Oh, his ideas are even stranger than that. Think of some of the implications, like the fact that his infinitesimal would be a small cube in shape! Since lines must have thickness, each side of the R3 "line" would be equally thick with the length being his fictional infinitesimal. A single infinitesimal would be defined by the intersection of two of these lines, orthogonal to each other, leaving you with a cube as the smallest possible unit of measurement or existence! This follows 100% from PJ's ideas, and it leads to the smallest thing possible having corners! His ideas on the nature of the very small only work if you don't think on them too hard. They confuse the eternal process of dividing things in half with the existence of a potential infinitesimal that can be used as a static concept. He then tries to have this non-zero entity act like zero by saying that an infinite number of them exist in any finite space. Think on that last sentence. The way to get around this impossibility is to define the object with the ludicrous property you are hoping to achieve, so you say "It is the thing which is so small that an infinite number of them fit within a finite space". Then, if you point out how impossible this is, you get the law of identity thrown back at you. It is a circular reasoning whose loop is smaller even than that of Christians who say that the Bible is truth because it says so in the Bible. :bugeye:
Wesmorris: I fail to see how this would be the case? For as the infinitely small allows for every single possible number till the infinitely large, five could be shown as the infinitely small point which its value (as -exactly- five) takes up. If you would read up, you'll see my mathematical arguments. They're with Swivel here and a little bit with Quantum Quack. Well really, lines having no depth is absurd. Moreover, even if we are only speaking of two dimensions, we still have the mathematical space of the conversion points.
Swivel: Actually, as I reject anything but the reality of three dimensions together (+time but that is irrelevant here) my infinitely small point would likely be spherical in nature. With the diameter of the sphere being infinitely small. The point would be this monad. Regarding your other claims, weren't you the one who just said a few posts ago that my system was -consistent-? Again, if you'd like to critique my system, go ahead. But I'd have you directly tackle my mathematical proofs I gave to you, especially the ones that refute the notion that it is "acting like zero".
I've seen you use numbers a few times to make points, but I haven't seen any mathematics in this thread, and nothing which resembles a proof. Please point me in their direction. A monad? You wish. Think about a line in your hypothetical universe. It must have thickness, since you do not allow zero dimensions spatially. A point would be defined as the union of two orthogonal lines. This is going to give you a cube. You can't have your lines be cylindrical, since each side can't be smaller than the infinitesimal. And I never said your system was internally consistent. I only granted you that some of the silly things you were saying would be consistent if the wholly incorrect axiom you stated was magically true. I was redirecting the focus back to the foundation of your ideas, which is where you are going madly wrong, and away from the rickety tower that you feel like you have erected on top of it. I respect your opinion all over this forum PJ, but I don't think you have said anything valid on this topic in three different threads. But, I am still enjoying the spectacle, so don't think that I am aggravated by this. More bemused and sad, really. Please Register or Log in to view the hidden image! Edit: And I agree that time is not a dimension. I wish we could get over that nonsense and move on (scientists as a whole).
Perhaps your comments on your dificulty with thinking about dimension stuff were sarcastic and too subtle for me. But it seems to me that that is exactly the difficulty. You demand space of that which lacks it because it's how you relate to it, and you cannot relate to it differently. You are a flatlander who scoffs the adventures of that one flatlander to swears he encountered three dimensional space. Please Register or Log in to view the hidden image! First of all, if you want to present a mathematical proof you should do it for the hardcore math guys here. I perused the thread and saw nothing I recognized as such, but it could be my ignorance in that arena. While I think it's kinda neat that you have an apparently unique perspective of mathematical space, I gather from your responses that you cannot see the problems I point out with your ideas. As such, I do not find myself of much use in the conversation.
Swivel: If you would like to refute my system, once again, I ask you to tackle the math I presented. If you have qualms with it, do it. Although you are now rescinding it and saying "it would be consistent if your axioms were correct", nonetheless I have presented math. If you would like to tackle it, go ahead. If not, then I suppose we're done here, as my arguments shan't be addressed and therefore, our conversation is fruitless. Actually, no: A point would not be defined as a union of two orthogonal lines in this system. Rather, it would be a sphere where the diameter is equal to the infinitely small. This would be the smallest possible length of every dimension, and as no dimension in this system can exist apart from the other two, this would be the only shape possible to serve as a true point. Likewise on all accounts.
Wesmorris: Actually, I'm more focused on coherence than the dogmatism that you demi-imply here. For instance, my major critique of any object with two dimensions is this: Suspend a two dimensional square of finite lengthed sides in a three-dimensional space. Then poke your finger on the square from above. What happens? As there is no depth, it goes right through. Yet if there is no depth, how can the sides be plane be connected? We're not really in the academic setting to necessitate, as you say, "a hardcore math guy approach". I provided none of that, no. But I provided a less hardcore approach - that is, I was not going into calculus and such to get my point across - throughout the last few pages. Well we were really arguing semantics for much of this discussion, as we were confused as to what notion of "space" I was refering to you. You (seemingly) thought that I meant physical space, as in I was demanding graphs be like rocks. But yes, I don't imagine we have much to discuss really, as that was the main pull of your argument, as far as I can tell.
PJ, your math relies on division by infinity, which is a joke. Go read up on the issue, here is a quick google result: http://mathforum.org/library/drmath/view/62486.html Since your concepts and mathematics rely on this, I believe everything you think you know about infinitesimals, space, time, the very small, etc... are completely wrong. What is frustrating for me is that I know that you are a smart fellow, but you have created a religion around some bizarre mathematical untruths, and you cling to those dogmatic axioms unquestioningly. You use bizarre examples (like poking a finger through a plane) and draw hasty conclusions from those examples that do not follow. You sound just like TruthSeeker, IAC, or Timetraveller in these threads. And I know you are not like those guys, which is why I enjoy laboring to help you out. Please do some studying on these matters. Stop trying to reach the conclusions based on intuition alone. And lose the religious fervor you have for your zany ideas. Over and over I have raised objections to your arguments which completely dismantle them, and you just go back to the law of identity and division by infinity and the endless process of division = infinitely small. You still haven't dealt with: No matter how many times you make a 'bit' smaller, it is still finite, and a certain number of those bits will fit in a finite space. An infinite number of anything, no matter how small, will still reach an infinite distance. This is axiomatic and unarguable. Making up a concept, which has an incorrect assumption, does not make that concept stand on its own. When you say "A thing so small that an infinite number of them will fit in a finite space", you are creating a concept which is internally inconsistent, which means you can not go on to use this concept to make other points. You can't have infinities bounded on both sides. .000...1 is impossible. It is the creation of a stretching line segment, which is not an infinite object, it is a dynamic process. You can't use a dynamic process as a static measuring tool. It created the illusion of an infinite space within finite confines, but it is an illusion created by an earlier mistake. There is no "smallest" unit of measurement. Any unit can be expressed in terms of any other. Pick one and use it. This is the way reality works. Points have zero size, and this is not a contradiction in concepts. When we talk about a coordinate in a plane, we are not pointing to a bit of matter, we are talking about a location which is a certain number of units from one side of the plane, and a certain number of units from the top or bottom. Poking your finger through this coordinate is not the same as interacting with actual matter. You are confusing geometric tools with the matter that we measure and describe with them. In short, you are 100%, objectively, wrong in all of this.
Swivel: Aren't you the one that was mentioning the Fallacy of Authority just a few weeks ago? So please, do not hold yourself to standards differing from what you hold others to. Actually, to be quite blunt? Your arguments have been laughably sophmoric. You also avoid every single one of my points with no refutation whatsoever. All within a package of amusing arrogance and pretension. Sir, it is truly you who have created a "zany religion". Yes, I did not deal with it because you said I did not deal with it. I gave you a refutation and you have ignored it. Continue to ignore it and we can cease discussion, because it is clear your dogmatism blinds you. If you'd like to critique my arguments from a rational basis, please do so. I'm waiting. I have never claimed otherwise...? I've given you a mathematical refutation. Your refutation is "whine, but I say different, whine!" Deal with the refutation and we can speak. Shown incorrect through an argument. Deal with said argument through reference to it, if you might? Incorrect, as shown by mathematical argument. I'm like a broken record with you, aren't I? If you'd like to tackle my proof, please do so. We're all waiting with baited breath for a real argument and not "I AM RIGHT!" Geometry = the mathematics of shape = mathematical forms relating to physical phenomena. Similarly, the claims of geometry may be critiqued on account of internal consistancy. A depthless plane has problems with consistancy of connection. Moreover, the definition of a point you just gave explicitly refutes its zero-size. You have placed it at the epicentre of two converging lines. This is a point with size - as such convergence is possible. A point which can be placed on a grid has definite position, which means definite place, which means definite size. In conclusion, you are not only 100 percent wrong in all manners, but your arguments lack reason and come from a distempered, arrogant mindset, without regard to refutations, only assertions. Please, save me and everyone else the time if you are going to answer back with no refutations whatsoever. If you are, simply say "goodbye" and we can end this. I tire of repetition.
I was only saying that from my perspective it seems you're forcing the mathematical space to behave "as in the real world". Just how it appears from here. By reference and reference only. There is no square except that which we project there via our reference to a pre-defined shape, which is defined purely by in this case, coordinates, which are references to locations on an imaginary grid. I think they may be aware of something that I am not, and would imagine this excercise has been undertaken before. I don't know, that's why I'd like their input. But yes you're right, this is not the setting and I think the philosophical differences have been well exposed. I do think you're have to in order to properly do so. And I still think that in a sense that's what you're doing, but I don't know that for sure of course. I'm going to post in the math nerd section and ask them.
Wesmorris: Please Register or Log in to view the hidden image! I'll be refering to this graph throughout. Regardless, the concepts must be coherent. I shall try to present a compelling case for why this is so. Consider the graph above. Let the outer diamond represent a hole in the two-dimensional plane. Let the inner diamond represent another shape passing through that hole in three-dimensionals. You shall admit that with a hole, clearly that inner diamond, so long as its size is not greater than the hole, can easily pass through, yes? With no obstruction, yes? Well what happens when the hole is closed? Where the plane is supposedly connected two dimensionally? Remember, this implies zero depth. Accordingly, would not the diamond still be able to pass through? As certainly, a hole in a plane also has zero depth? If so, then the ramifications are clear: A two dimensional plane cannot be differentiated from a hole in a plane. Ergo, the notion of a connected plane is incoherent. Assuming, of course, that in neither case the hole is not obstructed on either side. But that goes basically without saying. In an academic setting, maybe. But really, I don't have the desire to do so here on Sciforums. Moreover, the substance of the argument would not change, as we're dealing with the logical ramifications of certain concepts, as well as well understood mathematical notions.
You are holding the concept of a plane to the same standards as material things? What point could possibly be made there? Nobody would argue that a plane actually exists, they are tools, like lines and points. Wondering why they don't collide is an attempt to disprove a claim that nobody is making. So, when you point out that a plane with a hole acts like a solid plane, therefore the entire plane is just like the hole, you have made an error in logic. Namely, you have pretended that the feature of "collidability" is a feature of planes, without first proving this. I could say "All humans have wings, since I do not have wings, I am not a human", and you have an exact copy of your mistake. _____________________________________________________________ And I'm sorry that you are upset with the way I am discussing this topic. I feel that I am replying to your points, and listing the problems with your ideas in a neat way, and that you are the one ignoring them. I've replied to all of your mathematics by pointing out that you can't divide by infinity, and you can't have constructs which are bounded infinities. You left these issues hanging and continued to do so. I've read this thread several times to stay fresh, and I see it differently than you do. I think the best thing would be if we could find someone who shares your unique ideas on space, so that we can have a different set of explanations of why they might have some credibility.
Swivel: A plane is held to be connected and not an empty space, yes? That is why it is neither drawn, referenced, or otherwise calculated as having a hole in it, yes? Yet if such is the case, then should it not be able to be shown to be different than one? Clearly no, for the results of whether or not a three-dimensional shape can penetrate it are the same whether it is a square with an interior hole or not. Accordingly, one cannot rightfully say that the prior conception of a plane as a two dimensional object which can be coherently said to exist as it is claimed, ergo, the concept is flawed and the notion of two dimensions, apart from a third, is refuted. This is not a matter of physical considerations. It is a matter of whether or not it counts that absence of a plane would act differently than the presence of one. It would seem that this is not the case, ergo, a plane cannot said to satisfy its requirements for being held to be as it is. If, on the other hand, we can show that a plane is possible to to be differentiated from a plane with a hole in its center, then we might be able to show that a two dimensional object is not, in and of itself, absurd. Apology accepted and note that I did not mean to respond so nastily as perhaps I came over. However, yes, perhaps we ought to get other people to join. It could breath new life, although clearly, we both seem to disagree on what we have established and countered and what we have not.
Who claims that a plane is connected? I do not. In this thread you will find that I explained what points, lines, planes, and cubes are, and how they should be visualized. I think you skipped over it because I cautioned that these where abstract ideas, and not related to actual solids. It was also a brilliant gift for people who want to know how to visualize higher dimensions. A plane is not a connected, continuous object. It is a collection of lines, which are distinct from one another. And lines are a collection of points, which are distinct from one another. How far apart these points, lines, and planes are is decided upon by our choice of measurable precision. If I give coordinates to three decimal places, that is the absolute measure of distance between two points or lines. .001 is the smallest increment between any two points on this plane, and it is a discrete jump from on to another. This is one way to reject your point, the other is to point out that you are injecting a third dimension into a two-dimensional world and trying to make a point. You simply can't do this. Even though you are using two R2 planes, you are using the relative motion of them with respect to one another in R3 to make your point. This can't be done. The planes do not "pass" through one another. There is a moment in time when the two planes are separated by whatever smallest distance you choose for precision, let's say .001. The next moment in time, you are attempting to have the two planes occupy the same space, which is impossible. The next moment in time, you have the plane at -.001. Again, there is no sense in this, and even if there was, you would not have made the point that you are attempting to make. I know that this is similar to the finger-poking idea, and I again ask you, "Where did you hear about this example, or how did you think it up, and why do you think this proves anything about zero dimensionality?"
Swivel: As you claimed they weren't applicable, I did indeed skip over them. Moreover, you will find that the notion that a plane is continuous is noted simply by the fact that we can speak of such things as the area of a plane. Yet if a hole can not be distinguished from the plane, then the notion of an area of a plane is similarly flawed. Our choice of measurable precision can certainly work in a fabricated system that assumes such validity. But if it fails on other levels - including presenting a coherent alternative to a hole in the middle of the plane - then it is a false concept that is demanding of us acquiscence to that which isn't demonstratably so. Actually, using higher dimensions in lower dimensions is regularly practiced. The famous Flatland example of a sphere passing through a plane. Or a plane wrapped around a sphere (specifically good for non-Euclidean geometries). Also, if they have no height, why cannot they be in the same space? They have no value for that... I thought it up for this discussion. And it points to the absurdity of anything less than three dimensions. You litterally get answers which are incompatible with a plane having area, which contradicts it being a plane.
A plane has area, not because of the continuous *mass* of the thing, but as a function of the perimeter. A rectangle has known area by the product of its sides, not because there is a bunch of connected *bits* making up the plane. The reason two planes cannot occupy the same space is because you would only have one plane there. Imagine a cube. There is a single plane through the origin which is orthogonal to the z axis. Only one. If you were to "slide" another plane down the z axis, when it got to the origin, they would occupy the same space. It would be one plane. They are not interacting, because it is impossible to designate one rather than the other. No problem. I think you are seeing in the Math and Physics section how unique your ideas are. I'm not sure if this thread is even needed because that one is much more interesting. I can tell that you are still reluctant to acknowledge that you can't divide by infinity, and that the limit of smallness is zero, and I admire your spunk. Just make sure that you are coming to conclusions because of their merit, and not because of how long you have cherished them. My respect for you is most certainly non-zero. See you in the other thread. Peace.
Just managed to get back and catch up. Boy !! you guys are hard at it..Hi Wes long time no talk to..... I noticed a comment way back about the divisibility of zero.... Can I pose a scenario and a question that might stir some thought? "Take one flat plane mirror, and place it in a volume of vacant space without light to reflect into it. Essentially there is nothing for the mirror to reflect so we have zero to be reflected ok? When you look into the mirror what do you see? Suggested answer: A reflection of zero.... Is the reflected zero in the mirror different to the non-reflected zero outside the mirror? Suggested answer is: It must be as it is a reflection of nothing and not the nothing itself. Does the reflected nothing have value more than the original nothing? Suggested answer: Yes because it is a reflection and yet nothing simultaneously. If it is a reflection of nothing can it still be claimed that nothing exists in the mirror? Suggested answer: you tell me....... And if nothing exists in the mirror according to the mirror does nothing exist outside the mirror? suggested answer : No because nothing exists as a reflection nothing must exist as a source. So nothing is both existant and nonexistant simultaneously. depending on the perspective you take and of course we cannot legitimately take the perspective of absolute nothingness because there is nothing to form the perspective from. Why am I mentioning this? Shit! I dunno......Please Register or Log in to view the hidden image!
I guess it still is but heavilly side tracked to rationals and logics that prohibit the ability to deal with the logic needed to even get close to understanding it. Lost in argument about the difference between infinite small and zero.... Originally this thread was created as an off shoot to a thread I started about the need to accept irrationality and illogicality prior to the understanding of that rational and logic. Pj and I were heavy in discussing this and so he starte this thread to allow better focus. It appears to me that the two issues inf, small and zero are a good example of irrational and illogical. IMO "Infinitely small" is in it self an irrational proposition yet the idea of zero is quite the opposite. There are many arguements That I could entertain to support my opinion but I feel it would be "irrational" to do so. I suggested a formula of instanteous logic 0,0|0,<0> to show how in the given moment of NOW all three aspects are present. Of course it appears to be total gibberish and nonsense.....and so it should with out the necessary support both in written and physical terms [ evidencial] Unfortunately to understand the formula we would have to set aside our current use of logic and scientific understanding which is tantamount to dumping 5000 odd years of knowledge growth and starting again with only hindsight expereince...scarey stuff and unfortunately virtually impossible to do. So are we prepared to dump atomic theory, light theory, relativity theory, conservation laws and the illusion of distance, thermodynamic theory etc etc.... nope..would be my guess. So Exnhillo stays in the too hard and too scarey basket and can never be discussed in a proper and rational way until we are prepared to leave the failing logic behind. For it must be said that in my opinion it is failing us badly. And of course if you know how the universe came into being you also know how to destroy it....entirely..... Sorry a bit of a rant...... QQ
