I suppose that it comes down to how you define "exhaustive".
Let's take an example (which I'm personally extremely familiar with, as it pertains to my job): Suppose you are given, let's say, 20 random letters, and a large dictionary of English words (let's take the sowpods dictionary, which is used for official scrabble tournaments, and contains 276663 words), and your task is to find every single word in that dictionary that can be formed with any amount of those 20 letters.
If you find every single such word, without missing a single one, you could arguably state that the search was "exhaustive". But how long does this take?
An extremely naive approach would be to create every single possible permutation of up to 20 letters from that given set, and check if it appears in the dictionary. The number of possible permutations is over 20 factorial, which is absolutely enormous. (20 factorial alone is over 1018, ie. over 2 quintillion in American notation. The actual number of permutations is larger because you also need to check all the possible combinations of 19 letters, 18 letters, and so on.)
Even if you could check one billion permutations per second, it would take about 2 billion seconds to go through all of them, which would be about 77 years.
But how long does it take in practice? In actuality, producing that list of words that can be formed with those letters takes a small fraction of a second, even in a slow computer.
The trick is that you don't need to go through all the possible permutations of those 20 letters. When creating permutations, when you have taken two letters, you can check if any words start with them, and if they don't, you can skip all permutations that begin with those two letters. (The same goes of course for permutations of the first three letters, and so on.) This reduces the number of permutations to check to a microscopic fraction of the total. (There are also other algorithms possible for this task, which do not involve going through permutations of the 20 letters, but they aren't completely dissimilar to this idea either.)
Technically speaking the search was exhaustive: The resulting list contains every single word that can be formed with those letters, without missing any. However, the task didn't require 77 years to complete, but a small fraction of a second.
The point of this whole thing is that just because something may have a ginormous amount possible permutations or combinations doesn't automatically and necessarily mean that an "exhaustive search" (which I take to mean "finds the optimal solution") requires an exponential amount of time. (It can mean that, especially if the task is provably NP, but it's not necessarily so.)
To start off, I heavily object to the name "exhaustive search bot". Just by a simple calculation at the size of the NES RAM and the possibility of inputs, it's pretty obvious that with current technology it's impossible to make a bot that's truly exhaustive. The amount of possibilities is too much, even for a computer to check.
Technically speaking that's not true in all cases, but that conversation would be a bit off-topic in this particular thread. I would write an essay about it, but maybe that would be better in a thread that's more on-topic with that subject.
So kudos for keeping silent? Are you suggesting that I should also keep silent and just pretend that all the negative votes and criticism towards our run make sense? So who's "shutting down that freedom to express"?
Just stop it. You aren't doing yourself any favors by continuing writing like this. I know this from personal experience, believe me.
You wouldn't have to invent anything, you'd just go with existing low-glitch categories like "No wrong warp" or "no IM/wrong warp". The only OoT TASes that invented categories themselves are those challenges like "all dungeons, no doors" or "100% 3 pause".
The good thing about MST is that (at least at speedrun.com) the BA, RBA and GIM glitches are banned. You need to get all the required items genuinely.
To me, "demonstration" means "doesn't complete the game (but does something else)".
We have exactly 0 movies in the monstrosity called "Demonstration" that are actually like that.
Perhaps I should have clarified that IMO that's what "demonstration" ought to mean. (I haven't followed very closely how tags are currently being used and assigned, so I don't have the most current information on that.)
As an example, a run that ACE's a game and starts running custom code in the console would be a "demonstration" (and could perhaps be more specifically tagged as "ACE demonstration", or have both "ACE" and "demonstration" tags.) Especially if it doesn't complete the game.
If the "demonstration" tag is being used too arbitrarily and subjectively, slapped into non-any% non-100% runs at a whim, them perhaps it could be cleaned up and clarified a bit.
OOT can definitely support a category between pure Any% and MST. This just isn't the right category.
I think it would be a better idea to just outright go for MST, because that category is very popular in unassisted OoT speedrunning, rather than invent a new category (or use a much more obscure category) that's half-way between.
Abstain from voting (since I haven't watched it), but I don't think this is publication-worthy. Just writing the six medallions into inventory (mostly with RBA), and then jumping to credits just isn't intriguing enough to watch.
Indeed, in normal conversation in the English language, most of the time "either ... or" is exclusive, or heavily implied to be exclusive even if not (e.g. the Wikipedia page which I just linked uses the term "either/or situation" with a specifically exclusive meaning). However it is also possible that "either" has a meaning indicating indifference to both cases being true (a possibly inclusive meaning).
In the vast majority of spoken languages the word "or" is ambiguous because it can be inclusive or exclusive. In English, as you say, the word "either" doesn't necessarily disambiguate it.
"The price of the meal includes either one cup of coffee or one cup of tea."
Based on cultural context, this is certainly an exclusive or. It would be extraordinary if an establishment would offer both a cup of coffee and a cup of tea for the same price as either one.
"The requirement to apply for this job is either a degree in electrical engineering or at least two years of work experience in the field."
Again, based on cultural context, this is most certainly an inclusive or. It would be baffling and extraordinarily unusual if the requirement would exclude someone who has both.
You can look at it differently. Reaching the end via a major skip glitch is primarily demonstrating the glitch itself, and the fact that it can be used to speed you up. It doesn't matter if you call that any%, or you call any% the fastest run that avoids that technique.
Don't get me wrong. If ACE and other forms of memory corruption were banned in all categories (except those demonstration categories explicitly showcasing such techniques), I would be the first (and perhaps only) one to give a standing ovation.
It's just that I try to be pragmatic and acknowledge that many people consider any% to mean "anything goes, no matter what, as long as the ending is reached".
I think that any goal that forms the TAS branch should be accomplished for real, instead of tricking the game into thinking it was accomplished. And I think the exception should be demonstrating the glitchy technique itself, like "box glitch" in Crash Bandicoot.
I think the spirit of "complete thing X" in a game is indeed that the thing is actually done via normal gameplay. If in real life you had a goal to visit all cities in your country via train, nobody (including you yourself) would accept you having achieved that goal if you simply forged train tickets to make it look like you have visited all those cities.
I suppose in any% any glitches are allowed because there is only one goal: Reach the end of the game as fast as possible. Actually playing the game through the "normal" way isn't a stated goal in that category (something I readily admit regardless of my personal feelings about it).
However, pretty much any other category has more goals than that, and I think they should be actually achieved, rather than just forging the achievement by writing the proper values into the proper memory locations. Doing the latter just defeats the spirit of the stated goal.
Correct.
Curiously, different chess frontends have varying degrees of accuracy on this, and might report 3-fold repetition too soon (ie. their algorithm for detecting actual 3-fold repetition is lacking). Not all of them have been properly programmed to detect it correctly.
I also hear that something like this is also used to test how well chess engines are programmed to detect by-the-book 3-fold repetition. (Although, to be fair, perfect implementation seldom affects the playing strength of the engine, given that having the same piece arrangement repeat just 3 times without it being 3-fold repetition is extraordinarily rare, not to talk about the longer cases. Engines probably at the very least check if it's the same side to play, because that's probably the most probable situation where extra repetitions can happen.)
The reason for this is simple: fun. People may be interested in obscure goals for various reasons, but the reason that seems most clear to me is simply the lack of prior work put into that goal. You get to do more of your own routing and finding strategies than optimizing previous people's work. For some, that is more fun to do.
It just baffles me that OoT seems to be the only game in existence for which this is happening. Why OoT in particular?
Imagine if, for example, Super Mario 64 were like that. In other words, nobody would be interested in making an any% run, or even a 100% run, but only creating some TAS-only or obscure category runs. That would be rather strange.
Luckily SM64 isn't in that situation, and we have had amazing any% runs (that have even influenced unassisted speedrunning of the game to great extents).
Patashu wrote:
OoT any% is also distinguished by the fact that the RTA any% route is not possible to TAS, since it relies on a glitch that crashes the game on N64 and only works in VC.
I seem to remember some kind of discussion about this, and the consensus was that Wii VC versions of games would probably be accepted. I might remember wrong.
I suppose this is only tangentially related to math, but perhaps it does fit.
I recently started wondering about this, and did my calculations and came up with a number, and then asked in a chess forum for other people's opinions, and the final consensus agreed. (Thus, if you google for this you'll probably find the answer. You might want to think about it yourself, though, for the challenge.)
In tournament chess, a player can claim draw if the same board position repeats a third time. (Also, in computer chess tournaments a game is usually automatically adjudicated a draw if this happens.) This is the so-called "three-fold repetition" rule. However, there are more rules to "position repeats" than simply the same pieces being on the same squares:
For the position to be considered repeated:
1) it has to be the same player to play, and
2) all the possible moves have to be the same.
The second restriction considers "being able to castle to king side" and "not being able to castle to king side" to make a difference, even if all the pieces are on the same squares. The same for castling to queen side. Likewise being able to capture en-passant vs. not being able, also makes the position to be considered "different".
So my question is: What is the theoretically absolute maximum number of times that the same arrangement of pieces can repeat on the board without the 3-fold repetition rule kicking in?
The irony isn't lost on me that "Special Goals" (implying it had player-enforced criteria) was criticized by someone for being too vague but "Demonstration" (when quite literally every video ever made in history is a "Demonstration". Demonstration, quite literally, says nothing about the video.) wasn't and was actually called a "valid substitute for the vague Special Goals idea".
To me, "demonstration" means "doesn't complete the game (but does something else)".
The former is a more succinct tag name than the latter.
I enjoyed the movie so I voted yes. However, the category combined with the methods used is incredibly arbitrary. Firstly, why only the medallions?
Technically there is an unassisted OoT speedrunning category for medallions only, and to my understanding it poses no limits on what glitches can be used for that goal. So, I suppose, this technically speaking isn't a TAS-only category.
OTOH, at speedrun.com this category is only in the "OoT category extensions" section, and isn't very popular (only 24 entries total. Compare that to the almost 900 entries in OoT any%.)
I feel compelled to repeat my puzzlement about why people seem so eager to create TASes of obscure unpopular categories, rather than the absolute holy grail of OoT speedrunning, by far the most popular category, ie. any%.
As we know, the continued fraction 1+1/(1+1/(1+1/(1+... = phi, ie. the golden ratio. One of the simplest and most traditional ways to see this, ie. to solve the value of the continued fraction is to notice that the first denominator is exactly the same as the whole thing. Thus we can say that if x is the continued fraction, then:
x = 1+1/x
We can convert that to polynomial form (by multiplying both sides by x and bringing everything to the left side):
x2 - x - 1 = 0
When you apply your favorite method of solving the quadratic equation, we get the famous result
x = (1 ± sqrt(5))/2, which is the definition of phi.
One of the two possible solutions is negative, approximately -0.618.
But this raises the question of how the continued fraction can give a negative value. Where is the negative answer coming from? Is there a step in the solution that made a wrong assumption, or missed something, giving two values for the continued fraction, one of them negative?
Friends and family gathering together to have a good fun time, socializing, and deepening bonds and friendships. Why would that be a negative thing?
"That should be every day!" Except that it's not reasonable to expect so many people to gather every single day and do the same things, plus it would lose its charm very, very quickly. When it happens rarely, it becomes special, and optimally people look forward to it, and take the most out of it.
So, Nickolas's remark is correct. Assuming the criteria in the videos you presented, there is no "second most irrational number", because an infinite amount of irrationals are tied on first place.
"The second most irrational number" would refer to the "most irrational" number that's not equal to those.
I suppose one could come up with infinite patterns of 1's and 2's in the continued fraction representation, a simple example would be alternating between them. I suppose it could be argued to be "more irrational" than sqrt(2), because the continued fraction approaches that value slower than the one for sqrt(2).
Out of curiosity I tried to solve what 1+1/(2+1/(1+1/(2+... equals to, and I got (1±sqrt(3))/2.
While root 2 is also fairly irrational in that sense, it's not "the second most irrational number", nor is that concept well-defined. Consider that for any number but phi, you can obtain a more irrational number by, say, prepending a 1 to the list of denominators in its continued fraction representation.
This is, of course, going quite a lot on the more philosophical side of things, but if you do that, you are essentially adding a rational number to an irrational one. Whether the end result is "more irrational" is a matter of definition. (Can you make an irrational number "more irrational" by adding a rational number to it?)
Creating (and to a large extent watching) TASes, and speedruns in general, is a rather nerd hobby, and these kinds of nerd hobbies tend to be populated mostly by males. This is not a statement on whether that's a good, bad or neutral thing; just stating a fact.
(Playing video games is different, because it's not such a "nerd hobby", but a rather "normal" hobby, especially nowadays, which is why it appeals to all demographics much more evenly.)
The Numberphile YouTube channel is quite famous and popular. Perhaps slightly less known and popular is the Mathologer channel.
I find the latter to be many times of much higher quality than the former, in that the presentation is often clearer and more understandable on many of the more complicated subjects. For example, Mathologer's explanation of the Kakeya needle problem is orders of magnitude clearer and easier to understand than the more obscure, technical and even boring explanation given in the Numberphile channel.
Sometimes it happens in the other direction, though. While Mathologer's video on "the most irrational number" was very good, recently Numberphile posted a video on that very same subject, and I actually found it even more illustrative and enlightening.
On that note, both argue that phi, ie. the golden ratio, is "the most irrational number". The latter video tangentially, and perhaps serendipitously, also gives an argument for what could be considered "the second most irrational number", which would be sqrt(2). (It's all about their continued fractions, and how fast they approximate the actual value.)
Indeed, it appears that if you need a "very irrational number" (that has the properties that their continued fractions have), sqrt(2) seems like an easy and good choice.
One of the arguments against using the term "timeattack" was that it was already widely used in many racing (and other such) games as a gameplay mode where you run against the clock (usually contrasted to racing against opponents for the first place). While the meaning could be seen as related, it's a bit too narrow in that context and could cause confusion. "Speedrun", on the other hand, was an already well-established term. ("Tool-assisted speedrun" might not have been as popular and well-established because back then it was limited to a really marginal set of speedruns, probably only in the Doom speedrunning scene, but it was established nevertheless, to mean the same as "speedrun", but using tools like slowdown and arbitrarily many segments.)
On a tangent, I have for long suggested we move away from using the term "movie" to denote the timed keypress recording file, precisely because of its potential for confusion. (To the average person there's little practical difference between "movie" and "video", and it may cause the misconception that we edit video files and consider them "tases".)
Note that by submitting the file, and accepting the Creative Commons license when doing so, that means that if somebody were to grab the file before it's cancelled, that somebody can do whatever said license allows, and there's little the author can do about it (other than ask politely for that person to forget the file).
