I think the point of disagreement between you and the article is that the article assumes a formula can't contain an infinite number of symbols; it has to be finite. I think this is a reasonable assumption.
Exactly. Any set of words of finite length over a finite alphabeth is countable. The reals are uncountable precisely because they contain every word of infinite length; cantor's diagonalization doesn't work otherwise. He constructs a symbol of infinite length not included in the enumeration, then he shows that said symbol belongs to the enumerated set. With finite words, you can do the first part, but the resulting symbol wouldn't belong to the initial set, so there's no contradiction.
Assuming finite proofs is not just a reasonable assumption, it's a requirement for any useful definition of "definable number". Otherwise, every real number could be defined by its infinite decimal expansion, which would make the definable numbers a rather boring set.
Here is a probability mess:
A parser for a fictional bytecode format has gotten desyncronized. Given a certain distribution (your answer should work no matter what it is) between instructions with various lengths, how many instructions on average need to be decoded before the parser resynchronizes by dumb luck?
I don't think it can be answered by that alone.
How is the length of an instruction encoded? If it's encoded in the first byte, we need to calculate the actual chances for that encoding to appear in the later bytes of the instructions.
If it's encoded as "first bit = 0: instruction ends here, first bit = 1: another byte follows.", it'll resynchronize at the next symbol.
Other encoding schemes yield different results.
How did it get desyncronized? Did you pick a random instruction, then a random byte except the first? Or did you just pick a random byte and start from there? The latter would make it more likely to start in a longer instruction.
Also, what happens if the parser gets an invalid (or unknown) instruction? Is there any immediate data inside the bytecode, and what's its distribution? I'd assume that unknown instructions are just skipped, and there's no immediate data.
4: Now add the horse to set C that was taken out of set A in step 1, and call it set D. Since it is of the same colour as the horses in set C, D is a set of N+1 horses all of the same colour.
I'm not sure that you mean what you've written there. No set was taken out of A in step 1, that's step 2. You haven't defined a set C anywhere, did you mean the one created in step 3?
I'd reject that "proof" based on the convoluted structure and the handwaving alone. If you have to reorder a proof until it makes sense, it's not a proof.
But your well disguised attempt at an induction falls flat, anyway. You've proven it for N = 1, you've proven the step from N to N + 1 for N >= 2, but you haven't proven it for N = 2. Your step isn't valid from 1 to 2, because you're talking about the color of an empty set of horses, which you haven't defined.
Never heard of this game. Reminds me a bit of smashtv, just with the spritelimit cranked up to 9000. I thought the first world was overkill, but obviously I hadn't watched anything yet.
guess that's a yes.
She sits at her computer, doing her own thing. Mostly research into things she's interested in (she's the smart one in our relationship), but often enough just watching stupid videos or playing casual flash games. She's free to join me in my games whenever she likes, but that's not all too often.
Energy in a physical sense is absolutely not the kind of energy we usually talk about. "There's energy coming out of that wall socket", "This light bulb uses 50 watts of energy".. nope.
Energy is a physical quantity defined in such a way that the sum of energy in a closed system cannot change. So you cannot "use" energy, and it's not quite like the thing your intuition tells you it is.
You can convert energy from one form into another. Ignite some black powder to convert it's chemical energy into kinetic energy in a bullet. The bullet disperses its kinetic energy into more kinetic energy (air turbulences) and heat as it flies along, slowing down.
Now shoot the bullet straight up in a vacuum. Its kinetic energy is reduced to zero by gravity. No new forms of energy (turbulences, heat) were created, but the total energy in the system cannot have changed. So where did it go?
The solution is to examine "potential energy". It is defined in such a way that regular energy can be converted into potential energy (raising the bullet into a higher position) and back (let it drop) without violating conservation of energy.
So no, it does not actually "exist". It is not a physical property of an object, there is no potential-energy-o-meter. Potential energy is a derived property of a system. Examine a closed system and you can calculate (but not "measure") the amount of potential energy in it.
Warp wrote:
Thus, and kind of back to the original point: If "potential energy" really is just a notion, not a physical entity, then how can it be "converted to heat", given that heat is a form of energy that physically exists?
Potential energy is created when you apply work against a constant force, like lifting a weight, or pulling apart two magnets.
Put some gas into a flexible container. Stretch the container, the gas expands and cools off. Let it go, the container shrinks back until pressures in- and outside the container have equalized, the gas gets hotter.
Derakon wrote:
So a 1kg ball 1m above the surface of the earth has 1kg * 1m * 9.8m/s^2 = 9.8J of potential energy. This is equal to the kinetic energy the ball will have right before it hits the ground.
It's not quite that simple.
Dig a hole in the floor below the ball. According to your formula, now the ball has more potential energy. Where'd that come from?
The ball has potential energy to get as far as the force he's resisting (gravity) can take him, straight to the center of the earth. Letting it drop to the floor only converts a part of its potential energy, but a lot of it remains.
If you're only interested in dropping it to the floor, your formula will yield a useful answer, but it's not the total potential energy the ball has.
Most games start by zero'ing all the RAM that they actually need, before they use it; some games omit that step. We had a lengthy debate about that just a month ago.
Thanks!
After finishing up on that thread, I maintain my no vote.
TASes in their purest form are about pressing buttons on a console to get results. My opinion has always been that we should stick to the purest form whenever possible. My opinion is also that any and all rules must be broken if it results in something awesome.
Abusing a 1 in 32 random chance to show off additional levels in cheetamen might qualify. We know it's possible on a real console (there are youtube videos), we could even console verify the TAS with a bit of patience if only someone had the cart. And using the hardware glitch can show off something that couldn't be shown otherwise.
Here, we have a 1 in 21000 chance[1], which is about 1 in 10301. Remembering that the amount of events our universe produced so far is lower than 10250 events [2] this isn't just claiming luck, it's breaking physics. It will never ever be console verifyable.
Is the result awesome enough to justify such breakage? Well, it looks like another movie that was rejected on entertainment grounds, just with shorter words. Audience reaction hasn't been too positive, either.
So I remain with my assessment that the solution is interesting, but the video terribly boring and the tas unsuitable for publication.[3]NitroGenesis wrote:
I voted no because Fractal keeps wasting his talent on shitty games.
I must wholeheartedly agree with this :)
[1] actually, the chance is way lower or even non-existant according to AnS's post.
[2] Multiply the age of the universe in planck time with the cubed length of the observable universe in planck length to get a very rough upper bound for a very rough definition of "event".
[3] and you know that my assessment is correct, because it has footnotes. ;)
It's a neat little optimization problem to read about, but a terribly boring video to watch.
The reset trick is clever, but if we assume a way to control the NES's ram on startup, then there's nothing superhuman about this TAS - blocking all but the desired words, then solving immediately could be done unassisted. Adding tool assistance gets you.. incredibly precise letter input.
So I'd have to vote no.
As an aside, aren't ram cells guaranteed to contain just zeros after power loss? Why exactly is the NES's ram "undefined"? Does reading of uninitialized ram on a real console really produce random bits?
Google didn't really answer these questions for me.
if, a zonktillion years after the heat death of our universe, another big bang occured, would the laws of physics be the same? Or might they be utterly different if the fundamental particles generated by that bang are different than ours?
http://forums.xkcd.com/viewtopic.php?f=18&t=107636
Tchebu suggested locality and lorentz invariance, with the unspoken premise that the universe is free of infinite or negative infinite energy. Just read the full thread.
Even just for console verification, it's possible to input about 3Kb of data per second (compared to Gameboy's 60 bytes per second). That's enough to get a lot done in just a few seconds.
The SNES has 128kB of Ram, 64kB of video ram and 64kB of audio ram.
Even if you need to fill all those to the brim, it takes no longer than 85 seconds (using tasbot) or 8.5 seconds (on an emulator).
Though if you're going through the trouble of programming something that large, you're sufficiently familiar with SNES programming to simply add a progress bar during loading.
The goal of the run was met when the payload took over; if anything needs to be timed for obsoletion purposes, that's the point. Everything else is just showing off the outro, so to speak.
When the whole difference between two runs is a choice to end input slightly earlier, or to keep input running to show off something weird in the credits, or even just to press a button to speed up the credits, then I cannot remember those differences ever having mattered wrt obsoletion.
Everything past the glitch is just artistic freedom for entertainment. While we all agree that it could have been better if there hadn't been such a tight deadline, audience reaction has been very positive anyway, and the point of arbitrary code execution has been brought across.
Obsoletion on non-speed sections has always been difficult. There's no frame counter on entertainment, and comparing audience reaction is a dark art at best. That hasn't stopped us from publishing playaround videos, and I don't think it should stop us this time. The payload playaround is not meant to be a speedrun.
I don't think we had this case yet, but a "1-frame improvement" on entertainment videos doesn't make sense. If anyone wants to improve this run on entertainment grounds, they'd better bring a substantial improvement, like an entirely new payload, and not a five-minute job of shaving a few frames off here and there.
(I'd personally like to see a run where the glitch just warps you to the end boss - of an entirely different game. Which you then proceed to kill.)
Personman wrote:
It is of immense historical and cultural importance for our community that this run be easily available in a user-friendly way on tasvideos.org.
It is also of immense historical and cultural importance for our community to discuss about rules and their special cases. :p
I am hoping that this will eventually be obsoleted by a run with better payload.
Until then, I think this deserves publication. Not only is it awesome enough, but its display in agdq2014 makes it an important milestone for both our communities, and it'd be sad to see it buried in the rejected submissions archive.
I also suggest linking the agdq presentation along with the publication.
However, it still kind of puzzles me if and why the host's overall strategy would affect what you should choose in one single round. After all, if you are playing one single round, and the host opens a goat door, the situation is identical regardless of whether the host always opens a goat door or a door at random...
The doors are identical, the host's strategy isn't. If you need to watch a few games to determine the host's strategy, then on the first game, you can only guess.
But if you know the host's strategy, then it doesn't matter if you play a single game or a hundred games. They're statistically independent, the expected value is the same each time.
If you think that MH boils down to "two doors on switch, one door on stay, so it's 2/3 vs 1/3", then you haven't grasped the problem yet. It's not about counting doors, but about knowing which doors to count. You need to draw the full decision tree for that, examine all paths that look like your current situation and compare the chances for "car in door 1" vs "car in door 2". Intuition really doesn't help here.
What might help your intuition is the following: without any additional knowledge, your chances are no better than 50/50. To gain any better strategy, you need more knowledge. Where does it come from?
Sure, in both cases, you gain the knowledge that one door is empty, reducing your choice to two doors. But that information merely increases your chances from 1/3 to 1/2, no more. You need knowledge about the car to get better than that.
In the original problem, that knowledge is coming from the host. The host knows where the car is hidden. He uses that knowledge to determine which door to open (never open the car door). Knowing his strategy and watching his action, you can gain some of his knowledge, and that's what improves your chances. The important information is to watch which door he chose to open, since that choice is influenced by his knowledge. "He might have picked that door randomly since the car is in door 1, but he probably opened door 3 because he isn't allowed to open door 2."
Now imagine the host not knowing where the car is hidden. He has no knowledge. You cannot gain any knowledge from him. No matter what he does, he cannot improve your chances above 1/3 for the whole game. Revealing that door improved your chance to 1/2, but by opening a door he could also have revealed the car, lowering your chance to 0 - on average, his actions neither helped nor hurt you.
You may as well just pick a door and stick with it, nothing the host does will matter, you will not gain any knowledge about the position of the car until the door with the car is opened. Needless to say, that's too late to formulate any strategy.
I don't think this actually beats the game. When link tried to jump-slash Gohma, he hit his head pretty badly against the wall. He went unconscious and started dreaming of an imagined evil called "Ganon" atop an evil tower.
You know it's just a dream because important parts of the plot are missing. A mere kid couldn't imagine how to kill Ganondorf, so he skipped that part of the dream and began right at the fun part, where he emerged a hero. Reality seems distorted, physics have no meaning, as is often the case in dreams. The tower he's walking through turns invisible every now and then, it hasn't manifested itself completely in his mind, since this dream is about something else: Saving the damsel in distress and getting a peek at her boobs. It is a boy's dream, after all.
So sorry, you didn't beat the game. Link is still lying inside the deku tree, unconscious, bleeding uncontrollably from his head, with a giant spider gnawing on his legs.
I'm sure no RTA runner would kill non-stop enemies or doing the gambling game
Oh, there have been RTA routes that went for the first dungeon to get 10 rupees, then went gambling twice. IIRC there was a run published on SDA with such a route.
It's not pleasant, but it's manageable if the gambling is early enough in the run.
To get back to Warp's original question: if Pi is indeed a Normal Number (which is yet unproven), then yes, it will contain every finite sequence you can think of.
Granted, for any sequence of a million digits, the chance for them to be all zeros is 1 / ( 10 ^ 1.000.000 ), a very very small number.
For example, if you were to pick a random spot (of planck length) in the observable universe, at a random moment (of planck time) since the big bang, then your chance of picking exactly the time and place of the first neuron firing inside baby Einstein's brain[1] is merely around 1 / ( 10 ^ 250).
So if you pick a truly random sequence of a million digits, it's very likely that there has never been, and will never be, a physical representation of said sequence in our universe.[2]
But Pi is different. Its decimal expansion is infinite. So we need to take a look at an estimated 10 ^ 1.000.000 subsequences of Pi until we find one that matches? How many subsequences are there in Pi? Infinitely many, which is not only enough to find one match with probability 1, but an infinite amount of matches.
[1] or baby hitler's brain, if you prefer. Or any other point in our spacetime.
[2] well, unless you pick a sequence by writing it down or storing it in your computer's memory. Sampling bias, hu?
The formula is correct, but only if you actually insert the toasted bread randomly into the stack. Who does that?
Your actual chances would be better. You're taking K pieces of bread, put them into the toaster, take them out and put them on the plate. Repeat with K pieces of bread (however many your toaster holds), stacking them onto the plate until you're done.
(This only applies when N > K, otherwise Bobo's formula holds.)
This means that the first K pieces are always at the bottom, the next K pieces above etc.
For each part of K pieces, there are K! * 2^k permutations, only one of which is correct. (only the reverse order is possible; the first slice you take will not end up on top of the stack).
So for N = n*K slices, your chances are 1 in (K! * 2^k) ^ n
Then again, you wouldn't randomly flip toast while putting it into the toaster or putting it onto the plate. You'd usually use the same hand movement each time, go about it in an orderly fashion... Depending on the way you do it, I'd say you either have sorted toast every time, or never.
I would have thought if there's wind involved. You'll want to run at the same speed and direction as it is blowing.
For the simplified block, that's true. Either tilting or moving means that no rain will hit the sides, but moving reduces the relative speed of the rain against the top surface, so you'll get a bit less rain.
For a human, anything but standing upright with legs closed and both arms straight next to your torso increases your surface area, so any form of walking or running is a bad idea unless you need to get somewhere.
But while we're at impractical theoretical movements: try free falling.
Granted, tilting parallel to the rainfall without falling over might require the ability to adjust your body's density at will so that the wind can support your stance. But if you can't do that, you deserve to be wet, right?
Imagine running infinitely quickly. You'll cut a path through the raindrops in the shape of your silhouette, but no drops will fall on you. Slowing down allows drops to fall on your head in addition to hitting you horizontally, therefore it will make you wetter.
Because I just noticed, I have to disagree with this.
a) Running at an infinite (or very high) speed, you'll sweep up an infinite (or very high) volume of rain-filled air with your front. Running slower, you'll sweep up less, which is good.
b) Even when running at high speeds, you still get the same amount of rain on your head as when standing still. Rain doesn't stop falling just because you're running! You would need relativistic effects or supersonic shockwaves for that to change.
Neither makes running a good idea.
To determine how much rain you get over time, all you care about are your exposed surfaces, their area and speed relative to the raindrops.
Let's assume you're a block of 2x1x0.5 meters, and you can run at 5 meters per second. Raindrops fall at about 10m/s. The rain is falling straight down and is uniformly distributed.
Standing still for a second, you'll be hit by all the raindrops that were up to 10 meters above you when we started measuring, and your exposed surface area is 0.5m², so you get 5 m³ worth of rain on your head.
In other words: the top surface of the block moves with 10m/s relative to the rain, so 10m/s * 0.5m² = 5m³ per second of rain.
Running at full speed for a second, you'll sweep up all the rain in front of you, which is 5m/s * 2m² = 10m³ per second. Clearly wetter. Additionally, you still get the full 5 m³ of rain on your head - the surface area is still 0.5m² and the relative speed to the rain is still 10m/s!
So over time, running will always make you wetter than standing still. You minimize your exposed surface area by standing upright parallel to the rainfall. If there's wind, tilt slightly against it.
Running will not only increase your surface area due to flailing limbs around, but will also pick up more rain due to the increased speed.
But it's rare to encounter a scenario where this is relevant. You're stranded in an infinite, empty parking lot and need to stay as dry as possible until the rain stops? Yeah, right. Doesn't matter, you'll be soaked.
The usual scenario is that you need to cross the street until the next cover, or you need to run from the car to your home's door. Is the additional wetness from running worth the savings from a shorter exposure? And then there's wind, often changing. And puddles. And everything. And the volume of water accumulated doesn't directly translate into being wet, much less into feeling wet and cold and miserable or into ruining your expensive leather purse. And that's where things get complicated.
Mitjitsu wrote:
because they should be weighing themselves, and not their overalls.
Unless they swallow the rain, that shouldn't matter much. The experiment is set up in such a way that most of the rain will be caught in the overalls. They were dry underneath.
But yes, like most experiments on an entertainment show, there are flaws to be found, and not all of their assumptions and ideas were explained well.
Dryer over a certain period of time, or dryer over a certain distance? Are you interested in a theoretical account (like Derakon answered) or also in practical effects, like splashing puddles or additional rain swept through flailing your arms?
There's a mythbusters episode about it, where they did some actual tests.
Presumably because the database has to allocate a fixed amount of memory per password to be able to be remotely efficient
No. VARCHAR(32) and CHAR(32) offer similar performance on mysql (even in 2001) unless the column is frequently updated. Password's aren't frequently updated.
Also, I really really hope that the site doesn't store passwords in plaintext, but stores a salted fixed-length hash instead.
An upper limit makes sense for usability purposes and to prevent DDoS-attacks, but that limit would be higher than 32.
It also applies to situations where the administrator of the website didn't personally sign off on some file upload to the site, so if the upload happened through an automatic process without site staff verifying the content prior to its online publication.
Yeah, that argument worked very well for rapidshare and other file hosters, didn't it?
Hosting a forum for squirrel lovers and some user posted a copyrighted image of a squirrel? Not a problem for the hoster.
Hosing a site designed to distribute copyrighted works and most users are posting copyrighted files? Well..
The thing is: if the copyright holders don't agree with your stance on that, they'll take you to court. And that court may decide either way. It may also require you to implement far-reaching mechanisms to prevent further uploads of unlicensed files. Can you do that?
In fact, can you do that before you start the service?
For example, wikipedia requires every upload to be tagged with a proper license. Unlicensed uploads require a small justification on why the use is considered fair use or otherwise legal. That puts them in a pretty strong position to show that they (as a provider) do everything they can to care about copyrights, thus it's likely they wouldn't be accountable for the occasional user error.
If such a tagging system would result in most of your files being tagged with "unknown, probably illegal", that's a problem. If you'll tag them with "nobody seems to care", that's still a problem. If you can tag them with "distibution allowed by netherlands law §42", go ahead.
Dada wrote:
one of the things I've been thinking about is limiting the site to soundtracks that were not separately released (and thus are very unlikely to have people looking for them).
Do the netherlands have a "fair use" clause, or any clauses about abandoned works, or anything else that might justify releasing them legally?
Under US fair use law, the fact that they're not separately released is good for you, since the copyright holder will have trouble citing damages. But that's just one of the four factors to be considered, and I doubt you'll pass the others.
Dada wrote:
Obviously there can't be any certainty—but the same applies to this website's videos (to a lesser degree, but still).
Indeed it does, but tasvideos is showing derivative works of the video games instead of just copying a part of them. And that's the central point of this site's position:
http://tasvideos.org/Nach/FairUse.html
Also, US law seems to apply for tasvideos (which is registered to adelikat under an US adress). I wouldn't dare running such a site in germany, where even posting a screenshot on a website is - strictly speaking - copyright infringement as long as the screenshot contains copyrighted elements. Like a video game character or an elaborate background texture or...
