Agreed with the above - but I don't want to see a profusion of pairs of movies which are basically the same on this site. This leads to a dilemma:
Let's say that an SM64 (WiiVC) 1-key TAS turns out to be a few frames faster than SM64 (N64), but otherwise basically the same. Now either:
a) They're treated as separate categories, and we have effectively the same run twice on the site (same reason as we don't generally have separate runs of American & Japanese versions of a game, and many examples of one localisation obsoleting the other).
b) WiiVC obsoletes N64. Now a user searching the site's movies by console is going to think "where the hell's SM64 1-key?"
I don't know why anyone should oppose this, so long as Dolphin emulates the VC game in question sufficiently accurately. In principle I'm even open to the games having publications separately, if there are glitches exclusive to one version that make the runs appreciably different.
One fact about Fibonacci numbers is they have the Mersenne-like property that Fmn is a multiple of Fm and Fn. Hence all Fibonacci numbers with composite indices are composite, except F4, which is an exception because F2 is 1.
Another way in which the Fibonacci numbers resemble the Mersenne numbers is their exponential growth rate. It seems the problems are similar to each other, and probably equally difficult.
Here's a more interesting twin prime problem: prove that the only Fibonacci numbers that are also twin primes are 3, 5 and 13.
(I can remember the result, and I have been shown a proof, but I can't remember the details and Google isn't helping. But I think it relies pretty heavily on recurrence formulas for the Fibonacci numbers, and for Fn+-2, that enable you to factorise them.)
To clarify:
Masterjun's SMW movie was the first to use arbitrary code execution to complete a game, although before that there were a great many TASes that completed games very quickly through wrong-warping to the end and similar techniques, (eg the original Pokemon Yellow save corruption movie).
Bobtreb's Pokemon Yellow movie was the first to go one stage further, to use arbitrary code execution to do something the game couldn't otherwise do by itself. Masterjun's movie had mastered the technical detail of how to hijack a video game; Bobrteb's was the first to establish the broader implications that ACE could be used to do literally anything the hardware could handle.
Not sure this is quite on newcomer level - newcomer TASes aren't necessarily the best TASes, newcomers are "what would get you hooked into watching more?" TASes.
Do love the TAS though. Was going to say "N64 TAS of the year so far" but amazingly we haven't had any published N64 TASes to this point, so it would have been something of a backhanded compliment.
All this e-chat reminded me of a relatively obscure property of e which turns up in the following problem:
A cheeky monkey is stealing bananas from a market stall. At the market, bananas come in boxes of a specific size. The monkey is very clever, and knows the vendor leaves his market stall unattended for a few minutes at the same time every day to pray, leaving a partially full box of bananas. At this time the monkey dashes to the box and takes it back to his lair, where he has his own box of the same size that he has also stolen from the vendor. He does this every day until his box is full of bananas. Show that, on average, it takes e days to fill the box.
There's a general formula here:
d/dx expn(x) = exp(expn-1(x)+expn-2x+...+exp2(x)+exp(x)+x)
Plugging this expression in for x=0, the functions exp(x), exp2(x), exp3(x), exp4(x) have gradients 1, e, ee+1, eee+e+1. This doesn't seem to make a particularly neat pattern on a graph, really.
Depends what you consider the definition of e. Most people are introduced to it through the following identity:
lim(n -> inf) (1+1/n)n = e
However, from an analytical standpoint, the really fundamental property is:
d/dx(ex) = ex
The second definition uses calculus, and is therefore more advanced in terms of the level of mathematical education required to understand it. However, it's also the reason it turns up everywhere in maths, including specifically here. Seen this way, the "compound interest" definition is really just a consequence of the more fundamental idea that ex is its own derivative - if you have money earning interest at 100% per year, then at any time the annual return on your money is going to be equal to the money you currently have, and so it's natural to look for a function which is its own derivative.
2) Let's stick specifically to positive real numbers here - raising a negative number to a fractional power leads us into the murkier waters since these functions are multi-valued, and can only be defined via somewhat artificial branch cuts.
xy > eylnx implies:
eylnx > exlny
ylnx > xlny
lnx/x > lny/y
So the easiest way to visualise this is to draw a graph of f(x) = lnx/x, and then substitute in x and y. If f(x) > f(y), then xy > yx. Interestingly, this gives the relation a transitive property: If xy > yx, and yz > zy, then you can guarantee that xz > zx.
1) Well that's a classic conundrum. I don't know how much mathematical training you've had (you need to know some calculus, specifically the chain rule and product rule), but if you rewrite the equation as y = e^lnx/x then it's a relatively trivial problem:
y = elnx/x
dy/dx = d/dx(lnx/x)*elnx/x (chain rule)
d/dx(lnx/x) = 1/x^2 - lnx/x^2 (product rule)
dy/dx = (1-lnx)elnx/x/x^2
Set dy/dx = 0: 1-lnx = 0, x = e
Therefore y = e1/e
I know this is a short game, but 1 rerecord? Really?
EDIT: Okay, I thought this would be a mistake, have read your notes now. So why does it say "1" in the rerecord count on the submission page?
I'm wondering whether perhaps [3371] PSX Rayman by scrimpeh & got4n in 1:02:37.67 might be worthy of a star.
- It has an 8.9 rating, and is riddled with superhuman physics exploits and glitches that you wouldn't see in an RTA. While at just over an hour it is a little long, there is very little down-time within that hour, and something interesting is usually happening.
- I was not the only person on the submission thread to call for a star.
- Finally, the game is really bloody hard. I got to half-way through world 2 before running out of alarm clocks as a kid. Seeing it torn apart like this is immensely satisfying, albeit perhaps a bit less to someone who hasn't played it themselves.
It feels a bit similar to the situation with the "vault" tier. I have been pushing for years the notion of elevating this tier to the top, rather than it being considered just a garbage dump for all the "mundane" and "boring" TASes. I have been pushing for the idea that getting your run published in vault would be a privilege, the highest possible prestige, very similar to getting to the top of a category list of a given game at speedrun.com. In other words, if you get your run published in vault, you hold the world record; you are the best of all.
But no, vault is still considered just a garbage dump where runs that don't get to moons get dumped. Rather than being a badge of honor, it's almost a badge of shame. And I seem to be in a very small minority who seem willing to have this notion reversed.
This boils down to a difference in philosophy between the real-time and tool-assisted approach to speedrunning.
The real-time community is primarily about pushing humans to their limits. It's fundamentally competitive (though of course, speedrunners still share their discoveries), and the aim is to play the game better than anyone else can.
Conversely, the tool-assisted community focuses on pushing the games themselves to their limits. It's more collaborative (though skilled or prolific TASers still have prestige) and the aim is to play the game perfectly.
This last point is key. TASes, while rarely if ever perfect, should not be obviously flawed, in the way that any non-trivial real-time run is bound to be. A TAS is pretty obviously flawed if someone else submits another TAS of the same game/branch with a lower completion time. At that point the old TAS is clearly not perfect. It absolutely should be considered obsolete.
"This game has a battle tutorial, a jumping tutorial, another battle tutorial, another jumping tutorial, a time travel tutorial, and 2 more jumping tutorials."
Still not as ridiculous as Superstar Saga where Luigi has a tutorial on walking backwards.
This is pretty funny, but this April Fools submission would have reached legendary status if you had included a photo of a homemade version of the final burger.
Why not just go the whole hog (pun intended) and have an "in real life" TAS? I'm sure someone somewhere's working on a reality emulator.
Further to recent discussion here http://tasvideos.org/forum/viewtopic.php?t=18845 (particularly Warp's comments over the last few days) it appears that, for all there has never been consensus on this site for a Demo Tier, that ACE in particular has over the last few years crept into demo territory. Lots of people like watching these kind of movies but there has generally been a feeling that "pure" demos don't belong on a website that is about optimising video game play. The issue with ACE is that boundaries are blurred as what starts off as playing a specific video game becomes anything that you can do with inputs and a processor.
Incidentally, I suspect there is a reason why we have never had a Demo Tier, and that the reasoning is circular. We don't accept demos because we don't have a Demo Tier; and we don't have a Demo Tier because we have no demos to put in it.
So, at the risk of raking over old sores, I see there being three different ways to go forward:
1) Have a specific tier for Demos. The sort of things that would be appropriate for this tier would be movies with tags like "Demonstration" and "Playaround".
2) A more radical version of the above, which accepts content which the current rules do not allow. This would significantly expand the remit of what tasvideos is all about.
3) Keep the status quo.
Thoughts?
I am pretty convinced the probability would tend to 50/50 as the pile of cards gets large.
If you have a completely random pack of N cards of two equally likely colours (ie a pack of N Bernoulli trials with p=1/2) then the standard deviation in the number of red cards in the pack is of the order sqrt(N). Of course this is not the case, but the point is that when N is enormous, for most of the time the number of cards in the two piles are going to be within sqrt(N) of each other, and hence the fact that one pile is bigger than the other gives you a negligibly better than 50% chance of guessing correctly.
One way you could attack this analytically is a Pascal's Triangle-like formula that works out the N reds, M blacks scenario from the N-1 reds, M blacks scenario and the N reds, M-1 blacks scenario. That probability will be given by:
p(N, M) = (N/(N+M))*p(N-1, M) + (M/(N+M))*p(N, M-1)
You could then build up a triangle of results quickly, but it would still take hundreds of calculations to get to p(26, 26).
EDIT: okay that formula doesn't work because it just produces a triangle full of ones. I don't know whether the formula just needs to be tweaked or whether the idea is totally wrong.
That doesn't work perfectly either. You could then find yourself in a scenario where players are using a route that is suboptimal in both real time and without-loads time, because the alternative is a faster route which has more loading screens, which are now being unduly penalised.
Warp: The problem with PC games is you more-or-less have to go by time without loads, otherwise you don't have a level playing field and players could bring down their times by shelling out thousands of dollars on a top-end PC. Then stuff like this is an unfortunate side-effect.