wes, You're right about my saying reason is the antithesis of reason, I chose the wrong word. I agree with you that it represents the boundary of objective reasoning. I also agree that by choosing a perspective you resolve the paradox - that's probably a better way of saying it than I did. Another way to restate that is that paradox is caused by a (faulty) perspective. The choice of perspective is the relevant thing: how do you know which perspective is more true? I think that any perspective explored deeply enough would lead to inconsistencies(paradoxes). If space is mathematically divisible into an infinite number of segments then it seems that Zeno is correct. Since we know that Zeno is not correct in the real world, we are left with a real head scratcher. Please Register or Log in to view the hidden image!
Hmm.. I disagree. Paradox only arises from THINKING about it. If you choose to think that doing so is faulty.. Hey I'm not responsible for your brain. Get a tune up. Please Register or Log in to view the hidden image! (teasing) Paradox arises from not DOING. That's not necessarily faulty. I'd say it's perfect actual. It's cool as shit to me. I love that paradox in a way defines the difference between the subjective and objective experience (doing). That's easy: Because you lived it. Hehe, seems like a different issue to me... your'e talking about the ability to maintain a consistent perspective in THINKING.. that will certainly be as you say.. but that's not exactly at issue. I don't see how he made a claim to be proven correct or untrue, except if the paradox is resolved... then your claim becomes subjective and you've resolved it via that manner, but not objectively. I think the division of space is technically irrelavent. Like drnihili said, it's about taking the last step without ever having taken it. It's definately a good brain drainer. (brain drain is my old title here too, so I'm totally clever for having used it like that. Please Register or Log in to view the hidden image! LOL)
Yes, this is the only way both distances can be equal. As much it concerns other questions, I think that there is a common mistake that guys here makes when it comes to the quantized space. There is two kinds of spaces (and distances!), one is pure abstraction - the geometrical continuous space. This space is scale-invariant, it is not discreet. The other space is the real physical space, which had to be discreet at some level. Geometrical space can approximate physical space correctly only in macro scales. At micro scales continious geometry becom irrelevant. I will demonstrate this to you in this way. Imagine 2D discreet space from the kind: .................M......................................................... ............................................................................. ........A........B........C............................................... ............................................................................... N......D........E........F......P........................................... ............................................................................... ........G........K.........L............................................... .............................................................................. ..................O......................................................... A,B,C and so on are the discreet points from the space. The space exist only in this points. Point E is the central point, its distance to all periphery points- M,A,N.........., expressed in el. steps is the same. Because of this in the geometrical continious space the above figure is mapped as circle and in this points of view all periphery points lies on a circle. Inthis way a romb in the physical space is mapped as a sphere in the geometrical space. I am interested from your proposal. Can I send you e-mail?
On what basis is E a central point rather than a point on the periphery of a circle with no central point? Also, can you explain how macro distance are constituted from micro distances? Email isn't good for another week or so. I'm in the middle of a move. Edit - *oops, I misread your post. My first question makes no sense. Scond one is still good, and I'll post again when I get some time.*
Let ADF be a triangle composed of the triangles ABC, DBE, and ECF. Suppose further that each of the smaller triangles is minimal in the sense that each side has a distance of 1 el. Am I right in assuming that ADF must have each side equal to 2 el? If so, how does one map a macro isoceles right triangle on to such a space while preserving ratios?
I agree with this point. But it amounts to a restatement of Zeno's paradox in quantum terms. Zeno knew that physically the arrow crosses the distance. Mathematically it is acceptable to postulate a geometrically continuous space even though this does not work physically. As an aside, is there a name for a quanta of space?
is it generally accepted that space is not continuous? so this arrow we are taking about takes really small steps through the air and the motion is not a continuos line, but instead points? what's in between the points?
For consistency's sake you have to say that there is no "between the points". They are adjacent. Motion would probably be dexcribed in terms of superposition and subsequent collapsing of the spatial eigenvalues. That's how I think it would have to go, but I'm willing to be corrected by someone who's actually familiar with the extant theory.
OK, I just want to get my feet wet; this is my first time to post (pop). So, my thoughts are these: 1) This is an infinite geometric series (which, in my experience, is to be encountered in third semester calculus). 2) This is distinct from the concept of a halflife for the reason that has been mentioned a few times about appropriately diminishing time increments. The second point is intimately related to time, but it has been mentioned that time has nothing to do with the question. My response to that is: If time has nothing to do with it, then what is meant by "never" crossing the room?
To finalize my view about Zeno paradox I had two things to remark. First : the crossing of the room or any movement of a body or any physical object is a physical process that is realized in the real physical space. Zeno paradox shows inconsistency of explaining this process using continious space. Thus to mingle math and physics is wrong. Second: There is indications that the real physical space is discreet. Then movement of any el. particle happens with a succession of el. steps in this discreet space. That is why movement between the two corners of the room is possible. In addition it is possible to be defined many other similar to Zeno's paradoxes. I will give you example with the Neuton law - F = ma. Suppose that you have a body that moves with velocity v0. Now suppose that on this body is acting constant force F contrary to its movement (gravity for example). It is clear that the body shoud stop at some time and invert its movement. The velocity will changes in this way - v = v0 - gt. Then after time t1, velocity of the body will be one half from the initial velocity v0, after another time t2 it will be one forth and so on. Since velocity will never become zero we can argue that if time and space are not discreet the body will never stops. It will approache to the inversion point ad infinitium.
