Simulating Competition and Logistic Growth

[@PrimerBlobs]

A number of people have commented that at 5:22, the green population should be expected to beat out the blue population because the blue population suffers from mutations while the green population benefits from them. That effect is real, but it's too small to tip the scales, and I determined it was too complex for the main message of the video. But because some people are interested, I thought I'd lay it out in more detail here. Only 1% of replications by blue creatures produce a green creature (4:52), and another 1% produce orange creatures. This means blue's replication rate is effectively only 98% of the stated value. 9.8% instead of 10%. The green population gets an expected influx of creatures each time step equal to 0.001 (a tenth of a percent) times the number of blue creatures. Here's a desmos graph of the expected changes per time step for blue and green, from the equation in the video. (The green equation has an added term for bonus creatures from blue's mutations.) www.desmos.com/calculator/zhig0dcftg x is the number of blue creatures, and there are sliders for the other parameters if you want to play with them. N is the total, and N-x is the number of green creatures. We can see that when there are 49 or more blue creatures we expect to gain green creatures and lose blue creatures. And if there are 44 or more blues, we expect to lose more blues than greens. But for any number of blues less than this, we expect green to do worse. Green is never expected to outnumber blue. This all assumes no oranges. The fact that the functions add to less than zero for any value reflects the fact that orange is gaining in any of these scenarios. So it's true that in this setup blue suffers losses from mutations to different colors while green benefits, but the magnitude of this effect with the given parameters is too small to make up the difference in base replication chance between green and blue. Additional sims I ran reflect this fact, with green regularly losing, but I chose to animate the first sim I ran because it was a good reminder of how chaotic this system is. I appreciate folks commenting with a critical eye, and this will help me know what to explain more clearly vs what to gloss over in future videos. It was also kind of fun to make the desmos graph. If you like it and want to see more desmos graphs when relevant to other videos, please reply to this comment and tell me so!

[@mehdibouchaffra868]

Thanks!

[@homeyworkey]

new subscriber here, whatever u put out i think im going to watch either way :)

[@SaganIII]

More of this ! 🤤

[@2haha447]

But dosn't this also influence the "death rate" because blue lose every mutation one who can not replicate you could maybe give both yellow and green a 1% mutation rate to get blue idk it is just an idea

[@Kamushy]

Primer wow

[@KDNG105]

sometimes youtube algorithm really gives you the good stuff like this

[@Blobbyboi986]

You are correct

[@timbo3406]

Yeah!

[@thinboxdictator6720]

if it is sometimes,then it is more likely a mistake

[@nicosalsa21]

Then we get actually happened videos only

[@dsi-films1264]

Yeah your right

[@scares009]

This is one of the only channels that I will drop everything to watch when a new video comes out. Love it!

[@MystGames]

nigga

[@bestbread3446]

rude

[@MystGames]

@@bestbread3446 not really, since it's not directed at anyone or anything. CHECK YO' PRIVILEGE, SON

[@vanthonvenus]

would you drop your child?

[@MystGames]

LillyCookies DDAENG no, but im sure you were dropped as a child.

[@budzikt]

My God, In collage I was unable to figure out from where numbers comes out and memorize all stuff related to logistic growth without understanding it at all just to pass my matlab laboratories. It's so hard to explain this so simple. Thank you, channels like this deserve gold medal and monetization factor of x100

[@erwinmoreno23]

Hahah your last sentence is what all of us think but couldnt quite express

[@rogeronslow1498]

That's the problem with most universities. They produce graduates that are good at remembering stuff, not necessarily understanding stuff.

[@poofy6959]

Collage btw

[@cqrcin0]

*College :\

[@umbuchscui]

College* And I’m 10

[@googly4038]

The way the blobs wiggle their hands.

[@Isvoor]

The way the blobs win our hearts.

[@henryg.8762]

'hands'

[@williamhuynh869]

The derp.... I love derpy stuff, like Quagsire and these blobs

[@awhahoo]

They vibin

[@bigmoniesponge]

@@henryg.8762 I need to watch his video now “5 ways NOT to think.”

[@rhysmartins8936]

Can't believe I've missed out on this superb content until now ! Keep up the good work man !

[@colleen9493]

Yeah same. Simulating natural selection just showed up in my recommended.

[@cartor7892]

Same just found this channel yesterday

[@NickNLouie]

I'm a fan for the excited orange blob

[@cgmelody6422]

Nick Louie bandwagon fan

[@Ziess]

I'd like this but it's at orange blob's favourite number, 69.

[@Poffean]

@@Ziess 87, let's get it to 420

[@extaponts2402]

Me too

[@outofcontext728]

You mean scp 999

[@BoneAppleTea]

If it's too crowded, you could also just snap your fingers

[@eclipserepeater2466]

At which point that whole "logistics curve" thing would quickly bring the population back up to carrying capacity. No matter how powerful the snap, its effects are ultimately temporary. :P

[@BoneAppleTea]

@@eclipserepeater2466 I know, Thanos was not a mathematician haha

[@Wm7forthewin]

+DEMON XD sorry boys we took over the planet and have gone to the moon and invented the internet

[@brendaajamu7152]

Love that sub

[@rage_2000]

*Orange blobs appear* Blue blobs: _I don’t feel so good_

[@VincentZalzal]

Clear and very well animated! For the mathematically inclined, you can read delta as the derivative of N with respect to time, since it is the variation of N. Thus, before adding the crowding term, you get dN/dt = aN, a differential equation whose solution is indeed exponential, N = exp(at) + c. By adding the crowding term, you get dN/dt = aN^2 + bN, and the solution to that differential equation is the logistic function, as stated.

[@PrimerBlobs]

++ Thanks for spelling it out. :)

[@hubierti]

Help me out here, if dN/dt = aN, then the integral of dN/dt with respect to t is N. Thus, integral of aNdt = aNt = N, right? What am I missing?

[@XenophonSoulis]

Thank you!

[@kvackkvackfrisk]

​@@hubierti No, since N actually is a function of t itself (you could write our differential equation as N'(t) = aN(t)) you can't just leave it be when you integrate with respect to t - what we're looking for is a function whose derivative has the original function as a factor. And in fact, the only function f(t) whose derivative f'(t) = some constant * f(t) is the exponential function, and the derivative of e^ax = a*e^ax so the solution must be, like Vincent stated, N(t) = e^at + C since this gives N'(t) = a*e^at = a*N(t).

[@Kryo_Ghost]

I am smol brain and i have no ide wat haf of dis is

[@gnikola2013]

You should simulate the predator-prey model I think it would be really fun

[@bodbn]

Blue blobs being sore losers

[@AltAccount-ko3pp]

I'm pretty sure he has done this in a later video now

[@biglefteye5017]

Kiritsu yes

[@ChaosAbandon]

He did

[@miniaturejayhawk8702]

@MsBizzyGurl na its more like gis first natural selection simulation. There he made it that when a blob was 20% bigger than the others it could simply eat them.

[@undead_boi]

This reminds me of some of my favorite teachers over the years. You take the time to explain a concept in detail, and show every step of your work, while explaining WHY it's changing and how it's affecting everything else. You also recap things we've gone over before, and recap when you finish a concept. It's wonderful, and honestly, has pushed me to add physics classes to the bio classes i was planning on when I return to school. You've rekindled my love of math, and I applaud you for it. Thank you.

[@oceanman_8370]

I love how when you run the simulations it's 3d models just sliding along a wall

[@purple_sky]

I believe it's a flat plane viewed from above, and they are just looking up because they know how to smile at the camera

[@conoroneill8067]

Thanks - I've been looking forward to this video for a while - you have a style that makes it very easy to listen to and understand. I'm looking forward to what comes next.

[@PrimerBlobs]

Thanks, I really appreciate the kind words.

[@kurzed4904]

so thanos should've just modified creature's stats to reach the ideal equilibrium at some point in time instead of killing the half of everything which is only a temporary solution. not so smart huh

[@MarkAlcarezBoston]

Yes

[@aquaphoenix-mt2iv]

He'd have to increase birth rates for almost all creatures (except humans, since they're the problem-) And increase how quickly plants grow (to sustain current human populations, and the soon to be increased animal populations from increasing their birthrates) And since he can't do both of those in one snap (those are seperate actions after all), he'd have to snap twice. Which would kill him more than likely. Also those variables would have to be very precisely changed So.. no, he really couldn't fix it that way. I do agree that decreasing population size was the dumbest possible solution though

[@TooHarshForYou]

Even if he didnt add , there was still a n equilibrium point , the thing is humans modified earth to increase ita carrying capacity to their own good and thus they influenced their own stats and caps

[@matyaskassay4346]

but don't forget that in real life the "stats" are determined by the environment of the creatures, and aren't fixed unconditionally.

[@user72974]

This guy literally just debunked Thanos.

[@tymorgan2107]

Sooo... you spent the first 3/4 of this video explaining the very basics of calculus? I'm not complaining. In fact I'm very glad you are doing this because it is very useful in explaining these kinds of situations where the rate changes over time. So good job, plus you made it more interesting than any lecture could be.

[@bingbong8761]

I'm horrible at maths and science so I don't always understand all the numbers in these videos but all the concepts are really well explained and easy to grasp with a second watch and well-worded google searches. The simulations are also really interesting, easy to follow, and incredibly entertaining, and all of this combines to make your videos some of the best I've seen on KZbin- thank you so much!

[@availablekjp0609]

"We've seen that creatures can grow exponentially-" (flip flop) "But in the real world-" (stop) "A realistic growth curve would look something like this." (HOW CAN YOU DO THIS TO ME)

[@Arkos.Knight]

"Sorry, buddy." Orange blob: *blank face*

[@theominouspigeon]

°vine boom°

[@ellathon2277]

Thanos’ plan layout when trying to *save the universe* .

[@yzraeloa]

ellathon22 this actually shows how futile Thanos strat is. Population would grow back in no time and even promote a higher replication ratio

[@TheRedMooncorp]

@@yzraeloa Plus you have an initial universal famine, since most logistics will be severly damaged due to the loss of half the officials, half the technicians, half the farmers etc. Thanos never really thought this through at all^^

[@IamCoalfoot]

@@TheRedMooncorp It took me about five seconds of thought when I heard his plan to realize he'd spent about zero seconds on it.

[@TheRedMooncorp]

@@IamCoalfoot I feel you. I mean even choosing specifically half is so stupid. Even if Thanos would be right, the optimal number of deaths would differ from world to world, but sure let's treat a well organized society with population controlls, a new colony with 500 people and a sprawling over populated world of slums the same 😂😅

[@cooperwright9515]

TheRedMooncorp population controls are a meme

[@zersetzung8550]

Oh how my AP Calculus teacher ruined variable specification for me, I know that if I didn't specify N' = Delta when doing a project like this I'd have gotten tossed out a window or something for not defining my variables sufficiently. Other than that petty observation which most people would just be able to figure out if they're not baboon-tier, this video is genuinely an excellently animated, excellently voiced, and phenomenally descriptive example of the fact that there truly are still amazing content creators on this platform. This will be the first patreon that I support, and I wholeheartedly look forward to your next videos in the future!

[@peterlewis2178]

I love how you condescendingly call people who are less mathematically gifted or educated "baboon-tier". It says a lot about you that you consider people to be tiered in that way, and consider yourself in a superior "tier".

[@h_3795]

Wowwww I wished my calc teacher taught it like this when we learnt logistical functions. Never realized why dN/dt=N is exponential and dN/dt=-N^2 logistical.

[@b1rd1e81]

I knew that it was exponential only from integration, cool to see the visuals though

[@h_3795]

B1rd1e yeah I know how to integrate it but it didn’t make sense conceptually.

[@dvirkomlosh4152]

@@h_3795 can you maybe explain? I really wanna know how to get the function of N from the Delta function

[@h_3795]

dvir komlosh shoot idk man. I can give you the proof with integration but idk conceptually. But here’s what I think. The reason why tho that dN/dt=N is exponential is that it doesn’t have to move to the right in order to increase faster. Simply increasing makes it increase faster. With dN/dt=t, which results in a quadratic, much slower, you have to increase t in order to increase faster, which lowers the slope.

[@h_3795]

dvir komlosh oh I’ve just figured it out. You know that the derivative of y=e^x is e^x, so dy/dx e^x=e^x. Since y=e^x, dy/dx=y

[@Sephirothfrank]

I absolutely adore this series of videos, I can't watch enough of them! please keep making them

[@joshuahudnut4992]

I have my BA in biology I wish a few of my professors would have used something like this, a lot of people have a hard time understanding population growth. Very informative

[@carlosbarzottowirti1895]

I should be studying... but as a former biology student, and as I'm fascinated by genetics, I just can't stop watching this series

[@konokaiza]

Please don't stop making videos, your videos are the beauty of KZbin and are really satisfying, enjoyable and interesting.

[@georgplaz]

*Edit* : read response by channel before liking my comment ;) I doubt that green won because of luck in the simulation at 5:19. Blue loses offsprings to mutation (both orange and green) which makes blue worse than the stats suggest. Additionally green has a higher birthrate as blue mutates into green. Although I have to admit that you didn't show the mutation rates, so they could be small enough to be negligible. I think for a better comparison both orange and green could mutate back to blue with the same likelyhood.

[@vantutri9571]

This white haired guy is right

[@PrimerBlobs]

I didn't add a label for the mutation rate, but I did say that orange and green each come out of 1% of blue's mutations. So blue is still 98% as good as the written stats suggest.

[@vantutri9571]

@@PrimerBlobs yeah 98% is only for one generation though. Blue is destined to extinction

[@vantutri9571]

@@PrimerBlobs oh your videos are lovely and almost unique btw. Can you make a video about yourself, how do you make these videos and how long does it take? Thanks a lot

[@georgplaz]

@@PrimerBlobs You are right. I missed that! And yes, 1% is pretty negligible. The mutation rate does really "feel" a lot higher though. But I'll take your word!

[@Zoova]

I love how this KZbinr just sprouted up with confidence and good quality. Most people start nervous and slow with no audio or something like that. I'm not saying that's a bad thing, I'm just saying that this is way better. It's awesome.

[@liamcourtney390]

You are the only KZbinr of quality

[@munzeralseed]

It's been 50 days! We miss your videos!

[@PrimerBlobs]

Haha, thanks for the enthusiasm. Rest assured that more are coming. I'm getting impatient too. :P

[@munzeralseed]

:D

[@theprofessor1554]

@@PrimerBlobs :D

[@Hansgilhaus]

Plz do a video on simulation of life and why these ameobas are pear shaped

[@Hansgilhaus]

They ameobas cuz they look squidgy and there hands stretch from their bodies so there pseudopods

[@Zoova]

I would like to say that I absolutely LOVE this. I also love the fact that so many people are on board with this series, this topic, and this channel! It actually surprises me how many people like this stuff besides me. Thanks Primer!!! Also since you're going this high so fast you might want to put that face reveal at a higher sub level. Just saying.

[@johnnyi1337]

Man your videos are fantastic, I'm sure many people would kill for more frequently released episodes

[@pnpgod7904]

I never understood graphs and stuff, like parabels (i don't know if that's the right word, i'm german, so i don't know the special terms for that) in school, but you are really outstanding when it comes to explaining something. Great job man!

[@atilacorreia]

Thanks for giving me a solid base to my next simulation game.

[@mangjyz6336]

0:28 could of been a really nice city landscape ya know

[@AndrewFaberProperty]

Just found this channel, fantastic videos! I’ve been looking for a good educational economics channel for a while

[@alfon375]

Thanos should watch your videos.

I like how you explain these differential equations in such an intuitive way.

[@randomizer01j23]

0:06 even though we have limits in the real world it’s still nice to see that the human population looks similar to that graph over the past 150-200 years

[@NickTheHunter]

The video, the music and the presentation of the information are excellent

[@jonnySmashes]

This guy could write codes for old school RuneScape. Lots of equations like this. Really helped me get good at math as a kid. Great vids

[@professionalmemeenthusiast2117]

Never forget that he retconned where the orange blobs came from. Personally, I prefer the original lore, and I'm not calling it 'Legends' or some dumb name like that.

[@alkali5841]

TELL US

[@fbiguy6096]

I can say that this is helping me with my trapping course because you talk about the carrying capacity. Keep it up, your vids are epic.

[@jordanmackenzie5279]

This is one of the best channels on KZbin. Huge fan.

[@guidocampostrini]

This quality videos are the reason why KZbin is an amazing place

[@erinnlynn7]

I wish there were more of these videos! They’re very interesting and informative.

[@tony_yt5967]

This is an awesome way to grasp derivatives too wow this is an insanely clear explanation too thank you 🙏🏽❤️

[@Bananappleboy]

0:12 *_"Sorry buddy."_*

[@danizk0]

I love how enthusiastic he sounds about creatures dying at 3:16

[@blacknoir2404]

Ooh differential equations in disguise

[@PrimerBlobs]

Shh

[@buygeorgeivegotit7203]

I will reply to not shh

[@buygeorgeivegotit7203]

And use my home account tomorrow

[@awhahoo]

@@buygeorgeivegotit7203 F

[@jacobchavez7876]

These videos are so simple, yet SO entertaining

[@BiIlDipperIy]

I really hope you're a teacher somewhere. I learn more in these short videos than I did sitting in a high school class lol. The simulations and animations are top notch

[@hstera]

This is like 3Blue1Brown standard quality! Good stuff man!

[@01Myst10]

shoutout to my guy for putting so much work for 7 minutes of goodness

[@michaelboyd8546]

A good lesson about logistic growth without a single mention of calculus.... Impressive. Clearly calculus is still evident, but the idea was presented flawlessly without it. Good job!

[@MrDoodleDood]

Those videos are amazing, very high quality. Thank you and great work!

[@jiffylou98]

I’m in a calc 2 class rn and just had a test on differential equations (of which logistic growth is one) and it just occurred to me that logistic growth is just the next polynomial step up from direct growth (adding one term)

[@aksiiboy]

Would love to see your take on something like the rabbit and fox problem, or some other version of populations that have growth rates variant of eachother. Love the videos!

[@vithushanjegatheeswaran5317]

I have multiple questions: Which programming language do you use ? How do you visualize all these stats ? Where can I learn/read more about genetic algorithms, which is related to this topic? Thank you so much for the videos I like each and every one of them

[@Reality-zs2mf]

I just stumbled upon these videos and I really /really/ enjoy how simplified they are. I enjoy watching these kind of things. Keep up the good work

[@weirdoalert194]

I have been watching this man's videos every night while I fall asleep, my plan is to absorb the knowledge that this man holds and I will eventually become unstoppable.

[@bluecometzola773]

i'm really mad you didn't simplify the bell curve into a quadratic equation. im so invested in how beautiful functions look

[@vlgado3895]

Hi. You have very nice content on your channel and it is very easy to understand. Personally I think you use the term "evolve" a little to much when "adapt" would be more appropriate. I see your point of view at 6:20 when the blobs turn into rooster and rabbit. I think the species barrier cannot be broken since all mutations are bad (if you ask a doctor instead of a biologist), and all attributes need to be there in the first place. Thank you again for your nice posts, I cannot wait for the next one.

[@doyo1111]

this is the best channel to procrastinate to.

[@ChooceMooce]

Really enjoying this series. Great work

[@kristapskarnitis9613]

Excellent quality for the visuals and commentary - great stuff!

[@martinleithe8251]

So calming and easy to enjoy. This is so satisfying

[@royprincipe4590]

Wow! I just love watching the blobs. Great animation by the way!

[@justgame5508]

With the current covid -19 situation, simulating logistic curves makes this video relevant once again, well done KZbin algorithm

[@marcushendriksen8415]

I learned about this channel from 3blue1brown's website, in his FAQ, the first question he answers is what does he use to animate his videos? He mentions you as an example of not only someone who took inspiration from him, but did the best in coming up with your own unique style, so I thought you were worth checking out based on that. I'm glad I did, and what's more, I liked this video so much that I've just subscribed :)

[@BriarValley]

These videos are so chill and fun to watch. I'm glad I clicked on one when it was randomly recommended. I love watching the adventures of these little blobs!

[@stephenlujan8512]

Surprised the math this guy used wasn't explained a bit more. You can solve for the crowding coefficient with algebra, plug 0 in for delta and any number you want as your equilibrium stable maximum population for N, and you can calculate the crowding coefficient that gets you there. Also the delta curve is the derivative of the population curve, while the population curve is the integral of the delta. With the formula for either you can use basic calculus to get the other.

[@thecityshanker8913]

I am so glad I found this channel It’s funny and I’m learning about something that is extremely complex easily

[@Jazzafritsch]

Dear God biology economics and maths. I love this channel 😍

[@ok-kk3ic]

Jazza Fritsch / Do you actually find economics interesting? How interesting? (seriously asking btw)

[@Jazzafritsch]

@@ok-kk3ic very I never took the class but I would've if I had more units too my friends becoming a economist so it's great hearing him talk about it and now these videos

[@harmitchhabra989]

Hey guys Delta is Just rate of change of N with time So you can write it as dN/dt and solve the differential eqiation yourself to get N as a funcation of time This allows you to experiment with the crowding death rate Say you want it to be dependent in the square of population Also you can try adding a food competition death rate ans solve to get a new function of N in time. Have Fun! The whole simulations is based upon this central idea of buildind dN/dt using terms we can comprehend and in a way tgat the rate makes sense to us And then we let the math do the magic tk get N as a fn of time. But also to implement this simulation you would have to apply a chance or probability fn too. Then you can make differential equation for all 3 blobs. Heck you van use OOP Classes to do so.

[@Akumasama]

Damn, now I want to tweak the code you're using to create random mutation, multiple environments, hunting, competing for mates... Sounds like a really fun hands off full "game of life" project ;)

[@Yato_q]

Episode 56 How the cReAtUrEs population goes on when you include anxiety, suicide, civil wars, revolutions, alcohol problems and the fact that the creatures are constantly using fossil energy instead of sunlight and water even though greenhouse effect does obscure damage to the creatures because of a lack of oxygen ps.: i like the videos :D

[@deveshangovender3825]

Finally KZbin recommended something stimulating... Keep up the great content

[@jacobr7729]

Just a hypothesis: the reason that green did better then blue was because blue had no way to "get founded" out of another species. When blue turned yellow or green, and eventually died out, it had no way of coming back. If green dies out though, it gan be brought back with blue.

[@shellyann1817]

5 seconds and I subscribed. God bless youtube recommendations for this good stuff!

[@vilanovitube]

This channel is incredible. Please, continue creating new videos! I love it!

[@PrimerBlobs]

Okay. For you.

[@henrikolsen5]

Excellent material. Very clear and informative. Great work!

[@tabbycatowo277]

I always love coming and watching your videos because I always learn something from it :3

[@ryann7466]

Schools need to teach lessons like this

[@amireinav1]

0:50 why use x as multiply, wouldn’t that be confusing?

[@davidp.7620]

5:50 Green is doing better than blue because the chance of blue turning into green is doing something equivalent to adding to "green replication chance" while also adding to "blue death chance"

[@XxKINGatLIFExX]

I'm binge watching all primers videos

[@livipup]

I love your videos! This is going to be useful in for future for sure :) It's nothing to complicated, but you always go over things that are easy to overlook.

[@FabioStuber]

Nice too see all the math about probability etc. in action^^

[@EnjoyCocaColaLight]

6:04 Also the blue always has a chance to mutate, whereas the green and orange cannot mutate and devolve back into a blue. So the blue will ALWAYS die out eventually. You forgot this part :(

[@jodieaustin4245]

KZbin recommended me your videos, and I've been binging since. I've been reading a lot about world leaders, especially the suffering going on in North Korea. I've always wondered how one person can end up on top like that, and it would be really interesting to see a simulation based on these structures. I'm still getting through these videos, so I might come across it, but I've just been so fascinated in the way that the world works, which has taken me 25 years to get to this level of curiosity. I saw the doves and hawks video, and I am wondering if it's a derivative of that, but at a way larger scale. Thank you for these videos, so much food for thought. I look forward to any videos you might make in the future :~)

[@tommywolmart265]

Man, your content is addictive.

[@twstf8905]

It's better to watch the videos in this playlist in their intended sequence. 🤜💥🤛

[@firstname8468]

These videos make math exciting for me

[@ff-jt8un]

This channel is amazing

[@DodgeThatAttack]

All I've picked up from these vids so far is that orange is the superior race

[@EugeneAyindolmah]

G E K O L O N I S E E R D

[@mememachine3029]

Trump is Orange

[@dezynjikReal]

@@mememachine3029 you are an orange

[@xandyreoch8d874]

these are really interesting videos, little tibits like this can make a morning so much better :D

[@uMaud]

6:03 "There's always a chance for unlikly events to happen" -Connor, Detroit become human

[@floatytrouty]

Me:Expecting to see cute colorful blob moving around collecting dot Primer with his Calculus equation:HELLO

[@destinygreycloud5189]

i love this channel bc it sceince/maths but i understand it and its fun bc its about things i will click on XD keep it up!!!!

[@CsharpPreza]

This is so entertaining, calming and educating. Great job!