How Fractals Make the Best Coffee
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- Опубликовано: 29 сен 2024
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There is suprising physics involved in making the perfect coffee. Here's a math-free dive down the rabbit hole of how fractals make the best cup of coffee, and answering just what the heck is a renormalization group.
I am trying to aim for quality over quantity with these videos. If you want to support the channel consider checking out my patreon: patreon.com/NotDavid
#physics #coffee #stem #stemeducation #maths
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Footnotes:
[1] 2:01 - More importantly its missing any concept of time. Fundamentally this doesn't change anything though but we will need to talk about this in a future video.
[2] 2:47 Link to code in github: github.com/not...
please note im not a frequent user of github, if something doesn't work please let me know!
[3] 3:20 - An excelent reference for percolation on networks (which is a huge field in and of itself) is Mark Newmans Networks: An Introduction
[4] 6:53 - Here I make it sound like FSE are a problem we need to get rid of, but actually we can also exploit finite size effects to learn even more about the thing we are trying to study.
[5] 8:48 - In actuality there are a few factors working together and forest fires as a critical phenomena are a big area of research. For example, the density of the forest can also play a role.
[6] 11:22 - Here I call Renormalization Group theory 'simple' and ... yeah ... its not. Its probably one of the most difficult pieces of mathematics I've had to do so far. However, there are things about this particular example that make it simple. The hardest thing in RG theory is typically renormalizing things like energy, as it can accidentally become infinite (this is, as far as I know, the big problem of reconciling gravity and quantum theory). If you're familiar with partition functions then the issue can be rephrased as 'is the partition function self-similar under renormalization?'. However, here there is no associated energy and no partition function, so we really don't have to worry about that.
[7] 12:24 - I tried to rephrase this so many times and had trouble with it so apologies if you didn't get it. Essentially, imagine that we DIDN'T have those extra tiles flying in. Then, starting with a grid of 9x9, renormalzing it brings it down to 3x3, and then once more 1x1 and we are done. Thats 3 zoom out steps. Keep in mind in physics we are talking about renormalization from the size of atoms to the size of black holes, so we want a near infinite number of zoom out steps. So to keep the grid small enough for blender I just do the renormalization off screen and 'replenish' the grid. There is a little bit more to it than that but thats essentially it (for the physicists im recalculating the density from the renormalization flow and then drawing grids from the new probability).
CREDITS:
All animations, editing, scripting, story boarding are done by not David
MODELS:
Persona 4 TV world by bunnxarts
TUTORIAL SHOUT OUTS (youtube):
Black Hole Blender - Iridesium
Mandelbrot Fractal - Igot Zdrowowicz
Various Davinci Resolve things - Essential Video Editing
Various Geometry node things - Open Class
ADDITIONAL THANKS:
P. Freeman
J. McClean
ATLUS for making Persona and SMT
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Yeah yeah, it's nice to know _why_ fractals make the best coffee, but... HOW DO I MAKE THE PERFECT FRACTAL COFFEE!?
Trial and error, unfortunately. The critical density doesn't guarantee you a balanced extraction. So you'll have to dial it in; there simply isn't any way around it.
Here's how you do it:
Brew a cup. If nothing goes through, grind coarser. Once you get coffee out, taste it. If it is sour, that means the water percolated too quickly and didn't have enough time to extract the sweet components to balance out the acidity. Hence, you need to grind finer for more resistance. If it is bitter, then you extracted too much and thus need to grind coarser. Rinse and repeat (literally) until you get something you're satisfied with.
And when you buy different beans the whole process starts anew.
@@lonestarr1490Also, with a professional machine, running two ounces through (double espresso) the classic metric is 26 seconds. Finer grinds go slower, coaser grinds go quicker. This "26-second rule" gives you an easy metric without necessarily needing to taste it all. With our professional machine, it actually times it, so you don't even need to have a timer. That said, some people like a 17 second shot with one bean, or a 30 second shot with another bean. All preferences :)
content: amazing and this is so good and i learned a ton.
graphic feedback: having the text pop up word for word on top of the images makes it almost impossible to watch the screen - I had to look away to keep my attention on what you were staying. Your graphics were interesting and then flashed with text on top. easily remadied by designating space for images OR text and giving us time to look at graphics OR text without them being chopped up discontinuously. In addition I really encourage you to only use orthographic images when it's needed- they are used in architecture to preserve measurements, but when you present a 2d graph orthographic it's impossible to make sense of it. If you are going to show a graph, there is an assumption that it is something to try to make sense of. For example 6:19 is challenging because it requires us to project it in our minds while listening to you.
0:35 LOL at "Tim Hortons" being cut off
not enough people appriciated that joke hahah, thank you
Here is a comment to please the gods of the algorithm!
Your channel is going to blow up like mad in the coming months. Absolutely fantastic job. This video was a pleasure to watch.
Thanks so much, I'm glad you enjoyed the video :)
It indeed blow up!
And the coming months is officially here.
10k subs under a week! 🎉
22k Sub Already! Amazing Channel
And an extra 3k subs in 5 days. David keep going! 😤
I don't think there has ever been a channel as underrated as yours
The videos are incredibly aesthetically pleasing and every single render is on point, the explanations are elegant and simple and as a whole they just make you wanna keep watching!
I truly believe the stuff you make is on a whole other level, keep going!
This is one of those comments that really motivates me to keep working on videos even though its so time consuming. You made my day haha, thank you!
I completely agree. The videos have a very high quality, and I believe are on par with million subscriber channels
another underated channel that springs to mind is 'lines in motion'. rly rly inciteful commentary about art in manga.
@@pilkin5378 ooo right up my alley. Thanks for the recommendation!
I completely agree.
This was a great video; it's apparent how much effort goes into these.
Please keep making them!
Thanks so much, the kind words are greatly appreciated :)
I don't know how I found my way to your channel, but these videos are amazing!
My dad asks me questions about my career (unrelated, but both mathematical), and has always told me I can't really fully understand what I do until I can explain it to him.
I think this goes to show you understand your field completely, as you're able to break complicated topics down and relate them into easily understandable and interesting every day scenarios.
You mentioned in another video about what your tutor may think about how you're applying your learning - I, for one, think your tutor should be very proud!
I don't think I understand my field completely, but I do think your dad is very right, and honestly if I could go back and tell my undergrad self what to focus on, it'd be just that because so much of getting a career or grant writing is expressing why your work matters to a group of people that have no idea about physics. Part of making these videos is also for me just to learn to do just that. Thanks so much for the kind words!
Your dad is smart. You can't teach somebody if you don't truly understand.
When I used to tutor maths, if I got the feeling the student knew how to do it, but needed practice, I'd make them explain it to me. 90% of the time, it's just confidence they were lacking
Hope you enjoyed the video!
(post-uhmms video edit) Looking back I have two critisims about this video:
-the first is that it is not explicit enough in saying the video is not actually about practical applications of making coffee. I think this is one of those things that im still trying to get better at as a writer and was just a blind spot I missed. I am working on addressing this (I hope my uhmms video is better in this regard).
- the second is much bigger in that i never explicitly say what the result is. Like its implied but i just kinda breeze past it. Namely, the result is that you would want to be as close to the fractal without going over it. Of course, this assumes you like a strong coffee.
Anyway, I still think the video is good and im proud of it, but im definitly learning a lot from the feedback so thank you everyone!
It's a really good and interesting one !
Thank you! I'm glad you enjoyed it :)
you deserve a lot more subscribers, the study behind your videos and the dedication are just incredible. Keep it up!!
I really did!
You explained the concept of percolation and critical density extremely well and I'm now very excited to find other applications.
Thank you very much!
I wish it was more in depth, but I liked it
so cool! well done! I would like more about the unrealistic societal expectations for fractals please
least insane coffee bro
y'know... I have nothing to say, but commenting helps the algorithm. more people NEED to see this.
i watched two of your videos and then looked at your sub count. i legitimately expected you to have a million subscribers, this has to be one of the most underrated channels on youtube. crazy shit you're doing man keep it up
Persona 5 makes me feel nostalgic... never played it myself, but I watched the gameplay walkthough! Favorite persona song is "Road Less Taken" from Q2 :)
I've had the side games like Q2 on my to-play list for such a long time but haven't had the time to get to them ... one day! I will listen to Road less taken though, my persona playlist needs more. For me it has to be P3's Memories of You or the opening to P3FES. Its such a jam.
A few comments from a coffee-loving physicist:
1. The idea of fractals not strictly repeating as you zoom in or out but merely maintaining the same statistical density is interesting. I'm honestly surprised I hadn't heard about it before.
2. Scale effects are really important in physics-the most significant is probably the quantum-classical transition, in that the further you zoom out from the atomic scale, the less apparent quantum mechanical effects are and the more things behave according to the laws of classical physics. It's also hugely important in trying to describe phenomena such as ferromagnetism and material properties. I also had some personal experience with finite size effects when I worked on synthesizing semiconducting lead sulfide nanoparticles in undergrad. Their cool trick was that while they would absorb visible light and emit infrared as a bulk crystal, once you got them down to a few hundred atoms in size, they would start absorbing and emitting mostly in the visible range due to quantum confinement.
3. Regarding renormalization and gravity, the longstanding issue is that while we have a classical theory of fields that works really well (describing electric fields, gravitational fields, flow fields, etc.) *and* we have a quantum theory of fields that works really well (describing quantum electrodynamics and the nuclear forces), every quantum theory of gravity has proven unrenormalizable. Even worse, because gravity is by far the weakest of the fundamental forces, it's impossible with current technology to test gravitational effects at the quantum scale. (Note: I'm not a professional cosmologist or particle physicist, so I'm neither current with every development in the field, nor can I give much more detail than already given here.)
4. An interesting complication to your model would be to include a range of particle sizes. James Hoffman once put some ground coffee through a laser particle size analyzer, and the results for 3 grinders all showed a slightly skewed Gaussian distribution around 1 mm, along with a long tail rising slightly at 40 μm.
5. Other weird coffee physics topics include the production of foams. Espresso crema is the most well-known foam, but Turkish coffee also produces a foam, which consists of air and water vapor dispersed in a matrix of coffee oils, water, and suspended grounds. I don't actually know what causes it, so I'm starting a research project to figure it out. It's great to do experiments where you can drink the results.
I hope you found some of that interesting; I certainly enjoyed your video. Thanks for making it, and best of luck getting your espresso technique down!
Thanks so much for the comments!
Regarding comment 1: A good reference for this would be the book by Christensen And Monloney. They give an excelent overview of the statistical definition of a fractal (e.g., their association with power-law distributions). I addmitedly don't know if this definition is or is not reconsilable with the "traditional" thing we think of when we think of fractal (e.g., mandelbrot, menger sponge, etc.) but I think it should be possible?
Regarding comment 4: I did think about this and I think that a distribution of particle sizes wouldn't effect the overall conclusions. If we assume that each grind is impermeable (which is not a great assumption but I think my model implicitely makes) then a distribution of grain sizes would mainly indirectly effect the density. Thats completely conjecture though. I'm reminded of whats apperently called the brazil nut effect, where larger particles rise to the top because smaller particles fill the spaces below. I think it'd be a similar thing where larger particles interfacing with smaller particles would just change the density.
Tangentially reagrding 5: In the original version of the script I had a section where I talked about how other coffees relate to this model, or more specifically how they don't. Turkish is actually probably my favourite type of coffee but it is not really modeled by this at all.
@@not_David Thanks for the thoughtful reply. I figured Turkish isn't modeled by this because instead of having a bed of compacted grounds with a fairly high coffee to water ratio, you have a slurry of grounds suspended in 10 times as much water. There I think you're dealing much more with convection currents and bubbles from heating the water, and the grounds are mostly just along for the ride.
The other thing I forgot to mention that I was curious about is that your percolation probability vs. density graph around 7:28 looks a lot like the Fermi-Dirac distribution, which describes the average number of fermions (such as electrons) in a given energy state ε as a function of ε, the chemical potential μ, and the temperature T. The functional form is 1/exp((ε-μ)/Τ+1), and as T goes to 0 it looks more and more like a step function. I haven't really encountered it elsewheres. Do you know if there's a theoretical/mathematical connection to your model? Because that would be really cool.
Interesting question... I'm not actually sure, I'd have to think of it some more...
My first instinct would be that if there is a connection it would not be with percolation model itself but rather the Ising model. The ising model also has a phase transition when the external magnetic field is 0 (which is required otherwise it breaks symmetery) and T = T_c (the currie temperature). I think if you plotted the existinace of the order parameter (in this case the net magnetization) against the temperature, you would see the same plot for different grid sizes.
The big stretch is making analogy between temperature (in the case of FD) and system size (in the case of percolation and ising model). Maybe the temperature (or more specifically \beta = 1/T) could be thought of some sort of abstract system size, and as \beta goes to infinity is similar to as if the grid size goes to infinity?
This is all just early morning pre-coffee guessing by me though, I'd have to think about it, but its a good point, thanks for bringing it up!
Since we're bringing James Hoffman into the equation 😁, I think it'd be interesting to consider channeling in the model (i.e. the formation of discrete "large" flow channels as opposed to an "even" percolation); he has demonstrated in several occasions (esp. reviews of subpar brewers) that the impact of channeling in extraction quality is definitely non-negligible.
One thought would be to maybe consider the number of coffee-water interfaces in the grid, but then I don't know enough about RGT to tell how that would change the subsequent theory (since it's no longer a boolean condition like the existence/nonexistence of a percolation path) 🤔
(Note: I'm neither a physicist nor a barista and I haven't had coffee yet either so all of this may or not be nonsense 😅)
I think the guy's name is actually David 🤔
This makes the statement "coffee people will learn quantum mechanics to make an extraction 0.0001% better" sound a lot less like a joke
How are you not one of the most well known science communicators on this platform?
It's a terrific melange of informative and entertaining content explained in a easily accessible way.
Thank you so much for your efforts.
Looking forward to what this channel is going to become.
I just discovered your channel, and have to say that videos like this are *amazing*. I’ve long had a penchant for aggregating data that others haven’t and analyzing them in ways that others haven’t, to gain insight and, often, solutions to complex problems that wouldn’t have been possible otherwise. It’s wonderful to find others who take a similar approach, and present the process in such an intuitive manner.
Thank you! I appriciate the kind words :)
An absolutely amazing introduction to the topic, thank you so much for making this!
Thank you! It means a lot to hear that :)
To make a cup of coffee…
you first have to invent renormalisation group theory.
I get it now. This makes sense why the ice cube doesn’t instantly turn into water once it warms up.
Very interesting. How doest it apply to practical coffe making though? I hoped for some sort of numerical result.
Me 2
This is a good point. The thing is that the video was more intended as a way to teach phase transitions, fractals, and renormalization groups (which are important in physics but can be difficult to understand) by way of something reltable like coffee making. You could in theory (assuming it does indeed exist) find the critical density by doing successive measurements at various densities, but obviously this is not practicle (or cheap). The issue is that i didn't really make that intention obvious (i kinda assumed it was when clearly it was not). This is largely due to my inexperience with writing still but its something im trying to take into account as i keep making videos (i think and hope the uhmm video is evidence of that? maybe?)
Your ability to take interesting science and math topics and apply them to more 'mundane' topics is really impressive and helps me grasp them more easily than I thought I would. Great video!
Bro wtf,me thinking about markov interations through the hole video
12:24 "Showing everything everywhere all at once would be too intensive for my computer" Folks, I think he's hiding the bagel in his PC 👀
Kinda wild how fractals appear absolutely everywhere. Fascinating video!
Brilliant animations and explanations. Thank you!
So... how do I do that coffee?
15:50 why is there one line that starts below the critical point, yet ends up above it, could the inverse happen?
that's a great question! I have to go back and look at that video (it's been a while) but my guess is that it has to do with what I was talking about at 5:33. The chart at 15:50 is with respect to the grid size and at low grid sizes the critical point is really well defined. Its a quantity that only truly uniquely exists as you have large grid sizes. Phrased differently, its the same thing as flipping a fair coin -- you should expect 50/50 heads/tails, but that's only true in the limit of many many coin flips. If you only flip 10, then you can get any weird ratio of heads and tails. The same thing is happening in that plot. So yes, the reverse could happen as well, but its only a thing that happens at small grid sizes.
At 1:50 you describe the square as "orange-y". Was that a reference to the Technology Connections video about brown being weird?
cannot confirm or deny but lets just say im a big fan of the refridgeration cycle
Wow simply stunning, you gotta be up there in no time man…
dude just tell me what the critical points value is
I was just hoping for a good coffee recipe, tbf
Dure, you need a machine with an overpressure valve so that the coffee doesn't get too densely packed by the pressure.
You missed your chance to say "Critical Moistness" ha!
Pardon the childishness but amazing video!
I'm actually shocked at the definition of fractals that you just laid out. Not only that but you definitely frightened me about the implications of universality. Really cool.
Not gonna lie at one point it was that but when it came to recording I couldn't bring myself to do it haha
Admittedly I did kinda handwave the definition of fractal there but thats largely because I wanted to save it for the next video. The 3blue1brown video on the topic I think does it pretty but obviously I wanted to present it very differently and if I recall correctly he doesn't go into unversality.
Thanks as always!
wow, your channel is such a treasure! I'm usually not very big on maths and physics but your videos really change my perspective, they're really interesting and it's so cool too see how math applies in everyday life! the cherry on top for me is just the Persona 4 and Persona 5 references and visuals. i seriously couldn't ask for more from a channel, great work!
Thank you! my goal is really to show people who aren't big into maths and physics that there is a lot of creativity in those fields even if thats not how it is usually taught, so your comment means a lot :)
This video felt like it was a lot of fun to make given the amount of jokes and puns in it! I've thoroughly enjoyed it as well as a viewer!
the video making process has its ups and downs but its worth it for the nice comments like yours, thank you :)
instructions not clear, my coffee is still terrible
This was really a fantastic video, when I started watching your stuff I thought that you must have like a million subscribers or something. All of the effort that you put into your videos is really clear and I love the style. Excited to be in the first 15k when you blow up.
♎So when I can't get the flow without the pressure going too high, and I release the pressure (I have a manual lever activated coffee maker with pressure gauge) almost completely, let some CO₂ out, and then reapply the pressure it starts to flow faster, did I just renormalize my coffee?🤔
I would be quite interested in a follow-up. In particular I bet things get more interesting with the same example but 3d. Maybe the part about 50% being a repelling fixed point holds, but in 3d I’m pretty sure you get a percolating path before 50%.
11:34 still waiting for the words "self-similarity" or "fractal" to pop up 😂 there is still a little time tho. 😶
Edit: 14:13 Pheww... It's like finally being able to take a dump after being constipated for days...
NO?
Just me?
Shaddap, it's you who's weird! 😶
PS: I mostly was thinking about my course in statistical thermodynamics (mechanics) which introduced me to the self-consistent field theory (to model e.g. polymers in solution by regarding the segments/solvent molecules as blocks. It has an energy associated with all neighbouring blocks. Minimise the energy and you can simulate the kinetics. If I am saying that correctly. Statistical mechanics was a little beyond me. Chemistry easier xD). But yeah I can imagine these ideas are super universal. Like eulers idenity. That one pops up everywhere too. Seems a lot things are just rotating stuff, or 1D-projections thereof (i.e. waves). Or, periodic? I digress!
Your videos are awesome btw! Have yet so find a bad one.
11:06 if quantum gravity is ever resolved, I guarantee it will definitely involve a lot of coffee, so I'd say your priorities are perfectly placed!
You never said what number the critcal point was at (or did I miss it?)
I was guessing somewhere around 0.382
This wasn't interesting way to introduce this math to people, but unfortunately there's a lot more to espresso than what you're saying here. For instance, if it is able to form a channel it can make all the water go through that channel and still under extract and cause problems even if the overall density is okay.
I feel like I'm in a strange minority. I actually already knew about critical points since I went to university for engineering. It was really important for my thermodynamics class... but I don't know, and still don't know how to make coffee T.T
This was such a well done video! And explained from such an interesting angle as well.
And yes, as a former physics master student I can relate to just wanting to dig into some everyday thing and ending up at renormalization group theory. XD
Hey fractals are awesome and a good cuppa coffee is awesome.... what's the mystery? ;*[}
If you want the best coffee, you want fresh 100% Kona coffee that is hand-picked in Hawaii. Not sure that fractals are relevant, but that coffee is an entirely different thing.
So now... how do I make a good coffee again?
well first you ... uhhhh ... oh, but then you should ... mmm .... go to some that knows what they're doing?
@@not_David what do you mean I can't just teach my coffee machine maths and get the best coffee in the world?
I'm pretty sure thats how skynet in the terminator series started. Might still be worth it for a better cup though.
It’s good to see that coffee is only a subliminal problem for you‼️ It’s not a problem for me either. . . As long as I have my cuppa joe in hand😅⁉️
Really nice video. Not many people can draw you in with coffee and spring some RG theory when you're not looking!
This picked up some of the stuff i learned in my degree, and brought a load of stuff together in an interesting way. There's a lot to enjoy about this video, 10/10
How do you make the blender animations? I've made some myself but I was always just manually keyframing the position/rotation of individual objects which would be pretty painful for a lot of the animations in this video so I assume you know something I don't.
cool vid btw
Most of it is geometry nodes, though in a couple of places I use the python API as well if i need to calculate stuff between objects (like the RG theory section)
What a waste of 18 1/2min. Im wondering if one should even think about making coffee if this video makes you understand it better🤔
this is gonna sound really far out and looney but when i was around 16 I took some mushrooms on top of a cliff where I had a view of a neighborhood below me and mountains around it. When the mushrooms kicked I began hallucinating that all of the roofs of the houses where connected and repeating fractals and all of the mountains where repeating fractals as well. Later trips would result in the same hallucinations in trees, bushes, and even the faces and bodies of my friends and family. Needless to say, the ending section of this video almost made me shit my pants.
Based critique of Timmies. Mcdicks got their blend, and it's never been the same.
12:00
that process of normalizing and zooming out reminds me of when you're diagonalizing a matrix (say 4x4) and you break it up into clusters of smaller matricies to help you out, but in the opposite way-ish
0:35 Tim Ho--really diluted watery coffee 😂😂😂😂😂😂😂😂😂
Your model is wrong. You model a density of 0.9 as a chance of each cell to contain coffee, but if you do it like that then only the expected density is 0.9. You should instead use a random chance of P=X for each cell, then measure the actual density and plot the chance of perculation based on actual density.
Love the unironic use of the default font in Blender, it is kinda fun.
yes...I have fallen down the coffee fractal rabbit hole... This video actually came at the perfect time
I'd appreciate it if you'd master the audio closer to 0dB. This video is stunning, but I wish it were a bit louder.
Wouldn't fractal coffee be a little bit too strong though? I would rather have more water than coffee grains but maybe that's just me.
oh god i just realised that everything is raytraced with multiple light bounces oh god
12:24 Also it would be a violation of copyright, I'm sure...
puns
i hate coffee. i clicked like and subscribe anyways. and i am very hyped about whatever david doesnt do next ^^
In postulating prospective percolating paths, you are not proposing perfect particle *positions* but the ideal percolating path *probability.* This posits not on a particular particle placement but rather the preferable particle *proportion.* Pinpointing this preferable percentage places a practical perimeter on the possible parameters particular to this problem. Plus, pondering prospective particulars permits a pointless penchant for prolonging ppthbbbb
Man, I love your videos, they really remind me of Vihart, I hope your channel is gonna blow up some day
Unrealistic societal expectations for how fractals should like - best line in math RUclips
I am currently studying food engineering, so this was particularly fun :)
It's crazy that I was able to understand all of this complex topic that I have never even learned a thing about before just through this video! You have great teaching skills.
i love this channel and how you take a random Topic of normal Human life and make it sience
Usually I'd watch this type of content on the background to fill time and maybe learn something new, but this? This (and much of your other work) is art, I feel like I'm missing out on so much more if I don't pull my full focus to watch. Although it might not mean much from a random person who's not even close to qualified in content making, bravo is all I can say.
very kind words, thank you :)
i watched this video for the coffe yet you never even said what the optimal density is!!! the other stuff is cool but i want my coffee optimized damnit!
more specifically im wondering what the critical density for the 2d and 3d cases are as youve replied to someone else saying the results are different
Yeah in retrospect I agree. I think I wasn't explicit enough in saying that the video wasn't *actually* about coffee but rather about phase transitions, fractals and renormalization groups (things that are taught in high level physics but can often be confusing), through the guise of something relatable like making coffee. To get the critical density you'd have to do essentially do the experiment over and over again for different densities until you saw the transition point... I just can't afford that much coffee but that would be a fun video in and of itself lol.
Using the way I set things up in the video in 2d the critical density is I believe like 0.59 (you can kinda read it off one of the graphs). In 3d I believe it'd be 0.3 (altho that seems low to me... it could be 1 - 0.3). Theres an entire wikipedia page called 'Percolation Thresholds' where they report all the different percolation critical densities for a whole lot of different geometries in 2d, 3d, and so on.
@@not_David neat, ill check that out tommorow when it isnt nearly midnight
I learn about PID in control theory the first time on coffee forum. Espresso world is full of engineers and nerds.
its not me
11:37 I distinctly remember doing this in my nuclear engineering class. We called it “homogenization” or something similar
Dude, just stir your coffee. Stop being lazy.
I clicked on this thinking it was a blender tutorial on how to make a more convincing 3d render of a cup of coffee.
So like, do people never use instant coffee? I’ve only ever seen coffee videos with ppl using beans n shit…
all that maths and such was interesting and really well explained, but how does this help me make my espresso :(
love the subtle references! your humor and writing is on point!
Your animations are so good that i feel like you copied the animations from a big RUclips channel
I don't know about that! I know how gerrymandering works.
i literally had the exact same thought looking at my coffee thats crazy
took me twenty minutes after i finished watching to realize i can do the same thing to find the optimal density for a bowl of weed
This the best physics-related coffee video I've ever seen, good job
personally I think we need to start conceptually tying more things to coffee. Thank you!
Okey, but did your modell predict the perfect Coffee/Water ratio?
wait... this had nothing to do with actually making coffee...
finally the optimal coffee recipe for my spherical cow to get her energised before her long shift in the frictionless plane
I still dont get how to turn the density to a perfect number of grinds and volum of water
1:50 I do have to say that is a nice orange (with context)
if this is a reference to what I think it is then this is my favourite comment so far
@@not_David yes it's from the same guy who once spent 30 minutes talking about percolators, I got you fam
coffe enthusiasts creating antimatter in order to have a 0.2% higher dopamine hit
The real reason we wanted to see if anti-matter falls up or down is just to improve our drip-coffee making technique.
🇨🇱
I have watched 1000's of YT, but normally don't subcribe☹️. Bad for me, I know.
But your so very underrated channel made the excepion‼️
Congrats!! Subscribed!!
Saludos de 🇨🇱
high praise, thank you :)
Awesome shit man. Perhaps the best introduction to renormalization I’ve ever seen
This channel is like 3blue1brown X Primer X Vsauce
I remember doing a mathsy project at uni where we basically used the spread of a virus through a household, then sort of used recombination group theory (though I had no idea it was called that) to apply the same maths to a system of multiple houses, basically assuming there was a tipping point in each household where everyone gets infected, and this exact same thing happens for cities, and then countries, and that is how to beat plague inc
I can't believe I didn't know about maths that was as important as this is until now
ohh thats interesting, im gonna have to take a look at that. Thanks for sharing!
a few questions: It would've been nice if you said what exactly the grid of coffee+water models: the (top or bottom) *surface* of the, eh, "brewing cup"? Or a cross-section? Does it change the outcome if instead you try to model a 3D cube of coffee grinds and water?
Also first you defined density as the ratio of coffee grinds to grid space, saying at density 0 there's only water and at density=1 there's only coffee, and for 0
great questions, I'll try to do them in order.
This is would be more of an "abstract" 2d coffee in this case, I don't think it could work as a layer or something like that. 3D would still work and be more interpretable, the only reason I didn't use it is just its harder to visualize. Everything remains true in 3d, the only thing that changes is the value of the critical density.
Whenever you talk about density, we have to assume like a nominal density. if i tell you the density of air in the room and then you take a cube and calculate the actual density within that cube, it will deviate from that true density, and the smaller that cube becomes the more it will deviate. Here the nominal density is fixed, but because the grid is so small when you pick random values the measured density in any given trial will vary, but averaged over all the individual trials you'll get the nominal density. Thats what the discussion around 4:43 is about. Of course as we increase the grid size the measured density will approach the nominal density as it does later in the video.
I would say this point is my biggest self-critisism of the video looking back. The idea is that, in theory, you should try to get the density as close to the critical point without going over it for the "perfect coffee". And the clsoer you get to that critical density the more the grinds will resemble a fractal. This of course assumes you like a strong coffee and does not take into account that some people would like a weaker coffee. In this case, you'd want to back away from the critical density instead. Of course in practice finding what this critical density is from a real espresso basket is not easy, but conceptually it would follow these same rules. I just wanted to use the idea of making coffee to motivate phase transitions, fractals, and RG theory, which are some of the most important tools in physics.
Instant coffee granules... Instant coffee will save you all this hassle lol.
I absolutely Love the Video, but I could not find the answer to the coffee Problem. Should it simply be half coffee/half air? It is it impossible to make a good coffee as it is impossible to Hit exactly 0.5?😂😂
Yeah I was still trying learning to make a good script at this point in time -_-
I kind of touch on this towards the end, but not explicitly. The exact point that you need to hit is not 0.5, and it will change for the exact geometry you use. In the case of a 2d square lattice with 4 neighbours its 0.6, with 8 neighbours its 0.4, in a triangular lattice it is 0.5, and all of these numbers will change if you change the lattice. These numbers will also change when you go from 2d to 3d.
The 'perfect cup' (though obviously this is hyperbolic) is then the one that gets closest to that critical density, without going over it.
Of course, in the real world, we don't really have a 'lattice', its more of an amalgum, so finding the critical density itself is going to be very difficult (though certainly if you did repeat measurments you could estimate it but that would waste a lot of perfectly good coffee). But the cool part is is that even though these densities will change as you change the lattice, the properties of the fractals that emerge are completly indepedent of how the grinds are arranged (so long as you don't change the dimension, but thats easy to do). So once you're at the critical point, you can learn about the system (e.g., coffee) regardless of how the grinds are actually arranged or 'connected' etc..
One application of this is in systems like the brain which are hypothesized to be at a critical point. Even though connections between neurons change from person to person, in theory the fractals that arrise from neuron firing patterns, should be independent from these differences between people, which allows us to learn more about the brain without worrying about these differences.