3/4 and Kleiber's Law - Numberphile

[DrPhr0]

It could be so many things, but I think we all agree that's not a mouse...

[averagejoe91741072]

"Wait 'til you see my elephant." Bahahaha

[StuziCamis]

Oooooops Numberphile not Numberphila sorry

[StuziCamis]

Thumbs up if you follow Sixty Symbols, Numberphila and Periodicvideos. Nice work Brady. Keep it up!!

[EvolutionXEngine]

funny.. i see spheres all around Mc Donalds... im Oval ..lol

[willghass]

so in other words a log graph- that's all the math mind is looking for

[ProfessorBorax]

Isn't this "~" the sign for proportional?

[ThePurpleIsland]

@ProfessorBorax That's the sign for similar in geometry.

[CJFRANKS7]

There are speherical whales! They're in pokemon! :P

[DarkSoraXIII]

This kinda implies why people live in cities; it's more efficient.

[dk6024]

Very neat.

[MrTanookiMario]

There was a cool TED talk on this.

[Solipsistically]

its all brady in the house yoooo

[clownstangler]

it took me 'till the end of the video to realise the whale was not waving.

[andwhyshouldwe]

The first nerd to admit that size matters!

[redcups21]

That didnt look like a mouse ;)

[rayomundo28]

NIce, but you didn't explain how does the fractal structure gives the number 3/4, not having done so made your video only 3/4 as good.

[greymattersblog]

This is the last video by Mr. Thomas Woolley. From now on, he's Dr. Thomas Woolley. Congrats, Dr. Woolley!

[JuanLeTwnz]

This system works quite well for endothermic species. However, animals with different thermal regulation and circulatory systems will have greatly varied values in their m/MR ratio. This would include pretty much all invertebrates and most vertebrates except mammals, birds and some reptiles.

Just try to compare a shrew and a large tarantula. The spider's mass might be way above this tiny mammal and its MR will still be lower.

[masterlink101]

number 6 - numberphile's law: a video about maths aprox 6 minutes long can be the most interesting 6 minutes of your day.

[CARMENvalentine]

oh my god. im pretty much of polish humanistic, but You, user, made me to come back, when i thought about science as a very interesting thing. good work. (still, i'm watching your videos, instead of writing an article about korean culture.)

[NeonShuriken]

So in theory, bigger cars ARE, in fact, more efficient.

[MrTobi48]

Talk about the number 8!!!!

[MegaMonkeyExtreme]

As seen on Math Fail?

[Noovil25]

this is really interesting, but where can I get a more detailed explanation on this?

[dewinthemorning]

My two favourite subjects combined! I wonder where on the graph is the human being?

Fav'ed

[hotdog12370]

wait.... wahhhhhhhhhhhhhhhhhhhhhhhhhhhh­?



[BrunoHP89IT]

Biology channel Brady pleeease =)

[gulllars]

Requests: Graham's Number, the Knuth up arrow notation, and Ackerman's Function.

I'd also love to see if XKCD's strip about horrifying mathematicians by calling Ackerman's with Graham's Number as both arguments is true.

BTW, loved the fractal comment on the circulatory system. Can we get more on fractals?

[Jeuhann]

does this only apply on mass? or does size matter too?

[gulllars]

@Jeuhann because of physics and biology, animals consist mainly of liquids with some heavier elements solved in them, and little open volumes of gas. Therefore the density of animals is fairly consistent across sizes, at least for mammals.

[HeyJD123]

I nearly thought this video was about Rule 34...

[PK0777]

a tutorial on fractals would also throw some light on this 3/4 rule !! 'fractals' by mandelbrot may also be avlbl on yt - the documentary is called 'the hidden dimension' !!

[sarvalal]

@PK0777 Sal @ khanacademy has a pretty substantial explanation for the Koch Snowflake, maybe it could satisfy you until Brady does a video on fractals. :)

[PK0777]

fantastic, fascinating !!

[WildZangoose]

This should be done on white boards.

[vincentleest]

golden ratio will be a great vid!! :D

[kylekeepers]

"Since the elephant is a thousand times heavier than the mouse..." That mouse must be HUGE!

[MonkeyNinjaDo]

1.618?

[quosmo1]

like the maths, but did not like the eco-science type biology theory here, seems to be assuming a lot mixing cause and effect very un-scientifically...

[ib9rt]

@quosmo1 Cause and effect is the very heart of science. You observe an effect (output or measurement on system) and you relate that to causes (inputs to system). If you find a consistent and repeatable relationship you codify that (model of system). Given a model, you attempt to determine why the model works--which often gives you whole new insights and new areas to investigate. See this video (parts 1, 2, 3) for a great example of this: ahXIMUkSXX0

[quosmo1]

@ib9rt yes, i know what cause and effect is as a method.

my point here is that there could be many many variables of cause to give the effect of a relationship between MASS and (our own made up) MR, and that the assumptions for 'cause' that he rattles on about are just conjecture, not science.

[ReasonableMe]

Thanks Brady for doing the videos that include math and graphs!

[letsrock1994]

Is this true for plants or just animals?

[culwin]

Some humans are spherical... I've seen them at Wal-Mart!

[insanic1]

dinosaurs must have needed heaps of food to eat

[iBLITZzz]

talk about dividing by zero!!

[gulllars]

@iBLITZzz you want them to bring up L'Hôpital's rule?

[enriqueDFTL]

@iBLITZzz That wouldn't be a very long video. The answer to any number divided by zero is indeterminate. All there is to it.

[TheGuyInUrCloset]

Talk about dividing zero by zero!

[ijustdontcarenemore]

hahaha assuming spherical animals

[SMFApples]

Please talk about fractals!

[KyosBlog]

@SMFApples i really don't know which number could make a good, easy example for fractals. keep in mind that it's numberphile, not mathphile ;)

[1KevinsFamousChili1]

Speaking of Spehrical animals here's a joke:

A farmer notices his chickens are getting sick, he calls in a physicist to help him. The physicist takes a good look at the chickens and does some calculations, he suddenly stops and says "Ive got it, but it would only work if the chickens were spherical and in a vacuum."

[ParadoxPerspective]

Thumbs up if you think where that curve tapers off is completely intertwined with earth's total mass.

[SharkyAteYew]

They always get the people with the worst handwriting.

[retepaskab]

Does this equation apply to non-mammals also?

How about slow vs. fast animals? Birds?

A flying dinosaur must had been vey inefficient.

[Dilophodd]

0:30, yes, a mouse...

[muffemod]

Heart rates vs animal size

[MrAmo123]

the graph need to go past the mass of a blue whale so we can understand the metabolic rate of Americans

[xXOrangutanXx]

@MrAmo123 BOOM!

lol

[QwoPhasaArius]

@MrAmo123 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO­OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO­OOOO

Haha, nice. 

[MrMooremetal]

Why do you guys always write on butcher paper?

[alfiestoppani]

He draws a mouse like a cock! LOL

[Theelepeltjel]

Isn't there like a joke about this? You know, about a farmer who hires a mathematician, and the report starts with "let's view the animals as perfect spheres"?

[morethanthesun52]

fractals are really awesome! im so glad they came up in this video

[AntonMatsson]

Make a video about the divine proportion!

[FHomeBrew]

I expected it to be 2^(-½) since that's pretty close to 3/4 but somehow more elegant :p

[z0tx]

A mouse?... Hm...

[DireStraitsInImpala]

@z0tx I know what you're thinking, heh.

[Darso2]

FRACTALS YAY.

More videos of fractals?

[iTmcb]

Seventeen numbers down, infinitely many to go :D

[Bt3am]

BIOLOGY!! YAY

[AlanKey86]

0:59 Cute whale. With chef's hat on.

[CubexDE]

Brady, I've learned more watching your videos than I have ever learned in college classes... and I actually had fun and was interested in the process! You rock.

[DemangoProductions]

The mighty testicular mouse!

[SkinCollecter2]

@TerenceHorsman singingbanana had a video about it

[Zeldakitteh]

Video about parametric representations? =3

[Gameboygenius]

Small mistake. I think where you said they expected MR ∝ r^(2/3) you actually meant to say MR ∝ m^(2/3). If you take the r/V/A relations and solve for A, you get A ∝ V^(2/3). Mass is proportional to volume, so roughly A ∝ m^(2/3). If we then assume MR is proportional to area, the final assumption would be MR ∝ m^(2/3).

[ThomasEWoolley]

G'ah, you are quite correct. As with the rest of the video we're on interested in how MR and mass are related not MR and radius. I'll mention it to Brady and hopefully he'll add an errata to the video information. Thanks for the close attention. @Gameboygenius

[LightLink1992]

so when ur really fat

and u have a higher mass u need less food?

[TheRealMaxion]

@LightLink1992 Proportionately less, so someone with twice the weight of someone else, needs less than twice the food of the other person, but still more than equal amounts.

[JABRANE4]

numberphile: whats ur favorit number between 1 and 9 ?

[sarindam7tube]

How about videos on: imaginary numbers, one (the number), zero (the number), infinity and the continuum hypothesis, golden ratio, Eeuler's number, metric and imperial units of measure, the Fibonacci sequence, binomial expansions, trigonometric functions - you guys literally have infinite potential. Looking forward to all of the above and more!

[andrewthebestes]

@sarindam7tube Yeah, this stuff is pretty interesting. Not a bloody video about how three quarters has something to do with elephants and biology.

[MrOldprof]

@sarindam7tube Thanks for the suggestions and for suggestion that we have infinite potential. One day I hope to do a video relating cubic equations to the birth of imaginary numbers; I'm sure Brady has material for the number zero. But any ideas which have a single number associated with it are welcome. Now if I could think of a nice story involving Imperial units... ?

[sarindam7tube]

@MrOldprof Thanks. And waiting for that story :)

[supergsx]

@sarindam7tube Well, I like the videos he's been posting, because it's all about stuff I don't already know. I know a whole lot about all of those numbers. I knew nothing about 3/4 and its relation to biology, before this video.

[sarindam7tube]

@supergsx Agree. But the channel has real potential for attracting kids to science. Bread and butter stuff would be great too :)

[MindLessWiz]

@sarindam7tube Sweet ideas. I'm all for 'em.

[teavea10]

So we can assume a fractal spherical cow now?

[DeoMachina]

So bigger cities use their infrastructure and resources more efficiently? This is really interesting stuff, weird how it applies to so many things.

[retepaskab]

@DeoMachina Only spherically proportionally bigger cities. But building against gravity needs more resources, so the perfect shape for a city should be ellipsoidal. I wonder how skyscraper cities fit this shape.

[recklessroges]

anyone else think that this video should have mentioned the idea of asymptote?

[ZiqqiPH]

@recklessroges Wouldn't be necessary I think, seeing as it's not that relevant to this specific subject, although it is obviously of importance to power functions.

[johnnymanhands]

Maybe I've seen too much bathroom graffiti in my life, but that's no mouse.... and I definitely don't want to see your "elephant"

[Psenas]

@johnnymanhands i dont see how any of your criticism is relevant to this video. Maybe youre just too miserable and desperate you have to pick on the smallest things...

[vibhavsinha91]

congrats!! for the ad.. :P

[Theraot]

@numberphile nevermind, do that video ( v=G_gUE74YVos ) again in the format of numberphile. Do it twice or more times if necesary. After reading the comment by @TheBananular I understand we need to get rid of that "common misconception".

[Komentuotoja]

I don't understand a thing but im still listening

[Louiseskybunker]

Waltz!

[jhonbus]

I thought for sure that mouse was going to be a pair of balls.

[juraj89]

wait... how do you get r^(2/3) by combining r^3 and r^2?

If you are dividing them you should get r^1 and by multiplying r^5

[persycon]

since when do you calculate the volume and surface area of a sphere like that??

[mkaatr]

Just wondering, does that mean a fractal structured pipe network could be used to distribute water in the most efficient way in a city?

[ashwinnarayanVlog]

Spherical cows!!! That cracked me up.

[AxiomBios]

Fantastic video. Its nice to see real world application of number used to undestand otherwise hidden system properties. If only I had appreciated math in school, oh well still time to learn.

[VormPCbinichnackt]

@TerenceHorsman /watch?v=G_gUE74YVos

[00beasis]

"wait till you see my elephant" - Cheeky!

[Qieerbushe]

watch?v=G_gUE74YVos For those what a video on 0.9999 and 1

[dswiigamer1]

this guy is fucking awesome

[BloodMech21]

do a vid on the 3/5ths rule.

[TerenceHorsman]

Can you guys make a video about "0.9999999999999 = 1" ?

[Aviatorsmith]

@TerenceHorsman You should place ... behind the 9's to show that it is recurring.

Nothing much to talk about that sequence anyway.

[TerenceHorsman]

@Aviatorsmith Well I think it's interesting:

x = 0.99...

10x = 9.99...

9x = 10x - x

9x = 9

x=1

[Aviatorsmith]

@TerenceHorsman Well, I deal with physics and we get recurring numbers all the time. Never thought much about it. My take on it is that the 9 recurring notation is coincidentally just supposed to be round off.

[chrisofnottingham]

@TerenceHorsman One way to approach it is to ask; if it isn't 1, then by how much is it less than 1?

The answer looks very much like zero.

[Qieerbushe]

@TerenceHorsman There is one... On singing banana s channel

[RadioAurum]

@TerenceHorsman I believe there's one by james already!

[BallawdeQuincewold]

@TerenceHorsman Let x = 0.99999999... Then 10x = 9.9999999... 10x - x = 9.9999999... - 0.999999... => 9x = 9 => x = 1 But we originally said x = 0.999... Therefore, 0.9999999 = 1.

[jewwwcee]

@BallawdeQuincewold i think he understands how it works, he just wants a video about how it shouldn't work mathematically, as they arent the same number

[BallawdeQuincewold]

@jewwwcee But they are the same number. That's what the proof shows. : ) The fact they don't look the same is inconsequential. It's the same thing as writing pi as the integral of the unit circle. Two different forms, same number.

[jamma246]

@jewwwcee Yes they are.

[jawayetti]

@TerenceHorsman That is only true depending on accuracy needed for a given application. The so-called "proofs" aren't actually proofs, but it is still fun to play with. ;-)

[numberphile]

@TerenceHorsman what are you guys going to discuss in the comments section when we actually do that video... Kleiber's Law presumably! :)

[VintageSnatchy]

@numberphile there is no point of that video. just take 1, devide it by 9 and instead of writing 0.111... write 1/9. then multyply with nine = 9/9

[Brambite]

@numberphile you forget to put "is" between section and when

[BenVdd]

@numberphile i saw in school how to prove this a long time ago. Still don't know what can explain it tho.. Google here i come!

[TheBananular]

@TerenceHorsman 0.999... =/= 1. It is just rounded up to one. It is a common misconception that 3/3 equals 0.999... X/3 are just fractals and trying to use their decimal form in base-10 only unnecessary confuses people in math. Just make it a habit of using fractal rules for repeating decimal numbers.

[MarkArandjus]

@TheBananular Okay how about this then.

x = 0.999...

10x = 9.999...

10x-x = 9

9x = 9

x = 1

And then you look at the beginning of it and you see it comes to 1 = x = 0.999... ;D

The fact is that it's an irrational number something about it just doesn't make sense, but it works in theory, even your calculator agrees with it :) I could be wrong, I'm not a mathematician, so let's hope they make a vid.

[jamma246]

@MarkArandjus It isn't an irrational number, why would you think that?

People who don't understand why 0.999...=1 in general don't understand the construction of the real numbers (which, to be fair, is a little complicated if you are rigorous).

Your proof is fine, another way to see that it's "obvious" is that the distance between the numbers 1 and 0.999... is zero, it's less than 1-0.9, 1-0.99, 1-0.999 etc. 0.999... is just a different representation of the number 1.

[jamma246]

@TheBananular If you don't know anything about maths, please don't talk as if you do. Pretty much everything you have said there is wrong.

[jamma246]

@TerenceHorsman Please don't do a video on this. Anyone who wants to understand why can look it up easily, the point of these videos is to bring us interesting facts about things we may not have seen before.

That's not to mention that 0.9999..=1 is trivial anyway.

[Theraot]

@TerenceHorsman @numberphile If I understand correctly... Jim has already done that video before, just not on numberphile but as @singingbanana check it out: v=G_gUE74YVos

[defaultuser88]

@TerenceHorsman I know that one!

0.99999999999inf = 1

the end.

[AdderSIG]

@TerenceHorsman The easiest explanation is a rather boring definition that every real number has another real number between it and any other real number. Since there is no number between 0.99... and 1, then either 0.99... is -not- a real number or it is the same as 1.

[mydonkers]

@TerenceHorsman go to singingbananas channel he already covered that

[kapwul5]

Brady, you should make a channel about biology

[Mycernius]

@kapwul5 Agree. After all there is the QMC right next door to the university, so human biology at least.

[KajsSwedishMeatBalls]

@kapwul5 Yeah, he should make a video about each and every species that has ever existed! No, seriously he should make something on biology.

[renamorcen]

that mouse ( 0:41) looks like male genital

[DaTux91]

I'm a physicist but I'm glad to see a video about biology here. Unfortunately maths are usually not very popular with most biologists, but I think it's essential that it becomes more frequently used for biology to keep becoming a more and more modernized science. Maths are everywhere in nature, in fact biology is one of the best fields to see this: statistics are after all very important there.

[TheExtractor1]

Sweat video! Keep up the good work!

[joshcryer]

I was the 3rd like and when I started watching it was 4 likes, woooot (now it's 7 likes). :) I'm loving how deep you're approaching the maths here, more graphs and stuff! :D props to Thomas Woolley for a fascinating overview of this! :)

[SoManyHTZ]

woah

[tttt637]

Second

[Mr4NiceOne]

oh new video :D