Motivation and a sense of accomplishment

Do you want to do something? It depends whether you imagine it will be pleasant or unpleasant. The anticipating self imagines whether something will be pleasant or unpleasant. This is in some sense, the pleasure of your mental model of your future self. We call this "motivation".

Do you enjoy what you're currently doing? We call this "enjoyment", or "pleasure".

After you finish something, when you think about to it, do you experience pleasure? Are you happy you did it? Do you remember experiencing pleasure then? This is the happiness of your remembered and future selves. We call this "satisfaction" and "accomplishment".

They are not in alignment. What you anticipate being unpleasant or pleasant, is not always so. I rarely remember experiences as being as pleasant, or unpleasant, as they were at the moment. When I imagine being satisfied after finishing a task, it may or may not be true -- but it is usually true I will forget the effort the task took, afterwards.

What is capability?

Can I compose a symphony? In some sense, no. I don't know anything about music. In some sense, yes. My fingers can certainly draw all the notes.

Can I paint my house? In some sense yes. I know how, and I possess enough money to buy paint and tools. In another sense, no. I don't have any paint at my house right now. I am afraid of heights. It sounds like a lot of work. I don't care what color the house is. I have never painted a house before. I am sleepy right now.

One goal we might pick is to "expand our capabilities". But what does that mean? A naive view might say that it would be useful to learn to paint a house. But imagine I disliked the color of my house, and wanted to change its color. It might be scary to learn to paint. If I learned to paint, I would "have to" paint it... and I have not fixed any of the other obstacles. So it might be good to expand our vocabulary, or increase the detail of our thinking, when we think about whether we will be capable of something.

An experiment

Today I'm experimenting with the idea of trying to expand my capabilities, in the sense that I would say "yes, I am capable of that" in response to each objection above.

I have no idea how it will go. Probably it will fail--most experiments do.

Perhaps I will expand my comfort zones. I might increase my energy levels with exercise or coffee. I might boost my confidence by succeeding at smaller, my planning the steps of something, or by completing subtasks. I might take a class on music theory. I might compose and share a heartfelt, and very bad poem, so that writing more poetry has less pressure on it (I won't, though).

I'm thinking about how to get the most new capabilities, for the least work, and ideally to do things which advance my goals, like helping others.

Recently I was making a villager trading hall in minecraft.

One of the main goals of a trading hall is to collect all villager trades. One of the trickiest is books, provided by a librarian. I got to wondering -- how long is this going to take?

Well, we can do some math to find out.

There are currently (as of Minecraft Java Edition 1.21.11) 40 trade-able books. 36 of them are available from the enchanting table, treasure chests[1], or trading.

4 are available only from treasure chests and trading. These are called Treasure enchantments.

• Curse of Binding
• Curse of Vanishing
• Frost Walker I and II
• Mending

There's also three books, which can be found only from treasure chests. We don't care about them for trading halls:

• Soul Speed
• Swift Sneak
• Wind Burst

There are no books available only from enchanting and not trading.

The core mechanic of searching for book trades is resetting. If we look at a librarian and find it has a trade we don't want, we reset it.

Villagers remember their profession and trades forever after trading. But if we haven't traded with a villager, we simply remove its profession, and then give it a profession again. Then we can see if we like the new starting trades better.

This is very useful for librarians, because they have every book available as a starting trade, so there's no need to investigate later trades for books.

These are the options to make the villager forget their profession I'm aware of:

• Ignore the villager and get a new one (for example with a breeder), moving or killing the old one. This isn't a "reset" per se, but it acts similarly.
• Break the profession block manually. In the case of a librarian, the lectern. When breaking the block, the villager loses their profession instantly.
• Block the path between the villager and their profession block. I haven't seen this documented, but they reset at the same time as trades reset (twice per minecraft day). I did this by dropping the villager 1 block using a piston.
• Move the villager at least 48 taxicab blocks from their profession block. (Not tested)
• Move the profession block with a piston. This is an instant reset, but you can't do it for a lectern in Java edition. (Not tested)

Some of these are instant, some take longer. Once villagers are shown a profession block, it only takes them a couple seconds to get their new profession, so that part is easy.

I found breaking and re-placing blocks to be annoying, so I settled on moving librarians up and down with pistons. It takes about 5 real-time minutes for them to reset, so I used about 50 librarians to counteract that. By the time I finished checking all 50 librarians, they were ready to reset again because 5 minutes had passed.

Then the question is: How many librarians do we need to look at, to get every book?

Well, the first question is: what are we interested in? Let's say we're interested in getting each of the 40 enchantments.

Well, it turns out each enchantment is equally likely: there's a 1/40 chance of getting it. Well actually, 1/60 -- there's a chance that no book trade is offered at all.

Then this is the coupon collector's problem, a classic math problem.

The number of trades to look at turns out to be: 3/2 x n x H(n) where H(n) is the n-th harmonic number. For n=40, H(40) = 1/1 + 1/2 + 1/3 + ... + 1/39 + 1/40 = 4.2785. So we need to check 257 librarians on average to get every enchantment.

But, are we really okay with that result? Given that Efficiency V is available as a starting trade, I want a librarian with Efficiency V, not Efficiency I!

There are:

• 9 tradable enchantments with a max level of I
• 4 with a max level of II
• 13 with a max level of III
• 7 with a max level of IV
• 7 with a max level of V

What's the chance of getting each level of enchantment? It's equal. So for Mending, there's a 1/60 chance to get Mending I, because it's the only choice. For Efficiency, there's a 2/3 * 1/40 x 1/5 = 1/200 chance to get Efficiency I, Efficiency II, or Efficiency V.

How do we calculate the coupon collector's problem for un-equal probabilities? Well... it's really complicated[2].

But the answer is that we will have to talk to an average of 933 librarians to get all enchants at max level.

But hey. We can buy Efficiency V for 17 emeralds, if we get the right trade. Are we really okay getting a 64 emerald trade? What if we want only the best trades?

Mostly, the price range is based only on the level, but there are a few minor complications:

• Some price ranges go above 64! In the game, these get capped. For this reason, you're 8 times more likely to get Efficiency V for 64 emeralds than any other number.
• Treasure enchantments (in bold above) are double the price of any other enchantment. This is actually a double -- they're never offered for odd numbers of emeralds. Interesting!

The chance of getting an Efficiency V book at the best possible price is: 1/16,500 = 2/3 x 1/40 x 1/5 x 1/55 (because there are 55 possible different prices -- counting ones above 64).

To get every book at the best price, we'd need to talk to 45,594 librarians[2] to get every max-level enchant at the best price.

[1]: I think [2]: Source code here. This uses the inclusion-exclusion principle to estimate set sizes, together with optimizations to take care of repeat probabilities.

Hack-a-Day is my self-imposed challenge to do one project a day, for all of November.

Today I made Kim's Game. It's a recreation of (or a riff on) a classic spy-training memory game from the 1901 book Kim.

You can play online here. The source code is on github.

Faces are from thispersondoesnotexist.com

Hack-a-Day is my self-imposed challenge to do one project a day, for all of November.

Today I make a clone of the classic game, Guess Who?.

You can play online here. The source code is on github.

Faces are from thispersondoesnotexist.com

Hack-a-Day is my self-imposed challenge to do one project a day, for all of November.

Today I took my previous golf game, and turned it into a little idle game. It takes about 30 minutes to finish.

You can play online here or view the source code on github.

Hack-a-Day is my self-imposed challenge to do one project a day, for all of November.

Today's project was mini-golf. I've seen these online, and I thought it was an easy problem (I was mostly right).

It turns out finding the intersection of two lines is really hard, though! It kind of seems easy mathematically, but in practice it's really fiddly with a lot of edge cases. Reflecting is also harder to figure out on a computer than by hand.

My little demo only has one level, but the hard part was the engine -- adding 8 more holes would be pretty easy, I think. There's no hilly slopes or other special features in this verion.

I stayed up too late finishing this one, heh. You can play online here or view the source code on github.

Hack-a-Day is my self-imposed challenge to do one project a day, for all of November.

Today's project was a simple platformer. I got something playable, but I wouldn't say it's to the point of actually being a game. Hopefully I'll have time to go back and finish it before the month is out.

I had a lot of fun making this one. I love visual stuff. You can play online here or view the source code on github.

Today's project struck me out of nowhere. What if connect-the-dots... but wrong?

You can play online here or see the source code on github.

Have fun.

Today's hack-a-day project was Pokétrace. Did you ever, as a little kid, trace stuff you liked? It's how we learn art! I made this as a way to relax for adult (and for kiddos, of course!). And to improve my art skills.

You can trace pokemon in your browser. Let me know if you want any generations other than the first one, or show me any fan art you make! I'd love to see it.

This one should work on phones and tablets. Let me know if you run into any problems.

You can save your finished pokemon as an HTML file, and it should save progress (but only on your computer).

Open offer: if you trace all 150 pokemon, I'll make it into a coloring book version for everyone. And if you draw fan art of all 150 pokemon, I'll send you a poster of your art! (as long as you don't live somewhere with crazy shipping for me)

Enjoy!

Today's hack-a-day project was the Cookbook 2.0. I wrote a collection of my recipes in 2020. I've updated it with what I've learned in the last 5 years. Among other things, it has 57 new recipes.

You can read it online in a couple formats.

Enjoy!