How did video games solve that problem?
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How did video games solve that problem?
How did video games solve that problem?
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By step 2 he's already at arms' length to grab the turtle.
If dist > turtle_distance
Dist = turtle_distance
Race_end()
suck a dick homosexual
tortoise do jack shit, they don't move, they do the frick they want, butthole
Seethe
t. Hare
Literally watching a tortoise move outside right now
>race_end()
If only it were that simple
You just pick up the damn turtle
This is the most moronic paradox ever that I don't even know where to start
you are just too stupid and do not understand it
heres explanation for morons
achilles is so dumb just run ahead of the tortoise isntead of catching up with it
why is this guy so red around his lips?
He looks like he shaves the front of his face for a straight hour every day, with a straight razor.
There's a minimum unit of meaningful distance in games, including in floating point numbers. Its the same in real life, Planck length.
Why would Achilles be chasing a turtle when he should be worried about his fleeting mortality and impermanent glory?
Only good point made in this thread.
Thanks! I'm rereading the Illiad, and the whole thing is just depressing and tragic. The fact that the author(s?) used such amazing descriptions for the tragedy of war is so impressive to me. Some of the deaths in particular are so damn tragic, like when Zeus finally turned against Hector and made him so scared he was chased around Ilium 4 times before begging for his life and dying in such an awful manner. Or the death of that one dude who was fighting Menelaus, tripped over a stone, and then grabbed the Spartans' knees pleading for his life, only for that dick Agememnon to gut him.
>There's an hypothesis that Panck length is the shortest distance in real life, according to the current models we have.
ftfy
Isn't it not even that but simply the admission that our current models break down at that scale?
That's what it is. The notion of length and a smallest length are just abstract ideas that don't exist physically. Nature doesn't need a smallest anything. The strongest formulation of this you can make is that it's the smallest relevant distance but it's not a criterion of existence.
There's nothing that precludes the existence of a smaller scale with distinct features even if it those features are physically inaccessible and can't be measured or distinguished but project their properties in the form of ordinary matter we interact with, not different from me being able to see LED light from afar but not the distinct features of the LED itself because its size at that length cannot be resolved by lens in my eyes physically even with perfect sight. I am not super familiar with it but I'm pretty sure that's what they're going for with holographic principle by taking it to its logical extreme but more so because it's mathematically convenient lol
According to current models, taking away all of the energy from an object is the same as putting an infinite amount of space near it.
it converges, plain and simple
any demand for further explanation beyond that is pure sophistry
this explanation is as dumb as it is wrong, reality cannot be discrete
even ignoring the overwhelming consensus of modern physics that reality is continuous, a simple thought experiment employed by presocratic philosophers over 2000 years ago shows that discrete reality is self-contradictory
planck length is also not the smallest unit in the way you think it is
the extremity of planck length is that it's the smallest scientifically significant length because science is empirical and you can't measure anything below it, you can still indirectly show "structure" or rather some phenomena of "stuff" that is "smaller" but English doesn't do it justice because you're trying to describe continuous space in discrete terms
the reality may very well be that there isn't a smallest thing but an infinite regress of increasingly more difficult to isolate fluctuations
I'm the anon you replied to about the Planck length; you're right. Merry Christmas.
This doesn't make sense. If the runner can never reach the turtle, then that suggests that the turtle is already an infinite distance away from the get go. If the runner is able to reach the turtle's first position at any point, then that means surpassing the turtle is inevitable. No amount of quantum infinity bullshit can explain how it can be otherwise.
It's a paradox in the sense that they didn't know how to mathematically represent that fact
they did kind know how to represent that but didnt know that infinite series can have a finite limit.
So, can Ganker do it?
>It's a paradox in the sense that they didn't know how to mathematically represent that fact
why do they need to?
No paradox, the turtle just wins
>achilles can never catch up to the turtle because every time he catches up the turtle can just move again
damn is this really what passes for a paradox in caveman times? lmao
The turtle was just a visualization. The real "paradox" is just an early thought experiment for what eventually became the concept of limits.
It's more that while he is catching up with the tortoise, the tortoise has moved from that position. It's still moronic because the equation is using where the Tortoise was at t as opposed to where the Tortoise will be at t+1, the latter of which is the point at which Achilles catches up with it.
With that logic your car moving at 100 mph could never reach a car moving at 20 mph if the second car got a head start. Guess what, you do reach and pass by.
proof?
Go look at a motorway
By not having this problem in the first place, pseud.
while(true) {
float amount = getFrameTime();
achilles.advance(amount * achilles.speed);
turtle.advance(amount * turtle.speed);
system.out.println("The leader is "+achilles.distance > turtle.distance ? "Achilles" : "the Turtle");
// TODO: add a fair tiebreaker Socr -437/04/17
for (Actor a in actors) { if (actor.distance > TARGET_DISTANCE) declareWinner(actor); }
}
What is the problem
by the time Achilles moves distance to catch tortoise he will move away by small amount, then that process repeats and Achilles is unable to ever catch up.
You substitute infinite number of steps with actual infinity then pretend there is a contradiction.
If Achilles wants to catch the tortoise, he must chase it. The turtle is running away, so by the time Achilles reaches where the tortoise was it's taken a few steps. Achilles continues but find that when he's at the next spot the turtle has taken another step. This continues with the gap becoming vanishingly small but never quite reaching zero. So despite being obviously faster, Achilles will never reach the tortoise because he must first complete an infinite series of steps to close the gap to zero. Thus, no one can ever catch anything that is moving. It's not supposed to be a gotcha for physics or anything, Zeno intended for his paradoxes to be just thought experiments.
>im moving
>tortoise is moving
>i move faster
>i reach the tortoise
You can walk next to it, walk into it, pick it up as you walk. However you define "reaching" it, both of you are in continuous motion. Most of these ancient thought exercises are asinine with only a few key exceptions, about as relevant today as chess.
But like other anons said it's an early idea of limits which are a key mathematical concept.
Am I stupid or is this easily solved by making two slopes and finding the point of intersection?
if Achilles molecules change while he's passing the tortoise, did Achilles really beat the tortoise?
if so, how many molecules could change before it stopped being Achilles?
We have arbitrarily distinguished this body of mass as "Achilles." What distinguishes Achilles from any other body of mass? Why don't we call you or me Achilles as well?
a problem introduced by arbitrary linguistics is solved by arbitrary linguistics
come back when you've found a real paradox
I hate this shit, sometimes philosophers can really go up their own ass.
very smart anon
behold, the new Achilles
>featherless
>not a biped
Thats no man
furthermore, if achilles could push a lever to make a carriage swerve on the other path where there a fat man that will stop it, would the lever make a sound?
it really is eye opening on how stupid nuGanker is its struggling to even grasp what this 2500 year old problem is about
I prefer the one where he applies the same limit logic to ALL movement. If Achilles wants to reach his destination he has to get half-way there first, but he also has to get half-way to the half-way point and so on, resulting in another infinite series meaning motion doesn't exist.
Eventually his feet and the tortoise are bigger than the steps themselves, making the example not work. Sorry but if you want to use a visual aid of two things that everyone knows the size of, you can't just expect our brains to only discuss their speed.
achilles is fictional and the turtle is not, therefore he will NEVER catch up to it, myth busted
But the turtle is also fictional, because that is a tortoise.
here visualization for morons, achiles is 10 times faster but starts 100m behind, when he sprints 100m turtle will move 10m away, then when achiles tries to catch up those 10m tortoise will move 1m away, then 1m and 0,1 and so on ...
>walk 120m
>turtle is at 122m
WOAG
Ok but we know that isn't what happens in real life, if you move faster than the tortoise you will be able to catch it, because your position will exceed the position of the tortoise. There's no paradox here it's just moronic.
>Ok but we know that isn't what happens in real life
thats the paradox
>Ok but we know that isn't what happens in real life
yeah no shit you imbecile, way to miss the point. Fricking grug-level specimen, I swear to god
What's the point in talking about madeup baby scenarios when the real world is out there ready to give you the answer?
>madeup baby scenarios
entire scenerio is valid representation of reality you are too moronic to realize that infinite sum
100+10+1+0,1+...........
is actually a finite number
Because we know the answer, but can't (couldn't) describe exactly why we have that answer, and figuring out how to do so can be useful in other places for math/science/whatever.
>Because we know the answer, but can't (couldn't) describe exactly why we have that answer
> You can catch up to something if you move faster than it
So hard.
Why are you asking these questions grugg? You know this is way above your paygrade. Go back to gnawing on bones as you await your next meal, you're wandering dangerous close into intylekshual territory by pursuing your curiosity.
>the point.
The point of what? "What if turtles couldn't be caught because the universe ignores basic logic and mathematics" Ok? What then? What's the point of this hypothetical? What the frick do you derive from this besides "Yeah the universe doesn't work like that because of math and shit"? It's pointless.
This "paradox" pretend that time does not exist. Assuming constant speed: the stick figure would get to 100 in 1 unit of time. 110 to 1.1 unit, 111 to 1.11 unit and so on and so forth. The stick figure's gain compared to the turtle only diminishes as quickly as the time frame in which it is observed diminishes. In other words, observed in constant time, there is no paradox.
I understand that the tortoise is a weak metaphor (which is what most people have a problem with), but it's crazy some people don't understand the concept, somewhere out there
I believe Socrates brought this up in Plato's Republic, people get too caught up in the imagery of the metaphor that they fail to see beyond the metaphor itself
14! possible combinations
14*13*12*11*10*9*8*7*6*5*4*3*2*1 possible combinations
87178291200 combinations * 14 episodes = 1.2204961e12 episodes.
hmmmm
nyo
you are correct that there are 14! combinations but you have failed to consider that you can overlap combinations in the same series
see me after class
I never went past high school math but I'm sure you're wrong.
1,2,3,4,5,6,7,8,9,10,11,12,13,14
and
2,3,4,5,6,7,8,9,10,11,12,13,14,1
can be combined as 1,2,3,4,5,6,7,8,9,10,11,12,13,14,1
WHY DOES THIS FEEL LIKE AN ADVENT OF CODE PROBLEM
ERIC YOU FRICKING b***h IM ALREADY DONE WITH THESE 25 DAYS FRICK OFF
>I never went past high school math but I'm sure you're wrong.
And it shows because a combination has distinct members. You can't have two ones in a set.
If both the order and multiplicity matters you have what is called words over alphabet which is the literal definition of a language.
>If both the order and multiplicity matters you have what is called words over alphabet which is the literal definition of a language.
This is a nonsense statement, it has nothing to do with the problem at hand.
Wrong. Let's consider the trivial case of 2 episodes.
According to your formula, it's 2!*2=4. However, the correct answer is 3. Because you need to watch 1->2->1.
I've never seen Haruhi. Is the episode watch order really this complicated? I don't know what the series is about
so there is a canonical chronological order to the series, and season 2 is in order. BUT, when S1 originally aired it was intentionally out of order, IIRC episode 6 is the 1st one chronologically and the final episode is 2nd chronologically. And when they released it on disk it was in a DIFFERENT order than the TV one.
Sounds interesting. What order would you recommend for a first time viewing?
The original scrambled order it aired in, always. That is the intended experience.
All right. Thanks
The fact that Anonymous is credited in a paper in superpermutations specifically because if this question makes me occasionally ponder how much untapped autistic power is just left out to fester due to the idea of publishing academic papers being entirely foreign unless youre on the inside.
as long as we phrase all questions in relations to anime, I think we can solve every problem known to man
I go to where the tortoise is going, not where it has been
he will move by the time you get there, never going to catch him that way!
There are infinite "steps" between achilles and the turtle but as they close distance the time between each step becomes infinitely short
Totrle slower rate slower than man by 75% slower
Man 1 rate tortle 0.25 rate
Compare two values if same game end
gg ez
Why come he doesn't just run faster?
>why come
because it feels good
skill issue
I think to solve this you either have to invent limits/infinitesimals, which ARE kind of a massive stretch of imagination but basically work.
Or just say that you can't divide distance and time infinitely. Which is how actual physics work, I think. You can't subdivide it more than Planck time and length.
The whole problem is kinda Greeks grappling with "what the frick even is infinity and does it make any sense". Which is actually pretty admirable at a time when zero was still too radical a concept.
>how can you have nothing of something? lol those wacky philosophers, always making up useless shit, why would I ever need to buy a zero amount of apples, those nerds
do you think the greeks made memes about this kind of stuff?
You can probably actually look it up, but without doing it, I bet they did. I think Greeks were a pretty argumentative bunch, and this looks like a mighty fine shitpost.
Only philosophers probably, though. I imagine an average citizen of Athens probably cared about all those debates as much as an average American today cares about breakthroughs in topology.
Shitposting is a timeless tradition.
it is a fun paradox because the 'steps' of the flow are the issue. When we think about these discrete cases, a step is usually a fixed, constant amount of time, like a second. If something is moving at 5 m/s, and in the starting position we assume 0 distance covered, then after 1s (one step) it's 5m, then after two more steps its 15m and so on
the paradox here is because we actually frick with the length of the step every step (or we can call it a 'snapshot'). If achilles is running at 1 m/s, and one step is equal to 1s, then after 5s he moved 5 meters. But here, the duration of the step gets smaller and smaller, infinitely so, at such a rate that we never allow Achilles to overtake the tortoise by the very definition of the question given.
This scenario, on a computer, could result in two outcomes - depending on whether at some point we round down the duration of the step to 0. In this case, at one point the simulation just stops - no one can move ever again, Achilles never overtakes the turtle. In the second case, we might reach the lowest possible number given a finite resolution, at which point the step will have a fixed duration, and we overtake the thing.
subtract the turtle's speed from Achilles' speed and now you measure the difference between their positions, since that speed is positive it will eventually reach 0 and Achilles will arrive to catch the tortoise
When the projectile travels y pixels, the invader will have moved x pixels, so the invader can never be hit.
>just add or subtract speeds
there never was a proof it actually works like that, in fact we now know Galilean transformation used in Newtonian physics is just approximation.
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Wh-what? How is this possible? Those cars were ahead before the guy speeding! How can the guy behind catch up and pass the previous cars!? Velocity is not real! Distance is a concept in the mind that cannot be altered!
> You can't catch up to the tortoise, because you just can't OK?!!!!
Was easily solved by Plato. The runner can only never catch to the turtle potentially, but in actuality the distance is finite and he can.
The frick is this thread? It's simple algebra achilles goes a certain distance per time unit so does turtle ao you just add the head start the turtle has and solve for time to find when he they meet
Video games generally do physics and movement calculations using a reasonably consistent time step, so you would never run into this problem unless the time between frames gets worse every frame. However, couldn't you solve the original artificial difficulty problem using limits? I don't remember my math classes well enough, but I feel like you should be able to write out an equation where when the number of steps to solve the problem goes to infinity, the time per step and distance between the human and tortoise would go to zero.
>light can never reach me because I have already moved by the time light reaches my position
I am a god
anyways to answer your question most games use some sort of leading or compensation so the video gem character aims where you are going to be rather than where you are at the moment
Zeno was just the ancient equivalent of a shitposter.
Presocratics in general were schizophrenic as frick. There was a guy claiming that up and down are the same and he somehow made it sound reasonable
They were also massively underrated and before Plato turned philosophy into ramblings about made up things, they made a lot of claims that would later be verified like the existence of an evolutionary process, Sun and stars being balls of fire, the Earth orbiting the Sun (and in general criticism of anthropocentrism), moon reflecting sunlight, atomism, surprisingly accurate cosmology, the idea of a pervasive (but not luminiferous) aether or spacetime and a lot more all from almost pure reason. Who knows how many centuries Plato set us back by essentially inventing Christianity and making scholars focus on nothing but hypotheticals for over a thousand years.
So Plato is bad, noted.
game engines are fully accurate physics simulators, so they take into account that achilles, by virtue of moving faster, is also experiencing time more slowly and is thus able to do more relative to the turtle. when the gap in distance reaches the equilibrium point against the time dilation gap, where achilles is about to catch up, the turtle is effectively frozen, allowing achilles to both close in and match the turtle's position which appears to be the same instant from the turtle's perspective.
Thank god science has made philosotardation obsolete.
Hawking stated that armchair philosophy has been useless for quite a while. They can act smug all they want with "unsolvable" shit.
What problem? You can clearly see the lines get shorter at the end of the diagram. Eventually their lines of position will overlap.