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51

General Discussion / Re: Maths thread.

« on: February 23, 2021, 11:02:10 am »

And it's useful because while the definition of a function doesn't require any particular formula or pattern for specifying what the elements of S are, often in practice functions do arise from formulas and writing something like "the function f(x)" is less clunky than "the function f defined by f(x) = ..." or "the function f: x -> f(x)" or whatever. 

How does this apply to f(x) \in O(g(x))? I *don't* object to f(x) = x^2 to define a function, but that's not what's happening here.

Well for one it keeps track of what the independent variable is in cases where it might be ambiguous.

52

General Discussion / Re: Maths thread.

« on: February 23, 2021, 10:57:36 am »

Pedantically f is a function (an ordered triple (X,Y,S) where S is a subset of XxY satisfying the function axioms, or really better an equivalence class of such ordered triples where (X,Y,S) ~ (X',Y', S') iff S = S') and f(x) is an element of the codomain Y.

But using f(x) in place of f is one of the more ubiquitous and mild abuses of notation in mathematics. And it's useful because while the definition of a function doesn't require any particular formula or pattern for specifying what the elements of S are, often in practice functions do arise from formulas and writing something like "the function f(x)" is less clunky than "the function f defined by f(x) = ..." or "the function f: x -> f(x)" or whatever. 

53

Other Games / Re: Hades

« on: February 22, 2021, 04:27:29 pm »

I've been really hooked on this lately. I've never really liked rouge-anythings. I played a bunch of slay the spire over the summer but it eventually started to feel like a waste of time. But the story of Hades is so good and just perfectly meshes with the gameplay; you always want one more run both to see how far you get and to see what you might have unlocked after it's done. Good times.

54

Dominion FAQ / Re: Undo rules in rated games

« on: August 29, 2020, 02:28:02 pm »

I've said this before, but I don't understand people's extreme aversion to opponents denying an undo. The very fact that the undo system exists is a nice-to-have extra that allows you to sometimes deal with misclicks. I think if the system were better-done, then undo would be automatic / not require approval if no information was revealed, and never allowed if information were revealed.

I would not approve of that. There is a setting for auto-allowing some undos, and that's good. But sometimes I want to allow information-revealed undos, if my opponent believably assures me that e.g. they would have drawn anyway, but wanted to play the Village before the Smithy, or something.

I also think revealed info undos should be normalized for situations like ending a turn by clicking on the wrong card to buy. If the request comes in fast enough I’ll tend to give those.

55

Dominion Articles / Re: Menagerie Hot Takes

« on: August 05, 2020, 02:15:20 pm »

Why is that a problem though? It changes the calculus for that game, but you still have to, like, build a deck to line up your exliler (?) with your green cards if you choose to green early. Sanctuary is no Rebuild.

56

Dominion General Discussion / Re: Neat and potentially useful card interactions

« on: August 04, 2020, 10:55:00 am »

Sceptor - Way of the Turtle

Replay any action in play at beginning of next turn.

57

General Discussion / Re: Brag Board

« on: July 31, 2020, 01:53:21 pm »

My son just took his first steps!! 

Awesome! My daughter is probably getting there any day now.

58

Dominion General Discussion / Re: Neat and potentially useful card interactions

« on: July 30, 2020, 04:03:50 pm »

IGG + Guildhall

Maybe everyone knows this already but I just got wrecked by IGG/Guildhall. In a normal IGG rush you drain IGG, Curse and usually Duchy. Pretty rare that it's the best strategy these days. With Guildhall those Duchies are Provinces instead, and it's, uh, quite good I think.

59

Forum Games / Re: Drunk Mafia 8: Quarantine Edition

« on: April 17, 2020, 12:09:16 am »

I can maybe join later on if things go for a while.

60

Introductions / Re: Hello again

« on: April 17, 2020, 12:02:29 am »

Oh dang, it's yuma

61

Other Games / Re: Outer Wilds

« on: April 05, 2020, 02:01:55 pm »

This sounds very up my alley. What platforms is it on?

62

Dominion General Discussion / Vox on Dominion

« on: April 04, 2020, 08:09:44 pm »

https://www.vox.com/2020/4/3/21197399/dominion-online-board-games

63

Dominion General Discussion / Re: Epic Fails Thread

« on: October 07, 2019, 01:38:29 pm »

I just had a classic example of failing to do basic math: I went for Masterpiece-Feodum in a game with Bandit Fort. I was thinking enough Feodum points would outweigh the Bandit Fort penalty. Then I actually did the math and realized I would need at least 7 Feodums for that to happen... which was no longer possible because my opponent was pursuing the same boneheaded strategy I was!

Fortunately in this situation you can always just trash the feodums and pivot to a new strategy.

64

Dominion General Discussion / Re: Combo: Explorer/Captain

« on: October 06, 2019, 04:31:21 pm »

Because the sails are different?

65

Other Games / Re: Celeste

« on: September 24, 2019, 09:10:36 am »

I stopped quite a few screens before the door. I was in one of the first screens with the blowfish, I was supposed to dash into it, boost myself across some spikes, then dash back to that fish so it would blow me into another and so on. I kept not being able to bounce hard enough from dashing into the fish to clear the spikes without using the dash I needed to go back to the fish afterwards. After feeling rather frustrated with some of the screens in Core (and beating them through sheer persistence rather than skill), I thought it was a good spot to end.

This is the exact one I’m stuck on as well. The great thing about this game is that each screen is two challenges: the puzzle of figuring out what to do to beat it, and then executing the platforming moves. In this one though it seems pretty obvious what to do, but very hard to pull off.

66

Dominion General Discussion / Re: COMBO: hunting party/patron

« on: September 16, 2019, 02:12:06 pm »

Snark aside, I don’t really see this. We’re talking about a two card combo, and it was asserted that hunting party is no better than menagerie with patron. How do menagerie and patron constitute an engine that will reliably draw your deck?

Well, I'll try hard to keep this thread in mind the next time I play Dominion with a 2-card kingdom and the cards happen to be Hunting Party and Patron. After all, there is no way I could possibly figure out on the spot that there's anything going on there.

And why is the +buy “easier to fit in?”

Because you're playing an engine, not a Hunting Party stack.

All right, I did say "snark aside," but cool.

67

Dominion General Discussion / Re: COMBO: hunting party/patron

« on: September 16, 2019, 01:40:23 pm »

This isn't really a combo; there isn't much of anything that makes hunting party differ from eg menagerie or any other reveal card here, and hunting party makes it difficult to actually find all your patrons

combo threads are generally for things that completely change the game when present: hermit / market square, lurker / hunting grounds, etc

(hunting party is much better than menagerie here because you reveal the patrons that you don't draw as well as the ones in your hand; point taken that the word "combo" is controversial)

Yeah, this is the entire point. Maybe try it out before declaring it "not a combo?" In a Hunting Party strategy you're revealing your *whole deck* *many times* *every turn* (edgecasesedgecases). There is no comparison with Menagerie.

In a typical Menagerie strategy (also known as an "engine"), you can easily be revealing your *whole deck* *many times* *every turn* and the +buy is a lot easier to fit in.

Snark aside, I don’t really see this. We’re talking about a two card combo, and it was asserted that hunting party is no better than menagerie with patron. How do menagerie and patron constitute an engine that will reliably draw your deck? And why is the +buy “easier to fit in?”

68

Dominion General Discussion / Re: COMBO: hunting party/patron

« on: September 16, 2019, 12:37:32 pm »

This isn't really a combo; there isn't much of anything that makes hunting party differ from eg menagerie or any other reveal card here, and hunting party makes it difficult to actually find all your patrons

combo threads are generally for things that completely change the game when present: hermit / market square, lurker / hunting grounds, etc

(hunting party is much better than menagerie here because you reveal the patrons that you don't draw as well as the ones in your hand; point taken that the word "combo" is controversial)

Yeah, this is the entire point. Maybe try it out before declaring it "not a combo?" In a Hunting Party strategy you're revealing your *whole deck* *many times* *every turn* (edgecasesedgecases). There is no comparison with Menagerie.

 It could really use some +Buy, but it's uh, really good.

69

Mafia Game Threads / Re: M124: GPT-2 Mafia (2^2 spots left)

« on: August 21, 2019, 11:46:59 am »

bah, /out, sorry

70

General Discussion / Re: Maths thread.

« on: August 08, 2019, 10:40:43 am »

How would you describe math to a layperson, in such a way as to try to break through their preconceived notions of what it is?

This doesn't precisely answer the question, but this classic essay by Thurston is a great read

https://arxiv.org/pdf/math/9404236.pdf

71

Mafia Game Threads / Re: M124: GPT-2 Mafia

« on: August 03, 2019, 08:56:29 pm »

/in

72

General Discussion / Re: Maths thread.

« on: June 26, 2019, 08:40:26 pm »

People were able to compute plenty of derivatives perfectly well far before any of the modern rigorous notions of limits, which was primarily due to Cauchy. They did so mostly with "handwaving."

The key issue here is more subtle, and it's more about being circular than being handwavy. The approximation e^h = 1+h when h is small is only valid for the number e. It's equivalent to the fact that the tangent line to the graph of e^x at x=0 is y=1+x, which can't be established without knowing that the derivative of e^x is e^x in the first place.

I don't think that's a different issue from what I said. Being handwavy is what allows the argument to get away with whatever wrong thing it's actually doing, like being circular. If it spelled out the argument explicitly, we would see what exactly it relies on.

Taking shortcuts is never a mistake in itself, it's always a black box where real mistakes may or may not be hiding.

My point was just that the answer the question:

The physicist's proof for the derivative of e^x:

(e^{x + h} - e^x)/h = e^x(e^h - 1)/h.  Because h is small, e^h = 1 + h, so e^x(e^h - 1)/h = e^x(1 + h - 1)/h = e^x(h/h) = e^x.

What prevents that from working with any number other than e?

is something we can specifically identify in the argument. It's exactly contained in the statement "Because h is small, e^h = 1 + h." It's not just a "there's some handwaving so it's all completely invalid" kind of thing.

73

General Discussion / Re: Maths thread.

« on: June 24, 2019, 07:23:25 pm »

The substitution step could be done rigorously if you use the infinite series definition of the exponential. That would give a different result if you have a number other than “e”.

I think without the infinite series definition of the exponential function (or the definition as the inverse of the logarithm), the farthest you can go with this is that the derivative of exp is proportional to exp.

EDIT: what cuzz said

Right, I claimed that you can't use that substitution without already knowing the derivative of e^x is itself, but in fact you can if you define the exponential function as its Maclaurin series. But then the fact that the derivative of the function defined by 1+x+x^2/2 + x^3/6 + ... is itself is completely trivial via term-by-term differentiation (modulo the fact that you'd need to prove or just accept both that the series converges and that functions defined by power series are differentiable term-by-term).

In fact, it's worth thinking about what your original definition of the exponential function even is, as this can make a difference as to whether any given fact about it is a theorem or a tautology. For example, it's also perfectly reasonable to define the exponential function as the unique function satisfying f'(x) = f(x) and f(0) = 1, once you prove that such a function exists and is unique.

74

General Discussion / Re: Maths thread.

« on: June 24, 2019, 07:03:11 pm »

People were able to compute plenty of derivatives perfectly well far before any of the modern rigorous notions of limits, which was primarily due to Cauchy. They did so mostly with "handwaving."

The key issue here is more subtle, and it's more about being circular than being handwavy. The approximation e^h = 1+h when h is small is only valid for the number e. It's equivalent to the fact that the tangent line to the graph of e^x at x=0 is y=1+x, which can't be established without knowing that the derivative of e^x is e^x in the first place.

75

General Discussion / Re: Drinking

« on: June 21, 2019, 10:55:25 am »

This recipe is the best frozen cocktail I’ve ever had. Not a trashy syrupy beach drink, not too sweet, perfect for summer. You can batch the mix in the freezer and then just blend with ice on demand. It’s amazing. https://www.seriouseats.com/2016/07/frozen-gin-and-tonic-blender-summer-drink-cocktail.html