[0:00] I have some major issues with this cereal packet. 
Imagine you walk into a supermarket, you look at
[0:08] the cereal section, pick up a packet, and on the 
back of it, you see this. I don't have an issue
[0:15] with the front of the box. I have a major issue 
with the back of the box because as well as Glazed
[0:22] is genius. Hang on, let me bring it over here. 
They've put Look at this. Look at that nightmare.
[0:29] What is this? We did the math. Donut 
holes are the perfect shape to deliver
[0:35] more glaze. The area of a sphere equals 
4 pi r². The area of a taurus equals
[0:45] uh 2 pi squar r r r r r r r r r r r r r r 
r r r r r r r. Max glaze equals max flavor.
[0:55] Oh yeah, I um printed them out.
[1:01] Okay, things we have to deal with straight away. 
First of all, putting a blueprint effect on a 3D
[1:07] object. I don't know what's going on there, but 
they are they're fun objects. I got to give it to
[1:12] Kelloggs in that regard. Um, there is a typo. So, 
they've got two equations there. One is for the
[1:18] equation of the surface area of a sphere. That 
is correct. They've also got the equation for
[1:23] the surface area of a Taurus, which features pi 
squ. Very nice. That's why pi is better than to
[1:28] tao. And they put it in brackets for no obvious 
reason. I can forgive that. And they put a two
[1:34] instead of a four. That's harder to forgive, but 
it is the mathematical equivalent of a typo. Like
[1:40] I wish they would fix it. If they had a spelling 
mistake, they would have fixed it. And people have
[1:44] been putting this out for a while that they've got 
a two instead of a four and they haven't changed
[1:49] it. So I am annoyed at that. But it is a little 
trivial. More important are the mathematical
[1:55] problems with the whole concept they're trying 
to get across. And oh, by the way, I'm not the
[2:00] first person to get annoyed at this box. Other 
people have done that, but we do have some new
[2:04] information. Very exciting. Get to that in a 
moment. All right, but the point is people are
[2:09] annoyed at just the maths. And I showed this to a 
few other mathematical friends of mine. Everyone
[2:14] got annoyed for subtly different reasons. And so I 
thought we just have a quick quick chat about what
[2:22] Kelloggs could mean and eventually what they do 
mean right off the bat. What is a donut hole? The
[2:31] void in the middle of the donut. Well, here's the 
thing. A while ago, Dunkin Donuts did this thing
[2:37] where they, as a marketing gimmick, sold the dough 
that would have been the holes in the donuts when
[2:44] they get punched out. And actually, I've scaled my 
models to represent that in theory, this is meant
[2:50] to be the hole from the middle of a donut, but 
it's like the hole, the bit that's removed to give
[2:54] you the hole. And a lot of people think that's 
ridiculous, myself included, until quite recently,
[2:58] because that's not how you make donuts. You just 
make a ring of thing and your machine puts it in
[3:02] some boiling oil or something. So, there is 
there is no dough in the middle. But then we
[3:07] looked it up. Producer Nicole found this a video 
of the machine that makes the donuts for Dunkin
[3:11] Donuts because obviously that's happening at some 
ridiculous scale and they start with just a sheet
[3:18] of doughut ooze and then they stamp out donuts 
leaving behind dough in the middle. So there is
[3:27] dough from the doughut holes. Now whether or not 
that dough actually becomes the doughut holes they
[3:33] sell feels very unlikely. I imagine it just gets 
mushed back in again. I mean, what about the dough
[3:38] in between the donuts? I don't see them selling 
doughut manifolds, like the leftover joiny bits.
[3:47] I'd buy that. What a delicious snack. You could, 
you know, distort it, make it hyperbolic. Anyway,
[3:52] the point is the gimmick was it's the dough from 
the middle. In reality, they actually do have
[3:56] dough in the middle. I don't think they actually 
just cook that as holes. But that's why now in
[4:00] American cuisine there is the notion of a donut 
hole just being a fancy way of saying an edible
[4:09] sphere. The second part of the name we need to 
unpack is glazed. So Kells haven't just got donut
[4:17] holes, they've glazed them, as I believe the kids 
say. So, this um is is a sphere that they're going
[4:24] to put this kind of pure sugar all over. And then 
this is a Taurus or a donut that they're going to
[4:32] put pure sugar all over. And they're trying to 
argue that the sphere is superior to the Taurus
[4:40] when you're smearing a sugary glaze on it. And 
the ones I've made, you think, well, hang on, just
[4:48] very naively. No, if this was the donut and that's 
the center to scale, that's got way more area.
[4:56] Like, if you had to glaze all of this, that's way 
more glaze than the sphere. So, that's that's not
[5:01] what we're talking about. In fact, the picture 
um the the sphere is bigger than the Taurus. So,
[5:08] we can already accept that no, we're not talking 
about to scale the literal hole out of the donut.
[5:16] But does that mean maybe big R is the same? 
Because the big R appears in both equations
[5:22] and you could solve for that like if you solved 
it and it was like pi on R, then you would have
[5:30] the same area for both. And if it was any bigger, 
you'd have more area on the Taurus. Any smaller,
[5:36] more area on the sphere. But that's just it's a 
fancy way of saying bigger things have more area
[5:45] to a certain extent. It depends obviously on the 
shape. Um and that's that's something to be said.
[5:52] Um but I don't think I don't think that's what 
we're talking about. I think the Rs in each of
[5:57] the equations just represent that radius of 
that object. Like we're not assuming the A's
[6:04] are the same. And when you look at a big list of 
equations for areas of things, you don't go, "Oh,
[6:08] they must all have the same height or whatever." 
It's just that R pertains to that object. So,
[6:13] I think what we're actually talking about is just 
comparing the concept of a sphere to a donut.
[6:21] Finally, we're going to get to the point a lot 
of you have been yelling at your screens from the
[6:24] very beginning of this video because they say, "We 
did the math. Donut holes are the perfect shape
[6:29] to deliver more glaze." And you've been yelling, 
"No, they're the perfect shape." mathematically,
[6:35] rigorously to deliver the minimum amount of glaze. 
Because famously, a sphere is the most efficient
[6:43] way to maximize your volume, the amount of cereal, 
and minimize your surface area, the amount of
[6:50] glaze. So, it's the exact opposite of what they're 
saying. If you wanted to minimize the amount of
[6:56] glaze you need, you'd go spheres. If you want more 
glaze, you want a more complicated shape like a
[7:02] Taurus. Now, side fact, proving that a sphere is 
the optimal 3D shape to minimize surface area to
[7:11] volume. Non-trivial. I think it was like the 
1970s. We I'll put a picture of the paper up
[7:17] somewhere, right? Like complicated. And we'll 
link to that paper if you want to go check it out,
[7:23] but it is true. This is if you want to minimize 
glaze, that would be the optimal. And actually,
[7:29] mind your decisions did a whole video about this. 
So I'll link to that below. They look at what
[7:34] happens when you donutify a sphere and how that 
changes the surface area. But the kind of founding
[7:42] principle of this argument is that would be if you 
always had the same amount of cereal per cereal.
[7:51] So, if every piece of cereal is the same amount 
of cereal, and it doesn't matter what shape,
[7:56] like you've got your your quantum of cereal and 
you're going to turn that into a shape. And for
[8:02] the record, Kelloggs don't even make loops of 
any form. I don't know why why they're going
[8:09] on about donuts. They don't do any donut shaped 
cereals. I What's a normal frosted flake? I mean,
[8:14] guess it's flake shaped. It's like a probably like 
a saddle or something. Anyway, point is if you go,
[8:20] oh, the machine gives a certain amount of 
cereal per per per thing. What shape should
[8:25] we mold it into? Sphere is the worst 
choice. But the founding assumption is
[8:32] equal cereal per cereal. Actually, how 
big are the spheres? It's pretty big.
[8:41] About yay big.
[8:52] Max flavor.
[8:57] The top two ingredients are 
sugar and then air. A sparsely
[9:04] infilled sphere purely as a mechanism to 
transport sugary glaze into your face.
[9:22] They somehow as piping submerged in 
milk crumble into dust as you eat them.
[9:32] I've made some weird career choices. I 
just realized no one's making me eat these.
[9:38] Just literally eating a bowl of cereal 
while paying someone to film me. Yeah,
[9:45] you better keep watching.
[9:52] Now, where this gets interesting is a Reddit 
user Nahan0407, real name I believe Nathan,
[10:00] reached out to Kelloggs, expressed the concerns 
we all have, and Kelloggs responded. We now have
[10:08] Kellogg's side of the story. Connie from their 
consumer affairs department engaged with Nathan.
[10:16] They had a bit of back and forth. I'm going 
to ignore most of the emails. The first email
[10:21] from Connie lays out their logic behind 
what they've done here. They did not say,
[10:28] "Oops, you got us." No, they came to play. As we 
considered the shape of our cereal, the sphere is
[10:36] the most efficient mass to surface area shape. 
Correct? Yeah, we agree. We agree. If anything,
[10:43] that's the founding premise of why people are 
so upset. The sphere is the most efficient. So,
[10:48] it's curious that they're establishing what seems 
to be like the silver bullet in their delicious
[10:56] argument. But there you are. At least we all 
agree on that. Up next. For a given serial piece,
[11:03] when holding the glaze percentage constant, both 
the sphere and the loop deliver the same glazing
[11:15] mass and serial mass. Okay, now this one takes 
some more unpacking. This is some weird mashup
[11:23] of marketing speak and maths babble. Uh uh what 
I think they're trying to say is the the other
[11:32] assumption we were discussing before if you've 
got the same first of all they're establishing
[11:38] it's the constant serial per serial. So when 
they're down here saying the same glazing mass
[11:44] and cereal mass I believe they're saying and 
this will be useful in a moment is that if you
[11:49] do loops or donut holes it's the same amount of 
cereal in either case. So we were trying to work
[11:55] out is it oh is it the one that matches etc. No 
they're just saying the volume of the loop and the
[12:00] volume of the sphere if you're choosing between 
them is the same. Where it gets interesting is
[12:05] they say it's the same glazing mass. So not only 
are they holding the amount of cereal constant,
[12:12] they're also holding the amount of glaze 
constant. On we go. The sphere itself has
[12:20] less surface area than a loop for the same serial 
mass and parocity. They don't. Is that like number
[12:31] of paws? Are they saying it's absorbent? Let's 
just Okay, let's ignore parocity and just Yeah,
[12:40] we agree. The sphere has less surface area than 
a loop if it's got the same serial mass. Again,
[12:45] all on the same page. Closing statement. When 
applying the glazing mass to the serial mass,
[12:51] why do they keep saying mass? The sphere will 
have a thicker glazing mass application layer due
[12:59] to the limited surface area in comparison to the 
loop. And there, my friends, is their argument. If
[13:09] you have the same amount of cereal in both cases 
and the same amount of glaze, if you apply it to
[13:14] the Taurus, you're going to have to spread it out 
because there's so much area. Whereas the sphere
[13:20] is the optimal shape to build up the thickest 
layer of glaze possible. And a thicker layer of
[13:29] glaze is indeed more for some definition of more. 
But that means we did the math. Donut holes are
[13:42] the perfect shape to deliver more glaze. They mean 
thicker glaze. In that regard, they're right. Now,
[13:51] we should ignore the fact that they they you can 
just sense them desperately wanting this to sound
[13:58] as mathsy as possible. They keep referring to 
the the glazing mass and paracity and, you know,
[14:05] percentages. Like, okay, we appreciate that, but 
all they're trying to say is the glaze is going
[14:11] to be thicker. And you know what? I I agree with 
them. They're 100% right. And for the avoidance of
[14:18] any possible doubt, I'm going to take take a leaf 
out of their recipe book. And um we're not going
[14:25] to we're not going to glaze some loops and some 
holes. Instead, we're going to ice some cakes.
[14:36] Here's the plan. I'm currently being very uplit 
because I have two mirror like cake plate tray
[14:45] things and producer Nicole here has first of all 
made a hemispherical cake. That's what flavor is
[14:52] this one? Uh this is plain plain plain sponge. 
But if I put that on the mirror, look what we
[14:58] now got. Hang on. Spherical cake. Right. So, we 
have to bake half as much and we get the full
[15:09] sphere. And more more in a moment on that. We now 
need a donut shaped cake. And so, what do we got
[15:16] here? This is coffee and walnut. Coffee and look 
at that. Isn't that incredible? And that's half a
[15:23] half a donut. So, in theory, again, hold that up. 
There's your There's your whole The donut fills
[15:29] in. It's adequate. Completely adequate. And these 
both have exactly the same amount of cake. Same
[15:37] amount of cake. There it is as a sphere. There 
it is as as a Taurus or half of each. The math
[15:43] still works. And finally, we have the frosting. 
So, I'm going to glaze these cakes and I'm going
[15:52] to put exactly the same amount of frosting on 
both. And to do that, I'm going to weigh the
[15:58] cakes as I put the frosting on them. How can this 
go wrong? Other than all the obvious ways this is
[16:06] going to go wrong. Oh, it's got a delicious skin. 
I'm going to have to spread this real thin. I'm
[16:13] calling it. There we Okay, all I got to do now, 
put the same amount of icing on this here sphere.
[16:24] So, I think I think we can all agree it's only 
a matter of time before I get the phone call
[16:31] for Celebrity Bake Off. Imagine this in a tent. 
But more to the point, the process of doing it,
[16:41] I had to spread the icing way thinner on this 
one. And even then, I mean, around the back,
[16:49] I didn't even have enough to really do that 
properly. Uh, it was really hard to spread it out.
[16:54] Exactly the same amount of cake. Exactly the same 
amount of icing. It's on thick as you like. And
[17:00] now if I cut uh permission to cut these in half. 
If I cut these in half, the crosssection. Okay,
[17:09] this one I'm going to do in two cuts. Stressed 
the crumb. Oh, it's going to be such a good crumb.
[17:17] You know, I'm going to do both cuts 
first and then we'll do a big reveal.
[17:22] So, here we go. Big reveal over here. You can see 
on the Taurus one, look how thin that icing layer
[17:31] ended up being. And I'm This is me doing the 
best I can to really load it up. Whereas over
[17:37] here in Sphere Town, look at that. There. So, 
it's a way thicker layer of icing on this. So,
[17:46] as you can see, the sphere is the perfect shape 
for more. Assuming you're not allowed anymore.
[17:58] You know what? Kelloggs have convinced me. I'm 
now on their side. They're right. If you want to
[18:04] have the thickest glaze possible without 
adding any more sugar, and I assure you,
[18:08] these dose do not need any more sugar. Sphere. 
It's great. thick glaze for no no added sugar
[18:14] for no more added sugar. You get a thicker glaze. 
They've just worded it very poorly. Like this like
[18:20] as red is not good and the typo. Fix the t. 
You know what Kelloggs? Fix that typo. And we
[18:27] have emailed you and you not responded and we've 
just asked you to fix that. Do that. Just fix the
[18:32] typo and we're cool because I think you've got a 
good point. You just don't have to dress it up in
[18:37] technobabble language. And more importantly, I 
don't think the rest of us should be dunking on
[18:43] Kelloggs or indeed any any brand who want to put 
more maths in their marketing. The fact that we
[18:50] get more maths and culture like this is clearly 
advertised at children, but they're putting maths
[18:56] there. That's great. We should encourage that 
and we should encourage them getting it right
[19:00] and fixing their typos and phrasing it better. But 
the point is something is better than nothing. So,
[19:06] so in conclusion, Kelloggs, your your maths, 
it's not great. But it's it's good. Good work.
[19:15] Keep it up. Just turn that turn that two into a 
four. Future Mad here. Kelloggs did reply to my
[19:22] email to say they don't reply to that sort of 
email. So, either they've learned their lesson
[19:28] or we're not getting through to the right person. 
Come on, Kelloggs. Let's talk. This has been fun.
[19:33] This is a fun video to do and I don't think that's 
just the sugar speaking. So, thanks for watching.
[19:37] I really appreciate that. Oh, I'm on tour again. 
Please come and see me on tour. It's all around
[19:42] the UK. Sorry people in America. You have to 
console yourself with your fantastic cereals. Um,
[19:48] we're doing the Reading Hexagon on the 4th of 
March. It's like over a kilo human worth of seats
[19:55] and it's called the Hexagon. And I insisted that 
they book me in to do my show there. And it'd be
[20:00] very embarrassing if we don't have enough people. 
So come along there. We're in Nottingham a couple
[20:04] nights before. Um they got a big paraboid at the 
front of um the Nottingham Art Center. That's
[20:11] a lot of fun. And we end in Manchester, Sulford, 
Manchester. So it's a huge amount of fun. The show
[20:17] well me to do. I assume the audience also have a 
good time called Getting Trigy with it. All the
[20:21] links are below. Last night, however, spoke about 
this live on stage at an evening of unnecessary
[20:26] detail. That's my uh intimate nerdy variety night 
that I run with Steve Mold and Heleni and us and
[20:33] our buddies talk about things in unnecessary level 
of detail. And I was on stage chatting about this,
[20:38] just talking to the audience, getting their 
thoughts. Had a lot of fun. Thank you everyone
[20:42] who comes along to Unnecessary Details. If you're 
anywhere near London, we have two more of them in
[20:47] March and June. Uh it's not a big room though, 
so it sells out pretty quick, but uh it's a lot
[20:52] of fun. Come along. Uh and that's it. Uh thanks 
for watching the show. I'll see you all see you
[20:59] all on tour. Why should I eat more and um if you 
see me after the show, I'll sign your calculators.
[21:06] It's a lot of fun. Or bring a box. I'll sign 
cereal boxes. Hey, you bring it. I'll sign it.
[21:15] They just get worse every mouthful. It's 
so bad. Hey, you you want some? Anyone?
[21:32] Cereal artificially flavored. Tony Glazo.