### The Algebra of Socks

Delightfully, there is a way to define an algebra on the different ways you can wear your socks. In this interactive Scratch game, you solve math puzzles using a humble pair of socks and learning a little bit of group theory on the way.

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### Comments

I thought that this was a very nice introduction to finite groups and isomorphism between them. While I ran into the occasional bug during my 'play through' there was nothing that made it impossible to continue. Sometimes the transitions were slow, and the UI elements sometimes got in the way of things, but overall, I thought it was fantastic at covering the basic intuition behind groups.

6.6It can be a bit confusing figuring out what a reversed sock is

4.1I absolutely loved this game, it is extremely impressively made, and explains the maths in an extremely intuitive way. Unfortunately, I couldn't finish it due to a few bugs, but that doesn't change how much I love it. If the bugs got fixed, it would be perfect, and it's amazing that this is made in scratch!

7.2Charming :)

7I'm probably not quite in the intended audience (current postdoc in algebraic geometry). So while I found it pretty clear early on where the game was headed, I'm not sure the motivation would have been so clear to people who don't already know about groups. Similarly, constructing the isomorphism in the end was pretty straightforward for me, but I wonder whether a layperson could use some hints there; e.g. starting with elements which aren't self-inverse and proceeding to their powers. Besides this, I thought the art was cute, but I had a couple of difficulties with the UI. For example, sometimes I can't get the "next" arrow to appear on page 14 of 17 even after trying all eight operations. The symmetries-of-a-square display also tends to bug out if I start one operation before the previous one's animation has completed. And I wish it were possible to skip forward in the game after I've completed it once.

5.4I lost interest really quickly in this one.

3.2Hey, where's my feedback gone? Hope it's not lost. I just called it cute but pointed out a couple of minor technical gremlins

6.2This is an amazing way to present group theory! It's a bit finicky; I had trouble putting on the socks at the beginning and lost many letters to the garbage bin accidentally, and the exponents of u were hard to read. But all these things are more than made up for by just how good this game is!

8.1Great idea to use Scratch and let the user interact and learn through active participation! With a little bit of refinement this could be very well used on schools. One negative point arises through the complexity of using your entry on a mobile phone.

7.6So glad this popped back into my queue after I somewhat unintentionally skipped it when I was having trouble submitting a grade. When this came up the first time, I had just about finished downloading World Of Goo 2. I completely forgot about the game until I had spent over 15 minutes on Algebra of Socks. I got stuck at slide 16 due to some issue I was having on my iPhone. Today I tracked down the link in my browser history and opened it on my laptop, then went through the entire thing from scratch, just to see the ending. Outstanding interactive demo of two different things being the same group. Or whatever is the right way to say it.

9I enjoyed the light hearted nature of the example to introduce groups. I also particularly do appreciate how the conveyor belt also helped to represent the operation of function composition which is done right to left, which is not so intuitive for most beginner learners when connecting it back to groups. Some of the functionality of not being able to go forward or backward on different screens depending on pacing can be better optimized. I'd think it would also be cool to also give a real life example as well at the end just to round up how group action can be applied there and give a sense of what's out there in the world as well.

7On my screen, "We will be exploring the exciting mathematic" is cut off. Some other texts are cut off too, like "We can also put the blue socks c" in the tutorial. I have fixed this by running in Chromium instead of Firefox. (Might be some quirk of my OS rather than browser.) Very good otherwise!

7.6I had a bug on the last page - the box for selecting which square symmetry to assign to H wasn't located on the machine in the middle of the page. Apart from that, very easy to use and fun - bravo!

7.9Interactives are best when optional. If I understand, I should be able to move on. Otherwise this is a great explainer with engaging examples.

7.7Text overflows at times and is slightly unclear but otherwise a very fun explanation of groups and action.

9