Can We Test if Cats are Chaotic?

If you'd like to support these videos:
/ notdavid
Resources:
1. Strogaz's Nonlinear Dynamics and Chaos is the go-to for anything in this field.
I also highly recommend Dr. Steve Brunton and Dr. Nathan Kutz's youtube channels. They have really good educational videos from their labs and how they combine these techniques with machine learning to important real world problems like hydrodynamics and seizure detection.
2. Audio from the channel ClaireCats. If you need some cat purring ASMR to ease your day/night please check her channel out / @clairecats6852
3. Cited paper is: A practical test for noisy chaotic dynamics by Ahmed BenSaida
Chapters:
0:00 I need a hobby lol
1:39 What is Chaos?
5:05 Shadow Manifold
8:17 Multi-dimensional Cat Purring
12:11 Bring it All Together Now
Music (in order):
RPG Store - Chris Doerksen chrisdoerksen.bandcamp.com/al...
Atlas - HOME open.spotify.com/artist/2exeb...
Road Trip - Chris Doerksen (see previous link)
Intermission - Stux.io and Vaporwavez stuxio.bandcamp.com/album/qua...
Broken Drum Machine - Godmode (youtube audio library)
It's nice to be home - Not David (not posted yet)
Killer Vacation - Chris Doerksen chrisdoerksen.bandcamp.com/al...
Fiesta de la Vida - Aaron Kenny (youtube audio library)
Notes (roughly in order):
Someone requested a blender copy of the caterfly so here y'all go:
github.com/notDavidsGit/Cater...
Petting Analysis: For each cat then I had 2 categories (pet and not pet) with multiple segments in each category. I extracted the audio in each segment and used Fourier analysis. I found the average spectrum for each cat (N = 6) using zero-padding and a hamming window. From these 6 average spectrum, I found the average shift for 5 of the cats was 3 Hz, and the last cat had no shift at all.
A hand wavey explanation for the time delay coordinates: If you want to go deeper into this method, its also often called 'Takens Embedding Theorem'. The reason this method works roughly speaking is because the past of one variable influences the present state of another variable. By plotting one variable against the past of itself, it is bringing out the influence of these other variables. However, this puts some conditions as well. First, the variable of interest needs to be a function of all the other variables. In the Lorenz system this means we cannot use what is traditionally labeled the z-coordinate (e.g., as seen on the wikipedia page for 'Lorenz system'). The z variable is only a function of x (and z itself). This means the shadow manifold would not accurately recover the Lorenz system because the past of z does not contain information about the y-coordinate. I actually would like to perhaps make a video on this because there was originally a 5ish minute long section in the video just on this topic, but I cut it for time. If you've read this and are interested let me know. If I have time I'll make it and put it on the secondary channel.
/ @notdavidsecondary9958
A small mistake(ish): The way I define the stretch factor is a bit loose. At 13:01 the new size is equal to the stretch factor times the initial size. This is fine, but then I say the stretch factor is normally called the lyapunov exponent and treat them interchangeably. But actually the way I've written it, it should be that stretch factor = exp(lyapunov exponent). Nothing conceptually really changes but this is why in my demo of the sphere deforming the stretch factor becomes negative -- its because I'm treating it equivalently to the lyapunov exponent which can be negative.
Heart analysis: While people do indeed use chaos analysis on heart beat recordings, heart rate variability derived from EKG recordings is more commonly studied, where as I am just using the EKG signal directly. A healthy heart should have small variability, but if it is too small then your heart cannot respond to changing demand. Thus it could be that heart beats are actually optimally slightly chaotic or operate at an edge of chaos transition. There was a good paper on this that I can't find at the time of writing. I'll update it if I find it, but in the mean time, here is a somewhat recent example paper ("Chaos-Based Analysis of Heart Rate Variability Time Series in Obstructive Sleep Apnea Subjects", 2020) and "Chaos Theory, Heart Rate Variability, and Arrhythmic Mortality" is a nice little review, but it is from 2000. It is still well written.

[@not_David]

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.

[@bradleymorgan8223]

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

[@not_David]

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.

[@namyx_71]

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.

[@derpiedoxie]

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!

[@not_David]

@@derpiedoxie this is like a christmas present, thank you I enjoyed every bulletpoint

[@samuelthecamel]

If cat purring is chaotic, does that mean that I can use it as a pseudo-random number generator?

[@not_David]

thats... actually a really good question....

[@nos9784]

Only if you keep petting the cat :) I assume that won't be a problem.

[@lbgstzockt8493]

Anything can be a random number generator if you sample it in the right way

[@vinching926]

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?

[@warleon9499]

More like a real random number generator... Or is it

[@zigzagcheef]

Fun fact, cougars and cheetahs can not only purr, but they can meow too!

[@michajanik9277]

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

[@BartoszBzdak6285]

Gougar

[@thesithofearth3617]

​@michajanik9277 it's just interesting because they're really big house cats

[@jellifygirl]

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))

[@jellifygirl]

ah shit I think my autism is leaking

[@an_asp]

The biggest thing I got out of this video is that I really need to spend more time on data visualization. It's amazing how much more visible important insights like the dynamics of these systems can be when you put the data into a more human-friendly format. I'm always blown away by the effort you put into the visuals on these videos!

[@not_David]

It is a very underrated skill (one that I'm still trying to get better at). I think university degrees in the sciences could do with having a data visualization course if they don't have one already. It goes well beyond academia and is useful in industry.

[@rnengy]

@not_David Do you go into detail about how the visualizations are made on your Patreon? I'd love to support you and learn some design stuff at the same time Bonus cat fact: did you know that snow leopards have a partially ossified hyoid bone, making them an edge case between purring cats and roaring cats?

[@MrTuneslol]

​@@not_DavidWhen I was doing linear algebra in my engineering degree, I was really really struggling. Then for a separate year end review run by the engineering program itself, the attending professor drew two lines and showed that the span function just meant what these two lines were showing and I had the proverbial aha! moment. Suddenly an entire year of work just fit into place and actually made sense. Something as simple as that revolutionized months and months of other people's attempts to help me understand. I truly believe the benefits of visualizations can't be overstated.

[@jeffreychandler8418]

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.

[@not_David]

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.

[@gopherbarney8707]

​@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.

[@gopherbarney8707]

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

[@DaGrEeNtEaCoNnOiSsEr]

"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. 😂

[@amateur-disco]

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.

[@not_David]

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.

[@KoneSkirata]

7:08 „Shadow looks like a much edgier version of the original“ Spit out my drink on that joke. Brilliant and unexpected.

[@Lelle_Berg]

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 :)

[@not_David]

this is a very nice comment, thank you and I appriciate it :)

[@gauthamnair6075]

I love the humor, visuals, and the actual explanations. I wouldn’t know anything about physics, but this was very educational.

[@mince1035]

this video slaps. i found the handwavey explanation pretty neat. it would be cool to see that explanation further developed.

[@not_David]

Thank you for letting me know!

[@pathagas]

i’ve been interested in synthesizing cat purr sounds through physical modeling synthesis, and this video was incredibly helpful! it looks like this means there are four different systems i’ll have to model and have feeding back into one another. i’m guessing the chaotic-ness comes from the feedback loops happening in the system, which is very common in physical modeling synthesis.

[@mysigt_]

That sounds really cool! I hope you post about it if and when you have anything to show off

[@NicholasMarshall]

Check out engine simulator it's simulates air flow to make engine noises. The dev is working on a generalized tool that will let you simulate any air flowing system, and record sounds it makes. Under the hood it's a fluid simulator to sound recorder.

[@bradybirdy]

Conclusion: it is purrrfectly chaotic 🐱

[@not_David]

im so disappointed I missed out on the 'purrfect' puns

[@SolTheIdiot]

@@not_David Yeah that's quite the CATastrophe, huh. Maybe a more purrfect integration of the puns would've made them seem more natural.

[@yoavshati]

@@not_David I was sure you'd say the data is "impurrfect"

[@LoyDizak]

Nice to see bird the physics explainer flying around

[@josukehigashikata1481]

Another banger from 'David'

[@not_David]

thank you best boy Josuke Higashikata

[@zegevlier7076]

I think a company 3d printing your cat's purr print would be neat

[@minotower_]

literally the best video on the internet consisting of an extremely underrated field of math, silly ideas, amazing cute cats and amazing really beautiful animations and all of that while being accessible to almost everyone!! i love your stuff a lot, hope you continue doing it

[@not_David]

Thank you for this very nice comment :)

[@coffeeandproofs]

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

[@not_David]

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?

[@michaeldamolsen]

@@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.

[@not_David]

@@michaeldamolsenoh right haha. I dont know what I was thinking thank you for correcting me lol

[@Hunter-et3iy]

nerds lmao

[@evansdenhere7859]

I really like your animation It makes it so much easier and fun to understand what is happening 😊

[@dantheman8041]

Hi David, first off fantastic video. I completely agree about a push for interdisciplinary approach for these problems. Chaos theory should have more applications/frameworks developed. In terms figuring out how to better relate chaos of cat purring, you should look into detrended fluctuation analysis(DFA) and pink noise. DFA considers the fluctuation of signal at multiple time scales. So it can assess for self similarity. It has a parameter named the Hurst exponent to measure this. A Hurst exponent close to 1 represents time scale invariant self similar signal, which characterizes pink noise, which is very common in physiological measures. This way of testing is nice because as opposed to needing multiple measurements or trajectories to calculate stretch factor, only one wave form is necessary to see the spectrum of correlation to straight noise. Hope this helps!

[@not_David]

Yeah I did do a bit of testing with the hurst exponent but just like the lyapunov exponent of 300 I calculated, it didn't really make sense (for suggesting chaos or non-chaos). I havn't used DFA too much however so I kind of chopped it up to my lack of familiaritiy, or possibly due to noise (I'm not particulaly familiar how robust standard DFA is or is not with respect to noise). In retrospect though I should have at least mentioned there are other methods (such as the hurst exponent), even if I wasn't going to use them in the video.

[@tylerwyka6495]

Goin into my grad degrees and sharing these with all my friends to stress the importance of science communication

[@not_David]

thank you for your other comment but thank you especially for this comment. Depending on where you are doing grad school sci comm can be extremely beneficial even if only for applying for grants and stuff like that. The majority of research funding is granted by people outside of your field and if you don't know how to explain why your research is important to them it will be harder to get funding.

[@logician1234]

This video is very chaotic by itself lol

[@owenl3929]

Amazing video as always, and the writing was so good! I loved the subtle (or maybe not subtle at all) Sonic references :)

[@lazerlord_lance]

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

[@slink1515]

I absolutely love your videos. Please keep making them

[@Me-0063]

Physics for the birds reference at 1:06?? Coincidence, I dont think so

[@Broski601]

Thank you for the immense quality of this video's production!

[@Jojo-210]

Wow, you deserve a lot more subscribers/viewers than you have. I think it’s fascinating how you can make a scientific topic so interesting yet so funny. Other science youtubers produce more serious videos (like Veritasium, Steve Mould, 3Blue1Brown, … (one exception may be Michael Stevens from VSauce, his older videos are also pretty humorous.) But I absolutely love this combination of humor, animation, science/maths, possible applications. Another great thing about this video is the information you don’t find that often on the internet. I’ve seen a couple of videos that explain chaos theory, but I still learned a ton of stuff from your video. Keep up the work, you definitely earned a curious viewer and subscriber! 👍

[@not_David]

Thank you, very kind comment :)

[@Eye-Of-The-Beholder]

I really enjoyed this video You did a great job explaining this "nerd stuff" with visuals and words, and you also shined a light on how we need to open more channels of communication between researchers of different fields if we want to have more well constructed answers! Now that siad channels have been open, let's cross our fingers and hope the video goes around and stumbles into the right people so that you can hopefully do a part 2, for research and most importantly, fun

[@WilliamSeeley-ho6ju]

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.

[@kelzling]

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. :)

[@not_David]

if it does help understand it, let me know! It would be high praise if it did

[@mathildeduhamel991]

Your videos are masterpieces:) love watching them !!

[@nathanielvanrumpt4126]

Amazing video. Super interesting and concise, super engaging. Thank you for making this!!

[@canvalid6373]

you should make more videos for sure... loved it!

[@f0rc376]

I love watching your videos! I think that you deserve way more subscribers

[@skilluber]

Hey just wanna say, love your content! We need more people like you that make math and statistics (or science in general) so interesting and fun as you can! Also love the Physics with the birds reference ^^

[@omidkhajehdehi7627]

I love watching science or cooking shows on youtube. Even though, you didn’t cook anything, but this was a purrfect combo of two for me (I don’t know how, but it felt like I’m watching a culinary art video with well explained chaos theory) Kudos to you! Loved it 🐈

[@linga6421]

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!

[@aislingmol]

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

[@edenontheair4168]

Love the Raidou/Gouto on the TV at the beginning, one of my favorite person-cat duos

[@aarushabrol3760]

I love the visuals!!

[@iamtraditi4075]

Dude this video is awesome! I hope you’re proud of this work :)

[@user-ho3hl6jd1n]

This video is beautiful and so well made!

[@cloudsofbacon6632]

This is an incredible video! Love it!

[@leonmcrostie6580]

Very cool video! I really like your way of teaching a topic by applying it to a real world example. It's a very engaging way to do it and you've presented it very well, bravo!

[@Notapizzathief]

Brilliant. Such professional editing, dude. Really interesting topic too. Deffo earned a subscriber out of me.

[@dvtye3378]

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.

[@Sonnell]

Amazingly animated, well done! :)

[@Fubbymaster]

Great video again!

[@babsibecause]

I‘m astonished of how well made your videos are. I truly hope that you become the next big thing on science KZbin:) 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.

[@not_David]

hah thank you. I agree though, I struggle with thumbnails, they are difficult to do well (for me)

[@saynator]

Really good video. Loved it as always :)

[@zwaffel]

great video Lawrence

[@arni21]

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

[@tylerwyka6495]

I love your videos so much

[@raosthegray7090]

This is a perfect conjuction of the kinds of videos I come to youtube for

[@EPMTUNES]

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?)

[@not_David]

high praise, thank you

[@Daniel-li6gu]

idk how ur channel is so small your videos are super high quality

[@maddsdraws6543]

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!

[@not_David]

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)

[@VHenrik007]

Absolutely peak content, in every aspect!

[@kaelhop]

@not_David You got a hobby, KZbin. We the viewers thank you for that. You are doing great.

[@zanderv.l5607]

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!

[@ck_cal]

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

[@not_David]

Thank you for both the kind words and the cat information. Congratz on the new kitty I am very excited for you!

[@jonachu13]

I learned a lot! Thanks!

[@Steamrick]

Very nice. I do hope this video takes off because more people could stand to see applied sciences.

[@zblurth855]

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

[@not_David]

thank you for the very kind words

[@rodrigoff7456]

I am very grateful for the opportunity to watch your neat excellent work! It's disheartening how most of what's consumed nowadays is mediocre views-oriented garbage... your work, on the other hand, along with other great and resilient creators, is worthy of our time, attention and appreciation! So thank you very much. It's always inspiring to see someone putting in the hard work! 🎉❤

[@GingerWaste]

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

[@Emile9186]

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

[@not_David]

lovely comment, thank you

[@skoovee]

wow another video from Craig!

[@tabsc3489]

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.

[@aislingmol]

15:52 the Physics for the Birds cross-over with the cats is so cute

[@josuelservin]

That fake segue to sponsors really got me, and thank you for explaining this in simple, jargon free terms, I thoroughly enjoy it, and consequently subscribed.

[@vidhoard]

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. 😂❤

[@apppples]

I knew time delay embedding would come up! awesome

[@Cj-cv4wb]

Petting a cat triggers a chain of events likely fully unique to itself for all of time and space, each time. Wild.

[@mattitewes]

Hi (not) David, I love watching your videos and since I am in my masters Programm of mathematics they are especially interesting for me because i can see applications of the abstract theory I learn about in university. I would be really interested in your academic background and the specific fields you study besides obviously network theory ;). Keep up the great work!

[@not_David]

Thank you, I'm glad you enjoyed them :) I did my undergrad in physics, masters in quantum mechanics, and phd in neurophysics/complexity sciences (which is where the topics of my videos come from)

[@YandiBanyu]

"And that's where today sponsor, nah I'm just kidding". That got me there laughing hard

[@jovialgg]

It is so fitting that cats enabled me to better understand chaos theory. Keep up the great work :)

[@not_David]

what can't they do?

[@PronteCo]

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]

thank you so much! 100% agree with your addition, that should have been included for contrast.

[@PronteCo]

@@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?

[@kackers]

the visuals of the shadow manifold vs. the original butterfly being coloured black/red and blue/beige is an excellent visual gag

[@primoultimo4272]

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

[@Frostything]

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.

[@not_David]

I would watch a video like that 100 times over.

[@kiranaun9593]

The inclined plane graphic at the start is brilliant

[@joefishy3312]

Super interesting video! The time delay technique seems quite closely related to the autocorrelation metric in time series analysis.

[@not_David]

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.

[@augm8184]

6:50 Not Bobby Hill cat im dyinggg

[@ReducedNaCl]

I read the handwavy explanation, and i'm interested in that second video

[@Flippy9979]

Aw you saying you got a sponsor actually got me really excited for a second lol

[@e.s.l.1083]

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

[@MarkVank]

He's back

[@williamdavis3658]

Nice video! The oscillatory nature of the waveform at 1:59 might just be a sampling phenomenon of a signal close to the Nyquist frequency that is being aliased

[@not_David]

Its always important to keep the the nyquist frequency in mind to make sure things like that don't happen! However, in this case, the sampling frequency is about 44.1 kHz and theres really not a lot of biological things (especially not breathing related things since it is mechanical) that happen even close to that frequency. For example, even neuron activations, some of the fastest things in the human body, can't go much higher than 200 Hz, still well below the nyquist frequency.

[@amsie02]

amazing video :)

[@not_David]

thank you, I'm glad you enjoyed it :)

[@bartg5418]

I love the concept of discovering cornerstone mathematics from going down the rabbit hole of a real world problem. Student's t-distribution is another great example of that.

[@matiastripaldi406]

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

[@save-scum]

yes please post the cut of the explanation!!!

[@simonvergel1942]

this is like the best video in all youtube

[@subiugetur]

This is some seriously fantastic content, holy shit.

[@loveless-savage]

15:23 "And that's where today's sponsor -- nah I'm just kidding" that moment earned a subscribe instantly

[@abduhawk8994]

Hello again 'David'

[@not_David]

hello again

[@Oler-yx7xj]

Shadow the caterfly and the cats of chaos. Got it

[@TheFinalMB]

That one moment in intermission 2. I was ready to start skipping and then BAM! Expectations subverted masterfully!