bunburry is right. Infinite is a mathematical concept. In reality, you hit planck length and cannot go smaller physically. This is a string(?) you cannot cut in half. Please Register or Log in to view the hidden image!
Off colour nerd joke. You have been warned! A mathematician, a physicist, and an engineer are at one end of this long room, and a beautiful stud is at the other end. The only problem is that to get across the room you can go half way across, then half way again, and again, etc. "You'll never get there!" the mathematician proclaims, "You can always go half way again!" So she doesn't even try. "O-yeah?" the physicist responds, "we'll see about that..." and he goes half way across the room, then halfway again, and again and then gives up. "She's right, you can always go halfway again...you'll never get there!". The engineer walks across the room, has a wonderful time, walks back, and says to the other two: "Well, I can get close enough for all practical purposes!"
You cannot even take the tiniest step, make the tiniest movement according to this simple mathematical demon-stration! Perhaps y'all's resistance to the obvious here is its counterintuitive component. The results of this bit of mathematical doggerel is that; 1) math is completely spurious and irrelevent as far as being a descriptor of 'reality' or.. 2) there is an inherent flaw in the simple mathematical proposition, or.. 3) motion is an illusion of perceptions and has no reality. No motion possible other than in our concepts. Naive realism dies a slow lingering death! Finally!
Hi yall i don't know what's the purposeof this argument or long term conversation, cause the answer is different for different views. First of all another paradox for yall: OK think there is a line and put one dot on one end and put the other one 5 cm ahead, now imagine that the two dots are two men running, the man who had a early start or advantage have a velocity of 5 cm per min and the other guy who start from the beging with the disadvantage of 5 cm have a velocity of 20 cm per min. Question will the second guy who is behind by 5 cm ever pass the first with a 5cm advantage? Well in naturality he will, and if you don't believe me go ask you dad to run with you... But i mean if you think in an i guess paradoxy or abstract way the answer will be the guy with a faster speed will never pass the other guy with a slower speed. Becuase in a line there are infinite dots, thus when the faster guy got to where the slower guy stands, the slower guy will be 5cm infront of him, and we can go for ever cause it's infinite..... The reason i said that i don't get why are you guys argueing about it is that it all depends. I mean you don't want to mix reality with abstract too much. If i believe, understand and include the idea of infinite then the answer to the arrow is that it will never touch the target(earlier post). but if you are practical you'll know that eventuraly the arrow wil hit the target and that's cool too. See ! don't mis reality with abstract thinking cause in theory the arrow won't hit but in reality it will.
No. Like everyone else who fall for this sort of "paradox", you are falling into the trap of thinking that the sum of an infinite number of discreet time intervals must end up equally an infinite amount of time. Each time the faster person has to catch up to where the lead person was standing, it will take less time. He will have to "catch up to the other person" an infinite number of times, but it will take him a finite amount of time to do it.
Thinking that illusion is reality is delusion. Just because motion seems apparent, does not make it reality. Speed means nothing in this problem. The tiniest movement becomes impossible because there are an infinite number of points that must be reached first. Speed is irrelevent. Motion is therefore impossible. Perhaps that which is 'apparent' aint necessarilly so?
The question is not 'is apparent motion possible within the holo-dream context of our perceptions and concepts, but is it possible in other more 'real' context than 'appearances'? This simplest of logic and math seem to say no rather definitively. If this is the case, what new world-view can encompass this new (possible) truth?
If by "simplest" you mean "faulty" then yes. As has already been explained, it can be easily proven mathematically that the sum of an infinitely long set of numbers is not necessarily infinite. Look in any introductory calculus textbook. I don't know why people keep going on about this sort of thing. I'm sure it was kind of interesting back in ancient Greece when Zeno proposed it and mathematics wasn't developed enough to prove that an infinite summation could give a finite result, but here in the 20th century we know better.
how I always understood this was: as nosor said, nobody ever said that it takes time to pass these things, and as the distance gets smaller your rate increases. t=d/r, if d->1/infinity and your r->infinity, the time it takes you to cross that inifinite number of points is 1/(infinity^2) essentially 0. (I know that what I just said is not exactly correct, but its a way to explain it to people without higher math education)
Absurd. The more that I hear of these math proofs, the less respect it deserves. It is not possible to add together an infinite string of numbers. How many points on a line? Exactly? If infinite means that there is always another number, another point, your position is untenable, an absurdity. If you can find some sort of math that can prove your supposition, then your math is of no more value in the finding and description of 'truth' than religion, belief in absurdities. I don't mean to disrespect your 'religion' (if that is what math is to you), but you can't piss down my neck and try to convince me that it is raining from any book or series of mental gyrations! That is fundamentalist thinking. Believe what you like, but a tangent never reaches either of its descriptor axes. Has modern math done away with that pesky 'tangent' while I was out? If not, your argument, however couched, is spurious. At least in my opinion. It is not that one cannot proceed from 'halfway' to 'all-the-way', but half-way can never be reached. Speed is irrelevent. Run as fast as you like, speed of light, turtle dance, whatever, to move at all, distance must be covered.. . How close does your 'tangent' come to the 'x' axis, ever closer but not reaching? If it was an alactrical circuit, it might get close enough to spark, but it never actually reaches. We are standing on the axis and attempting to step onto the tangent when it touches our feet. Never happen. Starting on the axis, the tangent remains forever, by very definition, beyond reach. What would be the point. Has the definition of tangent changed? If not, then you fundamnentalistically grope and grasp for validation of your preexisting beliefs, presumptions and prejudices. Motion remains impossible. Naive realism be damned! There are, bye the way, vastly superior explanations supporting my position. Just look it up on the net. It is available for sincere 'seekers' of truth. I think, after cutting edge quantum understanding has successfully discarded the concept of time as a 'reality', motion followed close behind. You really are living in some past paradigm. Once there is a belief, thought is no longer necessary. If what I am saying (anyone) has any meaning to you, then feel free to incorporate into a (new, uppncoming) worldview. If they are meaningless words to you, then ignore and move on. Whatever works for you. This is not an argument. It is a sharing. Peace..
Well since X & Y are arbitrary points with no real meaning then any half-way point is, similarly, an imaginary hypothetical point with no reality and so any distance towards it is an estimation based on hypohteticals. Any movement towards a point (time/space) is an estimation of potential that can never be fulfilled, because by fulfilling it one reaches an absolute and so falls out of space/time and into a singularity. A singularity is always hypothetical and can never Be because only things that exist in time/space exist, that is phenomena with a potential of Being actually exist and those that theoretically ARE cease existing in the spatial/temporal dimensions we are accustomed to. Either that or I’m drinking too much.
ROFL!!!!!!!! *whipes tear of laughter from eye* are you insane? ever heard of an integral? not to mention that you can prove yourself wrong by simply walking across the room. how many midlines did you cross when you walked from one side of your room to the other? answer:infinite
Well, cato, I hope that you didn't get all dusty from that roll on the floor, and laughter is truly the best medicine! So, I'm happy to have been of help in that way. If I was insane, do you think that it is an act of sanity to ask the suspected insane whether or not he is insane? You remember that I have mentioned naive realism a couple of times? Naive realism is a belief system in the ability of our sensory 'evidence', our perceptions, to accurately depict 'Reality/Truth' as it is. This has been thoroughly refuted long ago. Do we 'bend' science to fit what we already believe/percieve (our set of prejudices regarding the 'world' that we pretty much have solidified by the time we reach 18 yrs), or do we alter our concepts of 'reality' as 'scientific understanding' is gained? Evidence of the eyes that the sun comes up in the morning. Evidence of the ears that there is a constant ringing sound behind all other sounds of day to day life... (oops, my tinnitis problem.. *__- ) Are you certain that all that your senses tell you is accurate 'reality'? Certain? You 'believe' that there is light and colors in front of your eyes? Do you really think that there is 'sound' beyond your ears? Odors in the 'world' beyond your nose? Watch a movie; looks like it is really people 'doing' things there in the monitor or on the screen. Believing your senses here is obvious error. The motion is illusion. You KNOW the truth about movies. You see 'motion', dont you, in the movie; flowing, temporal, linear motion, yet we know that the APPARENT motion of a movie is a trick of perception. There are a huge pile of still, motionless pictures (cells), all existing at once, together, in that film in the cannister in your hand. You visit each of them, consciously aware (hypothetically speaking) singularly. One at a time. In an APPARENT sequence thus forming the illusion of motion and sequential linearity, time. For the moment, we suspend our 'knowledge', our understanding of basics, and enjoy the ride. Please understand the hyperbole, the analog. There IS no motion, any more than there is light or sound or odors, etc.. beyond your nose. What you weren't getting about the construct is that there is no question of getting halfway anywhere as we would have to make the very first movement in the first place. The road (tangent) gets closer and closer to our feet (here on the axis) all the time, but never actually reaches us. We cannot take that first step. BUT, like the 'still shots' in the movie, all (Planck) 'moments of existence' are co-existent, simultaneously. Like the willing suspension of 'disbelief' when at the movie, the same principle acts in our 'day to day life'. Unfortunately we forget that we 'know better' and begin to believe the illusions of the senses to be 'reality'. That is delusion. Time, motion, linearity, cause and effect... all 'screen tricks' that we delude ourselves to be 'reality'. And we teach this delusion to our (originally) clear-sighted children, we 'adult-erate' them.
It is true that it would be impossible to sit down and add up an infinite series of numbers. However, it is possible to calculate what the result would be if you were to do so.
