If you want to reach out or touch something, there are always a infinite number of "halfs" you have to go though, but you get there eventually, so infinity tasks does not take infinite time to be completed?does nowdays science has a say in this? have our compreension of infinite changed? how far goes our knowledge on time and infinite?>not sure if this is the right place to post about paradox, if this is not the place it was not intentional, i am very new to 4chan postings
It's a supertask. The time it takes to complete each half step also decreases when in constant motion.
>>16260335And you haven't even learned about the continuum hypothesis.
>>16260335Here's my AI's response
>>16260372Trying to apply algebra/calculus to this is beyond stupid. That's the whole point of the paradox that finite distance is travelled in a finite time. Calculating the infinite sum does nothing but restate the paradox (which is stupid in and of itself)
>>16260348>there will always be a half of something>will time ever reach 0 since there will always be a lower time?lets say 1 second, there will always be 0.5 seconds, then half of half a second, etc.
>>16260414Say you travel 1 m/s to a point 10 m away.The 5m takes 5s to traverse.The next 2.5m takes 2.5s to traverse....The next 0.00001m take 0.00001s to traverse...You travel all infinity segments in finite time because the time taken for each segment also becomes infinitely small.
>>16260335Usually I think of the paradox as a variant of this problem but correct me if I'm wrong:>Object A has x length>Object B has y length>x is greater than y>Since x and y are both infintinly divisble, their respective values are indeterminate and differences can be considered neglible>Thus Objects A and B may have same lengthThe solution to the paradox isn't that there's anything flawed in the logic but that numbers must not be thought of as essentialist universals. Numbers, and thus mathematics, are self-referential and can explain the values of one object in terms of another but never in an absolute sense independent of the object, which explains why there is no objective and universal unit of measurement. I believe the eleatics used this premise to argue that time and space are illusory and have no definitive objective basis, a form of mathematical fictionism or nominalism. It's really more a philosophical argument rather than a scientific or empirical since its making an epistomelogical argument. Outside of perhaps economics, the problem is not really applicable to the hard sciences. But if anything, l'Hopital's rule might also support the paradox.
>>16260446I don't really go into the infinitesimal thought experiments. Haven't touched them since 2012. If reality is something like infinitesimal reals, the bottom of the turtle stack is a paused state. And derivatives become a ghost driving these paused entities at different velocities. Assuming a materialist position, this differentiation would lead to a strange phenomenon of contextualization of indistinguishable parts. To demonstrate the point, consider a spring compressed and released at different times under different compression forces. And pretend we perfectly capture it in the infinite sequence form and that we could review such a thing in its entirety - starting to remind myself why I don't go down this rabbit hole anymore.Under conventional infinitesimals, there would be no way to distinguish which images have the spring compressed under a higher force and moving faster, up until it surpasses the smaller at either end of equilibrium. At every level, the two are equivalent and then suddenly one keeps going. Materially, we would have to posit something like a tachyon which bind states together.
>does nowdays science has a say in this?Science says you can't actually touch stuff cause electricity and shit.
>>16260335zenos paradox is easily solved by making time and space discrete.
>>16260335>infinity tasks does not take infinite time to be completed?No, an infinite task, by definition, would take an infinite amount of time. But the task is not infinite, that's what it means, because the distance is covered by a velocity that covers the distance, eventually. The paradox would only occur if the velocity would keep on decreasing as you progress, but it does not: the first half gets covered at some speed "V", then the half of the next remaining half the distance (1/4) also gets covered at speed V, and so does the next (1/8), etc, and so the entire distance does get covered. Done, that's it.Who gives a shit about a what theoretical idea says if it doesn't match reality? It's wrong, period.
>>16260685hand waving =/= solving
>>16260335Anything can be turned into infinite, infinitely small subdivisions. It doesn't have to involve time either, you can apply this to anything.
>>16260335>filtered by 1/(1-x)lol
>>16260335there are different kind of infinities if that's what you're asking. for example if you wanted to count from one to ten from the set of natural numbers, then it would take you secondsBUT if you wanted to count from one to ten from the set of real numbers, then it would take you an eternity. to be fair it is actually impossible to do so.so some infinities are bigger than other infinities
>>16260335give it more thought and you would get the same result as Cantor :)
>>16261198You can't count real numbers what are you talking about?
>>16260335The entirety of the paradox lies in the problems with defining the problem in linguistic language surely.Achilles does not travel in an infinite number of "halves", he travels in a number of absolute distances assuming constant motion. He does not choose to travel a relative "half" distance, he chooses to travel an absolute "x" distance. He overtakes.
>>16260335What a fucking retard>infinity tasks take finite timeno you dumbfuck you can also divide each time interval on half so it is infinity tasks over infinity time segmentsbut since each of the infinity tasks and time segments are infinitesimal the end result is a finite distance traveled in a finite time period which is a single task
>>16261206>to be fair it is actually impossible to do so
>>16261209>then it would take you an eternity.
>>16260335infinitely divisible =/= infinite in lengthMathematical abstracts are not the same as empirical physical properties
>>16261218say op was given a task to count from 1 to 10 from the set of natural numbers, op would be delighted to do sonow if op was given a task to count from 1 to 10 from the set of real numbers, and say op starts counting from 0.1, I'll say there's real numbers much more less than that. op would probably say 0.01 and so on. how much time would op be taking for the second task?
>>16260335The paradox was meant to lead you to think that the physical world was an illusione, and that everything is ultimately one singular object to be contemplated.In other words, it's stuff for /his/, not /sci/ and trying to solve it mathematically is futile once you recognize that zero exists, since saying "zero is nothing" breaks the premise, which hinges on "nothing" being not real
>>16261202evil
>>16261207The reality of a thing is not necessarily anything like the proposed problem. Again, at the infinitesimal level, the world would be a paused state independent of whatever velocity a thing is moving. There would be no way to distinguish state evolution.The illusion of time is baggage brought in under your premise of constant motion. Suppose the motion is watched by a camera with a frame rate approaching infinity, and there is also a stop watch in view. There is no way to count the number of frames between 0 second and 1 second. The constant motion divisor is meaningless because it is effectively saying one motion took fewer infinities than another.It is impractical to superimpose infinitesimals over the universe. Those that did were primarily in the early development of calculus, but you can't even pretend the notion is something taken seriously since Dirac. Physics doesn't really care that reality doesn't behave like mathematical infinitesimals, but rather, it is an abstraction they butcher the ever loving shit out of to describe reality despite that. You may still be really considering the case. And I would point to the picture from this fag >>16261219Even if the universe is bounded on some conditional infinite descent, we would end up with fractals which violate differentiation anyways. This is because the further you zoom-in the more the same everything is - that is, it is closer and closer to nothing, or to the smallest possible transactions. And that the variations in this nothing are infinitely far apart, but these distant variations are similar across all spaces. This would be the idealist case.The materialist case would be a transformation of substances, layer after layer quark-quarks and quark-quark fields.
>>16260335Paradoxes of this kind are false because everything in the universe is discrete.
>>16261453Failure to understand the instrument, the experimenter and the experiment.
>>16260784>discrete computations are hand wavinggood try kike
>>16261503failure to realize discrete systems dont have zenos paradox for a reason
Wannabe philosophers in this thread.
>>16261436The paradox is already solved by infinite series of a finite sum.
>>16260335Space is discrete and that solves the supposed paradox.Let’s do a little thought experiment. If space is continuous, then you could fit unlimited computing power in any given volume of space. And the smaller you make a computer, the less energy it would take to operate for the same computational power since you’re moving smaller parts around. Unlimited computing power for near 0 energy is complete lunacy.There’s also the fact that no object with infinite detail has ever been observed in reality ever, so to assume every single small volume of space to be an infinitely detailed object in itself is VERY bold.
>>16261912>Space is discreteprove it
>>16261229Then it wouldn't take an eternity to do the process since the process could never even get started, there is no doing the process, let alone doing it for eternity.
>>16261903>infinitegood try shekelstein
