how taxes work

I’ve heard income tax compared to a bunch of men going to a restaurant and splitting the bill for the meal in some rather strange way, like there’s 10 men who all ate the same meal and the total bill is $100 but five of them pay nothing and four of them pay $8 and the 10th man has to pay $68 blah blah blah. But the person who wrote this little drama is assuming right from the start that progressive taxation is unfair and they created this narrative to illustrate their point. I could just as easily create a narrative which proves the exact opposite, like in my story it wouldn’t be 10 adult men, it would be two infants, a teenager, a paraplegic veteran in a wheelchair, a pregnant woman who just lost her job, a middle-aged husband and wife who are both school teachers, a retired couple, and a recent college graduate who has never had a job but just inherited $80,000,000 when his rich uncle died. Now tell me if you think it’s totally fair that the infants should have to pay for their own meals. Or the vet. Or if they can’t pay, tell me you think they shouldn’t be allowed to eat. Do you think it would be fair to ask the rich guy to pay most of the bill? What if I told you that all 10 people are members of the same family, would that change your answer?

If you ask me, it is totally fair to let people who are struggling pay very little and people who have more than they need pay a lot. And given that the one-percenters control such a huge fraction of the money, it only makes sense that they would end up paying a huge fraction of the taxes. If you asked me “Is it true that the rich pay very little tax?” I would answer “That depends on your definition of ‘very little’. If ‘very little’ means a smaller total than what the average person pays, then no. If ‘very little’ means a smaller fraction of their income than what the average person pays, then maybe. If ‘very little’ means an amount so small that it is not a hardship for them to pay it and losing that money has no effect on their standard of living, then yes it’s true, the rich pay very little tax.”


How to win 2048 (short version)

  1. Keep your highest number in the lower right corner.
  2. Put your second highest number just to the left of the highest, and put your third highest number just to the left of the second.
  3. Swipe Down 80% of the time. Swiping Right is also good.
  4. Swiping Left is a bad thing if it messes up #1, otherwise Left is good.
  5. Sometimes when Left is a bad move you have to do it anyway because Down and Right aren’t legal.
  6. Swiping Up is very bad. Don’t do it unless that’s your only legal move.
  7. When your bottom row looks like [ 256][ 256][ 512][1024] swipe Right three times and you win.

How to win the 2048 game

2048 is a very addictive game. It combines three classic games into one: (1) the fifteen puzzle (2) the Tower of Hanoi puzzle, and (3) Tetris.

It’s addictive like Tetris because every new bit of order is threatened with random chaos. It uses a 4×4 grid with tiles that move, like the fifteen puzzle. And moving up from one level to the next roughly doubles the playing time, like the Tower of Hanoi puzzle.

Starting with the Tower of Hanoi puzzle, the key is to first figure out how to move 3 disks. It takes 7 steps. Once you’ve figure that out, let’s call that sequence of 7 moves “A”. Now, how you do move 4 disks? Simple. You do the “A” move from the first peg to the second, then you move the #4 disk to the second peg, then you do the “A” move from the second peg to the third. That whole process takes 15 steps. Let’s call it “B”. So… how do you move 5 disks? First you do B from first to second then you move disk #5 from the first to the third, then you do the B move again from the second to the third. The process takes 31 steps.

The 2048 game has a similar structure to it. You try to combine 2’s and 4’s to make an 8. Then once you’ve got an 8, you make another 8, then you put them together. It takes at least 3 moves to get an 8, then at least 3 more moves to get another 8, then it takes at least 1 more move to put them together into a 16 tile, total of 7 moves. So… how do you get a 32 tile? Simple, first you get a 16 (7 moves) then you get another 16 (7 moves) then you put them together (1 more move, total of 15 moves). How do you get a 64 tile? First you get a 32 (15 moves) then another 32 (15 moves) then put them together (15+15+1=31 moves). See how much this resembles the Tower of Hanoi Puzzle?

Okay, down to strategy. This is my suggestion of how to play, which I worked out for myself. It’s by no means the only way to do it.

First, you need to play around with the game a little bit and get the feel for it. I assume you’ve already done that before you’re reading this. If not, go play around for a while and then come back.

Now suppose you have this on the bottom row of your board: [  2  ][  2  ][  4  ][  8  ] Don’t worry about what’s on the rows above that; it doesn’t matter right now. Imagine what would happen if you swiped Right 3 times. The two [ 2 ]’s would combine to make a [ 4 ], then the two [ 4 ]’s would combine to make an [ 8 ], then the two [ 8 ]’s would combine to make a [ 16 ]. Neat huh? Okay, see if you can figure out how to make that happen. Get [  2  ][  2  ][  4  ][  8  ] on the bottom row. I’ll give you some help: Rule #1: Don’t swipe Up. The time to break this rule is when that’s the only legal move. Otherwise, only swipe Down, or Left, or Right. Also, try to avoid putting a [ 4 ] in between two [ 2 ]’s. Okay, go and play around until you manage to get [  2  ][  2  ][  4  ][  8  ]. Then swipe Right three times.

Woohoo! You now have a [ 32 ] in the lower right corner. Now add Rule #2: Keep your highest numbered tile in the lower right corner. If you only swipe Down and Right, then you’ll be following Rule #2. But sometimes you can swipe Left without moving that tile. Here’s an example: Suppose you have [ 4 ][ 2 ][ 4 ][ 32 ]. Swiping Left won’t cause anything to combine on that row. So Left is a safe move here without breaking Rule #2. But if you had [ 2 ][ 4 ][ 4 ][ 32 ] then swiping Left would break Rule #2. Don’t do that unless Down and Right aren’t legal moves.

Remember what I said about not putting a [ 4 ] in between two [ 2 ]’s ? Generally, you want to avoid having isolated singles of any size. For example, if you get a [ 4 ] stuck between two [ 8 ]s then you’ll have a hard time combining the [ 4 ] with another [ 4 ]. That’s Rule #3, tiles need to be in pairs, so don’t isolate them. Keep swiping Down and Right (and throw in an occasional Left, breaking Rule #2 as little as possible). Hopefully, you’ll end up with another [ 32 ] right next to the [ 32 ] you already have in the lower right corner. Now combine them with a Right swipe and voila, you have a [ 64 ] in your lower right corner.

Suppose you could get this on your bottom row: [ 16 ][ 16 ][ 32 ][ 64 ]. Wouldn’t that be sweet? Try to do it by swiping Down and Right. You can also swipe Left, assuming it won’t dislodge the [ 64 ]. If swiping Left would move the [ 64 ] tile, don’t do it unless you have to. If there’s a moment where Down isn’t a legal move and Right isn’t either, then you have to swipe Left. But what if Down and Right and Left are all illegal moves at some point? What if Up is your only move? Then you have to break Rule #1. When that happens, all your carefully cultivated order will quickly descend into chaos. It’s difficult to regain control after that.

If you manage to get [ 16 ][ 16 ][ 32 ][ 64 ] on your bottom row, swipe Right three times and wham! you have a [128] in the lower right corner. Now keep on following those same three rules and try to get [ 32 ][ 32 ][ 64 ][128].

Maybe you see what I’m leading up to here. Your goal is that you want the bottom row to look like this: [ 256][ 256][ 512][1024] and then you could swipe Right three times and boom! you win the game.