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### Course: Math for fun and glory > Unit 1

Lesson 7: Thanksgiving math# Thanksgiving turduckenen-duckenen

Forget turducken... I'm stuffing my turkey with two ducks, stuffed with four hens, stuffed with eight quail eggs. Honestly, I do not recommend trying this yourself.
So what's your favourite naming scheme: breadth-first, depth-first, or inordered binary tree traversal?
Mathed Potatoes: http://youtu.be/F5RyVWI4Onk
Green Bean Matherole: http://youtu.be/XwIs1nlDQ2I
Borromean Onion Rings: http://youtu.be/4tsjCND2ZfM. Created by Vi Hart.

## Want to join the conversation?

- What is an abacaba pattern?(38 votes)
- An abacabadabacaba pattern is sort of a fractal fraction thing. Vi explanes it more in the Fractal Fractions video.(40 votes)

- i wonder if that tastes good?(12 votes)
- I bet it tastes good. My tumy tum tum started growling when I looked at it.(3 votes)

- At3:54, it shows the egg with the whites still surrounding the yolk. How did she get it to stay together instead of all smushing around? Did she leave it inside of the shells? If so, then how do you eat it?(4 votes)
- You just boil the eggs for, what, i think its somewhere around 20 minutes, until they're hard boiled. Then you run cold water over them and peel off the shells, and then you put them inside your hen. And viola!(2 votes)

- How is this mathematical?(3 votes)
- It is a fractal and can be represented by a binary tree.

The pronunciation is binary tree traversal. (a fun mathy thing too think about.)(8 votes)

- Check out these videos for info on the number Tau: https://www.khanacademy.org/math/trigonometry/basic-trigonometry/long_live_tau/v/pi-is--still--wrong(10 votes)

- At 1:5 what happened?(3 votes)
- she was trying to find ways to say what she was making(4 votes)

- At1:05, why does it sound like multiple people are speaking(2 votes)
- Before3:00, how does Vi Hart make a sort of number tree like that?(2 votes)
- Try this: take on line, split into two, split each of those into two and on and on and on. the average sheet of paper can hold as many as 4000 trillion of these iterations.(1 vote)

- how did the thanksgiving turduckenen-duckenen taste(1 vote)
- Make it yourself and find out! But, at3:54, bby the looks of it, it looks yummy.(1 vote)

- will you give me a vote if you think this looks tasty?(2 votes)

## Video transcript

You may have heard
of turkducken, a turkey stuffed with a
duck, stuffed with a chicken. Yeah, it's a cute idea, but
mathematically uninspiring. Much more interesting
would be some sort of fractal-fowl arrangement. Say the turkey were
stuffed with two ducks, and say each duck were
stuffed with two hens. You'd get a turduckduckenenenen,
or turduckenenduckenen. I'm not sure yet. Then each hen could be stuffed
with two quails, or whatever. And by the time you
get down to sparrows, you have a whole flock
of them in there. That sounds fun and practical. Let's do it! But being an extremely
practical person who realizes that exponential
quails will not fit inside of one turkey, I am
using tiny unborn quails. Eight of them inside four
hens, inside two ducks, inside one turkey. This structure is
much more interesting because birds belong in
trees, binary trees, that is. Obviously this is superior to
the old linear bird-stuffing paradigm, and while you're
deboning seven birds, you have lots of
time to consider the question of binary
bird stuffing nomenclature. How do you traverse
this tree of syllables? Unless you can say lots of words
that once, like turduckenail, you'll have to say the
syllables in a linear order. You could go layer by
layer, biggest birds first, like
turduckenenenenailailailailailailailail. Or, you could go down
through the layers, like
turduckenailailenailailduckenailailenailail. The second one is certainly
more complicated to say, but I like the way
the structure of it suggests the structure
of the whole. And say you've made two of
these and put them in a goose. In the first scheme,
the new bird names get inserted into
the name to get gooturturduckduckduckenenenenenenenenailailailailailailailailailailailailailailailail,
while for the second, you start with goose and then
just repeat the old word twice to get
gooturduckenailailenailailduckenailailenailailturduckenailailenailailduckenailailenailail. So it's nice that part
of it stays the same. Of course, those aren't the
only possible naming schemes. Maybe you go from left
to right on the tree. So this would be,
quailenquailduckquailenquailkeyquailenquailduckquailenquail ooh, [? abba cabba ?] pattern. OK, so in 1807, a guy
roasted a bustard-- whatever that is-- stuffed with a
turkey, stuffed with a goose, stuffed with a pheasant,
chicken, duck, guinea fowl, teal, woodcock, partridge,
plover, lapwing quail, thrush, lark, bunting,
and warbler to get at
buskeygooseantenduckneatealcockridgeerwingailusharktinbler. But say he had done this
with the new exponential bird-stuffing paradigm. I mean, you'd need over
100,000 birds to do it, but the world has a
lot of birds in it. And if you can consistently
say four syllables a second, you can say the name of it
in only like nine hours. It might seem like a
lot, but it's really not compared to if you
used, say just twice as many kinds of birds. Then you'd need over 8.5
billion individual birds. And if you started naming
it as soon as you learned to talk and take breaks
to sleep at night, you'd still probably
die before you finish. So I can't say I recommend it,
buy hey, maybe with advances in medicine, it will become
a more feasible goal. And even there it
is-- two quail eggs in each hen, two
hens in each duck, two ducks in this turkey--
if I can close it. Eventually I had
to go for sewing up the turkey most of the way with
the one duckenailailenailail, and then stuffing the other
duckenailailenailail in. Now you can arrange it nicely
with the original legs, and wings, and stuffing to
make it look perfectly natural. There. Anyway, once you've
got that, you're pretty much good to go as far
as Thanksgiving is concerned. You should already have your
gelatinous cranberry cylinder, bread spheres with butter
prism, masked potatoes with organic hyperbolic
plain, string bean vector field with Borromean onion rings
on top, double helix cut ham, pi, tau, and so on. And now, finally,
you've got your turduckenailailenailailduckenailailenailail,
or quailenquailduckquailenquailkeyquailenquailduckquailenquail,
or turduckduckenenenenailailailailailailailail
whatever. Each slice gives
a different cross section of this binary bird. Here, you can see
a quail egg wrapped in the light meat of the
hen, wrapped in the darker meat of the duck, wrapped in
the light meat of the turkey. Another cross section
shows two eggs. Now you can sit down, eat your
mathematically-inspired food and be thankful that no
matter how crazy people are, at least mathematics is
always there for you, making sense, and truth,
and beauty, and birds. Lots of birds.