corvi

1. A smartphone app that will send a push notification (beep, buzz, whatever your phone uses) when there is a good chance the aurora borealis is going to be visible in your area in the next couple hours. There are already apps that do this, but I feel strongly there should be a free one so anyone can see it.
2. Flashcard smartphone app for learning Mongolian and mongol bichig.
3. I wanted to make a flow chart of cheesemaking processes and what sort of cheese you got, but it turns out to be too complex to lay out in any sort of useful form. So I am now making a Cheese Your Own Adventure Game! Which is a less useful way to convey information, but hopefully fun anyway. juli  thought of the title. :)
4. The long-suffering Dream Atlas: scrape facebook for people writing status updates about their dreams, extract geographical terms (mountain, river, etc) and produce an Atlas of the Dreamlands based on what kind of geography people see in their dreams and where they live.

juli

• The Boat of a Million Years (Pol Anderson) follows ten naturally immortal humans over about four thousand years as they weave in and out of eachother's lives and history.
• Red Mars and Green Mars by Kim Stanley Robinson are told from the point of view of the first hundred Martian colonists. They cover fifty years, and even after Mars is fully colonized and they have dispersed into the general population following their own concerns, the First Hundred spent so long as the only human beings on the world that they can easily recognize each other, no matter how distant or disguised.
• First Among Equals (Jeffrey Archer) is about four fictional British MPs, following their careers from 1964 to 1981 and their reactions to changes in politics and the world.
• The Years of Rice and Salt is another Kim Stanley Robinson book about a group of people reincarnated together repeatedly through an alternate history (though they don't know it) 

• A longish timespan
• Not focused around a single crisis or problem
• Multiple viewpoint characters...
• ... who don't interact very closely
• ...but share a bond which affects each differently

juli and I have been talking about Faro or Pharaoh Shuffles, which is a common shuffling technique for card games or magic tricks. It goes like this: 

1. Divide the 52-card deck into two half-decks of 26 cards, deck A and deck B.
2. Merge the two half-decks together so that cards alternate, one from half-deck A, one from half-deck B, but the individual half-decks stay in order.

So if your deck starts out numbered like this:

1,   2,   3,   4,   5,   6,   7,   8 … 49,   50,   51,   52

You divide it into two decks, 1-26, and 27-52, and then merge them together like this:

1,   27,   2,   28,   3,   29,   4,   30, … 25,   51,   26,   52.

If you do this perfectly eight times with a deck of 52 cards, you will get back to the original order. I had trouble believing that, so we sat in a diner and carefully shuffled cards. Six cards return to their original positions after four shuffles. Eight cards take three, twelve takes ten shuffles and three restarts after losing my place.

Of course we both announced we would write a script when we got home, but Juli got hers done first. Go look at it here.

A graph of how many perfect faro shuffles it takes to bring a deck of N cards back into its original order:

 
And here is an image of the patterns formed by shuffling 52 cards. Each horizontal line is the deck before or after shuffling, and each rectangle is a card. Black is card #1, red is card #52.


 

  
What about some other sized decks of cards? Decks that contain a power of two cards return to their original state in log-2 shuffles. Here are the patterns for decks of 16 (4 shuffles), 32 (5 shuffles), 64(6 shuffles), and 128(7 shuffles) cards:

Decks with two more cards than a power of two take twice as many shuffles as the power of two. First the shuffling arranges every card in the deck except the first and last (which never move) in reverse order, then it turns them around again. Here are 18(8 shuffles), 34(10 shuffles), and 66 cards (12 shuffles) card decks:

  

The slowest decks take two less shuffles than they have cards. Here's 84 (82 shuffles required to return to original state), which does include a "reversed-except-for-the-outside" state, but I don't know how to characterize any of the rest of it.

 

There is some discussion of the math here, but I wish it went into more detail.