I'm going to try making plaited bread. This will involve some group theory.
Follow along with me!
First, here's some dough that I've left to rise and just knocked back

18 favourites 6 retweets

In reply to @christianp

I've divided it into 8 by cutting in half three times

1 favourite 0 retweets

In reply to @christianp

Now I've rolled the bits into strands of equal length.
OK, similar length.

1 favourite 0 retweets

In reply to @christianp

Next I have to connect them up like this, which reminds me of that puzzle about the hydra that I can never solve.

1 favourite 0 retweets

In reply to @christianp

Your man Paul says: "Step 1: place 8 under 7 and over 1 Step 2: place 8 over 5 Step 3: place 2 under 3 and over 8 Step 4: place 1 over 4 Step 5: place 7 under 6 and over 1"
I need to label these tentacles

2 favourites 0 retweets

In reply to @christianp

That looks like this. I think. I might not have done exactly the right thing, but I've definitely done some overs and unders.
To answer a comment: the numbers refer to positions, not tentacles, so you relabel after each step

2 favourites 0 retweets

In reply to @christianp

So the immediate question is: where did each strand end up?
The steps are, in permutation notation (I say where each strand ends up) :
(2,3,4,5,6,7,8,1)
(1,2,3,4,6,7,8,5)
(1,8,2,3,4,5,6,7)
(2,3,4,1,5,6,7,8)
(2,3,4,5,6,7,1,8)

1 favourite 0 retweets

In reply to @christianp

You can work out the final permutation by applying those in turn, to get:

(8,4,5,6,7,1,2,3)

So things don't end up where they started.

So... how many times do I have to do this to get them back where they started?

1 favourite 0 retweets

In reply to @christianp

(brief intermission while some parenting happens)

4 favourites 0 retweets

In reply to @christianp

One dance recital, one full potty and a cuddle later, I'm back!

0 favourites 0 retweets

In reply to @christianp

You can write that permutation, (8,4, 5,6,7,1,2,3) as a cycle: now (a, b, c) means "a goes to b goes to c goes to a"

That is:
(1,8,3,5,7,2,4,6)

0 favourites 0 retweets

In reply to @christianp

This cycle includes every strand, so I don't get to do a fun bit of maths. I was hoping it'd be several disjoint cycles - cycles that don't share any strands.

This cycle is 8 elements long, so if I apply it 8 times I get back where I started.

0 favourites 0 retweets

In reply to @christianp

Fans, I forgot to keep count. Let's say I did it a multiple of 8 times so everything's back where it started.

(ignore the big mush of I-got-bored at the end of this plait)

2 favourites 0 retweets

In reply to @christianp

If the permutation *had been* a product of disjoint cycles, I could use a cool fact to work out how many times I need to apply it: the least common multiple of the lengths of all the cycles.

That's what I get for trying to apply maths in the real world...

4 favourites 0 retweets

In reply to @christianp

We'll see if the bread is as good as the maths!

Some books about maths and baking:

0 favourites 0 retweets

In reply to @christianp

The Proof and the Pudding by Jim Henle
press.princeton.edu/books/hardcove…

2 favourites 0 retweets

In reply to @christianp

And How to Bake Pi by Eugenia Cheng
profilebooks.com/how-to-bake-pi…

1 favourite 0 retweets

In reply to @christianp

That's it! I'll try to add a photo when it's baked.

1 favourite 0 retweets

In reply to @christianp

lol 🌈

5 favourites 0 retweets

View this tweet on twitter.com

This tweet as JSON