In lieu of pictures, please tell me about your cat in great enough detail that I can visualize them in my head thank you (or dog or other pet, or if you don't have one (like me) I accept house plants) edit: I've been keeping up with all of these and love them all, if I happen to not respond to your comment please know I've read it and probably went 'awwweee' to it. Thank you :) EDIT: I just realized I never stayed the delay I used for Helga's caterfly - it was about 35 time steps. Audacity says the recording is sampled at 44.1 kHz, so 1 time step is about 22 microseconds. However, A viewer made their own caterfly (!!) and it does look quite a bit different to the one shown in the video. For example, their caterfly does not have two clear lobes and the delay they used was very different as well (still looks awesome though imo). It very could be that it depends on the recording method and probably even the cat.
We have a neighborhood stray cat, he's a gray tabby. He's a little skittish and wary of loud noises and sudden movements, but we've slowly gained his trust with food. We call him Jackson
Olga came to us from our neighbours who had 100 cats and they roamed the neighbourhood. Olga was only a month or two old and was meowing on our doorstep for a whole night and we took her in to feed her and she just stayed with us.
His name is biscuit because looks like a biscuit, the type you put into tiramisu. He was very mischievous at first but now he's a resident lap sitter. His meows are very cute and gentle and his purring is very heartwarming.
Ok so I have five cats, in order of age: Laia: - “my cat”, my “Familaia”, basically the cat that loves me the most - white belly with a a dark brown, almost green looking upper half with black stripes and green eyes - absolute darling, will cuddle you immediately - has the cutest little meow - has a “I am so done with this” looking face Cutie: - Laia’s sister - patterning almost identical to her sister - nickname: chainsaw - will be super cute and cuddly one moment, will scratch your arm into confetti the next - unpredictable - ironically enough the most friendly looking face Fluffy: - extremely fluffy - probably a Maine coon mix, since she has the fluff, but isn’t as big as one - black boots, black gloves, black lip stick - sometimes we call her a little goth - kinda reddish and cream with black stripes - extremely chatty with the loudest meow - loves to just appear, cuddle for like five minutes and then vanish Boba: - cat with adhd - looks almost identical to Laia and Cutie, only slimmer - will follow fluffy around to annoy her - similar behaviour as cutie, tho les dangerous - very playful Odin: - Bobas brother - the stalker -completely cream with black stripes and paws -will follow the other cats around and my family - will just appear in random places - can’t really meow properly Phew, that was a lot to type out. Hope you enjoy all the cute cat descriptions!
I think any biometric could be formulated into RNGs even not the pseudo one, did you mean that using multiple recording of purring for RNG data pools and use pseudo RNG selector to extract a random value from cat's purring?
I think what "cat purring is chaotic" actually means is more as a fun proof of concept. Small starting point changes in the position, airflow, etc of the mouth, vocal tracts, esophagus, etc results in disjunct responses. I found a study trying to see if voices are chaotic ("Chaos in Voice, From Modeling to Measurement" Jiang et al 2006) and they in fact seem to make a voice logistic map xD, which is pretty cool.
woah thats interesting, I'll check it out, thanks for pointing it out! I tried doing a literature search but I dont think I went broad enough to look at human voices as well.
@not_David do you happen to play an instrument? I was recently looking into alternative options for effects pedals for my bass and it opened my eyes to similar concepts of visualizing delay, octave, reverb, pitch shift, distance and position of the microphone to the Amp. (Though I suppose for the purpose of this experiment where Amp=Cat you'd need a collar with some kind of 3d tracking and another on the mic to record distance/position if you felt you needed to) One might find those datapoints of use when attempting to make a butterfly from audio alone instead of needing to creating a delay shadow... though I'm not exactly sure as to what else you'd record audio data for to find out if it's chaotic... or why... I'm sure someone smarter than I might be interested. I know this video was for educational purposes and I very much appreciate the message in your final thoughts. It's a goal of mine this year to read sheet music for the very purpose of being able to communicate musical concepts to people who don't play guitar. It's been a while since I played the trumpet lol My entire experience with chaos theory was until now limited to a joke bit in Futurama or some cartoon or maybe the Big Bang Theory where someone was trying to explain it and eventually said, . "Stick out your hand. This dropper is full of water." *he squeeze the dropper and the liquid burns the other characters hand* "yeah it was actually acid, anyway..." Fascinating mechanism for data analysis thank you for the video.
"Biologist" here. It's in quotation marks since I'm a wet lab biologist that's moved into computational biology. It's a struggle to make this transition at times but videos like this one really makes learning and transitioning easier. The video is well done and breaks down concepts super clearly. Never thought I'd learn so much from cat purrs on chaos theory. Great work and I'm excited to learn more from ur vids. :) P.S. I don't know much about cats so can't help with explaining why cat purrs would be chaotic even though I am a biologist. 😂
all cats can meow, all do as younglings. It's basicly cat for "feed me, idiot" so young ones do to their mother. House cats never stop since it doesn't stop working :D
The reason they can purr is the same reason they can't roar, and why every cat that can roar can't purr! It's something to do with the structure of their vocal chords; the specialisations needed to be able to properly roar all simultaneously get rid of the stuff (easiest example to explain is the whole ass BONE they're missing) that's needed to purr. Panthera and Felis are even coloquially considered the "roaring/purring cats" respectively. Just, uh, ignore snow leopards, cus they're actually purring cats in the Panthera genus. (apparently there's debate on if they should even be in Panthera, and I'm just assuming that's why lol) ((also, don't ignore snow leopards. they're really fuckin cool and if you see one you better SAVOUR it))
This is honestly one of the most well explained and entertaining (16:55) videos I have seen of such a complicated topic. I would never have read about this otherwise, but I'm very happy to have seen the video. Looking forward to seeing this channel grow :)
hey -- math phd (& cat owner!) here, this video is AMAZING. regarding the curiosity on the chaos embedded in cats purring, it also got me wondering. i'd be happy to talk more on this -- could it be the percision of measurements when purring was recorded? i go back and forth on this as the heart data you visualized was clearly periodic and non-chaotic, so i suppose i now wonder how they measured that data... the reason i wonder on about the chaos of purring is because of two ideas that came to mind: (1) there's a neat paper, and quanta had a nice article explaining it, on "non-deterministic approaches to physics" in relation to this neat concept called "intuitionism" developed by brouwer, a mathematician from ages ago -- and how our inability to measure to "infinite-precision" requires "fuzz" in our measurements, which would mean, as you fantastically noted, everything in our real life is chaotic! reason (2) i wondered about the chaos being likely, related to (1) slightly, concerns what's called the "dense line on the torus" -- lets say Earth is a donut, and you're standing somewhere on it. the direction towards the "hole" from you, lets call that the y-axis direction, and the direction "around" the hole, is the x-axis direction. you are the origin. (this is called an "affine chart"/"local chart"/etc etc). now, if you walk off in the x-direction, you just loop all around and are back (same with y-direction). but if you point at some random direction, say it makes a *rational* angle θ with your finger and the x-axis, then walk that direction, that will be *periodic*, you'll eventually get back to your original spot. (rational means it's some fraction, like angle is 326/728, etc.) if it so happened you pointed at *irrational* angle with the x-axis, you get the dense line on the torus. in other words, you will never get back to where you started, always and forever walking somewhere you haven't been. i am curious and wonder if it's this, embedded in some shape or form here, that causes the chaos. for instance, what if you change the "time-shift" interval you mentioned doing? maybe instead of 1 second, it's 0.9 seconds? how does that change the structure? does there exist a correct shift such that it *isn't* chaotic? what if you had (unobtainably...) perfect recording equipment, with no noise? but i suppose maybe most likely, like us trying to sing a consistent *note* and hold it still -- that biological beings just "can't be consistent"? though, this loops back to the strangeness of that heart diagram... hmmmm... ok brb i need to go record my cat purring
There is a lot to parse here so I will try to do my best to answer haha. Regarding your dense torus idea - there is something similar going on in chaos. The chaos can be attributed to a strange attractor being present. I don't know how much you know about attractors so I will be as broad as possible, but if you imagine a sink that pulls things into it, that would be a point attractor. The strange attractor is similar but its 'strange' because instead of being a point, its actually a fractal. This generates a manifold (like the butterfly shape) that the dynamics are dense on exactly like in the torus example you made (though in your example I don't think you need a torus, couldn't you do the same with a sphere?) Reagrding the time shift question. It is possible that changing the shift changes the result, but this is not a property of the time delay coordinates but rather because the data/computer has finite resolution. In theory changing the shift would not change the conclusions (though the percsies values for the stretchfactor/lyapunov exponent could change, but the sign shouldn't). There is a lot of work going into then picking the "correct delay" but because this issue is a problem with technological limitations and not theory of time delay coordinates (or more generally manifold reconstruction, of which time delay coordinates is just one exmaple), there isn't really a concensus. The gold standard is to use information theoretic techniques and find the delay that minimizes the mutual information of the signal against itself. However, this technique doesn't work for autoregressive signals, which is actually a very catagory of real life signals (I believe the cat purring potentially falls into this catagory). So thats why I didn't spend too much time on this aspect because there really isn't an agreed upon method. Hopefully those kind of answered your thoughts?
@@not_David "... I don't think you need a torus, couldn't you do the same with a sphere?" - No, on a sphere any chosen direction would form a great circle assuming you walk in a 'straight line", so rational angles wouldn't generate a dense path. Your answer that the torus is not a point attractor but is also not a strange attractor (because it isn't a fractal) is very insightful.
For dogs, I'm just gonna throw out there that I would love seeing anything related to the non-verbal communication that takes place between our species.
So much lovely attention to detail, including crediting the music at the beginning AND throughout (and I do notice there's some originals too!) and striving for colorblind friendliness. I also love the reuse of that background with the orange splotchy-painted cat. It does so much to spice up a scene w/ just a rotating curve.
Thank you, comments like this make those extra bits of efforts worth it. I think my videos would not be the same without the music made by those creators so the least I could do is to make it as easy for others to find them as well.
Well you got your target audience here. I know nothing about physics or whatever it is you're talking about here, I just like cats and random very specific scientific topics from people who are actually good at explaining them and I have ADHD so the random jokes and cat pictures keep me engaged. 😂❤
On a serious note, you have an incredible ability to take complex concepts and show their core in an almost painfully simple yet respectful way. Truly wonderful. The only addition I would have considered would be showing how a non-chaotic signal performed on the same test
@@not_David oh by the way, let's see if I can exploit your superpower:D every year I use dominos as an example to explain proofs by induction to my students (if the ith falls, the i+1th will fall too..) but I feel it's not really enough. Do you have any idea for a better example?
11:50 Using color as the representation for the 4th dimension was genius! It helped explain the difference in dimension in an incredibly intuitive way!
Probably one of the best explanations of Chaos Theory I've come across so far, well put together and I love the animations! I saw someone give a talk about looking for chaos at a programming conference a few months ago, and I didn't take all that much out of it because I didn't understand enough of the background. I might have to go back and rewatch the recording now, see if I can get some more insights. :)
I just wanna say I really appreciate you mentioning the importance of interdisciplinary work. I'm kind of a generalist although I'm mostly focused on art/graphics and programming and it's just nice having someone else appreciate this kind of work where most employers only see that I do both and automatically assume I'm worse at both than most others. Even though understanding the whole process of how graphics are made to how they are ultimately displayed and animated on your screen has helped me both to figure out graphical errors when programming as well as helping me understand my tools to create graphics way better than I would've otherwise
The sheer fact - that the effort, itself, is to 'predict' chaos - is scrambling my brain. I simply, might be too ignorant to the subject matter... (i will like 👍 it for the 'tilt' factor, because thats always a curious sensation though) and i will come back in the future for further attempts at comprehension. TY
Thank you for making a video for me, who likes physics but struggles with math. This kind of content helps me approach both. And cats are extra motivating.
Not a biologist, but I am a complexity researcher with some (limited) background in chaos theory. The 'what does it mean for a cat purr to be chaotic', when plotting the single-dimension topology in phase space of the amplitude of a sound wave question, could be addressed by asking 'what would it mean for it not to be chaotic'? In other words, say the sound wave, when plotted against itself, turned out to be non-chaotic, then it would imply that the sound wave is generated by equilibria mechanisms. For equilibria to really exist in the context, there must be identical generators and transmission of the sound, with some parametric variation. This would be manifest as steady oscillations around a certain amplitude. As the sound is being generated by vocal chords, which require pressure to activate, and is being recorded outside of a vocal chamber, which generates distortions based on the physical position of the cat's body, there are many interactive effects from multiple variables that influence the physical acoustics of the sound measure. These could include the amount of pressure on the vocal chords, relative to the position of the head, relative to the intensity of the vocal trigger...etc... In other words, what you get is both chaotic and complex, in that the 'measure of' the purr (as a sound wave within a physical acoustic chamber) is an emergent property of many interacting influences. When plotted as an attractor, it cannot manifest order, as the endogenous effects are simply too great for the sound wave to be pulled toward equilibria. Without equilibria, the 4 embedded starting points result in wild variations from initial conditions. You would probably notice the same phenomena if you plotted the start of the purr against the start of the presumed cause of the purr (i.e. the stroke), but not if you plotted each individual 'click' of the purr against each subsequent 'click', as the time delay between each individual click will have a single biological mechanism (although it will stop existing as a single causal mechanism above a certain microscopic resolution).
That was a very interesting read and I like the way you phrased it. It made me wonder if perhaps by saying 'what would it mean for cat purrig to be chaotic' that I was unintentionally engendering the same sort of 'mysticism' (might not be the right word) that is often attached to chaos theory in popular media. Perhaps the better way to have phrased that section would be to say something along the lines of chaos being everywhere and finding it in this one particular area is not suprising, and in fact could be argued that it would have been more suprising had it been non-chaotic. (I hope I am understanding your argument correctly, I have not had my morning coffee yet, please correct me if you feel like I misinterprated something)
@@not_David Yes, I think you make a good point. But, in reflection, I think I framed my above explanation incorrectly. Rather than assuming a dichotomy between 'chaotic' and 'ordered', I think the better question would be why is it chaotic and not 'random', as would be implied by a purely complex system? That question is still better answered by a biologist. Chaos implies a deterministic structure. As you identified chaos across a certain number of dimensions, it would imply that, at least in those dimensions, the specific underlying rules or mechanisms are being captured, which may be insightful to explore further.
I really really love your visualy and your subtle (or sometimes less so) use of humor. I think it's one thing to make an explainer that relays the information in a comprehensible way and an entirely different thing to do so in a sympathetic and fun manner. I actually took like 30-35h in the last few days to work on an explainer video project for school, which was fun but also very much exhausting. Now I have even more appreciation for the work you do and I really hope that you'll continue because I'm very much enjoying it :) thank you
As someone who is studying Data Science with Computer Science this is a really great video, it just shows how science and math can be really fun. Sometimes the best experiment/study are the ones where you expect a certain outcome and then get the complete opposite. Please keep making videos!
Thank you so much for sharing this, this time shifted coordinate idea is a simple solution to a problem that at first sight i would have thought to be impossible! I feel like i really learned something of value here!
It's rare that I see a video that I think is so beautiful, beyond the animations. The idea of printing a cat's purr is incredible and I hope that one day I get to do it for my own cat. Don't worry not going to monetize it or anything that's for you
As a computational biologist i would say that"what it means for cat purring to be chaotic" it depends on how and what those original dimensions are intertwined. But in general like for the classical lorenz butterfly weather case you know that you have periods and oscillations (sunny and rainy, different kinds of purrs), but over long times the slight differences in event length doesn't let you forecast what event will be happening at a time T. Need more pictures of cats thought
I recently took a course on Dynamical Systems which used the same textbook that you referenced for this video. It was very helpful to see an example like this and I would absolutely love for more videos of a similar nature.
Regardless of practicality, accuracy, or whatnot, the 3D rendered 4D shadow manifold of a cat purr makes a pretty cool image. I might try to render one out with my brother's cat and give a resulting image to him.
So this is just how I made the data make sense to myself, but I think it's useful to remember how our data was obtained. In physics, we think of the starting conditions in a system and see how small changes in the starting conditions are reflected in the outcome. Going back to the weather example, we interpret the chaos as meaning that small changes in starting horiztonal/vertical temperature and convection lead to big changes in the ending temperatures and convection. We can also isolate these variables by only changing one factor at a time. From this, we might find that the system is not chaotic with respect to vertical temepraure, but is chaotic with respect to convection (just a hypothetical). So, now taking that and going back to the purring example, what is being compared? Well, we are comparing the waveform of a cat pur to the waveform of a cat pur. So what do the starting conditions represent? They represent different starting amplitudes along the pur wave forns. Thus, the small changes in the starting conditions correspond to starting with slightly different amplitudes across the 4 waveforms (as represented by slightly different coordinates). Finally, the big question, what does it mean for cat purring to be chaotic? It means that if you have a slightly different set of starting amplitudes between two coordinates, then you will have very different final amplitudes between the two coordinates. In other (more sensible) words, the amplitude pattern of each "pur cycle" (an in and out breath) differs somewhat from one cycle to the next. This means that the amplitude pattern for each consective "pur cycle" drifts significantly from the previous pur cycle to the next. From this, what I think you have shown is that cat purs are irregular and, thus, unpredictable in their variations. I'm not sure whether this is an interesting result or not, mostly because we don't even know why cats pur in the first place, but i still find it intriguing regardless P.s. amazing video by the way, your content is always top-notch and amazing
Nice! Love this brain storm. Regarding your last point -- is it interesting? At the start I wanted to emphasize that chaos isn't that wierd or anything and in fact it is actually very much 'every-day' math. However, I feel like when it came time to interprating the results I was getting I was falling into the trap of thinking chaos was something special. In reality for many things chaos is the norm and non-chaos would be more suprising. Though, to give myself a little bit of credit, what I actually thought was going on was a non-chaotic oscillating system with noise, which can often look like chaos. However, a lot of people have chimed in and maybe now I am more on the, it is chaotic side. Whether or not that is interesting I would argue is in the eye of the beholder lol.
@@not_David a few thoughts: did you see if applying noise reduction caused the "stretch factor" to reduce? Also you could isolate the pur cycles into individual sets, zero them at their first spike, and from there you can do myriad things. You could make an "animation" by presenting each pur cycle, one after the other to see if the cycles are changing over time, and how. This can be even more visually enticing if you then apply a morph transition to the "frames" (made up of each pur cycle) to see if a) there is a drift and b) if that drift is linear or non-linear You could also take the isolated cycles and find the intra-spike distance, intra-spike distance variation, cycle duration (measured from first spike up to last spike down), cycle duration variations, etc.. because counting spikes is just a matter of thresholding (and these spikes are very clear and obvious), it'd be really easy to identify spikes vs. noise and run any kind of data analysis you want.
I did use some filtering to see how things change. I used a low pass filter with a fairly high stop frequency and tried lowering it. For the most part the stretch factor did not change, however it wasn't clear to me how low I should go and felt that it was a rabbit hole that wasn't worth going down for this video. I did not do what you suggested for the cat purring, however I did do it for the heart beat analysis. This was important because you want to be able to better compare across patients (in the PTB data set I had about 150 if I recall correctly). In that case I chose the peak of the heart beat action potential. There I could make a peak triggered average signal for each patient (i.e., the average shape of a single heart beat), which was interesting and potentially related to chaos, but it wasn't direct enough to include in the video.
@@not_David makes a lot of sense that you did this for the heart beats since I thought of the suggestion from my work with event-triggered action potential averages in the C. elegans cortex. As far as finding out how much to push the threshold, the answer that is used in neuroscience research often is "whatever looks right". The trick is that once you establish a noise threshold, you need to continue applying it for the remainder of your samples. You only have one sample, so if you wanted to do this then you would want to cut it into equal parts, determine a good threshold, and then check that it makes sense on the other parts you cut. Finally, another way to see if noise is the culprit is a bottom up approach. Take one pur cycle and repeat it many times after itself, it should then have a very low stretch factor. Then, run a few simulations (with many trials per simulation) seeing how much randomly-generated artificial noise is needed to achieve the same stretch factor as you started with. If noise is not playing an important role in the stretch factor, then you should have to add an absurd amount of noise before seeing a large change in the stretch factor. Otherwise, adding a relatively small amount of noise (as compared to the average height of the peaks) should noticeably add to the stretch factor. Oh, and then try the same thing, but with randomly contracting or dilating the timing of each cycle by some factor. I hypothesize that small variations in the timing of each cycle will result in a higher stretch factor (assuming my first comment in this thread is correct) It's been great talking to you and I look forward to all your future uploads!
I‘m astonished of how well made your videos are. I truly hope that you become the next big thing on science UA-cam:) I only think that the thumbnail doesn‘t do justice to your beautiful visuals in the video. But the rest - your humour, your voice, the math and the explanation is sooo good.
I hope you can keep up the videos man. When i first binged through your videos i was sure you would fall into the set of small science youtubers that went viral then disappeared. Now im much more optimistic about you. If you keep your current pace you can become one of the top science channels on here
Oh, wonderful! I wasn't quite sure what I was getting into when I saw this video, but as usual, I could trust that it was gonna be a fun, extremely well animated and easily digestible exploration of math, and you delivered! I really appreciate chaos theory, even though I'm not particularly well-versed in the actual math behind it. And to have this related to cats? It's great! I love seeing videos just talking about things because they're fun and cool, without necessarily a goal in mind, and this was a great example of that. Every time you post I find myself being so glad I found your channel many months ago, you're so passionate about it!!! Keep going! P.S. I just got a kitty cat one month ago, and it's the loveliest and most demonic ball of fur possible, haha! It's a tuxedo cat with wonderful white socks (and a whole white hind leg! delightful) who loves to be a menace in the morning and right before bedtime, but sleeps and cuddles for the rest of the day It's still a kitten, but it's already so big! Basically a grown cat at three months, which is. A bit scary. But I personally can't wait to see how much it grows! Oh, and it loves to make the weirdest belly up poses when it sleeps (one time it looked like it wanted to be a superhero!) Hope your day is delightful and you receive many more cat descriptions from us! :3
Awesome video. You and physics for the birds are masters of this genre of videos. (im not sure what you would call the genre; intro to some physics or math concept with some relatable application?)
Inclined planes are important to form people that don't think Aristotelian Physics is the real Physics, taken them from the 15th century and bringing them at least to the 16th century. We may say people are chaotic too: I remember reading on a book from Prygogine about the relation of respiratory frequency and frequency steps of a person walking , walking fast and running (or something like that) and there was chaos involved.
Just found your channel through this video and honestly I didnt know I could put so much attention into the chaos of cats purring 😂 The concept of lorenz butterflies is beautiful and i thank you for introducing me to such an interesting topic. Very entertaining watch, I may need to check out more of your videos!
I'm glad you enjoyed it :) I don't have a lot of videos but I hope you enjoy them too (or least the more recent ones its okay if you dont enjoy the first couple haha)
biology and citology enthusiast here, not at all qualified to speak up as a biologist, but i still wanted to give my two cents; i think it has to do with the "randomness" of nervous and neural responses. simplifying it a lot, our nervous cells use sodium and potassium ions to signal "on" and "off" to surrounding cells, be they muscle cells that can contract or relax or other nervous cells. either way, these "on" and "off" states can be traced as a kind of wave from 0% "on"ness to 100% "on"ness, where depending on the sensitivity of the cell, it would consider different percentages as "on" or "off". due to the nature of the surrounding "body juice" (technical term) not having the exact same concentrations of potassium and sodium ions everytime the neuron/nervous cell turns "on", that results in small imperfections in the oscillation between "on" and "off", and those stack to the point where the macrostructures, although having their own oscillatory behaviour (like the cat purr having a inhaling and exhaling part), the addition of all the different oscillations from different nervous cells, that translate to relaxation and contraction of muscle cells, ends up making the system chaotic. i guess if you could replicate every single one of the oscillations given by the nervous cells exactly, you could get a "copy" of the exact same purr, but i think that would be as likely as randomly shuffling a stack of cards to have the same order, twice in a row.
I wonder what kind of results you would get if you ran the recording through different notch filters to select for different frequencies. Maybe the lower frequency components wouldn’t appear chaotic?
I was wondering this too. The reason I didn't do it is because I felt like it really opened up a big rabbit hole because there are so many ways you could filter things. I agree with your guess and I think if I low passed it there would potentially be a transition from chaos to non-chaos, but what does that really mean for cat purring as a whole? Its something I'd need to do more reading about in the broader chaos literature what the appropriate filtering methods are when doing this kind of analysis.
Your guess will be better than mine, how many dimensions do you think it is? Is the dimension just a the order of the system of equations that model the cat's purring? @@not_David
I've dedicated a part of my life to chaos as how it relates to sound, and the reason I am dedicated is because I believe chaotic sounds are objectively more pleasing than non-chaotic sounds... for certain genres of music anyway. Synthwave is an example of using very little to no chaotic sounds. I don't know of a music genre that focuses on chaotic sounds but Dubstep gets close. Objectively bad vs good dubstep may come down to majority non-chaotic vs chaotic sounds. Edit: And the reason for this is because our ears like organic sounds... which are usually chaotic. Hence why car enthusiasts like a good roaring car engine (which I hypothesize is a chaotic sound). Edit2: One of my goals in life is to invent a music genre that focuses on chaotic sounds. I'm in the process of programming the synthesizer for that.
Very curious as to why time delay analysis to generate a chaotic caterfly shadow manifold is valid. Would love that video explaning this that you mentioned in the description bc it really does seem like magic fr
I use incline plane education all the time, I understand how things roll down them based on their weight, this is a skill I use while driving all the time to determine when to downshift and hit the brakes relative to the weight of my car and its cargo, Not a physics student and I found that knowledge helpful
Haha I'm super glad you did. My intention there was not to say that that stuff is useless (it's very obviously not), more that the experience of many non-physics students to that material is that of indifference. Though I'm primarily drawing from my experience TA'ing life science/biology students who often did not see the point of that material. Which is a shame because I think you could still teach that material while still making it engaging for them. For example, I tried to make the labs incorporate using spreadsheets, which is a really applicable skill anywhere you go, and the reception was fairly positive and the students were much more engaged in the labs.
You should make your youtube opening phrase "hello nerrrrds". Completely unrelated, I'm sure many would enjoy seeing some more nitty grittys on your second channel
Great observation! There are some similarities, mainly the delay aspect. The autocorrelation sweeps through all delays (it is a convolution, though I really like to think of it more as a time-dependenat dot product), where as in time delay coordinates you just pick one delay. However, one of the possible metrics you could use to pick that delay time is to use the autocorrelation (often times you want to pick the first zero of the autocorrelation). This isn't very recommended because many signals, especially chaotic ones, are nonlinear and autocorrelation does not work there. Instead you'd use more generalized techniques like mutual information between the signal and its delayed copy, but broadly speaking the idea is the exact same as the autocorrelation you mentioned.
In lieu of pictures, please tell me about your cat in great enough detail that I can visualize them in my head thank you (or dog or other pet, or if you don't have one (like me) I accept house plants) edit: I've been keeping up with all of these and love them all, if I happen to not respond to your comment please know I've read it and probably went 'awwweee' to it. Thank you :)
EDIT: I just realized I never stayed the delay I used for Helga's caterfly - it was about 35 time steps. Audacity says the recording is sampled at 44.1 kHz, so 1 time step is about 22 microseconds. However, A viewer made their own caterfly (!!) and it does look quite a bit different to the one shown in the video. For example, their caterfly does not have two clear lobes and the delay they used was very different as well (still looks awesome though imo). It very could be that it depends on the recording method and probably even the cat.
We have a neighborhood stray cat, he's a gray tabby. He's a little skittish and wary of loud noises and sudden movements, but we've slowly gained his trust with food. We call him Jackson
Olga came to us from our neighbours who had 100 cats and they roamed the neighbourhood. Olga was only a month or two old and was meowing on our doorstep for a whole night and we took her in to feed her and she just stayed with us.
His name is biscuit because looks like a biscuit, the type you put into tiramisu. He was very mischievous at first but now he's a resident lap sitter. His meows are very cute and gentle and his purring is very heartwarming.
Ok so I have five cats, in order of age:
Laia:
- “my cat”, my “Familaia”, basically the cat that loves me the most
- white belly with a a dark brown, almost green looking upper half with black stripes and green eyes
- absolute darling, will cuddle you immediately
- has the cutest little meow
- has a “I am so done with this” looking face
Cutie:
- Laia’s sister
- patterning almost identical to her sister
- nickname: chainsaw
- will be super cute and cuddly one moment, will scratch your arm into confetti the next
- unpredictable
- ironically enough the most friendly looking face
Fluffy:
- extremely fluffy
- probably a Maine coon mix, since she has the fluff, but isn’t as big as one
- black boots, black gloves, black lip stick
- sometimes we call her a little goth
- kinda reddish and cream with black stripes
- extremely chatty with the loudest meow
- loves to just appear, cuddle for like five minutes and then vanish
Boba:
- cat with adhd
- looks almost identical to Laia and Cutie, only slimmer
- will follow fluffy around to annoy her
- similar behaviour as cutie, tho les dangerous
- very playful
Odin:
- Bobas brother
- the stalker
-completely cream with black stripes and paws
-will follow the other cats around and my family
- will just appear in random places
- can’t really meow properly
Phew, that was a lot to type out. Hope you enjoy all the cute cat descriptions!
@@derpiedoxie this is like a christmas present, thank you I enjoyed every bulletpoint
If cat purring is chaotic, does that mean that I can use it as a pseudo-random number generator?
thats... actually a really good question....
Only if you keep petting the cat :)
I assume that won't be a problem.
Anything can be a random number generator if you sample it in the right way
I think any biometric could be formulated into RNGs even not the pseudo one, did you mean that using multiple recording of purring for RNG data pools and use pseudo RNG selector to extract a random value from cat's purring?
More like a real random number generator... Or is it
7:08 „Shadow looks like a much edgier version of the original“
Spit out my drink on that joke. Brilliant and unexpected.
hedg hog
@@Axcyantol sognog the hoghog
@@Thirty_Fiveshagdo the hegd hog
JEVIL IS A CAT
KRIS IS NOT THE KNIGHT
the visuals of the shadow manifold vs. the original butterfly being coloured black/red and blue/beige is an excellent visual gag
I think what "cat purring is chaotic" actually means is more as a fun proof of concept. Small starting point changes in the position, airflow, etc of the mouth, vocal tracts, esophagus, etc results in disjunct responses. I found a study trying to see if voices are chaotic ("Chaos in Voice, From Modeling to Measurement" Jiang et al 2006) and they in fact seem to make a voice logistic map xD, which is pretty cool.
woah thats interesting, I'll check it out, thanks for pointing it out! I tried doing a literature search but I dont think I went broad enough to look at human voices as well.
@not_David do you happen to play an instrument?
I was recently looking into alternative options for effects pedals for my bass and it opened my eyes to similar concepts of visualizing delay, octave, reverb, pitch shift, distance and position of the microphone to the Amp.
(Though I suppose for the purpose of this experiment where Amp=Cat you'd need a collar with some kind of 3d tracking and another on the mic to record distance/position if you felt you needed to)
One might find those datapoints of use when attempting to make a butterfly from audio alone instead of needing to creating a delay shadow... though I'm not exactly sure as to what else you'd record audio data for to find out if it's chaotic... or why... I'm sure someone smarter than I might be interested.
I know this video was for educational purposes and I very much appreciate the message in your final thoughts. It's a goal of mine this year to read sheet music for the very purpose of being able to communicate musical concepts to people who don't play guitar. It's been a while since I played the trumpet lol
My entire experience with chaos theory was until now limited to a joke bit in Futurama or some cartoon or maybe the Big Bang Theory where someone was trying to explain it and eventually said, .
"Stick out your hand. This dropper is full of water."
*he squeeze the dropper and the liquid burns the other characters hand*
"yeah it was actually acid, anyway..."
Fascinating mechanism for data analysis thank you for the video.
TLDR: Cat=Amp
The second I read "changes in position" it gave me a brain blast to when I tried to design my own effect pedal lol
"Biologist" here. It's in quotation marks since I'm a wet lab biologist that's moved into computational biology. It's a struggle to make this transition at times but videos like this one really makes learning and transitioning easier. The video is well done and breaks down concepts super clearly. Never thought I'd learn so much from cat purrs on chaos theory. Great work and I'm excited to learn more from ur vids. :)
P.S. I don't know much about cats so can't help with explaining why cat purrs would be chaotic even though I am a biologist. 😂
Fun fact, cougars and cheetahs can not only purr, but they can meow too!
all cats can meow, all do as younglings. It's basicly cat for "feed me, idiot" so young ones do to their mother. House cats never stop since it doesn't stop working :D
Gougar
@michajanik9277 it's just interesting because they're really big house cats
The reason they can purr is the same reason they can't roar, and why every cat that can roar can't purr! It's something to do with the structure of their vocal chords; the specialisations needed to be able to properly roar all simultaneously get rid of the stuff (easiest example to explain is the whole ass BONE they're missing) that's needed to purr.
Panthera and Felis are even coloquially considered the "roaring/purring cats" respectively. Just, uh, ignore snow leopards, cus they're actually purring cats in the Panthera genus. (apparently there's debate on if they should even be in Panthera, and I'm just assuming that's why lol) ((also, don't ignore snow leopards. they're really fuckin cool and if you see one you better SAVOUR it))
ah shit I think my autism is leaking
I love the humor, visuals, and the actual explanations. I wouldn’t know anything about physics, but this was very educational.
this video slaps. i found the handwavey explanation pretty neat. it would be cool to see that explanation further developed.
Thank you for letting me know!
I think a company 3d printing your cat's purr print would be neat
Nice to see bird the physics explainer flying around
This is honestly one of the most well explained and entertaining (16:55) videos I have seen of such a complicated topic. I would never have read about this otherwise, but I'm very happy to have seen the video.
Looking forward to seeing this channel grow :)
this is a very nice comment, thank you and I appriciate it :)
0:30 I forgot the name of the video and thought "aww"
hey -- math phd (& cat owner!) here, this video is AMAZING. regarding the curiosity on the chaos embedded in cats purring, it also got me wondering. i'd be happy to talk more on this -- could it be the percision of measurements when purring was recorded? i go back and forth on this as the heart data you visualized was clearly periodic and non-chaotic, so i suppose i now wonder how they measured that data...
the reason i wonder on about the chaos of purring is because of two ideas that came to mind: (1) there's a neat paper, and quanta had a nice article explaining it, on "non-deterministic approaches to physics" in relation to this neat concept called "intuitionism" developed by brouwer, a mathematician from ages ago -- and how our inability to measure to "infinite-precision" requires "fuzz" in our measurements, which would mean, as you fantastically noted, everything in our real life is chaotic!
reason (2) i wondered about the chaos being likely, related to (1) slightly, concerns what's called the "dense line on the torus" -- lets say Earth is a donut, and you're standing somewhere on it. the direction towards the "hole" from you, lets call that the y-axis direction, and the direction "around" the hole, is the x-axis direction. you are the origin. (this is called an "affine chart"/"local chart"/etc etc).
now, if you walk off in the x-direction, you just loop all around and are back (same with y-direction). but if you point at some random direction, say it makes a *rational* angle θ with your finger and the x-axis, then walk that direction, that will be *periodic*, you'll eventually get back to your original spot. (rational means it's some fraction, like angle is 326/728, etc.)
if it so happened you pointed at *irrational* angle with the x-axis, you get the dense line on the torus. in other words, you will never get back to where you started, always and forever walking somewhere you haven't been.
i am curious and wonder if it's this, embedded in some shape or form here, that causes the chaos.
for instance, what if you change the "time-shift" interval you mentioned doing? maybe instead of 1 second, it's 0.9 seconds? how does that change the structure? does there exist a correct shift such that it *isn't* chaotic?
what if you had (unobtainably...) perfect recording equipment, with no noise?
but i suppose maybe most likely, like us trying to sing a consistent *note* and hold it still -- that biological beings just "can't be consistent"? though, this loops back to the strangeness of that heart diagram... hmmmm...
ok brb i need to go record my cat purring
There is a lot to parse here so I will try to do my best to answer haha.
Regarding your dense torus idea - there is something similar going on in chaos. The chaos can be attributed to a strange attractor being present. I don't know how much you know about attractors so I will be as broad as possible, but if you imagine a sink that pulls things into it, that would be a point attractor. The strange attractor is similar but its 'strange' because instead of being a point, its actually a fractal. This generates a manifold (like the butterfly shape) that the dynamics are dense on exactly like in the torus example you made (though in your example I don't think you need a torus, couldn't you do the same with a sphere?)
Reagrding the time shift question. It is possible that changing the shift changes the result, but this is not a property of the time delay coordinates but rather because the data/computer has finite resolution. In theory changing the shift would not change the conclusions (though the percsies values for the stretchfactor/lyapunov exponent could change, but the sign shouldn't). There is a lot of work going into then picking the "correct delay" but because this issue is a problem with technological limitations and not theory of time delay coordinates (or more generally manifold reconstruction, of which time delay coordinates is just one exmaple), there isn't really a concensus. The gold standard is to use information theoretic techniques and find the delay that minimizes the mutual information of the signal against itself. However, this technique doesn't work for autoregressive signals, which is actually a very catagory of real life signals (I believe the cat purring potentially falls into this catagory). So thats why I didn't spend too much time on this aspect because there really isn't an agreed upon method.
Hopefully those kind of answered your thoughts?
@@not_David "... I don't think you need a torus, couldn't you do the same with a sphere?"
- No, on a sphere any chosen direction would form a great circle assuming you walk in a 'straight line", so rational angles wouldn't generate a dense path.
Your answer that the torus is not a point attractor but is also not a strange attractor (because it isn't a fractal) is very insightful.
@@michaeldamolsenoh right haha. I dont know what I was thinking thank you for correcting me lol
nerds lmao
This video is very chaotic by itself lol
Physics for the birds reference at 1:06?? Coincidence, I dont think so
Petting a cat triggers a chain of events likely fully unique to itself for all of time and space, each time. Wild.
"And that's where today sponsor, nah I'm just kidding". That got me there laughing hard
For dogs, I'm just gonna throw out there that I would love seeing anything related to the non-verbal communication that takes place between our species.
I would watch a video like that 100 times over.
Love the Raidou/Gouto on the TV at the beginning, one of my favorite person-cat duos
So much lovely attention to detail, including crediting the music at the beginning AND throughout (and I do notice there's some originals too!) and striving for colorblind friendliness.
I also love the reuse of that background with the orange splotchy-painted cat. It does so much to spice up a scene w/ just a rotating curve.
Thank you, comments like this make those extra bits of efforts worth it. I think my videos would not be the same without the music made by those creators so the least I could do is to make it as easy for others to find them as well.
@not_David You got a hobby, UA-cam. We the viewers thank you for that. You are doing great.
Hello again 'David'
hello again
Well you got your target audience here. I know nothing about physics or whatever it is you're talking about here, I just like cats and random very specific scientific topics from people who are actually good at explaining them and I have ADHD so the random jokes and cat pictures keep me engaged. 😂❤
Am a biologist and i feel attacked by the last part. Definitely need a beer (or two) after lab work during this horrible week between holidays
On a serious note, you have an incredible ability to take complex concepts and show their core in an almost painfully simple yet respectful way. Truly wonderful.
The only addition I would have considered would be showing how a non-chaotic signal performed on the same test
thank you so much! 100% agree with your addition, that should have been included for contrast.
@@not_David oh by the way, let's see if I can exploit your superpower:D every year I use dominos as an example to explain proofs by induction to my students (if the ith falls, the i+1th will fall too..) but I feel it's not really enough. Do you have any idea for a better example?
6:50 Not Bobby Hill cat im dyinggg
It is so fitting that cats enabled me to better understand chaos theory. Keep up the great work :)
what can't they do?
11:50 Using color as the representation for the 4th dimension was genius! It helped explain the difference in dimension in an incredibly intuitive way!
Probably one of the best explanations of Chaos Theory I've come across so far, well put together and I love the animations! I saw someone give a talk about looking for chaos at a programming conference a few months ago, and I didn't take all that much out of it because I didn't understand enough of the background. I might have to go back and rewatch the recording now, see if I can get some more insights. :)
if it does help understand it, let me know! It would be high praise if it did
Amazing video as always, and the writing was so good! I loved the subtle (or maybe not subtle at all) Sonic references :)
The only things I truly understood from this video were the “Shadow Clone Manifold” and “Shadow the Manifold”. Quite the man of culture you are.
The way the starting points spread out reminds me of how debris in orbit spreads out due to having slightly different orbits.
My cat loves to sit outside my bedroom door and scream. When I let her in, she tackles me and sounds like a dying motor boat.
cats that sound like broken transportation vehicles are my favourite genre of cat
@@not_David it's so cute ;_;
This video is so effective at explaining chaos theory that I'm gonna go learn how to read sheet music for guitar instead of tablature.
This is a perfect conjuction of the kinds of videos I come to youtube for
I just wanna say I really appreciate you mentioning the importance of interdisciplinary work. I'm kind of a generalist although I'm mostly focused on art/graphics and programming and it's just nice having someone else appreciate this kind of work where most employers only see that I do both and automatically assume I'm worse at both than most others. Even though understanding the whole process of how graphics are made to how they are ultimately displayed and animated on your screen has helped me both to figure out graphical errors when programming as well as helping me understand my tools to create graphics way better than I would've otherwise
lovely comment, thank you
The sheer fact - that the effort, itself, is to 'predict' chaos - is scrambling my brain. I simply, might be too ignorant to the subject matter... (i will like 👍 it for the 'tilt' factor, because thats always a curious sensation though) and i will come back in the future for further attempts at comprehension. TY
Thank you for making a video for me, who likes physics but struggles with math. This kind of content helps me approach both.
And cats are extra motivating.
comments like these are my favourite, thank you :)
That one moment in intermission 2. I was ready to start skipping and then BAM! Expectations subverted masterfully!
Not a biologist, but I am a complexity researcher with some (limited) background in chaos theory. The 'what does it mean for a cat purr to be chaotic', when plotting the single-dimension topology in phase space of the amplitude of a sound wave question, could be addressed by asking 'what would it mean for it not to be chaotic'? In other words, say the sound wave, when plotted against itself, turned out to be non-chaotic, then it would imply that the sound wave is generated by equilibria mechanisms. For equilibria to really exist in the context, there must be identical generators and transmission of the sound, with some parametric variation. This would be manifest as steady oscillations around a certain amplitude. As the sound is being generated by vocal chords, which require pressure to activate, and is being recorded outside of a vocal chamber, which generates distortions based on the physical position of the cat's body, there are many interactive effects from multiple variables that influence the physical acoustics of the sound measure. These could include the amount of pressure on the vocal chords, relative to the position of the head, relative to the intensity of the vocal trigger...etc... In other words, what you get is both chaotic and complex, in that the 'measure of' the purr (as a sound wave within a physical acoustic chamber) is an emergent property of many interacting influences. When plotted as an attractor, it cannot manifest order, as the endogenous effects are simply too great for the sound wave to be pulled toward equilibria. Without equilibria, the 4 embedded starting points result in wild variations from initial conditions.
You would probably notice the same phenomena if you plotted the start of the purr against the start of the presumed cause of the purr (i.e. the stroke), but not if you plotted each individual 'click' of the purr against each subsequent 'click', as the time delay between each individual click will have a single biological mechanism (although it will stop existing as a single causal mechanism above a certain microscopic resolution).
That was a very interesting read and I like the way you phrased it. It made me wonder if perhaps by saying 'what would it mean for cat purrig to be chaotic' that I was unintentionally engendering the same sort of 'mysticism' (might not be the right word) that is often attached to chaos theory in popular media. Perhaps the better way to have phrased that section would be to say something along the lines of chaos being everywhere and finding it in this one particular area is not suprising, and in fact could be argued that it would have been more suprising had it been non-chaotic. (I hope I am understanding your argument correctly, I have not had my morning coffee yet, please correct me if you feel like I misinterprated something)
@@not_David Yes, I think you make a good point. But, in reflection, I think I framed my above explanation incorrectly. Rather than assuming a dichotomy between 'chaotic' and 'ordered', I think the better question would be why is it chaotic and not 'random', as would be implied by a purely complex system? That question is still better answered by a biologist. Chaos implies a deterministic structure. As you identified chaos across a certain number of dimensions, it would imply that, at least in those dimensions, the specific underlying rules or mechanisms are being captured, which may be insightful to explore further.
I really really love your visualy and your subtle (or sometimes less so) use of humor. I think it's one thing to make an explainer that relays the information in a comprehensible way and an entirely different thing to do so in a sympathetic and fun manner.
I actually took like 30-35h in the last few days to work on an explainer video project for school, which was fun but also very much exhausting. Now I have even more appreciation for the work you do and I really hope that you'll continue because I'm very much enjoying it :) thank you
you should make more videos for sure... loved it!
Just found your channel via this video. So, you've got science, cats (especially cats) and humour all in one: subbed and liked!
Should have called it the "ooh big stretch factor" instead of just stretch factor
This made me realize I would actually understand math if everything wasn't named after people
As someone who is studying Data Science with Computer Science this is a really great video, it just shows how science and math can be really fun. Sometimes the best experiment/study are the ones where you expect a certain outcome and then get the complete opposite. Please keep making videos!
Thank you so much for sharing this, this time shifted coordinate idea is a simple solution to a problem that at first sight i would have thought to be impossible! I feel like i really learned something of value here!
Absolutely peak content, in every aspect!
My quest log has been updated: Create an app that gives you a visual of how chaotic a sound is.
It's rare that I see a video that I think is so beautiful, beyond the animations. The idea of printing a cat's purr is incredible and I hope that one day I get to do it for my own cat. Don't worry not going to monetize it or anything that's for you
so the butterfly effect was just a proverb in some sense. like a drawn picture in a stretch? amazing
"this is my sister's cat not Schrodinger's cat" NICE
Aw you saying you got a sponsor actually got me really excited for a second lol
As a computational biologist i would say that"what it means for cat purring to be chaotic" it depends on how and what those original dimensions are intertwined. But in general like for the classical lorenz butterfly weather case you know that you have periods and oscillations (sunny and rainy, different kinds of purrs), but over long times the slight differences in event length doesn't let you forecast what event will be happening at a time T.
Need more pictures of cats thought
I recently took a course on Dynamical Systems which used the same textbook that you referenced for this video. It was very helpful to see an example like this and I would absolutely love for more videos of a similar nature.
Regardless of practicality, accuracy, or whatnot, the 3D rendered 4D shadow manifold of a cat purr makes a pretty cool image. I might try to render one out with my brother's cat and give a resulting image to him.
So this is just how I made the data make sense to myself, but I think it's useful to remember how our data was obtained.
In physics, we think of the starting conditions in a system and see how small changes in the starting conditions are reflected in the outcome. Going back to the weather example, we interpret the chaos as meaning that small changes in starting horiztonal/vertical temperature and convection lead to big changes in the ending temperatures and convection.
We can also isolate these variables by only changing one factor at a time. From this, we might find that the system is not chaotic with respect to vertical temepraure, but is chaotic with respect to convection (just a hypothetical).
So, now taking that and going back to the purring example, what is being compared? Well, we are comparing the waveform of a cat pur to the waveform of a cat pur. So what do the starting conditions represent? They represent different starting amplitudes along the pur wave forns. Thus, the small changes in the starting conditions correspond to starting with slightly different amplitudes across the 4 waveforms (as represented by slightly different coordinates).
Finally, the big question, what does it mean for cat purring to be chaotic? It means that if you have a slightly different set of starting amplitudes between two coordinates, then you will have very different final amplitudes between the two coordinates. In other (more sensible) words, the amplitude pattern of each "pur cycle" (an in and out breath) differs somewhat from one cycle to the next. This means that the amplitude pattern for each consective "pur cycle" drifts significantly from the previous pur cycle to the next.
From this, what I think you have shown is that cat purs are irregular and, thus, unpredictable in their variations. I'm not sure whether this is an interesting result or not, mostly because we don't even know why cats pur in the first place, but i still find it intriguing regardless
P.s. amazing video by the way, your content is always top-notch and amazing
Nice! Love this brain storm.
Regarding your last point -- is it interesting?
At the start I wanted to emphasize that chaos isn't that wierd or anything and in fact it is actually very much 'every-day' math. However, I feel like when it came time to interprating the results I was getting I was falling into the trap of thinking chaos was something special. In reality for many things chaos is the norm and non-chaos would be more suprising. Though, to give myself a little bit of credit, what I actually thought was going on was a non-chaotic oscillating system with noise, which can often look like chaos. However, a lot of people have chimed in and maybe now I am more on the, it is chaotic side.
Whether or not that is interesting I would argue is in the eye of the beholder lol.
@@not_David a few thoughts:
did you see if applying noise reduction caused the "stretch factor" to reduce?
Also you could isolate the pur cycles into individual sets, zero them at their first spike, and from there you can do myriad things.
You could make an "animation" by presenting each pur cycle, one after the other to see if the cycles are changing over time, and how. This can be even more visually enticing if you then apply a morph transition to the "frames" (made up of each pur cycle) to see if a) there is a drift and b) if that drift is linear or non-linear
You could also take the isolated cycles and find the intra-spike distance, intra-spike distance variation, cycle duration (measured from first spike up to last spike down), cycle duration variations, etc.. because counting spikes is just a matter of thresholding (and these spikes are very clear and obvious), it'd be really easy to identify spikes vs. noise and run any kind of data analysis you want.
I did use some filtering to see how things change. I used a low pass filter with a fairly high stop frequency and tried lowering it. For the most part the stretch factor did not change, however it wasn't clear to me how low I should go and felt that it was a rabbit hole that wasn't worth going down for this video.
I did not do what you suggested for the cat purring, however I did do it for the heart beat analysis. This was important because you want to be able to better compare across patients (in the PTB data set I had about 150 if I recall correctly). In that case I chose the peak of the heart beat action potential. There I could make a peak triggered average signal for each patient (i.e., the average shape of a single heart beat), which was interesting and potentially related to chaos, but it wasn't direct enough to include in the video.
@@not_David makes a lot of sense that you did this for the heart beats since I thought of the suggestion from my work with event-triggered action potential averages in the C. elegans cortex.
As far as finding out how much to push the threshold, the answer that is used in neuroscience research often is "whatever looks right". The trick is that once you establish a noise threshold, you need to continue applying it for the remainder of your samples. You only have one sample, so if you wanted to do this then you would want to cut it into equal parts, determine a good threshold, and then check that it makes sense on the other parts you cut.
Finally, another way to see if noise is the culprit is a bottom up approach. Take one pur cycle and repeat it many times after itself, it should then have a very low stretch factor. Then, run a few simulations (with many trials per simulation) seeing how much randomly-generated artificial noise is needed to achieve the same stretch factor as you started with. If noise is not playing an important role in the stretch factor, then you should have to add an absurd amount of noise before seeing a large change in the stretch factor. Otherwise, adding a relatively small amount of noise (as compared to the average height of the peaks) should noticeably add to the stretch factor. Oh, and then try the same thing, but with randomly contracting or dilating the timing of each cycle by some factor. I hypothesize that small variations in the timing of each cycle will result in a higher stretch factor (assuming my first comment in this thread is correct)
It's been great talking to you and I look forward to all your future uploads!
I haven't laughed out loud to a youtube video in too long... loving all the references, jokes, and the quality animation and cat vids.
15:52 the Physics for the Birds cross-over with the cats is so cute
I love watching your videos! I think that you deserve way more subscribers
I‘m astonished of how well made your videos are. I truly hope that you become the next big thing on science UA-cam:)
I only think that the thumbnail doesn‘t do justice to your beautiful visuals in the video. But the rest - your humour, your voice, the math and the explanation is sooo good.
hah thank you. I agree though, I struggle with thumbnails, they are difficult to do well (for me)
Maybe a hummingbird is more chaotic since it seems like it's everywhere it wants almost like a dragonfly
6:40 is that Julia Drawfee's Bobby Hill? very very close if not lmao
I read the handwavy explanation, and i'm interested in that second video
this is like the best video in all youtube
I hope you can keep up the videos man. When i first binged through your videos i was sure you would fall into the set of small science youtubers that went viral then disappeared. Now im much more optimistic about you. If you keep your current pace you can become one of the top science channels on here
I love the visuals!!
NO NO NO NOT THE BOBBY CAT I CANT ESCAPE IT
this video is so great, it actually helped me contextualise my own final year project and think of a way to tackle the second half of it :) thank you
Oh, wonderful! I wasn't quite sure what I was getting into when I saw this video, but as usual, I could trust that it was gonna be a fun, extremely well animated and easily digestible exploration of math, and you delivered!
I really appreciate chaos theory, even though I'm not particularly well-versed in the actual math behind it. And to have this related to cats? It's great!
I love seeing videos just talking about things because they're fun and cool, without necessarily a goal in mind, and this was a great example of that. Every time you post I find myself being so glad I found your channel many months ago, you're so passionate about it!!! Keep going!
P.S. I just got a kitty cat one month ago, and it's the loveliest and most demonic ball of fur possible, haha! It's a tuxedo cat with wonderful white socks (and a whole white hind leg! delightful) who loves to be a menace in the morning and right before bedtime, but sleeps and cuddles for the rest of the day
It's still a kitten, but it's already so big! Basically a grown cat at three months, which is. A bit scary. But I personally can't wait to see how much it grows!
Oh, and it loves to make the weirdest belly up poses when it sleeps (one time it looked like it wanted to be a superhero!)
Hope your day is delightful and you receive many more cat descriptions from us! :3
Thank you for both the kind words and the cat information. Congratz on the new kitty I am very excited for you!
Woah, I didn’t know Louie Zong had a physics channel
i will take this as a high compliment
I read the hand-wavey explanation and want to know more!
idk how ur channel is so small your videos are super high quality
Your videos are masterpieces:) love watching them !!
This is a really cool video, I’m really appreciative of the way you care for the research you did and you show to others.
Awesome video. You and physics for the birds are masters of this genre of videos. (im not sure what you would call the genre; intro to some physics or math concept with some relatable application?)
high praise, thank you
Inclined planes are important to form people that don't think Aristotelian Physics is the real Physics, taken them from the 15th century and bringing them at least to the 16th century.
We may say people are chaotic too: I remember reading on a book from Prygogine about the relation of respiratory frequency and frequency steps of a person walking , walking fast and running (or something like that) and there was chaos involved.
Brilliant. Such professional editing, dude. Really interesting topic too. Deffo earned a subscriber out of me.
Just found your channel through this video and honestly I didnt know I could put so much attention into the chaos of cats purring 😂 The concept of lorenz butterflies is beautiful and i thank you for introducing me to such an interesting topic. Very entertaining watch, I may need to check out more of your videos!
I'm glad you enjoyed it :) I don't have a lot of videos but I hope you enjoy them too (or least the more recent ones its okay if you dont enjoy the first couple haha)
11:12 just update to Blender 4.0 it clearly have 4D support, probably hidden in one of the many mesh nodes.🤣
probably in one of the new collapse-able menus
Those little planet-headed cats are funny. I should make one that's a security camera.
biology and citology enthusiast here, not at all qualified to speak up as a biologist, but i still wanted to give my two cents; i think it has to do with the "randomness" of nervous and neural responses. simplifying it a lot, our nervous cells use sodium and potassium ions to signal "on" and "off" to surrounding cells, be they muscle cells that can contract or relax or other nervous cells. either way, these "on" and "off" states can be traced as a kind of wave from 0% "on"ness to 100% "on"ness, where depending on the sensitivity of the cell, it would consider different percentages as "on" or "off". due to the nature of the surrounding "body juice" (technical term) not having the exact same concentrations of potassium and sodium ions everytime the neuron/nervous cell turns "on", that results in small imperfections in the oscillation between "on" and "off", and those stack to the point where the macrostructures, although having their own oscillatory behaviour (like the cat purr having a inhaling and exhaling part), the addition of all the different oscillations from different nervous cells, that translate to relaxation and contraction of muscle cells, ends up making the system chaotic. i guess if you could replicate every single one of the oscillations given by the nervous cells exactly, you could get a "copy" of the exact same purr, but i think that would be as likely as randomly shuffling a stack of cards to have the same order, twice in a row.
Dude this video is awesome! I hope you’re proud of this work :)
6:12 buddy were all nerds here
I wonder what kind of results you would get if you ran the recording through different notch filters to select for different frequencies. Maybe the lower frequency components wouldn’t appear chaotic?
I was wondering this too. The reason I didn't do it is because I felt like it really opened up a big rabbit hole because there are so many ways you could filter things. I agree with your guess and I think if I low passed it there would potentially be a transition from chaos to non-chaos, but what does that really mean for cat purring as a whole? Its something I'd need to do more reading about in the broader chaos literature what the appropriate filtering methods are when doing this kind of analysis.
Cats purr in 4D, got it
*preliminary result
Your guess will be better than mine, how many dimensions do you think it is? Is the dimension just a the order of the system of equations that model the cat's purring? @@not_David
great video Lawrence
I've dedicated a part of my life to chaos as how it relates to sound, and the reason I am dedicated is because I believe chaotic sounds are objectively more pleasing than non-chaotic sounds... for certain genres of music anyway. Synthwave is an example of using very little to no chaotic sounds. I don't know of a music genre that focuses on chaotic sounds but Dubstep gets close. Objectively bad vs good dubstep may come down to majority non-chaotic vs chaotic sounds. Edit: And the reason for this is because our ears like organic sounds... which are usually chaotic. Hence why car enthusiasts like a good roaring car engine (which I hypothesize is a chaotic sound). Edit2: One of my goals in life is to invent a music genre that focuses on chaotic sounds. I'm in the process of programming the synthesizer for that.
Very curious as to why time delay analysis to generate a chaotic caterfly shadow manifold is valid. Would love that video explaning this that you mentioned in the description bc it really does seem like magic fr
I learned a lot! Thanks!
Amazing video. Super interesting and concise, super engaging. Thank you for making this!!
A shame this video isn’t as popular as your other larger ones. It’s such information and features both cats and the butterfly effect!
comments like this are worth thousands of views so I'm happy with it :)
One of my favorite channel rign now, so much effort be it in visual or writing on surprisingly interesting subject
What can we ask for more
thank you for the very kind words
Amazingly animated, well done! :)
I use incline plane education all the time, I understand how things roll down them based on their weight, this is a skill I use while driving all the time to determine when to downshift and hit the brakes relative to the weight of my car and its cargo,
Not a physics student and I found that knowledge helpful
Haha I'm super glad you did. My intention there was not to say that that stuff is useless (it's very obviously not), more that the experience of many non-physics students to that material is that of indifference. Though I'm primarily drawing from my experience TA'ing life science/biology students who often did not see the point of that material.
Which is a shame because I think you could still teach that material while still making it engaging for them. For example, I tried to make the labs incorporate using spreadsheets, which is a really applicable skill anywhere you go, and the reception was fairly positive and the students were much more engaged in the labs.
You should make your youtube opening phrase "hello nerrrrds".
Completely unrelated, I'm sure many would enjoy seeing some more nitty grittys on your second channel
Super interesting video!
The time delay technique seems quite closely related to the autocorrelation metric in time series analysis.
Great observation! There are some similarities, mainly the delay aspect. The autocorrelation sweeps through all delays (it is a convolution, though I really like to think of it more as a time-dependenat dot product), where as in time delay coordinates you just pick one delay. However, one of the possible metrics you could use to pick that delay time is to use the autocorrelation (often times you want to pick the first zero of the autocorrelation). This isn't very recommended because many signals, especially chaotic ones, are nonlinear and autocorrelation does not work there. Instead you'd use more generalized techniques like mutual information between the signal and its delayed copy, but broadly speaking the idea is the exact same as the autocorrelation you mentioned.
I knew time delay embedding would come up! awesome
Very nice. I do hope this video takes off because more people could stand to see applied sciences.