The Statistics of Microwave Popcorn

[@mgostIH]

11:00 The pdf is the derivative of the cdf, so that's the inverse function theorem on the cdf (1 / f'(f^-1(p))), giving you the derivative of the inverse of the cdf, the inverse cdf is the quantile so this is the quantile density function (qdf)

[@physicsforthebirds]

That's beautiful! It's even already in the right form for the inverse function theorem. Thanks!

[@kaidestructor7350]

Exactly what I was thinking, BTW, is it a PDF or a WORD?

[@incredulity]

Omg GD hacker

[@Nice-jd2sl]

​@@kaidestructor7350 a document file on computers😁

[@BruceWayne-eh1pz]

Swear to god I stopped for about 5 solid minutes and looked at your comment at least 10 times and I still can't read it, it's some sort of elvish ...

[@SepiaSapien]

I like how something useless as gravitational waves helped humanity understand more meaningful stuff such as popcorn pop's

[@LuskyMJ]

Ah yes. Gravitational waves are useless and defintively not one of the fundemental forces that define how our entire universe works.

[@Periwinkleaccount]

Can someone _else_ point out this person’s spelling mistake?

[@realperson9951]

@@Periwinkleaccount sure meaningful*

[@Periwinkleaccount]

@@realperson9951 there’s a second one.

[@belischluple6329]

@@Periwinkleaccount keyboard warrior lmao

[@badguy562]

I like how you connect so many fields of science just in one topic

[@MahBor]

That's the beauty of science! Everything is connected! It's surprising what similarities a whale and asphalt have for example. I wish science was taught like this at school.

[@zuz-ve4ro]

that's how you do serious science lol

[@GeofreySanders]

I like popcorn.

[@unlisted9494]

That is because all spatial dimensions exist in the same space so all forms of math are connected, because being connected is what allows base 10 math to work at all

[@NexusOfChaos]

and even better "fail" at the "original purpose" of the video, ending up not giving a new way to pop your popcorn. *obviously* the original purpose was to go through all those different fields of science using something familiar, but im just running with the script

[@nirajmehta6424]

I wonder if the popcorn companies looked into this same kind of statistical analysis, or if they arrived at "wait 1-2 seconds between pops to pull out" as a gut check, from years of experience making popcorn. Great video, and the first of yours that I've seen. I'm definitely subscribing

[@Hyperbolic_G]

There is R&D but not quite this in depth. You quickly find that popping any longer burns the popcorn and ruins the flavor, less is underdeveloped and lots of unpopped.

[@winebartender6653]

​@@Hyperbolic_G The other variable not taken into account here is the power of the microwave. As an example, we have a 1250w here and man, you are really pushing towards the 1 second or less between pops before it is burnt lol.

[@hotketchup100]

@@winebartender6653 I have seen a few bags that had different instructions for different power settings.

[@mixiekins]

I dunno, seeing shows like How It's Made and ザ・メイキング have shown a lot of food industry quality control testing, which implies there was R&D to establish said protocols.

[@nolansprojects2840]

@@winebartender6653most microwaves you can adjust power settings, but I really like imagining a group of frat guys freaking out as they try to listen for popping to slow, but not too much. 🤣

[@jamprer860]

I've just started my first course on data analytics and I could see this video being shown to all students as a way to show the applications (and I'll definitely recommend it to others). Amazing work!

[@rlrfproductions]

This channel has been a fantastic discovery because it's someone with my exact intersection of niche interests and hobbies, but importantly also the drive and energy to actually go through with the crazy ideas like mathematically model popcorn intervals in code. I live vicariously through this content.

[@franciscopostigogarcia2694]

adhd

[@utamari]

Adhd doesn’t mean it’s not fun

[@Sestaak]

Here's another tip! Shake the bag shortly after you notice the popping slowing down, helps spread the heat, just be careful not to burn yourself. I get noticeably less unpopped kernels that way.

[@PewPewCricket]

but its still in the microwave?

[@Sestaak]

@@PewPewCricket You take it out for a few seconds, then put it back in, dummy.

[@isengrom6883]

@@PewPewCricket yea but it doesn’t remain in the microwave, you eventually take it out

[@MFKitten]

I was just thinking "how much does the kernel-to-kernel heat transfer factor in?

[@svps169]

​@@isengrom6883so y'all are saying after the popping has slowed down, if I shake the bag, it will help pop more kernels even after it's been taken out of the microwave? 🤔

[@aayushde9346]

Man, this channel is popping off! Another great explanation, which covered a variety of topics.. Definitely one the best channels to come about in the last few months... Keep up the good work, Physics Bird.

[@level_breaded5364]

Nice pun bro

[@aayushde9346]

@@level_breaded5364 I hoped it wasn't too corny..

[@level_breaded5364]

@@aayushde9346 ok now you’re pushing your luck

[@LinusTechTipsTemporary]

@bradynlee0933 lma wut

[@uga7473]

lmao good one

[@gao1812]

Fun Fact: You can make delicious microwave popcorn that is CHEAPER and SOFT (doesn't get stuck between your teeth). Simply buy popcorn corn, put it in a large glass bowl (only enough to cover the bottom of bowl), add a thin layer of water (very little, only covering the kernels halfway), place a glass dish on top of bowl. Microwave at highest potency until just before popping sound stops (timing is finicky and can be tricky, might burn a few times before you get it just right).

[@Milark]

This channel just randomly popped up and started prolifically making some of the best science videos I’ve seen. They’re so nice to watch.

[@john_lemon4205]

Man literally proved that popcorn popping slowing down in a microwave means that most of the kernels have already opened, using complex mathematical analysis. I love this channel.

[@bluetube8824]

I lobe that this video does a ton of math and experimentation and detailed exploration of the science of popping corn, and then concludes with "Yep, the instructions are right." More seriously, confirmation studies are far too uncommon in science. This sort of thing should happen more often, not just on KZbin, but also in academia. Brilliant.

[@monicarenee7949]

My favorite part of physics class in college was that we would do labs to confirm the formulas we learned in class. It made it all make sense to me

[@cenotaph152]

The thing I love about science and engineering is that the practical application of mathematical concepts, even to seemingly random situations like this, can give insights that allow objects and processes to be further refined and optimized to improve our daily lives. I’m Glad the algorithm recommended this video.

[@jackkrell4238]

Unfortuantely, some people take this kind of cience for granted and just think that these concepts should be taught in a classroom or reserved for more overarching phenomena. The calculus puts me off a little bit, but the rest of the content is easy to understand.

[@Onoesmahpie]

@@jackkrell4238 It's easy to understand if you don't use your brain. His use of the central limit theorem is at worse flat out incorrect and at best not properly explained, to the point that he doesn't really justify its use.

[@ajplays-gamesandmusic4568]

If you want more of the kernels to pop, unfold the bag and use your fingers to rip the adhesive on the bottom left and bottom right of the bag, this allows the bottom of the bag to expand more as the popcorn pops, and because there's more space, the popped kernels have more time before they burn, thus allowing the unpopped kernels more time to pop.

[@SnowyYukiThe2nd]

That’s pretty cool,it seems worth it to count. That 10% that’s unpopable always made it feel like there wasn’t really a right way so long as it didn’t burn

[@rowgesage936]

I did a project for university where we needed to find a wolf's howl in a large dataset and use the time-delay between different microphones to triangulate it's position, and we used the exact same method of detecting signals as you did! We did however not use the [-1,1] trick for the moving average to find the starting time so it gave us a lot of headaches! You just solved my internal conflict for not finding a short/satisfying solution for that problem. Thanks!

[@RodrigoCastroAngelo]

Great video! Just one small detail, the central limit theorem requires that the variables are independent and have the same distribution for their sum to converge to a gaussian

[@chrispiech]

Super important comment

[@primenumberbuster404]

This channel is like oversimplified but for science instead of history.

[@geosultan4]

The algorithm recommended this video to me, and I decided to watch as I washed some dishes. All the popcorn talk made me want to go microwave a bag, then I wound up watching two more of your videos. Great content! I love your narration style and your simple explanations of difficult concepts that I would have loved when I was struggling through 100-level physics!

[@remiwi2399]

I literally subscribed like 2 days ago and at the same time have started making microwave popcorn more frequently. This video is for ME

[@Telectricity]

The use of the Central limit theorem here is not exact, it's correct for sums (or averages) of variables coming from the same distribution, so not for sum of the different things that cause popcorn to pop at a certain time. I'd say the reason that you should expect pops to be distributed normally is because you are averaging over many kernels that might pop but not because you are summing over the reasons. regardless, I really like the channel and I'm happy to see it's really gaining attention.

[@dario8863]

I am a student in economics at the ENS and I have in my study plan Statistical Physics, I am loving the patterns that repeat themselves for all these different phenomenon, the fact that aggregation of these simple events gives birth to complex system approaches gives me the idea that the scientific method talks in the same way, we are only separated because every human is limited

[@wertacus]

I can't believe I only recently discovered this channel. What hard hitting science. I pop my popcorn methodically as well

[@SapientPearwood]

This channel is way too good for how few videos you've made. I really love the way you attack the whole problem, incorporating as many flavors of physics as neccessary to get to a satisfying explanation. I'm a fluid dynamicist, so I especially like when you dip into the wonderfully confusing world of fluids, but really all the physics explored in these vids are interesting and described exceedingly well. Also the art is great. Just all around excellent work!

[@juancruzbaudino7389]

I’m really amazed by how many different concepts are condensed into one video. Not only do you spot the similarities between them, but also do the math and draw great conclusions! You need way more subs

[@adancastro2220]

Some years ago I've discussed with a Matemathician and a Physicist friend the popcorn topic... I asume the "popping" as a logístic function depending on time, comparing the process of popping with a second order transition phase. The density of "poppings" in the microwave time Interval must obey a probability distribution, althoug at beginig my Friends laughed at me they concluded it would be interesting to do some experimentation and get the data... Sadly it was a tough moment of My lfe and I had not resources (time, money, entusiasm) to do this research for fun. After all this years I've learned new concepts and realized My idea for popcorn experiment translated into a logístic map may show interesting aspects of dinámics and criticality... Wee know that logístic function has proven to be more than the eye catch ;) PD great channel, great content! ... I. Suscribed Yesterday after watching your vídeo on why we like Jazz.

[@jaskatharina]

i love that the internet has become a place where you can watch a well produced in depth video about microwave popcorn. great video

[@mrlindsay123456]

Dude you just made so much of my time in college start clicking together. These aren’t just abstract concepts…they’re tools! Tools that can be used to do awesome things!

[@ldx8492]

6:38 you can pinpoint the precise moment I fell in love with you and your channel and instantly subscribed

[@thomasrokicki]

This channel needs to blow up more - so here I am in the comments. The content is unmatched. Great stuff!

[@christiannipales9937]

What a world we live in. To put so much scientific knowledge to understand the mundane. Truly, we are blessed

[@zacharynolan9553]

I love the nerdiness of how you pop your popcorn. It is unbelievably cute :) Another great video!

[@kraftzion]

Dude. Anybody that can connect popcorn popping and black holes merging has earned my subscription.

[@ilyakiselev4209]

Brilliant video! Live the style of presentation, the homemade scientific experiment and the opportunity to learn a whole lot of different concepts and ideas on one video. Glad I subscribed 😊

[@imsleepy620]

bro really just did a long mathematical and statistical derivation to get the same number as the bag really glad im subbed tho

[@andymoo00]

Great video I really enjoyed it! However 4:30 is not what the Central Limit Theorem says, and it leads to an unfair assumption that the the time it takes for a popcorn to pop is normal. The CLT says that the sum of i.i.d random variables tends to a normal distribution as the number of RVs increases. The CLT really doesn't say anything about adding distributions in general. The example with the dice illustrates the CLT well. However 4:30 what you're doing is adding a simply adding distributions together (a small number at that), the problem here is the distributions are definitely not identically distributed (if we assume the distributions for strength, volume etc. are represented by the drawings you've shown then you can clearly see that they aren't identically distributed). The reason why it works for the dice example is 1) because for any die there's a 1/6 chance of rolling each number, so the each dice throw is identically distributed, and 2) they're clearly independent and also you in the video you show what happens in the limit (i.e involving a large number of dice). Applied to popcorn popping times the CLT would say something like: if you take a bunch of popcorn and pop them, and add up the time it takes each one to pop, then "the sum of the time it takes for each popcorn to pop" follows a normal distribution. Note that it importantly doesn't say anything about the underlying distribution of the time it takes a single popcorn to pop.

[@seanflancrisco]

Came here hoping someone would have pointed this out

[@renyhp]

I agree that the video could've used a bit more rigour in that point, but I do think you can use the CLT to say it's gaussian. The point is, the distribution that he shows on the left are not added in any way (how could you even add volume and position?!), but, the thing is, each of those variables contribute for some dt to the popping time of a single kernel. In other words, the popping time of a kernel is a sum of many values that depend on many different variables. Even if those variables are not normal, their sum can be approximated as such, because they are many. This is very similar to the assumption of normal errors when doing regression.

[@lc7269]

Hey, I don't know if you'll read this, but I think this will be super helpful for your lisp. I used to pronounce my 's', 'sh' and 'ch' sounds from the side of my teeth. This created the same sound you are currently making. When I asked a friend how they made theirs, they said they produce it at the front of their teeth, like theyre about to say 't' but blow out instead to make their 's'. To make their 'sh' sound, they would curl their lips like theyre about to kiss and blow To do 'ch', they did the same but with a rapid stop. I tried to copy this myself and it completely got rid of my own lisp. It was a bit hard to get used to, but it's now second nature to me. I hope you actually manage to see this and I hope it helps you along your KZbin journey :D

[@utkarshsinghal4291]

Really cool video! PS: Could you share the popcorn audio and the pop times? I'd love to play around with the data.

[@zoidsfan12]

I genuinely love the fact you straight up count each time you pop popcorn lol. For me I figured out years ago that 2:25 in my microwave gets it pretty perfect and just go do something else while I wait on it. 2 different mindsets, the "good enough" mindset and the "there has to be a perfect formula for this".

[@endopol]

The normality argument (4:34) seemed very suspicious to me. You could use the same argument (that a random variable has many contributing factors) to show that, for instance, mealtimes are normally distributed throughout the day. To apply the CLT, you have to believe that each independent factor has a negligible effect on the sum.

[@Onoesmahpie]

I agree, I was disappointed to hit a wall so quickly when using my critical mathematical thinking. Shame so many pop science channels have to be so lazy and hand wavy with math.

[@robertviragh6527]

I just got started watching this video but it raises a good productive point about instructions, whether on microwave things or other products. Very important!

[@crazychashews]

For those who hate having extra kernels, before putting the bag in the microwave flatten the seeds evenly throughout the bag so they're not clumped up If you just tear off the plastic and pop it in, it will be too clumpy and won't cook evenly. I always spread out the kernels till everything is flat and I only get like 3-4 kernals.

[@ThatRandomNova]

oh my gosh, I need to try this, thanks!

[@kuratse205]

This is the most physicist way of telling people to read the instructions on the packaging. I love it.

[@andreasflensmark8616]

That was very cool, would love to know more on the subject. I study chemistry and found your statistics very interesting

[@hedgehog3180]

It is really clever how they managed to turn a fairly complex problem into instructions this simple.

[@ImBarryScottCSS]

Cosmic pop 😊

[@Beastw1ck]

I feel so overstimulated by most of the screeching KZbin content vying for my attention so I VERY much appreciate the chill demeanor of this channel.

[@frederiksvane9787]

Rarely comment, but I have to say that this video is outstanding! The style, the pace, the wit, it's almost perfect! Please make more!!!

[@Volvith]

"So before we can explain how long you should microwave your popcorn, _let me explain astrophysics."_ Yep. Found the reputable and needlessly in depth source. _Bless you._

[@Andrew-yr6ig]

I love that there are many of us that want to rewrite users manuals using the same techniques that the original engineers probably used to develop their guidelines.

[@Potoaster]

I absolutely adore the interdisciplinary education aspect of this channel! So many disparate fields of math and science working in a lovely tandem!

[@MuonRay]

Great video and touches on the topic of the dichotomy between closed "black box" system and environment in which many systems such as complex, quantum and unobservable systems fall under. The thing that always blows my mind is how complexity, in the signal space which can be represented as the networks graph space, always seems to emerge here. Once you go down this rabbit hole it never ceases to amaze how much deep structures are hidden and find commonality across the scales. Something about the interplay between the physical laws that govern heat transfer and percolation in a bag of popcorn and similar effects in Bose-Einstein condensates give me big "theory of everything" vibes!

[@fdmugen4724]

Im not surprised the instructions are spot on. People who love popcorn LOVE popcorn

[@conween]

the amount of detail is astounding, i love it

[@silvesterreen2902]

This short video made me spend so, so much extra time reading up on concepts and honestly is absolutely amazing

[@mattgach1779]

I just found this channel last night and watched all the videos back-to-back, and as soon as I’m done a new video comes out. I’ll take that as a sign that I should stick around and subscribe lol

[@emilybaker8175]

As someone who is an animator, loves birds, and wanted to be a physicist for a while, this channel is insanely well recommended to me

[@jackkrell4238]

I'm still dissapointed that this channel wasn't about the physics behind avian biomechanic( as that was the impression I got froms tumblign upon one of his videos), as the channels name is 'physics for the birds'. The fact that music theory, differential calculus, data analytics, theoretical physics, and some biology content has been organically interwoven into this masterfully produced video series makes up for the lack of ornithology information.

[@tjacob5603]

The amount of work to get the same answer is beautiful. More content like this.

[@JamieCracker]

I heard your voice and immediately subscribed. I don't know what it is about your voice but it's very lovely and fills me with joy.

[@googleyoutubechannel8554]

I like how this shows the very common approach every experimental physicist (or any problem solver really) quickly learns: auto fitting a curve to real data beats assuming simple stat model dynamics every time. Understanding CLM and gaussian distributions is nice and all, but basically the most de minimis part in the process of trying to model a system.

[@MeDoMeer]

God I love statistics. Idk why I'm also so satisfied that you just checked whether the bag instructions are right or not.

[@korne341]

You have the potential to rival Minute Physics and Minute Earth! Such great contents connecting so many fields together! Thank you so much for the great work!

[@lmackenzie89]

I LOVE this video. I've thought about this sort of analysis every time I've made microwave popcorn and always wondered why popcorn companies don't make an analysis app to help with achieving optimal popcorn.

[@viktortodosijevic3270]

I'm amazed at how creative you've been at sneaking in signal processing into a video.

[@grantm.9109]

Wow! It takes a lot of skill to make educational content that is genuinely informative and useful, while remaining accessible and engaging for all audiences. Multi-objective optimization really is one of your strong suits 😉.

[@nouwenlaroche]

Another wonderful exploration prompted by curiosity! Hope your birds have a nice day!

[@ardavalilable]

This channel is becoming my favorite, very enjoyable videos and kudos to the curator for making the whole thing investing and entertaining

[@daryan3033]

I love this channel and I'm not even 3 mins in, it's just the vibe, I want to listen

[@NorthRoyalton]

OMG I just got done doing my Discrete Signals and Systems homework and I was finally able to eat dinner and watch KZbin. But, then I heard the word Convolution and realized I could not escape my classes. Great video I love your channel. You make learning fun!

[@franksloe5087]

This is such great way to teach kids about scientific approach to problem solving

[@tobs82]

late night searching of youtube never disappoints, your channel was just recommended and i watched all your videos and they are all amazing, keep up the great content, the way you explain everything in all your videos is amazing and so well said. keep it up

[@theboogerbomb]

I've mastered the art of microwaving popcorn, I have 5 to 10 kernels MAXIMUM in the bag after I'm done with it!

[@bradarmstrong3952]

Great videos on your channel. Explaining a topic clearly and completely, without dumbing it down, is a real skill. Doing it in a way that turns out to be interesting, educational, and understanding is rare indeed. Keep up the great work!

[@fenderchen182]

You may not have taught us anything new. But you proved what we already knew, with statistics!!

[@felipecaetano15]

Thank you KZbin for this amazing suggestion. Loved the video! Gonna rush to watch the rest of the channel now.

[@p8p877]

this channel is so underappreciated

[@aaronrdaniels]

This video is fantastic! Helps frame some other concepts quite well, more to be learned here than fluffy corn balls being birthed in a small wave machine.

[@Carla-or1ls]

just watched all of your vids in this one sitting, you make really good content and i cant wait for more

[@hoodie_cat]

Loved this video so much, it reignited my love for mathematics.

[@sirradical]

I love this! We often forget that physics governs even the most mundane thing in our lives. Thank you for reminding me :)

[@jsimm00zonian]

Also worth mentioning your great graphics skills which helps present complicated statistical theories in an enjoyable manner. Good job!

[@roygbiv163]

I have a very rudimentary grasp of mathematics…but I still love watching your videos. Keep it up!

[@cola98765]

I'm so happy to be as early here as I am. This channel has such a potential. Animation, explanation of how problems are connected across multiple subjects, and non trivial calculations not hidden just becasue they are not trivial.

[@Phatxual]

You've changed the way we see popcorn, for the better!💯❤️‍🔥

[@toasture9119]

I love how im gonna learn more from this than i do in my math books and actually enjoy learning it

[@danielbraddock8648]

I'm so glad I found this channel, such a hidden gem.

[@shmackydoo]

One of the best physics videos I've seen in a long time. The work you put in and showed was covered in great detail. Nerds rejoice! A new KZbin Physics Saint has cometh!

[@CalvinG973]

YT just recommended this video to me. Great job!! :) I usually wait 5 seconds until the final pop, and it doesn’t burn anything.

[@FippeFi]

wow the signal convolution just solved an edge detection issue i was having with a problem and i actually have leads to research more as a result, thanks

[@TheBaxes]

Finally, an actual application of statistical analysis! After working with ML for a few years and feeling that I'm only using it as a black box is refreshing seeing someone use actual statistics to solve a problem. Can't wait to see the rest of your videos :)

[@JDogA-uh6mn]

Wonderful video! I’m halfway through a physics degree and I love seeing some of the concepts I come across in class put to good use

[@MervDeGriff]

Yes, you may not have taught us anything new... but you have empirically validated what we knew. That's important too!

[@alexanderkruszewski7306]

Another brilliant video! Love the channel, and a follow up point: if you want maximum kernels popped, make it on the stove the old fashioned way. I’ve been enjoying the luxury of all kernels popped for years now with a little olive oil, butter, a saucepan, and a bag or organic popcorn kernels which you can buy in bulk at the store. Add a dash of sea salt and you’re in heaven.

[@craigcraig6248]

What a gem of a channel

[@matti1770]

Never knew I could be so invested about a popcorn video. You pop off queen 🥲

[@utamari]

This covers nearly exactly what we’re covering in calculus, I’m showing this to my teachers

[@arduous222]

For the first time, I subbed to a wonderful education channel before it reachs million subscribers. I feel privileged that I could proudly say, I came here early!

[@MiguelGarcia-zx1qj]

I'm teaching statistics for engineers right now, and about to start explaining the Gaussian distribution next week. So your video comes out handy for the occasion, as a good example of the Central Limit Theorem that relies on every day experience, not on some arcane mathematical function shuffling. In any case I've enjoyed the experimental approach a lot; I'm also an occasional amateur home scientist. Thanks a lot.

[@lunaponta594]

7:10 I CANNOT BELIEVE THIS not in a million years would i have thought this weird channel youtube's been begging for me to watch interesting videos of, just throws the LICC on the FIRST video i actually watch instead of putting on watch later. it's not even related to anything so i really wasnt expecting. i love you and will now actually watch your videos out of sheer respect. may the power of the licc be with you.

[@brysonsmith1523]

this is by far my favorite youtube channel! Covers topics I love with enough rigor and topics I am interested in an easy to understand way ❤❤❤

[@Snadker]

Just ate some popcorn today and asked myself the same exact question as the video introduction. 😂