Zeno's "Paradox of the Arrow"

Tags: paradoxes
Posted in Time


It's just an exercise in logic by an ancient philosopher. It's unfortunate that you can't wrap your head around the idea, but that doesn't make the one who thought of it stupid. It's actually the opposite. Also, Learn to capitalize before you tell anyone to go back to school.
Posted by jamesisiadouche on 6/2/2011 9:16:23 PM
'Also,Learn to capitalize' that was funny!
Posted by not really here on 6/2/2011 9:25:42 PM
Zeno had a lot of these paradoxes. His error was to assume the arrow is ever at rest. At all points in the arrow's flight it has momentum and instantaneous velocity. The arrow is always in motion until the momentum and instantaneous velocity equal zero. Further, a "series of separate events" requires time in which to manifest. Without time, the notion of an orderly, unfolding series is meaningless. As to Lanza's conclusion, time passes whether you are conscious or not. Were it to be a manifestation of our minds, you would go to sleep, (or into surgical anesthesia where NO conscious thought occurs from my own experience - or lack of it), and when you woke up, it would still be night at precisely the moment in which you nodded off. This is a good exercise for the brain, but that's all it is. Lanza is wrong, and so is Zeno.
Posted by Alan Wortman on 6/2/2011 9:31:14 PM
James, if you're going to explain yourself, at least do it in a somewhat intelligent manor. Also, be right.
Posted by wow on 6/2/2011 9:51:22 PM
Alan, Lanza's saying that time is just a function of how we perceive things, not that it's dependent on our observation.
Posted by Mat on 6/2/2011 10:10:58 PM
wow, I don't believe James needs to be in an intelligent manor to explain himself, I am sure whatever home he is in will be just fine.
Posted by gENTLEMAN on 6/2/2011 11:24:24 PM
Time, a feature of this world, not of our minds, is what holds this universe together. Without it, we'd perceive everything as an endless dream, moving from one instance to another with no transition. It seems to me that without calendars and clocks, time would still exist. If there were no calendars or clocks, our perception may cause time to appear either slower or faster than usual, but time would still exist. So like Zeno, I believe that what we call time is the way we treat math. Everything on this earth can be calculated and measured by numbers, however we were the ones who created the numbers
Posted by Jesse on 6/3/2011 12:07:23 AM
Utter bullshit...
Posted by Cyrus on 6/3/2011 12:32:58 AM
But if it is in only one place, it must be momentarily at rest? What kind of silly leap o' logic is this? Position and velocity are entirely independent. You can conclude nothing whatsoever about an object's velocity from knowing its position. This is like saying because every point on a mountain's surface has a definite height above sea level, the slope of the ground there must be zero -- and since this can be said about every point, there must be no such thing as mountains, ah ha! Additional proof that logic is quite often merely a way of going wrong with confidence.
Posted by Carl Pham on 6/3/2011 1:39:05 AM
@alan time would not stop with sleep or under anesthesia as your mind does not completely lose consciousness while you are not awake. The only way time would cease to exist is with a complete loss of brain function which in that case it wouldn't matter because you would also no longer exist. The biggest fault to me in this theory is that the only way to view as an object in one place at a given time would be stop time itself. Because while everything we observe is a continuous series of events that does not make our observations some type of giant flip book. @Carl you can't say that about a mountain because the slope is determined by two points or the slope of a line it is impossible to determine the slope of a point as there is nothing to measure it wouldn't be zero it would n/a. The philosopher says nothing about determining velocity from position but rather that at any point in time the arrow is in a unique place along it's trajectory.
Posted by Dt on 6/3/2011 2:47:29 AM
Some typos in there whatever it's late read through them
Posted by Dt on 6/3/2011 2:48:42 AM
@Alan, I'm afraid your argument does not prove Lanza or Zeno 'wrong', although it does explain why 'you' disagree with them, which is fine. Sorry, a bug bear of mine on declarations of 'wrong'. As to why, there is a question to the argumentative position of both, one can turn to recent developments in quantum theory which suggests that under certain circumstances an object can be in two places at one. Thus it is an observational problem. Again we know that light can be observed as both a particle and a wave thus both Lanza and Alan's viewpoints have some validity. But of course neither proves either 'wrong'. One could also point out quantum limits, we live in a Newtonian world from most observational perspective, however as time is not a Newtonian constant, Alan's argument of time thus is that of a human perspective, however Zeno's argument, although written from the perspective of Ancient Greek knowledge does not require this. I suggest Alan read Foucault's Order of Things to understand the historical relevance of his argument (somewhere mid 18 century) more up to date than Zeno but... Oh and Jesse, a bit more up to date but you could do with checking out some Relativity Theory, but hey that means reading Einstein so don't be hard on yourself. But still pre 1920s. However Zeno caused interest again with the advent of Film as the experiment describes what we observe in the film making process. However as this is something that is merely observable in the visual arena as a spectacle and so says a lot about the influence of this thought experiment and the elective affinities that relate to its interpretation with regard to current socio-politoco-historical economic understandings. I also find it amusing that Lanza is an MD.
Posted by Schizo Stroller on 6/3/2011 3:37:05 AM
Alan, even reaching and then returning from a state of no consciousness in a future time does not provide evidence that consciousness is not necessary in our understanding of time. According to what Lanza is suggesting in his interpretation, time is a feature of consciousness so while your body and others would continue to experience time, you would not until you awoke at which point you would be assured that time had passed in the objective realm. BUT to you it had actually discontinued when your subjective perspective ceased to exist though all that was physical continued on. As for the "giant flipbook" issue, even though "a moment" in the sense of the argument has no duration, where does one end and one begin? Even a frame of video represents some miniscule passage of time. If you're going to have a moment with no duration you cannot compare it to any other moment or the idea becomes paradoxical. This is what Zeno was getting at, this is not what Lanza was getting at. However I would suggest that time IS a feature of our minds and is one of the crucial ways (along with all of our senses) we use our unique consciousness to separate reality as opposed to Lanza's idea of a stringing it together. Our perception of time takes one moment the one "moment" (though it exists outside of time so its strange to call it even that) and separates it for our brain into pieces which can then be strung together. So everything has happened is happening and will happen. We are locked into time, the only one who ever supposedly became unstuck was Billy Pilgrim... but he probably just had PTSD. Anyways... It is already a popular idea that time can only be understood through the context of an observer, and that mere observation can change the outcome of physical events, I would be very excited to see what could happen if theories developed where time and microscopic physical reality could be seen as relative to the so called "motion" of consciousness, but exploring such subjective material seems impossible within our scientific world based on undeniable, prevailing truth, ha! maybe that's why our doctor Lanza is an MD and not a physicist! There are better examples for Lanza's conclusion, which of course is not by any means his own. Great for talking about film though and a cool idea regardless.
Posted by Sim Sala Bim on 6/3/2011 6:21:46 AM
time only exists so that everything doesn't happen all at once. p.s. it is not impossible for something to exist in two places at the same moment in time. i'm sure is zeno knew about quantum physics (or the characteristics of motion) he might revise his statement
Posted by Kevin on 6/3/2011 9:46:06 AM
The author of this quote clearly knows nothing about calculus. With even a basic understanding of limits and infinite summations, the paradox is easily resolved.
Posted by Michael on 6/3/2011 10:40:08 AM
The great thing about philosophy is that they are mainly theories... None of which he says needs to be true. Furthermore, every philosophy has flaws but that is to be expected until it is possible to probe further and deeper into understanding certain ideas -- just how people had assumed Earth was flat prior to realizing that it is actually a globe. Also, the idea that time is an actual natural thing is a false claim; man-kind created the idea of Time to help give us a sense of perception in comparison to reality. Reality is just what is perceived by the individual - just how if a tree falls in a forest and no one is there to hear it, does it make a sound? I think that Lanza is just giving food for thought. He gave us an idea and we can derive what we wish from it; to agree or not to agree is not the same from right and wrong.
Posted by violentendencies on 6/3/2011 5:29:59 PM
This is scientifically true according to Einstein's Theory of Relativity
Posted by Jack Nibsty on 6/3/2011 7:45:08 PM
While an object cannot be in two places at the same time.. Isn't it also true that this only works if we decide that time is real? Meaning if time is real and there are points in time then there is a moment where something is still and in an exact place.. So its only a paradox if time is a real thing right???? (Silly kid here trying to understand)
Posted by Daniel P on 6/5/2011 12:29:12 PM
The response that depends on calculus relies on the realist positivism that the post responds against, and doesn't necessarily then demonstrate or diffuse any features of the post. Also, the way that this is set up here is in no way paradoxical. The arrow paradox is a paradox only from a positivist point of view, and since the author here disputes that, we are left with an assertion instead.
Posted by Abraham R. on 6/5/2011 1:12:27 PM
In other words, what Daniel P. said. (hadn't read his post yet).
Posted by Abraham R. on 6/5/2011 1:13:12 PM
both lanza and zeno are wrong. allan is also wrong, but much less so. time is not linear as we perceive it to be. our perception of time gives us the idea that time is actually a series of separate moments strung together, when in fact all the moments occur simultaneously. our brains cannot process all of the dimensions that are believed to exist, so they instead resort to interpreting these dimensions (one of them being time) in whatever way is appropriate, and since we humans exist only in 3 dimensions, our brains cannot properly understand the fourth (time). therefore, although we live in linear time and perceive time to be linear, it isn't actually so, we are just unable to understand more dimensions than the three we live in. there are no separate moments of flight, because all the particles of the arrow are not confined to existence in the space that they occupy at any given moment, they exist over all the space they will ever occupy, because the concept of a moment contradicts physics, expect in our limited existence/perception. for lack of a better word, time is mobius, not linear. QED
Posted by stuart on 6/6/2011 9:28:49 PM
The sun may rise and fall each day ,we may sleep,we may die,this is all one reality of our own perception,depending on when where and how we began and came about,the future the past ,its all been a hell of a long day in reality, we can only appreciate this potential .
Posted by jordan Hardin on 6/6/2011 10:50:07 PM
This is a pretty popular theory... it's also remarkably similar to Parmenides theory of time and change, which he came up with about 2,500 years ago...
Posted by Benjamin on 6/7/2011 1:17:40 PM
Interesting discussion; it certainly seems the origional writer misunderstood the paradox, but perhaps some of those commenting understand it a little better. The essential developments in how we should treat this paradox, or any of zenos three paradoxes of motion, start with the invention of calculus by Newton (or leibniz, depending on whom you believe). Calculus gives us the differential, it is the property of differentials (velocity is the differential of displacement with respect to time) that they take their two variables to tend to the limit of zero whilst having a finite value (i.e. quantity of displacement and time tend to zero), this allows the mathematical formalism of summing a set of dimensionless points to give a line. Through this we can describe motion without entering Zeno's paradox. With respect to time and conciousness there are several interesting new theories on this in both physics and philosophy, (for physicist see Barbour - The End of Time, for philosophy see Wickes on 'the eternal present'). It does seem at least possible that time, as Einstein stated, 'is the most persistent of all ilusions' and does not exist in the way we perceive it to. It certainly has a dinstinctive role in Minkowski spacetime with respect to the other three dimensions. The history of this discussion in both Physics and Philosophy is extensive, and there is evidence to support many views, but modern physicists and philosophers generally no longer regard Zeno as posing a problem, even if the conclusions argued due to this paradox are still under contention.
Posted by Guy on 6/7/2011 1:18:34 PM
P.S. In response to Abraham, whilst I agree that this discussion assumes a realist approach it should be noted that so does Zeno's paradox. Either you have to take a Kantian transendental idealist stance, in which case this is all the world of representation and so what we mean by the words used is simply altered, or your forced into some kind of natural ontological argument which doesn't seem to prevent the relevance of calculus either. So I don't think it alters the fact that the use of calculus is the correct response to the mathemtaics of the issue.
Posted by Guy on 6/7/2011 1:33:03 PM
Is it not possible that the arrow is always stationary, and jumps from point to point using some kind of quantum effect? I think this is what some of the more recent 'brane theories suggest... with quantised space/time...
Posted by Pos on 6/7/2011 4:55:58 PM
i believe you fellow opionist are taking it to literally. In my mind, I've come to conclude this: That the arrow is at a constant movement, always having a place in it's path. It's neither here, nor there, but where we choose to place it. For example let's talk about humans here instead of an arrow, we can't be at two places at once correct, that physically impossible, but what if humanly, that's true, but not consciously. We physically are bound to one area, what if the idea of "us" is a free traveler to roam about. Leaving it's physical shell. I know it doesn't make much sense but, try to understand, physically we are chained to an area, someone out there giving us meaning to exist can hallucinate our bodies to form a delusional life form. Not real, but yet there, but because our concsiouness is giving it reason to be there.
Posted by Him on 6/7/2011 9:39:43 PM
I agree with everyone.
Posted by Bob on 6/7/2011 9:46:11 PM
is it a paradox or are we just incapable of understanding it yet. also what about the heisenberg (sp) uncertainty principle. as i am sure some of you know, to observe is to effect. what if movement at all is to transition an infinite number of universes. i won't even go into what i believe time is. oh! by the way it will never reach its target since it only transitions a partial amount of the distance in any moment of time.
Posted by GERM on 6/7/2011 11:40:27 PM
Can half of you look up what a paradox is first. Second, time was there at day one if you believe in evolution or whatever.....times there......deal with it. Why so serious?
Posted by Hittler on 6/8/2011 1:07:30 AM
no paradox. the arrow constantly has a certain velocity (in the direction tangent to it's motion), however it is in a different position at each moment. This does not mean that it doesn't have any "speed" (velocity would be a better term) at each instantaneous moment.
Posted by matthew on 6/8/2011 3:58:27 AM
An interesting way of thinking about it, but he errs in thinking that the arrow must be momentarily at rest. Though he is correct in assuming that no object can be in two places at once (at least according to classical physics) but he neglects the fact that position and velocity are independent. Though the arrow is in one place at one instant, for which the interval of time that passes is absolutely zero, that does not mean that it will not be in another place at another instant. The arrow is going somewhere at that instant, but it does not move during that instant because there is no such thing as "during" an instant, since the time interval is zero.
Posted by Sean on 6/8/2011 5:43:05 AM
Without going into quantum physics and calculus, there is a fundamental logical flaw which Carl identifies correctly and Dt falsely refutes. The philosopher DOES determine velocity from position, he says that because it is at a unique position it must be at rest, ie that its velocity is zero.
Posted by Marten on 6/8/2011 7:22:23 AM
Life is lived at 24 frames a second
Posted by Charles on 6/8/2011 10:59:35 AM
It is not a paradox of reality, time or physics but it is a paradox of defining the continuity in mathematics. In particular, consider the question "do two points on the real line touch each other or not?" If you consider points as 1-dimensional objects, then this question is even more fun. (without going into hyperreals) I would recommend the book "Where Mathematics Come From?" by Lakoff and Nuñez. A boring but superb book. Especially the second half pays off.
Posted by dude on 6/8/2011 4:45:40 PM
time is money. remember? and money is the root of all evil. therefore time is the devil.
Posted by duh on 6/8/2011 7:13:03 PM
Not to pop any one's bubble but ..Man invented time...otherwise it doesn't exist. It's for our own purpose that it exists at all. Also it has been proven that an atom can be in two places at once. And motion is only a product one point after another, which can also be proven.
Posted by meinid2011 on 6/8/2011 8:20:59 PM
Guys, it's just like the sun and the tides. They go up and down, in and out and we don't know why. It's simply inexplainable.
Posted by badasinine on 6/9/2011 12:22:40 AM
An object can be in two places at the same time if it goes through a portal.
Posted by Portals on 6/9/2011 4:42:46 AM
this is absolute bulcrap. this shit should not be on stumble
Posted by tim on 6/9/2011 9:33:25 AM
I think the point in all of this is everything is subject to our version of reality. We think the sky is blue because we see blue, but that doesn't means thats actually what it is. Even you get all the way down to the quantum physics of it, that's all based on structures and systems that we have created to help us define and understand our universe. I think the real statement that Lanza is trying to make is that time is just another creation of our minds to allow us to function in a universe with limits we can comprehend. We can never definitively prove it one way or another because we can't escape our own minds.
Posted by Sam on 6/9/2011 4:57:28 PM
In Calculus we learn that an object frozen in a moment has a position as well as a velocity and an acceleration. In other words, the fact that an arrow -seems- to be at rest because we are looking at an individual point in time is the illusion. In reality, the arrow has a velocity in every moment of its flight from release to landing.
Posted by Rob on 6/9/2011 7:57:47 PM
The Planck length is the smallest division of energy and distance between "points" (in fact they define themselves as points). So yes, an arrow can be at rest at infinite (practically) points along it's path.
Posted by Thor on 6/9/2011 8:53:42 PM
Newton solved that puzzle. It's called a derivative.
Posted by annoymus on 6/9/2011 9:04:36 PM
I think my eyes are bleeding...
Posted by Sicarus on 6/10/2011 3:19:56 AM
Isn't time as we know it just a feature of our dimension? So if we were in another dimension (I think higher?), each point could be it's own individual occurrence, but all happening at once. This makes me think that it has to be a series of events that we perceive as fluid time. In our dimension we travel time in a linear way, but it is perceived differently in other dimensions. That's what I've read. But don't say Zeno is an idiot. Without his questioning the subject way back when, we might not be where we are today.
Posted by Bill on 6/10/2011 8:57:38 AM
Posted by GERM on 6/10/2011 3:31:16 PM
I like this site! interesting points of view! (n_n)//
Posted by GABE on 6/10/2011 4:15:29 PM
@ meinid2011. Are you sure that it's an atom that can be in two places at once, and not just an electron?
Posted by Keener on 6/10/2011 8:43:19 PM
Paradoxes (paradoxi?) like these do not stand up to scientific analysis. They are thought problems - metaphors - meant to spur philosophical discussion about the nature of things and the nature of life.
Posted by FreddyZ on 6/11/2011 11:47:46 AM
I really don't have time to explain it all, it takes forever :)
Posted by god on 6/11/2011 1:58:59 PM
I ban anyone who has not taken at least one philosophy class from entering into a debate on a philosophical problem.
Posted by alieraek on 6/11/2011 8:30:29 PM
what exactly is philosophy anyway? You have Past, Present, and Future. The Past and Future are both perceptions. However, the instant of Present, the millisecond of time that is now, is a snapshot in time, before it instantly becomes the Past. Therefore anything we perceive as in motion, is just a series of these instant snapshots in time, the instant of Present. Just because we cant percieve the object ... um lost my train of thought
Posted by axslinger on 6/11/2011 10:47:22 PM
This is all well and fine... until the arrow hits THAT'S when Time slows down
Posted by Timothy on 6/12/2011 12:22:50 AM
Time and Space are just perceptive qualities that are used by our conscious mind to order our world. I however do not see the paradox. If a single moment in time is observed everything that has momentum would be frozen in that moment. The arrow just occupies different areas of space at different times
Posted by Matt on 6/12/2011 9:45:06 AM
Didn't read anything else posted. But how we perceive time, can be considered very much similar to how we perceive light. Where as there are many levels to the electromagnetic spectrum, we acknowledge only a small percentage as what we can see, time in itself is experienced differently throughout nature as well. This calls me to think whether the question is really just questioning logic of a generalized understanding of perceptual time. To put it simply, we live in and for the future.
Posted by Basker on 6/13/2011 6:46:22 AM
My head is bleeding..
Posted by Vedette on 6/13/2011 10:24:32 AM
recently it has been discovered and proven by quantum physics that particles can exist in two places at the same same. as everything that is shacks or wobbles constantly.. fact..
Posted by joe mc on 6/13/2011 12:28:03 PM
Time is an object of human creation to give an explanation for the evolution of moments and action. Although using the idea of moments suggests time, this argument seems to have a scientific basis, so consider the Big Bang into this. The universe is constantly changing an expanding. It all started, according to the Big Bang Theory, in a singular infinitely dense point. Everything that happens is nothing more than a reaction, taking into account the Laws of Newton. From the first expansion to the current expansion, the only reason anything is evolving or changing is due to reactions, which are being created still from the first moment of our universe. Time is nothing more than a word used to describe a constant evolution of this reality. Although "time" still passes without consciousness, doesnt mean life isnt just moments. Motion is not what is happening, it is reaction. Basically what im trying to say is, with or without clocks, calendars, and all other forms of grasping what "time" it is, reactions will still happen. And the only reason we came up with the word time, is so we can grasp that concept, constant change. Time is not real, only evolution. Humans created time to describe the constant evolution of our universe.
Posted by Andrew on 6/13/2011 3:27:45 PM
I'm going to help reference Joe. Just look into M-Theory. http://www.youtube.com/watch?v=Fb2vWj6ITGo
Posted by Basker on 6/13/2011 7:51:46 PM
Time is not an energy, process or function of physics. It is a dimension. The motion of time is an illusion because all of our equally accelerating bodies experience time in much the same way. Therefore, many assume time to be a constant direction, when really, it is already mapped out. Time... is the finger that flips life's flip-book of space.
Posted by Greg on 6/13/2011 9:36:07 PM
Andrew, for the win.
Posted by Dominic on 6/14/2011 12:47:56 AM
While ancient greek philosophy is at least amusing, your transition of it to science-language is just as ridiculous as it is blatantly ill-manered to always use "we" as in "the way WE perceive time". You should seek out the origins of science, maybe then you will actually get it.
Posted by stumbler on 6/14/2011 4:22:19 PM
But, you were still late for work.
Posted by Sean on 6/15/2011 1:47:47 AM
Zeno is an idiot
Posted by damien wraith on 6/15/2011 12:12:51 PM
According to the theory of special relativity Zeno is right in a sense. The motion of all systems is relative; the arrow is at rest in its own frame of reference. The theory goes on to prove that time itself is relative, and not definite, as was thought by Newton.
Posted by Ben on 6/15/2011 12:46:59 PM
so zeno's right after all. Good job, einstein!
Posted by stumbler on 6/15/2011 3:49:48 PM
Before I wrote this comment I had to type the first...
Posted by ariyatsu on 6/15/2011 4:52:47 PM
...half; and then the third quarter.
Posted by ariyatsu on 6/15/2011 4:53:47 PM
7th 8th.
Posted by ariyatsu on 6/15/2011 4:54:45 PM
Posted by ariyatsu on 6/15/2011 4:55:02 PM
An infinite number of infinitesimals equals 1.
Posted by ariyatsu on 6/15/2011 6:09:15 PM
This philosophy is easily disproved. Rather than time being a human's way of piecing together many, separate-occurring events, I believe that seeing time as pieced together separate-occurring events is man's way of attempting to understand time. Just like in the fundamental theorem of calculus, if you take the limit of the size of many different pieces as it approaches zero, then the item at hand becomes continuous. The same would apply for time in this logic.
Posted by Dustin on 6/15/2011 7:43:11 PM
This ignores the fact that this series of spatial "snapshots", if that is the way the world works, would be defined as motion. Also, Zenos paradox, which actually involves the infinite division of the arrows trajectory, is invalidated by the Planck length.
Posted by FoeHammer on 6/15/2011 7:46:28 PM
Perhaps trivial in the context of this argument is that the arrow itself is by design a linear object, so constructed that in flight it retains a specific sequence of its parts as it passes: the head, the shaft, the tail. Anyone who doubts the significance of that is cordially invited to stand in the way of its trajectory.
Posted by Will Owen on 6/15/2011 8:14:22 PM
absolutely ludicrous how people try to rationalize. Our human condition is feeble at best. Constant redirection of reality is filtered through our senses and any idea that works against this must be grasped and explained by these great minds above. You know the minds that point out grammatical mistakes? Yah those minds. We are ingrained in the fiber of God, the all-one, universe etc,etc,etc... It never started , it never ended and yes there is only now and that now is depending on where you are. The fact that we age is not the conclusion of this train of thought. Take a closer look....lots of motion right? When did it start? where does it go? =it didnt, it doesnt. Go get laid everyone and get off yer hi-fuckin horse. You dont know anything other than your attitude towards thought.
Posted by Bostonsbetter2 on 6/16/2011 10:30:31 AM
....Hey, I am big into philosophy. My grammar will be off, idc, listen to what i mean, not what i say. I actually just published a book this year on a lot of logic and philosophy. This is the first time i read zeno, it is brilliant. Thank you for enlightening my day :)
Posted by Luke LaChac on 6/16/2011 11:59:02 PM
Rather now is dependent upon where we are going and how we have understood where we came from to improve the betterment of the future. We are all in this together and we should help each other out. A world of peace and love can be created if we strive for it. Humble your ego to the unseen wisdom of the man standing next to you and work to a common goal. We are God. We create our own reality. How do you want to live? In a world of war, famine, unemployment, collapsing economy, and an exponentially growing large sum of the worlds cash in so few hands. Greedy hand which only wish to keep themselves in power and care not of the needs of humanity. Look around, the world is an urban jungle that is destroying the perpetual system of life that has been sustained for so many thousands of years on this planet. If the planet dies we die, end of story. I believe we are ment to live forever, but that can only happen if we allow ourselves to continue to exist. We've already stated that the possibilities are endless. Infinite realties!. i see no physical reason why we can not create a reality where everyone can be supported to a reasonable standard of living. the conditions of our planet are unacceptable and there is no reason we can't have peace, love, and life.
Posted by Karl on 6/17/2011 12:20:20 AM
So, even though this was thought up around 2500 years ago, because Robert Lanza restated it, the quote goes to him? Hmmm. Um, E=mc2. Someone quote me on that, please.
Posted by jolancka burgeus on 6/17/2011 1:40:25 PM
Ahhh....Zeno's paradox - causing trouble for 2500 years! Having a degree in Philosophy and having studied the Pre-Socratics in my day - I still love to use Zeno's paradox to spark lively discussion. Glad to see it's till working for others too!
Posted by Borge on 6/18/2011 9:35:56 AM
"But if it is only in one place, it must momentarily be at rest". I'm terribly sorry old boy, but why?
Posted by Tower on 6/19/2011 12:07:06 PM
Motion and time are inextricably linked. One is a consequence of the other. As the period of time across which motion is measured tends to zero, so the motion possible in that time tends to zero. Anything above zero enables both motion and time to occur. This is true if we consider that 'motion' addresses all aspects of matter down to it's most fundamental particles. The arrow is made from these particles, as is its surrounding environment, as is any measuring device including the brain of a human observer watching the arrow. Whilst these fundamental particles are in motion so time can be considered to be passing, if they stop, or are all frozen, then time effectively ceases, time restarts when motion restarts. So the only way this arrow can be at rest is when time has stopped, at which point any possible observation of the effect also stops.
Posted by an inarticulate man on 6/21/2011 1:52:31 AM
There's no need for serious debate here. The quotation is just a musing, so all that should be elicited by the reader is further contemplation. Plus, the assumption the being in one place in instance means having no movement has no support.
Posted by Luke on 6/22/2011 1:51:09 AM
If you put something like this up on the internet together with the ability to comment, you are going to get debate!
Posted by Myrtle on 6/22/2011 2:15:34 AM
I think the point here is to expand your mind's way of thinking instead of accepting the common thought. Most great inventors and philosophers never created their ideas through reciting common knowledge but by expanding on it or viewing it from a different angle and perspective.
Posted by Zeltarius on 6/22/2011 12:05:20 PM
I think that it's our mind that devides the outside world into little steps (and instants), but in reality the steps don't exist, its a flow. So "being in one place" is created by our mind. The arrow never is in one place at one instant.
Posted by Bosj on 6/24/2011 7:21:13 AM
You can measure time but cannot grasp it. Zeno just says time is a commodity we use to bind events together. And even now none of our knowledge can PROVE it wrong. All critics in this comments are based on the assumption of absolute time (example: momentum) that make the reasoning circular. To solve the paradox you can't use anything related to time to prove the necessity of time. If someone can really resolve the paradox ... OMG you're a genius ;)
Posted by Kairos on 6/25/2011 4:47:05 AM
A moving arrow has energy and will have slightly more mass then a stationary arrow. Therefore the two are fundamentally different.
Posted by ptrux on 6/27/2011 7:41:42 PM
I'm amazed of how much I've learned reading this blog, and all the intelligent people discussing the topic. I'm starving for knowledge right now! :P
Posted by sandy on 6/28/2011 1:29:32 AM
It seems to almost pertain to the concept of Relativity as per the workings Galileo and Einstein. There is no such thing as "absolute" Time or Space. Each are entirely relative to the observer.
Posted by Jimmy Kruger on 6/29/2011 12:01:09 PM
This is known in science as the Heisenberg Uncertainty Principle. It just means that the more you know about an objects velocity the less you know about its position in space and vise versa. Its nothing special and is not a paradox.
Posted by Willy on 6/29/2011 4:54:29 PM
I am of the opinion that it is important for mankind to consider these questions. I am not of the opinion that it is important for us to solve them. The mental expansion occurs during the contemplation and, for a given problem, shuts down almost immediately upon its solution.
Posted by Bill on 7/1/2011 1:03:40 AM
Bill explains it all
Posted by I am Yum! on 7/1/2011 1:40:18 AM
Time is merely a word. To think such passion and thought came out of this truly simple statement. I would love to see some of this energy dedicated to real questions... But alas I too am here posting my garbage for all to see
Posted by young and dum on 7/1/2011 7:04:10 AM
Posted by Brittany Marie on 7/1/2011 7:51:20 PM
Yeah, Zeno was right.And as some have mentioned on here, Einstein validated it mathematically. Time and space are actually the same thing. You can't move in space without moving in time as well. This is a necessary practicality of the 'space' we exist in. The human mind does have kind of a "refresh rate" which takes snapshots of reality for us in such rapid succession that to us it appears to be seamless. I think that is what Zeno noticed. I love debates like this. I agree with Bill that the process is important.
Posted by Hugh on 7/3/2011 11:19:13 AM
It's a shame Zeno hasn't taken an avanced physics class, otherwise idiots would be wasting time. When the time period where the arrow is in its position is infinitely short, it can still have velocity while it travels.
Posted by benji on 7/3/2011 1:53:53 PM
Bill, time has actually been labeled an extra dimension by popular science. However, there is no true way to measure time only perceptions of it. Even with an atomic clock we are saying that something that might not have a constant "time" has a constant time. It is indeed a product of our consciousness, rationalizing the world in a way that will allow us to survive and multiply. In other words our perception of time is a product of evolution necessary for life to survive in our perceived universe. As far as labeling time as a dimension, I find that to be faulty. I have many experiments and diagrams that explain why time is(most likely) not a dimension but our perception of movement through a higher dimension caused by a warping of an even higher dimension. The fact that(by our limited tools of measurement) we have noticed a fluctuation in time related to speed is what sparked this idea. I however follow physics as a hobby and have no "formal" schooling in physics so fear that my temporal theories would just be chastised by the scientific community that has a piece of paper saying they know better than me. It has also been recently proven that everything is digital and therefore everything is finite including time if it even exists at all. This means that the arrow is indeed at one place at any given moment and indeed is at rest. The reason for this is that motion, like time, is also perception. Just because we use our very primitive(as far as understanding or measuring quantum physics and cosmological physics) tools to measure what those tools were designed with our intent to measure doesn't mean that there isn't something that our tools aren't measuring.
Posted by US ARMY SPC on 7/7/2011 8:01:48 PM
I was cheered up by seeing so many discuss such well thought out speculations on the nature of time. I believe most of the contributors here are among the upper 20% of the population with whom I so rarely get interact. I further assume less fairly Im' sure that we all abide in our parents basements.
Posted by interested bystander on 7/9/2011 11:36:52 AM
if you have ever done lsd then you know time is only relative it slows down time
Posted by whatthe on 7/10/2011 4:04:40 PM
Duh. Time cannot be measured. There is an infinite amount of time in a second.
Posted by trebory6 on 7/11/2011 11:10:21 PM
Whereas everything in the universe is in constant motion, "stillness" only refers to a thing in motion relative to another chosen point of reference which, as it happens, is in motion too. He's correct that "time" is simply our way of refering to a sequence of changed states. One isn't apt to ever cut the process of change down to a size small enough to be reasonably considered "still" or "changeless" which means that "time" is divisible to ever smaller bits without end.
Posted by Naumadd on 7/14/2011 12:17:00 AM
If it weren't for time, then everything would happen at once.
Posted by Brian Ross on 7/14/2011 2:50:21 AM
Robert is correct. Besides, culture is behavior LEARNT from the individuals around you (of the same species). Monkeys, apes (not the same!), whales and dolphins have culture too. Maybe other species have culture as well. We are still to find out.
Posted by RokcetScientist@yahoo.com on 7/16/2011 1:56:20 PM
dis guy was dumb and probs did a lot of drugs and had aids and died.
Posted by poopsickle on 7/20/2011 11:54:15 AM
If he was any dumber he would be really dumb
Posted by nipple on 7/20/2011 11:55:10 AM
Taken From Occupants of the 2 dimensional world: At each moment, we are at the edge of a paradox known as “The square-o”, first described 25 hundred years ago by the philosopher Zeno of Elea. Starting logically with the premise that nothing can be on two planes at once, He reasoned that a square is only on one plane during any instant of its extrusion. But if it is only on one plane, it must momentarily be a square. The square must be present somewhere, at some specific depth, at every plane of its extrusion. Logically then, a cube per se is not what’s really being created. Rather, it is a series of separate squares. This may be the further indication that the depth of space in which the square's extrusion is embodiment- is not a feature of the external world but a projection of something within us, as we tie together things we are observing. By this reasoning, space is not an absolute reality but a feature of our minds.
Posted by Aristotle on 7/24/2011 9:58:24 PM
I never thought of it that way. :)
Posted by Lila on 8/2/2011 10:08:14 PM
Time does not exist as a reference for our minds, it is an independent force tied to the space of the universe. That's why we have the space-time continuum. If time existed only as references for our own perceptions then we would live our lives totally alone since everyone and everything else would exist simultaneously at the exact same minuscule moment while you would live out your days stretched out over seventy or eighty years. Time stops everything from happening all at the same time.
Posted by Ian on 9/4/2011 5:23:43 PM
There is one problem which is shared by every person who has posted so far, and that is that they are deaf to each other. There is one group of idiots who say "Zeno is stupid; calculus has proven him wrong and velocity exists instantaneously", and another group of idiots who say "Man has just invented time; we need it to understand things." But not one person has considered that there might be a grain of truth in the opposite argument. Calculus does indeed stop Zeno's observation from being paradoxical, but instantaneous velocity is nonetheless a ridiculous concept invented by physicists who are scared of tackling this very problem. Conversely, calling Time a human concept helps just as little, and in fact the whole point of saying that it exists only in our minds is merely a way of illustrating its inescapability, for no matter how many times we break things up into infinitesimal events, we still have to have the events occur as a progression for them to make any sense. If we really are moving through a bunch of infinitesimal freeze-frames, then the real question is "What about the part of us moving through the frames?" This mind/spirit whatever still needs to progress chronologically to perceive events at all. We could break that up as well, and keep adding multiple dimensions ad infinitum to compensate, but eventually we find that something can move if and only if time exists. Yes, it is annoying, and yes, it means we can't remove time from any equation. The challenge is to find a way around it, and that's not going to happen unless you accept that the idiots who say Zeno is wrong are just as correct as the idiots who say Zeno is right.
Posted by Polymath on 9/5/2011 7:06:41 AM
Zeno’s Achilles paradox and Arrow paradox came from Parmenides. Parmenides made Achilles paradox to help Pythagoras’ students – Pythagoreans to laugh at Pythagoras’ students – Mathematicians’ logic (idealism logic), when he was learning from Pythagoreans. Parmenides made Arrow paradox to laugh at Pythagoreans’ logic (materialism logic) after he had had his own unity logic (usually it is called digital logic today) and left them. Human brains’ the parts that support to idealism logic, is autonomic nerve system center. Human brains’ the parts that support to materialism logic, is sex center. Human brains’ the parts that support to the digital logic (the unity logic), is parasympathetic nerve system center. The idealism logic (human autonomic nerve system function), the materialism logic (human sex function), and the digital logic (human parasympathetic nerve system function) are as teamwork of ZEN. Yun Zeng (yun.zeng@att.net)
Posted by Yun Zeng on 10/14/2011 10:34:50 PM
I have thought it could be loosly resolved using heisenbergs uncertainty principle
Posted by Petey on 12/19/2011 7:52:53 AM
@Peter hahaha, it was hard to understand it from a philosophical view no you are suggesting physics. Good luck.
Posted by PHY on 12/21/2011 5:04:10 AM
No shit Sherlock. As if someone actually thought they had found something new. Fascinating.
Posted by Kimberly on 3/9/2012 2:51:28 PM
Ask him to stand in the direction of travel of the arrow and ask him his thoughts once the arro strikes him.
Posted by jojo on 5/6/2012 7:33:04 PM
Don't (doesn't?) Quantum Mechanics kinda put this whole thing to rest?
Posted by LaRubia on 8/29/2012 7:46:10 PM
"A series of separate events." It's all so brilliant, you just have to take the time to sit back and observe, no iphone or mac!
Posted by Samantha M on 4/23/2013 10:49:35 AM
Pls. see I. Kant "Critique of Pure Reason" 1789 which argues convincingly for just this idea, and includes space as well.
Posted by Alex on 10/28/2014 11:26:34 PM

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