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General Discussion / Re: Maths thread.
« on: January 20, 2019, 12:28:40 pm »
The main reason I don't like the term is that it's confusing to beginners.  It's usually the first time that something that is called multiplication doesn't behave like any other type of multiplication that they are used to.  I know I at first was wondering why in the world it was defined in the way that it is.  "Why not make it like matrix addition and use the component-wise product?  That has all of the standard properties of multiplication."  Of course we don't use the component-wise product because it's rarely useful, but back then it was radically different than any other kind of multiplication I had seen, and it seemed so arbitrary.

This kind of reminds me of tau vs. pi, or whether we should really call imaginary numbers "imaginary" numbers.  It's probably too late to change things now, but it would make more sense, especially for beginners, if the terms were different.

This is all totally valid. Two things I would say:

 1. Some terminology, while being confusing to beginners, is very intuitive and natural in a higher level context, or sometimes it's just so well established that you just have to deal with the fact that it's what everyone uses. In either case, though, we preumably want some of these beginners to become non-beginners some day, and we should think about the trade-offs between using counter-intuitive terminology in the introduction of a topic vs. making people re-learn proper terminology later on so that they can communicate with the rest of the community. (As an aside, this reminds me a little bit of learning how to ski. We teach young kids to make wedge-turns and then have to have them un-learn this and make proper turns later on).

2. I like your point about how "we don't use the component-wise product because it's rarely useful, but back then it was radically different than any other kind of multiplication I had seen, and it seemed so arbitrary." I think in a well-taught class there should be some serious time spent on getting students to understand why a component-wise product would be rarely useful, and why the proper definition is in fact not so arbitrary. The problem is that so many classes just introduce matrices and show how to multiply them with no context as to why we might want to do such a thing.

You can define anything you want, but the things worth studying in mathematics have a reason for the definition being what it is and not something else. I can define a binary operation on the set of all functions from the reals to the reals by

(f#g)(x) = f(x)g(x-2)+f(-2x)[g(x)]^2

Perfectly good binary operation. I could even prove theorems about it. But what's it good for? Not much as far as I know. Whereas the binary operation defined by

(f*g)(x) = int_{-infty}^infty f(y)g(x-y)dy (when convergent)

is good for lots of things.

Hmm; I'm not sure if I've ever posted in this thread.  Anyway, Linear Algebra is hard to teach.

This is very true. It's also somewhat unique among introductory math courses in that there are two pretty radically different ways to approach the subject, which I generally think of as the "Begin with systems of linear equations"  approach and the "Begin with the definition of an abstract vector space" approach. Courses titled "Linear Algebra" might be either one and they have a very different feel to them.

General Discussion / Re: Maths thread.
« on: January 19, 2019, 12:48:09 am »
Barely related, but I feel like matrix multiplication isn't "multiplication".  It's more like composition.

Eh, what is "multiplication" then? It's a binary operation and it distributes over addition, might as well call it that.

Do you call the composition of two functions a multiplication?

Well, I'm a dynamicist so kinda. By which I just mean that for me the notation f^2(x) generally means f(f(x)) and not [f(x)*f(x)] (exceptions being things like trig functions where the notation is standard but annoyingly inconsistent). But this is maybe confusing the issue...

To get at the heart of it, there are two things at play here:
(i) Terms in math mean whatever they are defined to mean and nothing else
(ii) Terms should ideally be chosen to be useful and consistent

Importantly, "multiplication" does not have a precise mathematical definition as a stand-alone term, so we can't appeal to (i). But there are certain binary operations on certain sets with certain properties that perhaps warrant using the same name for all of them, to highlight exactly those common properties.

On sets that already have a commutative binary operation which we've agreed to call "addition" and have agreed to denote with the symbol "+",  we often have another binary operation (which we maybe denote by *) satisfying a*(b+c) = a*b+a*c and (a+b)*c = a*c+b*c. Seems useful and consistent to refer to such operations as "multiplication."

For general functions, composition definitely does not satisfy this property (sin(a+b) =/= sin a +sin b), so it seems less useful to call it "multiplication." Could we? Sure, but then what property is shared by all "multiplications?"

You can debate these things of course. I've avoided using the word "ring" but maybe you want to restrict "multiplication" to only refer to a ring operation. But multiplication in rings must be associative. Is that important to you? Maybe, but then you lose the ability to call the cross product of vectors in R^3 "multiplication." Do you care?

Now of course in the realm of matrices, we have such a binary operation which distributes over addition, so we do tend to call it "multiplication". It also happens to relate to linear transformations of vector spaces, and in a sense coincides with the notion of "composition" in that context (where you should now think about what a useful and consistent definition of "composition" would be).

At the end of the day I'd argue that it's better to talk about multiplying matrices as opposed to composing them. You'd not be insane to take the operation we call matrix multiplication and call it something else, as long as it is defined precisely, but you should think about whether that term is useful and consistent. In this case, you'd be clashing with established nomenclature, though, which is hard to overcome even when it's not useful or consistent (like sin^2(x) v. sin^(-1)(x)).

As a final quiz, how should we define multiplication of ordered pairs of positive integers? For a,b,c,d positive integers, which is more natural (consistent and useful)?
(i) (a,b)*(c,d) = (ac,bd)
(ii) (a,b)*(c,d) = (ac-bd, ad+bc)

General Discussion / Re: Maths thread.
« on: January 18, 2019, 11:29:27 pm »
Barely related, but I feel like matrix multiplication isn't "multiplication".  It's more like composition.

Eh, what is "multiplication" then? It's a binary operation and it distributes over addition, might as well call it that.

Dominion Articles / Re: The Top 20 Best Designed Cards
« on: January 14, 2019, 03:38:27 pm »
Doctor was the first card I ever owned where I am not to date able to tell you what it does by heart. It's some trashing, top of deck, I think with matches? And then it does the same thing as overpay, or no, a very similar but not identical thing... Maybe it makes sense once you play a few games with it, but this never left our box.
We had this experience during Renaissance testing. Doctor was in the game, and someone said, man I don't want to read that.
For me it's mostly the fact that both things are so similar, really. It would be easier if the parts felt like they complimented each other, like on the other overpay cards, or were actually the same, like on Noble Brigand. I don't even know whether the card is good or bad, just that I never felt I could explain it in short words to my play group. That said, Guilds is still one of our favourite expansions, and sees a lot of use at our table. Baker's setup is perfect.

This is a similar issue I have with Graverobber. You're upgrading or pulling from the trash, there are some cost restrictions, something has to be an action, sometimes it goes on top of deck, but I cannot ever remember which goes with what.

General Discussion / Re: Movies: Any movie buffs?
« on: January 02, 2019, 12:48:26 pm »
I was expecting to be annoyed by Spider-Ham. He was just in small enough doses that I was able to accept him.

John Mulaney is a national treasure.

This movie was fantastic, and gives further evidence that basically everything from Lord/Miller is worth watching. There was even a Clone High billboard easter egg in the background!

General Discussion / Re: Drinking
« on: December 21, 2018, 12:24:56 pm »
Cuzz, are we still in the same hood? Cause I definitely want an invite to the next cocktail party. :)

Also, congrats on the upcoming little one!

Alas, no. I moved to Chicago about 3 years ago.

General Discussion / Re: Drinking
« on: December 21, 2018, 11:37:48 am »
Hey, joth is back!

I threw a cocktail party a few months ago and made huge batches of whiskey smashes (the signature cocktail from my wedding), mai tais, and a sort of paloma-type thing with an IPA float that came out really delicious. I tend to wildly swing between trying to make precise versions of classic cocktails and inventing my own with whatever I have on hand. Mixed results on both counts.

Since my wife got pregnant I've been leaning more into beer, though. My local bottle shop sells a beer advent calendar that I ended up with two of as gifts from people, so I've been working my way through those. A Metropolitan Dunkel Rye and a Half Acre IPL were standouts so far.

Dominion General Discussion / Re: Taking Notes - Against the Rules?
« on: December 17, 2018, 02:38:55 pm »
After consideration of my opponents inability to memorize certain aspects of the game (they cannot remember if they bought all of the cards for Museum), I prefer to make the game more 'playable' for them (if they prefer to take notes, then I can take notes myself, but I would rather want them to play the game and enjoy it.  Just because I can remember things better should be my advantage.  I want my ability to know how to play the kingdom at hand to be the deciding factor, not my ability that I have the advantage of having more VP then they do, and end the game on piles.

No problem playing that way if you want; so long as you recognize that you are playing a variant.

Yes to be safe you'll want everyone to fill out the Variant Contract in which all players affirm their understanding that an actual game of Dominion has not been played, and that they will under no circumstances claim that they have played a game of Dominion in speech, print or semaphore to any other entity living, dead, or fictional.

General Discussion / Re: The Legend of Zelda: Ocarina of Time turns 20
« on: December 12, 2018, 04:59:43 pm »
Ha, I read that piece today and was wondering how you pitched it to them.

Yeah, I generally don't have to get my pitches pre-approved at my normal place of business.

Yeah, I don't know how these things work in media. But I don't think I had seen any other video game pieces there so I just thought it was cool that you were able to write something like that for them.

General Discussion / Re: The Legend of Zelda: Ocarina of Time turns 20
« on: December 11, 2018, 07:58:33 pm »
Ha, I read that piece today and was wondering how you pitched it to them.

I'm not much of a gamer at all but man do I love that game. Every time I start it up again I feel immediately transported to my parent's family room on Christmas morning in 1998. I haven't touched a console in months but now I feel like I need to play it this weekend.

Dominion: Renaissance Previews / Re: Renaissance rulebook is up
« on: November 07, 2018, 08:01:40 am »
Patron gets added to the list of cards that clearly only exist to stick it to people like me who have responded to fan cards by saying "it's not a good idea to have a reaction that reacts to being revealed".

Why was this not considered to be a good idea?

Mine becomes a discount Expand for your new treasures.

Mint becomes a Disciple variant (buy it before you buy Capitalism).

Dominion: Renaissance Previews / Re: Renaissance rulebook is up
« on: November 05, 2018, 11:16:44 am »
Some of the Teaser cards: Patron has "reveal" in quotations, Scepter, Capitalism, and Inovation let you play Actions in your Buy phase, Fleet gives players extra turns, and you can't turn off Cathedral.
I'm kind of dissapointed that Border Guard uses both Lantern and Horn, meaning that there are only four kingdom cards that use Artifacts. I hope he uses them again in another expansion.

Don't count on it. He's already gone on record saying that he'd remove them from Renaissance if he had to do it all over.

Where was this? It seems odd to already have such strong regrets about a set that is just hitting shelves and that essentially no one has played with yet.

Black Market will enable some serious craziness as well.

Storyteller playing actions with "+ Coin" (obviously) and "+ 1 Action" enables village-like effects.

Oh yeah Storyteller becomes ridiculous in two ways. Mostly you think about the effect of Capitalism during the Buy phase, where Storyteller can now be used for draw even if drawn dead. But now it also gets a huge buff as an engine component during the action phase since it can play all of your new action/treasures for draw and other effects.

How does Capitalism work with the $ token from Adventures?

Giant gets a buff

Other Games / Re: Fireball Island
« on: October 29, 2018, 10:30:39 pm »
I joined the backerkit and am really excited for my copy to show up. I'd never heard of the original, but I think Restoration Games' premise of revitalizing older games is fantastic.

I likewise joined the backerkit, having missed the Kickstarter.

I had a copy of Fireball Island when I was a kid, but I'm not sure I ever played a game of it using the actual rules. Specifically, I don't remember ever using the cards.

EDIT: I am also likewise really excited.

I also had it as a kid and also remember it as one of the games where the components were so much fun we didn't usually bother with the rules. Mousetrap, grape escape and the omega virus also were along those lines.

Dominion Articles / Re: Draw-to-X engines
« on: October 10, 2018, 10:44:46 am »
I think it would be worth it to include a list of draw-to-x cards, since really only 4 cards say "draw until you have x cards in your hand" (and Jack isn't that great of an engine card). I mean, at this point we all probably know, but for newer players it's good to mention that Minion, Menagerie, and Scholar are lumped in with the other cards.

Menagerie, Minion, Tactician, Library, Watchtower, Jack of all Trades, Guide, Cursed Village, Scholar. Did I miss any?

Tactician doesn't work more than once each turn and double Tactician is its own strategy altogether.
Jack of all Trades is hard to make work because it only gives you five cards and it gives you a Silver on each play.
Guide doesn't work, as you can only play it at the start of your turn, before any actions. Although it synergizes well with start-of-turn trashers (but how many of those are there? Amulet... Ratcatcher... Transmogrify not so much... Prince...)

I think based on the way the article is written, we're effectively really only talking about Library, Watchtower, and Cursed Village. You mentioned the issues with Tac, Jack and Guide, but Menagerie is not at all Draw to X (although some of the same principles apply), and the discarding with Scholar and Minion are large enough wrinkles that they'd need their own subsection.

Dominion: Renaissance

Dominion: Renaissance Previews / Re: Renaissance name BINGO
« on: September 27, 2018, 09:29:06 am »
Grand* Merchant, DAMMIT. Asper I want credit for that when it comes up.

Dominion: Renaissance Previews / Re: Renaissance name BINGO
« on: September 27, 2018, 09:07:38 am »
I would have rejected Silk Merchant based on the fact that we already have Silk Road and a bunch of merchants, though in hindsight I guess the namespace is pretty cramped already.

Yeah I'm kinda banking on that for my card:

Silk Market                 Wine Road              Grant Merchant

Market Ship                Merchant Square     Market Guild

Farmer's Merchant       Spice Market          Merchant Market

Nice, three more cards that Lord Rattington has no idea what to do with!

Some plausible future card names that would be doublets of existing cards: Peon, Money, State, Esquire, Eremite, Fief, Fee

Less likely ones: Bench, Fabric, Place, Guy, Wit, Fjord

Pawn, Mine, Estate, Squire, Hermit, Feodum, ?

What do you expect to do with it? Trash your Estates and accelerate by not needing villages for a few rounds, or use gainers to feed it?


It can get bonkers with gainers in particular though, especially silver gainers. If you can feed Recruiter consistently, your terminal space utterly explodes, sometimes essentially to Champion level, and it draws.

"Draws." But doesn't actually increase your hand size.

Sure. My point is itís very very good.

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