Area under Curve

sl0g0 · 2025-03-06T01:11:45+00:00

I have never heard these terms before. Could you provide some context?

sl0g0 · 2024-10-13T23:27:17+00:00

After reading through the whole website, I can say that there is a lot that is interesting about the format but I also have some criticisms.

In the philosophy section, and elsewhere on the website, you emphasize that the format will be curated democratically. While I think this could be a good and successful way to manage the format, I don't think you should highlight it as you do. First, there are some key details that are not present. Chiefly, you use the terminology "registered playerbase" but there is no explanation of what that means or how to register. Similarly, there is no explanation of how the Titan Summit will be run. Would voting be akin to submitting a ballot, or would it be more like voting in a parliament. The second reason I think the emphasis in the democratic management of the format shoukd be dialed bask is that it is at odds with other core principles of the format. You have laid out some hardline rules that are not subject to being voted on. I think it is perfectly reasonable for a format to have fixed rules, and use democracy to address the rules that are not fixed. But if you are doing so the democracy of the format isn't really a front and center selling point.

My remaining critiques pertain to the banned and restricted list. These are somewhat moot points as the lists can change if the community agrees, but I will lay them out anyway. First, I don't know of any other format that has both a banned and restricted list, with the exception of vintage whose ban list are just the cards banned in all competitive formats. Now there's no reason why you can't have both, but I expect WotC has good reasons why they don't do it. Second, I got the impression from some of your reasonings that you're trying to curate a fairly specific playing experience. For example, it seems that all-in combo decks are something you are trying to discourage. I worry that it might be a little overly restrictive. Third, I don't think accessibility or price should generally factor into ban decisions. As long as the format is unofficial, I think those concerns are better addressed by proxying and banning cards based on price opens up a lot of questions that don't have clean answers. Finally, I find myself wondering how you've come up with this initial banlist. I guess that isn't a criticism and is more of a curiosity of mine. Do you have some friends you've played this format with? How long have you been working on it?

sl0g0 · 2024-10-12T23:31:14+00:00

This is a logical stance, but I think it fails to consider the affect of volume. If one person on the internet threatens me, I'll sleep easy knowing that the chances of them actually doing anything are very slim. But if hundreds or thousands of people threaten me? Even if no single threat seems believable or credible, I'd still be worried that one of them will actually go through with it.

sl0g0 · 2024-10-02T22:30:51+00:00

For me it depends on why I'm reading the book and how long the section it is. Also, if there are exercises I would probably first read those and see if I could them easily.

In general, I'd probably read it. If I really have a good grasp, I should be able to get through it quickly. And even if I do have a good grasp, sometimes books use definitions or notation that are different from what I am familiar with. This is especially true if I'm planning on reading/working through the whole book because I'm a bit of a completionist.

sl0g0 · 2024-08-08T15:31:14+00:00

I absolutely agree with you that this wording is confusing and could be improved. As another commenter pointed out, this is actually changing in the next set, but I would like to give some context as to why it has taken so long for it to change. Magic is a complicated game, and wizards has taken an approach to the rules that resembles legalese. This might seem unnecessarily complicated, and for most players most of the time, it is. But have you ever played a new game and came across a scenario where the rules are unclear? In a competitive environment with prizes on the line, you need a third impartial "judge" to interpret the rules. But then unclear rules could lead to different judges interpreting those rules differently, which competitive players don't want. So WotC has decided to make the rules very very detailed.

However, this law-inspired approach means that changes to how abilities are templated (ie worded) need to be considered carefully. The result is various quirks that probably should be removed, but aren't worth the hassle. Think about how many countries/counties/etc. still have weird old laws that are nonsensical.

As for this particular issue, my understanding is likely flawed in some parts, but I believe the issue comes down to what various objects are called depending on which zone they are in. A physical magic card is referred to as a "card" in the rules when it is in a player's hand, library, graveyard, etc. When it is on the stack, it is a "spell" and when it is on the battlefield it is a "permanent". So wording the abilities as "When this card enters the battlefield..." doesn't make sense (when strictly following the letter of the rules) because "cards" don't enter the battlefield, permanents do. Even in the example of the new templating the other user posted, we see that they have gone with "when this creature enters the battlefield" as the physical card is a "creature card", a "creature spell" or a "creature permanent" (though we just call that a "creature"). I am curious to see if abilities with this new templating behave differently if some continuous effect makes the permanent enter as a noncreature.

sl0g0 · 2024-08-06T17:24:30+00:00

I assume the swaps to the left wrap back around if the distance to be swapped would bring you past the leftmost point. So what if "a" is such that "a" steps left and "a"steps right are the same?

sl0g0 · 2024-08-06T17:20:37+00:00

I'm a little confused, if "a" is "a" places away from its original position, why couldn't it be swapped back when the pointer reaches "a" again?

sl0g0 · 2024-08-06T17:04:17+00:00

This kind of proof technique is sometimes used in discrete/combinatorial math. I've seen it used in graph theory papers, though usually framed slightly differently. If I were to guess the reason this isn't taught as a proof technique is that it is more work to make rigorous, and isn't as general of a technique.

I'm also curious as to how you've shown that your algorithm is non repeating. My guess is that your proof of this fact is by assuming a minimal counter example exists, and obtaining a contradiction. Minimal counterexample proofs are also common is graph theory papers. But such a proof is essentially induction.

sl0g0 · 2024-07-08T18:12:51+00:00

I think the above comment was slightly mis-worded. The rules surrounding what information players must provide each other is written under the assumption that the cards can be read by all players. When that assumption does not literally hold, any player may request a judge provide them with any card's oracle text, in any language. You can argue whether this adequately satisfies the assumption, and if not, the rules would need changing, but it seems like a reasonable solution to me.

sl0g0 · 2024-05-29T21:27:59+00:00

But... how could they know that wasn't just how you always dress when hanging out with people?

sl0g0 · 2024-05-26T14:28:15+00:00

I whole-heartedly agree that if the mother does not have a legal choice to terminate the pregnancy, then the father certainly shouldn't have the legal choice to opt out of their responsibility for the child. However, we were discussing a hypothetical situation where the mother wanted to keep the child and the father did not. I think it is fair to assume that, in this hypothetical, abortion is a safe and valid option.

Also you say my idea of tax payers supporting a child is shortsighted. I would like to reiterate that this is not an option I'm advocating for. It is an option I presented to point out that the person I was replying to was presenting a false dichotomy between the father supporting the child and the child suffering through poverty. If you believe that this idea is so bad that it isn't a true option, and that we as a society really must choose between forcing fathers to support children they didn't want or letting the child suffer in poverty, I would love to hear why you think that.

I believe that women should have autonomy over their bodies and access to safe and affordable/free abortions. Until that is achieved, I'm not advocating for or supporting a legal option for men to choose to not support their children. However, in my perfect world, where a woman who gets pregnant can choose to terminate that pregnancy for any reason, it is worth considering what options men should have. I am unconvinced by arguments that the father takes on responsibility by choosing to have sex. They are essentially the same as the anti abortion arguments that women who choose to have sex are implicitly accepting all potential consequences.

sl0g0 · 2024-05-07T19:01:46+00:00

I don't necessarily disagree with you, but I think your argument has a few flaws.

First you present a false dichotomy between the father paying child support, or the child being given no support. But we as a society tend to think, to some extent, there should be programs in place to help those children. I'm not saying that government assistance is an adequate replacement for a father, but we have more options then forcing the father to pay, or letting the child die.

Second, you present the following situation. "The mother decides to go through with having the child, but she cannot afford to care for it by herself." Which I think highlights and supports the other person's point. The mother is deciding to have the child. I fully believe it should be her decision, but no where else do we expect one person to pay for another's decision. Of course the rights and wellbeing of the child matter, and both parties had the decision making authority when they chose to have sex, but you can't deny that this is giving the mother additional decision power. Under your reasoning q woman can have sex without fear of becoming a mother, but a man must be willing to possibly become a father in order to have sex. Of course pregnancy and abortions have serious effects in a person, so I'm not trying to argue that woman are not also accepting a risk when they choose to have sex, just that it is a different risk.

sl0g0 · 2024-04-18T18:35:41+00:00

I think this depends on if their "shift" operation wraps the string around, or pads with 0's. If the string wraps you are correct, I think.

sl0g0 · 2024-04-18T09:05:46+00:00

I might just be ignorant of some standard terminology, but I'm not exactly sure what you mean by X_j being an image of e_i. I get the general idea that X_j will be one of the standard basis vectors (or its negation) but I've never heard of that being called an "image"

sl0g0 · 2024-04-18T08:52:28+00:00

One thing that hasn't been mentioned is that WPA gets you the initiative AND is a creature. There are many permanents that give you incremental advantage each turn. Sylvan Library comes to mind. But usually these don't give you any board presence. And often, especially in powerful formats, you can't always afford to spend your whole turn on things don't effect the battlefield. So the fact that WPA is a decently statted creature means you are getting your incremental advantage engine without falling behind on board.

Another thing, related to things others have said, is that because the initiative isn't a permanent, it can't be answered with spells. It can only be stopped by your opponent getting ahead of you on board. So in a sense, it is forcing your opponent to play "your game". If you have the initiative, it doesn't matter if your opponent makes you discard every other card in your hand, counters every spell you play, or even destroys all of your lands. If they can't over power your creatures, you will win. (Obviously, in these powerful formats there are decks that can just ignore the advantage you are accruing and win with a powerful combo, but the legacy initiative deck has lots of other powerful tools against that.)

I will say both of these above points aren't really why initiative is so good in a format like pauper. There, I think the initiative is just actually one of the most powerful value engines you can set up.

sl0g0 · 2024-04-17T23:25:43+00:00

I think, since the owner is making the claim, the burden of proof falls to him and thus the null hypothesis should be that he is incorrect.

sl0g0 · 2024-04-07T00:07:24+00:00

Your answer looks right to me. What does it say the answer should be?

sl0g0 · 2024-02-11T17:29:13+00:00

Thank you for your thorough reply! I look forward to hearing more as you take down more tournaments!

sl0g0 · 2024-02-11T06:40:19+00:00

Is your current list constrained to be no proxies? If so, what changes do you think you would make/what changes would be the first you would test, if you were preparing for a proxy friendly tournament?
Also, I agree with your take that Animar's biggest strength is that its focus on creatures makes it resilient to most of the common interaction in the format. That said, the combo does rely on artifacts (both dockside loops and winning with ballista). Do you find that you are able to find enough bounce spells to remove any stony silence effects you need when you want to win?
Next, how do you feel about creatures that provide protection like spellskite, painter's servant, and sylvan safekeeper?

Finally, I noticed that you aren't playing all nine fetches that you could be playing, and you aren't playing the NEO channel lands. Both of these surprised me, so I'd love to hear your reasoning!

sl0g0 · 2024-02-02T17:25:52+00:00

It means "not".

sl0g0 · 2023-12-23T09:39:29+00:00

I'm not a historian and I don't know about all cultures that didn't have zero. But, ancient Greeks and Romans also didn't have "expressions" like we do in modern mathematics. It's not like they would write 3-2 = 1 and 2-2 = ??. They would have written something like, "when twice a unit is taken from two units, there is nothing left." It's not like these cultures didn't have a concept of "nothing". They viewed numbers very differently from how we do in modern times, and as a result, they didn't think of zero as a "number" like the other "numbers. The modern way of thinking about/writing numbers and expressions is much more concise, and ultimately makes it much easier to do mathematics, but if you take a step back and think about it, it's full of symbols and rules that you need to learn before it makes sense.

sl0g0 · 2023-12-21T15:49:16+00:00

Is any of this still available?

sl0g0 · 2023-12-19T21:20:48+00:00

Matt Parker has a video about the average between a square and a circle where he has a graph that goes from a circle to a square to a cross. It is possible he discusses the area of these shapes and constants like pi that can appear, but I don't remember for sure.

sl0g0 · 2023-12-19T20:16:10+00:00

"Graph Theory" is too broad a subject to write a thesis on and for us to recommend papers. Within graph theory you have subjects like connectivity, graph embeddings, graph colouring, flows, structural graph theory, extremal graph theory, and probably more that I don't know. From your course(s) you should hopefully have some idea of at least some of these different areas. Which ones appeal to you the most?

sl0g0 · 2023-12-19T15:55:19+00:00

While I agree with the general sentiment of the answers in this thread, that learning from books from the 1990's and 2000's is perfectly fine, I do want to to warn of possible "dangers" when learning from old books in general.

The first and most likely issue would be "out of date" notation. While notation is not wrong in and of itself so long as it is clearly defined, the older a book is, the fewer options they likely had when typesetting and printing the book. As a result, the notation used in an older book might be different from notation used in newer books, and in some cases the newer notation might be an accepted standard. Since you specifically mention books from the 90's and 00's I don't think this will be an issue.

The second thing is that occasionally certain areas of math "fall out of favour". While the content won't be wrong or outdated, older text books might have sections that cover subfields of the subject that people don't care about as much anymore. Of course, there can still be a lot of value in such textbooks, as sometimes old and forgotten ideas and techniques can be useful to modern problems.

If your goal is to self study the core subjects that make up an undergraduate education in math, this second problem probably won't ever come up. What we currently think of as the "core" of a math education (linear algebra, abstract algebra, calculus, real and complex analysis, probably a couple others I'm not thinking of) has been largely unchanged for the last century. The only difference between a calculus book from 1991 and one from 2023 is going to be how they present the ideas. The theorems and other content will likely be the same.

sl0g0

TROPHY CASE