While it's quite inefficient, one way that would guarantee getting every combination would be to create an algorithm that first creates all the length-n strings of stars and bars (2^n combinations), then counts the number of stars in each string and returns the strings with exactly m of them.
Some other examples (which you may wish to Google for more info):
The Mertens Conjecture is false, but the smallest counterexample is at least 1014 and may be as large as 101040.
A computer search of Happy numbers might lead one to think that there are never more than five of them in a row. The smallest such example of five consecutive happy numbers is {44888, 44889, 44890, 44891, 44892}. The smallest run of six consecutive happy numbers, meanwhile, starts at 7899999999999959999999996, and it has in fact been proven that for any number N, there are N consecutive happy numbers, though the smallest example grows very rapidly as a function of N.
In addition to these examples, there are many unsolved mathematical problems which, if they have a counterexample, it is very large indeed. For example, if there are any counterexamples to the Riemann Hypothesis, they are not among the first 1013 non-trivial zeroes. Any counterexample to the Goldbach Conjecture is at least 4 x 1018. If odd perfect numbers exist then the smallest one is at least 101500.
I suppose that my problem is that I still don't understand "potential energy". I still can't grasp the concept that it's not just an abstract mathematical tool invented to make calculations easier, but it's actually a real, physical thing, with actual mass (according to GR).
It's also hard to grasp the concept that the total mass of a system can be more (or sometimes even less) than the sum of the masses of its individual particles.
Whether energy exists or is merely a mathematical construct is really more of a philosophical question than a scientific one. In classical physics it generally acts as a book-keeping device to simplify calculations. However, at the beginning of the twentieth century special relativity was formulated, explaining how "abstract" energy could be converted into "real" matter and vice-versa. Then quantum mechanics explained how energy was discrete, and systems changed their "abstract" energy by emitting or absorbing "real" particles. So I doubt there are many physicists still around who view energy as merely a mathematical construct.
In any case, this philosophical question doesn't affect any of the mathematics, so in a sense it doesn't matter (though personally I find the philosophy of science, and particularly physics, very interesting).
As for the sum-of-masses thing, it's a special relativistic effect because it comes out of mass-energy equivalence (because forces and relative motions between particles add additional energy terms to the system, and this energy can be thought of as mass). You wouldn't get any such term in classical physics; and for most systems it tends to be pretty small anyway. For example the Earth has a mass of around 6*10^24 kg. Its effective mass would be changed very slightly because the gravitational binding energy holding its particles together has an effective negative contribution to the mass, but this correction is only about 2.5*10^15 kg, less than a billionth of the total mass.
So I had a really detailed answer written up... and then out of curiosity I read the article and realised they'd explained everything a thousand times better than I had.
My advice is to console yourself with the thought that this will never actually happen.
Actually, thinking about it, this is pretty much the reverse of the mass defect you were asking about a while ago in the thread. In an atomic nucleus, the particles attract each other*. so there is a negative binding energy, and this means that the total mass/energy is less than the sum of its parts. In this weird electron moon, the particles repel each other and so the total mass/energy is greater than the sum of its parts.
*(even though they have similar charges, there's another, attractive force called the strong interaction which dominates the system at nuclear length scales)
CoolKirby do you or have you ever watched Extra Credits? I'm sure they'd have plenty to say on the subject.
Anyway I responded via the Google Doc. Good luck with the project and I would love to look at the results :)
I'll give it a yes. If it had dragged on any longer, it might have been a different story, but it did enough to hold my attention for two minutes.
Dun, dun, duh duh duh dun, dun...
If the problem the site is suffering is overlong movie lists draining the servers, then maybe a more basic solution is needed. Instead of having movie lists which contain full publications, complete with resource-heavy YouTube encodes, just replace each publication with a simple hyperlink which, when clicked on, leads to the publication.
I'm no web designer so there's probably something obvious I'm missing with this idea, otherwise we'd have done it by now...
I think HPP is a little repetitive, to be honest. It's incredible and shows off the essence of TASing as well as any movie, but within a few minutes it's shown you pretty much everything it has. However, ISS and SSBM I wholeheartedly agree with, precisely because they show such fantastic variety throughout their runtimes.
Warp: No, no, no.
The point in the Vault/Moon distinction is to resolve the fundamental conflict between two very different aims of tasvideos: to entertain its viewers, and to be an archive of tool-assisted speedruns that catalogues the fastest possible completion times for every game. Hence the Moon tier is set up to house movies that get to exist on the site because they are entertaining (and who cares what crazy goal choice those movies might have, as long as they're entertaining?), and all other movies go to the Vault.
But the other crucial thing about the Vault is that Vault movies are hidden away, out of sight of newcomers. This is designed to prevent newcomers being warded off the site by early exposure to boring TASes. If we had all any%/100% movies in the same tier then Where In Time Is Carmen Sandiego (for example) would be mixed in with some very entertaining movies, and, in some sense, would be more "respectable" than BLJ-less Mario 64, for example. Does anyone really want that?
Archanfel: the thing is that, in 98% of cases, whether a movie is publishable is objective and fairly obvious, and in the other 2% of cases there's a strong argument that such a judgement is best left to the judge (hence the name). In any case, the judge would not be swayed by a poll answer but rather submission thread comments which have had time and thought put into them. Note that, while the site did use to have the "should this movie be published?" question, that was only in the pre-Vault era when a movie had to be entertaining to be published.
This movie is far better than I could have expected given that the previous version is languishing in the vault. I also really appreciate the comprehensive submission notes: it really helped me appreciate the little micro-optimisations a lot more.
Okay, I've re-watched Kriole's old TAS, and I really don't feel there's too much of a difference between them to warrant a new category. The "major glitch" branching is designed to allow TASes that show some sort of normal playing through the game in games where a glitch makes it possible to skip straight to the end, making any% runs very short. But this is a 100%, collect-all-the-tokens TAS, so being able to use a glitch to skip to the end isn't able remove all the gameplay - you still have to jump around the map collecting souls - and there is still plenty of zipping all over the place, crushing bosses and manipulation of highly unlikely drops that Kriole's movie had.
Will watch when there's a YouTube encode - don't have a niconico account and can't be bothered to make one just to watch this video. I will vote yes (obviously) but will wait until I've watched it.
I personally believe that this should not be a new category, but should obsolete Creole's movie. The closest precedent I can think of is http://tasvideos.org/2653M.html versus http://tasvideos.org/1840M.html - even though MrWint's movie warps all over the place, it isn't a new category.
moozooh's criteria are an excellent starting point. I may not agree with the fine detail on all of them but they encapsulate the purpose of the "notable improvement label" fairly accurately.
Archanfel wrote:
Notable changes is not the same as notable improvement. It would be wrong to use this tier for all MK tases and for all other playarounds..
I disagree, I think there are some playaround-style TASes which warrant the tag. Brain Age and Pokemon Yellow ACE are two such movies, though you could make an argument that they are demonstrations rather than playarounds. Gradius, which moozooh mentioned, definitely qualifies too. Not sure about Mortal Kombat because I can't remember too much about the TASes.
Perhaps some (non-strict, flexible) rules of thumb could be outlined, to aid in deciding whether a run deserves the "notable improvement" tag or not?
Something like the run meeting one or more of these:
- The run is at least 10% shorter than the previous version.
- It uses new notable glitches or techniques that are very visible.
- It uses a drastically different route.
- It may be of great interest to the community, or to the fans of the game.
I'm not a fan of the fourth criterion (every TAS of a game is of interest to that game's speedrunning community), and the the first criterion is pretty arbitrary (why 10%?), though I agree the time save should certainly be a factor. The other two are pretty much what I think of as a notable improvement.
In particular, I think "notable improvement" should be a tag that says to the audience: "don't worry if you watched the previous version, this is different enough to be worth watching". This will normally be because a significantly different route is used, often due to the discovery of new sequence breaks; it might occasionally be because a movement optimisation was discovered that, when applied throughout the run, saves a lot of time; sometimes it might be because entertainment during autoscrollers and other downtime is improved.
Another thought - when a game-breaking glitch is discovered that splits the game into two categories, should the first run in the "skip to the end" category be considered a notable improvement? It fits the criteria but is not technically an improvement, but rather a run in a new category.
So moozooh linked this thread after the topic was brought up in another forum (http://tasvideos.org/forum/viewtopic.php?t=6606&start=83) - it appears this debate was never resolved.
I can't even find the Movie Tags page on the wiki. Shouldn't it be made more visible?
Perhaps the simple act of changing the word "technical" to "effort" might in fact be enough. The latter gives a much better idea of what the rating is about than the former. And using one single word. I like it.
I personally prefer the word "difficulty", since I feel technical ratings should incorporate the level of TASing skill required to make the TAS as well as the sheer volume of gruntwork. Highly botted TASes, for example, should not get lower technical ratings because the bot cuts down the manpower; on the contrary, they should get higher ratings because skilful bot use is a cut above bog-standard TASing, and because the bot, with its millions of calculations per second, can help achieve a higher level of perfection/superhuman-ness than manual re-records could alone.
Actually, that's another reason I don't like the technical rating being purely a metric of effort. We already have one of those - it's called the re-record count.
Warp, your suggestion is probably more trouble than it's worth, given that even a highly experienced and skilled TASer like MUGG has a dubious interpretation of the what technical ratings mean. (I always understood the technical rating to be "how much effort and/or skill was used in this movie?" whereas MUGG interprets it as "how frame-perfect is the movie?")
We don't need funny algorithms, we just need to establish consensus on the meaning of the technical rating, or even whether it is necessary. If that requires a community-wide discussion, so be it.
EDIT: And I quote directly from the Rating Guidelines wiki page:
"A common misconception is to think that "technical quality" is a synonym for "frame perfection" (in other words, how optimal the run is). This is not so. Frame perfection is part of what constitutes the technical quality of a run, but only a part."
Well, I wasn't expecting this...
Unfortunately, it ends up being one of those classic "fascinating concept, not very entertaining, definitely not vaultable" cases, like bobtreb's original Pokemon Yellow total control run (the one with the MLP music). It's entertaining for a minute or so, but after that there is nothing more to show really.
It's a real shame that the snake can't be made to move faster. Is this a limit imposed by the calculator's processing power?
So as I understand it, the quoted time 58:53.93 is inaccurate, as the originally submitted movie file had a lot of blank input at the end.
However, I can't find the PCE frame rate conversion factor anywhere. Can someone else calculate the correct time for this TAS?
OmnipotentEntity is right, log(x) (or ln(x) or whatever, all logarithms are the same to within a multiplicative constant) grows slower than any x^k for k>0. Somewhat informally, when you multiply x by 10, you multiply x^k by 10^k; when you multiply x by 10 you add 1 to log(x). Even if k is tiny (so 10^k is only a little bit bigger than 1), when x^k is large enough then multiplying it by a number close to 1 has more of an effect than adding 1 - in other words at large enough x it grows faster. And out of two functions, the one that grows faster must eventually become bigger.
So for sufficiently large x, x^k > log x for all k>0.
Also calculus makes this pretty easy. You differentiate both sides: d/dx log(x) = 1/x = x^-1; d/dx x^k = k*x^(k-1), so for k>0 it is clear that the derivative of x^k grows faster (or rather, decays slower) than the derivative of ln(x). Then you just integrate both sides :)
Personman - realistically, are there any examples of where easy mode and hard mode runs of the same game would be different enough to warrant separate categories?
The thing is, the fact that the loops exist is entertaining; but actually watching those loops isn't. I did appreciate that you tried to vary the loops as much as possible in 8-4 though.
I'm with Mothrayas on this one. If there is little difference between easy and hard, use hard. If there is significant difference and you choose easy then the onus is on you to justify your choice.
However, I don't like that using easy mode can be used as an argument not to publish, given that, for the majority of TASes (especially platformers) there is minimal difference.