have a likelihood of it being rainy that's where that likelihood comes from because you have you use the difference in the results to kind of predict how I guess um not like how much I really don't want to swap out like standard deviation but like how much the outcomes are spread and if there's a large spread then it's going to be more unpredictable and more likely that things you know might happen
a lot likely and so that's when you get these weather predictions or weather forecasts of things being highly likely or 95 chance of rain where they kind of get that number from I think it's I don't think it's directly related to the maths but it's where they kind of use it just tell people in a way that they'll understand I've never really thought about it in this way when people have talked about predicting the weather so I've just assumed it requires a lot of data right
and they kind of look at the past and find Trends and the more data they have the more Trends they can support but I've never really thought about using a theory from like really fundamental physics to try and make something that's actually genuinely useful I have to say a lot of the times weather forecasts aren't that useful when it says there's a 50 chance of rain I'm like so do I take an umbrella or do I know I take one anywhere I guess I guess it depends how much how much you
like to live on the side of risk do you risk getting wet for carrying an umbrella around that you didn't need or I don't like being wet and cold I prefer to be prepared but I feel like it it must apply to other things like any chaotic system so like I guess it could apply to financial markets as well because they must be really chaotic yeah people are inherently chaotic right yeah then it comes down to what occasions and subscribes a person smooth though I don't know what factors are coming into
that I guess it depends how how detailed a model you want on a single person or do you try and model A group of people that or what I what I heard was sentiment sentiment of the market those kind of words and that and I think that is maybe how people are represented they're not they're not saying people think exactly this they just feel like this isn't going well for this market and so the price is going down you know I've I've seen this happen before uh I genuinely saw a report a few years ago
that said the price of the um stock markets are going down because people are worried that prices are going to go down yes not necessarily even like action it's just people thinking it causing it wow so yeah the idea that you can sort of capture that kind of very human interaction using physics I think is quite interesting it sounds very odd but it also looks like people are actually doing this using Chaos Theory to kind of look at how like the economy and how social science works I
should rephrase that the social scientist would say it's not about looking at social science works yeah I did look up a a bunch of applications for chaos theory and it seemed like it could be you could apply it to anything you really could if you thought of a thing that you wanted to try and represent mathematically you could try it with Chaos Theory yeah I think it just if you have us like an equation describing how a system evolves in time especially I think that's that's always
inherently chaotic because it always depends on the exact incident that you start something or do something like that like I feel like it's entirely dependent on I mean that's what chaos is but that's why you know if you had like you do an experiment with like water or something it would change depending on even just a slight change in the temperature would affect how fast the water molecules move and it would change the result in like a change in the outcome so I feel like it
definitely does apply to everything but it's like used to help understand why systems change so much and why and how that is actually useful like with the weather forecast it's useful to understand how the predictions would change with a slight change in initial conditions because then you can start to evaluate how varying your um weather forecast is and if it's very variable then you're not very certain on what's going to happen but if it's very kind of similar which is very possible
with chaos series doesn't always result in this I mean it doesn't I was gonna say it doesn't always result in chaos I think with time it will always result in chaos but there's like moments in this areas of um kind of patterns and synchronicity that kind of arise throughout different time evolutions and so you can get periods of time where your system is not actually that chaotic because that's also chaotic it's having patterns in chaos is getting like a bit inspection
now yeah speaking of inception I think you mentioned there was one particular book that explained Chaos Theory so well that that's why we keep hearing about chaos theory in the in popular media yeah it was um my lecture actually was the one of the textbooks for our course um it's if anybody wants to read it it's the Stephen straggartz um non-linear Dynamics and Chaos textbook but it's very readable to kind of most audiences um and she mentioned that when this book
came out it kind of became a bit more popular but not just in like the scientific Community but also kind of in in just like the public and popular culture and so after the release of this book and like around the time of the release of the book um it's clear that some like screenwriters or directors had had read somebody I've read some of it or somebody told them about it because it kind of came up with this like really cool concept that um started to make its way into films and
so I do love talking about a Jurassic Park and so I'm gonna bring it off again um but that's when I first heard of chaos theory was because um uh Dr Malcolm no can I not remember his last name now I don't know isn't it funny how everyone just refers to him as Jeff Goldblum it is Jeff Goldblum but it's not the character's name Ian Malcolm it's Ian Malcolm I knew I knew I'd have it but um but he's like this cool guy who wears a leather jacket who's not a scientist
he's a chaos mathematician and so like he gets introduced like initially as this cool concept and so then it starts to make its way into kind of further media and I mean like you said with the with the butterfly effect that's that's entirely Chaos Theory because the whole there's a the famous like sentence of Chaos Theory that's like if a butterfly flaps its wings and then you have an earthquake that's the butterfly effect by definition and then so they've obviously used like a concept to make a
film out of it um but it's always betrayed as this really like cool not like the other Sciences type of it's it's different it's different to physics it's not maths it's chaos it's chaos math so yeah I don't know I feel like it started to make its way into things and even now you know with it kind of ties into non-linearity and like multiverses that's essentially like still based in chaos so it's making its way around so in everything everywhere all at once when they were calculating
the strangest thing you could do that would make you most likely to jump into a particular Universe they never said it in the film but do you think they were using alluding to the fact that Chaos Theory could potentially do that I did not watch it yeah I would say yes I think that based on my understanding of Chaos Theory now after Emma has explained it I I think that that's what they were using you know that they had they had calculation based with probability and ultimately it
was swing chaotic that could happen with some predictability but it was all um it was only in a specific moment in time like they had a window to do these strange things oh Emma you've just got to watch it that [Laughter] I know I do I've been mean to do so much [ __ ] because it definitely the Oscars as well so I feel like I'm behind on everybody yeah they're not watching it I I watched it and it really uh got me it really it really got me because it was a little too real
oh wow I think that was not what I got out of it but okay yeah why was it real real I guess because like a lot of the topics that they talked about was very relatable and I could see a lot of similarities coming from my my background um literally being being a Chinese immigrant um descendant so yeah there's there's a lot of there's a lot of relatable things I don't want to talk about on a podcast laughs fair enough so in the butterfly effect there were lots of negative things that
happened in that film um it's been a long time since I've seen it 20 years old man um but it it seemed like every time you try to do something to fix something by sort of going back in time and having a second chance he just seemed to make it worse so is yeah it almost suggested chaos is always a bad thing it's always negative and you know we don't think of chaos as being a good thing necessarily anyway let's see yeah I also think um it's kind of you know what I'm in Back to the Future as
well they kind of touch on it there like you don't want to go back and make a change and then mess things up because you don't know what world you're gonna move back into so it always it always yeah it always feels like a negative thing but I think I mean I just thought about it like literally just a second ago is it just is it I mean a lot of stuff bad stuff does happen to have things but you're in the multiply fact but um is it just that change is bad like or is it unpredictability that is bad
or like the externalities of yeah you know time travel and changing swing in the past yeah not to bring up another film but I don't know if anybody listening a scene about time but that's also a sort of thing he goes back in time to change and have an effect and then there's one scene where he goes back in time and then he uh changes something and then he comes back and he's like kid is like a different child of course yeah because it's like in that instance of like conception it's a
different it's just a different child and so he goes back and re-changes it but um I mean is having a different child a bad thing know if that's what you always had do you know what I mean I think the fact that it's it's changed it allows you to make a direct comparison yeah with things and so I think maybe I think it's portrayed as like a bad thing because it's like the fabric of like space and time is so weak that if you just change it you don't know what you're going to end up
with but um I think is that just people not liking change but it's good yeah but it's good in evolution because you know these random changes happen sometimes it doesn't help you as a species but sometimes it's it's actually something great and it wouldn't have occurred otherwise because it was completely random so it's like a random genetic change presumably caused by something that also causes protein folding to be a bit weird it's difficult to understand I should say not weird yeah
um yeah yeah because you have the um that your whole genome you have genes that you don't get turned on and different environmental factors can change which genes get turned on and turned off so like you can just be in like a different environment to somebody with the same exact genetic code and have different genes being expressed which I think is yeah but it's really into okay into the territory of the X-Men and how that's like the evolution of human species yeah
how many film references can we fit in is that the x is that what the X-Men is is that like they're like scientific yeah they had a genetic mutation and apparently each one is such wild and crazy powers like one shoots ice one shoots lasers from his eyes another one literally can die and be reborn I mean that that I mean I don't know how like your DNA enables that but um but yeah imagine like all these all these possibilities thanks to chaos yeah yeah well in in all these films you
know they never make a change and then come back as like I don't know King and have all these good things going on for them so all these superpowers but maybe maybe there needs to be a film about chaos in that sense somebody makes a change it doesn't hand in their homework one day and then they go back to the future and then they I don't know they're like the president or something I feel I feel like there's sort of a moral point to those stories like don't
wish for something that you can't really control there's got to be some way of making a film that points out the benefits of using Chaos Theory to not quite predict what might happen but make it obvious how it can be useful because we just mentioned quite a few useful applications of it so flipping the film Narrative of chaos being negative on its head how can chaos be made to be a positive thing I think it's I think it's inherently a positive thing because it helps you understand things
but I don't know if that's got like a Mass Appeal to people if somebody can understand why it behaves that way I don't know who's I don't know who's improving from that imagine you know somebody had a pendulum join that man or woman has appeared on the scene and their superpowers I understand how to pendulums act instead of one but wait there's more I could also predict how three pendulums would interact well you're going into a crazy territory there okay I think that's a good place to
leave it we've gone so far off topic we've just started talking about how we can write better films using Chaos Theory so I'm just gonna summarize what what I think I've learned from today um so I think I've learned that chaos theory is the study of physical systems where small changes in initial conditions can lead to large effects the these systems actually might not be as unpredictable as we thought because they can be modeled with some repeatability but there comes some uncertainty
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