**1. **** ****O****ne of three hypothetical segmented lines that pictorially depict the three mutually-perpendicular**

**directions an object can move in.**

**The three vectors of Physics are called depth, breadth, and elevation****,**** with the convention that **

**height**** is typically oriented parallel with the direction of gravity of the celestial body used as **

**reference and**** width****, with the observer's horizon.**** Dimensions**** should under no circumstances be **

**confused with ****coordinates**** (****longitude, latitude, and altitude) ****or with ****vectors**** (****depth, breadth, ****and **

**elevation).**

**In Science, ****dimensions**** are static concepts. They have two properties: direction and orthogonality.**** **

**There is no such thing as a ****dimension**** without the other two. Whenever we talk about ****width****, ****we are **

**implicitly alluding to length and height****.**

**In the religion of Mathematical Physics, ****dimensions**** are ****treated as ****dynamic**** concepts****. ****The **

**dimensions**** of Mathematics have magnitude, ****but ****lack**** direction. Direction is conceptually static and **

**'made' of a single piece (i.e.continuous).**** The '****dimensions****' of ****M****ath are segmented, meaning that they **

**are composed of countless numbers. You cannot reconcile ***segmented*** with ***direction***! The idiots of **

**Mathematics are ****referring to**** number lines**** and calling them 'dimensions.'**** Number lines fit the **

**description**** of what the mathematicians are talking about****: no direction and segmented. ****Now you **

**know**** how the idiots of ****relativity**** converted ***time*** into a '****dimension****.'**** **

**In their zeal to define words ever more abstractly, the mathematicians have put so much effort in defining **

**the word vector that they have made it circular and meaningless. Contemporary definitions merely say that **

**a vector is an element of a vector space. [1] The mathematicians say that these vectors can be added, **

**subtracted, and multiplied, but you have to guess what they are talking about. There is no hint as to what a **

**vector is or what it represents. A vector space, for its part, is defined as the object of study of linear algebra. **

**And, of course, linear algebra is the study of vectors and vector spaces.**

**Fortunately, and before the record vanishes completely, we still have some documents bequeathed from **

**days of old that give us a vague idea of what a vector used to be. A vector was until recently defined as ‘a **

**directed line segment’. [2] The most popular examples were force and velocity, parameters that the **

**mathematical vector is allowed to depict pictorially because all three appear to have two properties in **

**common: magnitude and direction. [3] Both force and velocity are dynamic concepts, and this is consistent **

**with the etymology of the word vector. The word vector comes from the Latin vehere, roughly translated as **

**‘carrier’ or ‘to carry’. Therefore, from the start the word vector was intended to be used in the context of **

**motion.**

**If a vector is further alleged to have direction, again we are talking about displacement or directed motion. **

**This contrasts significantly against the conceptually static words dimension, which is reserved for contexts **

**dealing with structure, and coordinate, which has to do strictly with orientation and location. Therefore, a **

**vector is not a directed line (static object) but displacement (motion), a notion that is incongruously **

**depicted with a line capped by an arrowhead. I say incongruously because motion implies that each **

**location is on a unique frame of the film. The static vector of mathematics – the line segment – is a collage of **

**locations.**

**The issue doesn’t end there. If a vector were only a pictorial representation of rectilinear motion, there **

**would be no difference between a vector and displacement. A vector additionally embodies yet another **

**feature: it is orthogonal with respect to the other two vectors. A single vector is one of three. An object can **

**move up (or down), sideways (left or right), or forward (or backward). Of course, there are countless angles **

**in between that an object can move in. We don’t have to move north/south or east/west; we can move **

**northeast or southwest or any direction in between. However, we must distinguish between the object **

**doing the motion and the observer visualizing the scene from afar. From the object’s vantage point if the **

**object is going forward, it is by definition moving along the vector of depth. If the object is facing ‘forward’ – **

**because this is where we choose to put our eyes – but moving sideways – perpendicular to this particular **

**line of sight – then we must talk about breadth. And so on. Hence, a vector embodies not only rectilinear **

**motion, but orthogonal direction with respect to the other two.**

**What a vector of Physics does not have is this mathematical property called magnitude. A magnitude is**

**and implies that there are perpendicular angles. The object However, any of these perspectives instantly **

**becomes one of the three from the observer’s standpoint and is subsequently used as a reference for the **

**other two. The word vector is simply a useful or popular convention to designate the main directions an **

**object can move in.**

**A vector is not really a straight line, but a segmented concept. it is not a curve but a movie, a series of **

**frames on a film. Therefore, when we see a line on a graph that a relativist tells us represents the motion of a **

**particle, we are not looking at a continuous curve of distance versus time, but a movie constructed with **

**individual frames. Unlike dimensions and coordinates which are photographs, vectors are movies. hence, a **

**'position vector' is perhaps the most ridiculous and incongruous notion in relativity. To see why let's **

**translate this term for laymen. Position vector is like saying position motion or moving standstill. Again, the **

**fact that relativists use the word vector to qualify dimensions and coordinates shows how they've lost track **

**of what they have been talking about all these years.**

**Vector a is translation from point P to point Q. Then he contradicts himself by saying that a vector is **

**defined by two points. Indelible proof that relativists confuse displacement (motion of ONE object) with **

**distance (a static separation between TWO objects). The distance vector conceptually belongs to a static **

**universe whereas the displacement vector belongs to a dynamic universe. The distance vector is not really **

**a vector because vectors represent motion, not static parameters such as distance, location or position. **

**Unlike with the definition of displacement, the definition of distance makes no provision for direction, and if **

**we judge by the arrowheads, we could just as well say that distance has two of them facing diametrically. In **

**Physics, direction means only ‘direction of motion.’ Direction is a dynamic parameter. When we point with **

**our finger, we are conceptually talking about orientation, not direction. The finger is tilted to orient the **

**person to the designated place. If a vector requires both magnitude and direction, a distance is not a vector **

**because it lacks direction.**

**Rectilinear displacement is a special type of displacement (motion). Displacement in general is simply **

**motion. If we wish to quantify distance traveled, we must establish a standard and perform a measurement, **

**a comparison between the ruler and the path. Then we can state the 'length' of the path in terms of the units **

**of rulers that fit in the trajectory. But both displacement and its special brand rectilinear displacement **

**without this quantification are qualitative concepts. Displacement is a property we associate with a **

**dynamic universe.**

**Distance (gap) is a static notion: the gap or separation between two objects. Distance is a qualitative notion **

**in principle. If we wish to quantify distance, we are implicitly making a standard: a ruler and performing a **

**comparison between the number of such units that fit in this distance between two objects -- not to be con **

**fused with trajectory of one object -- and the itinerary. A measurement of gap distance or distance traveled **

**is conceptually the same. The moment we obtain a value, that value is valid only for the cross-section of **

**time, that frame of the film in which we obtained it. But this should not let us lose sight of the fact that the **

**original distance traveled (one object from its starting point) and the gap distance (between two objects) are **

**qualitative and distinct.**

**The null or position vector for its part has neither direction nor magnitude, so it does not meet either **

**requirement of a vector. The novice may have to think about the direction argument, but will likely protest **

**the magnitude issue. He’ll argue that the magnitude of the null vector is zero. The trouble is that zero is not **

**a number or magnitude. (see section xx). Null or position vectors are oxymorons. A null vector reduces to **

**‘single location’ motion. vector curvature. P. 126. direction curvature.**

**Vectors are typically drawn as straight arrows representing displacement -- sequential positions of a noun. **

**However, if the definition of vector incorporates the concepts magnitude and direction as relativists allege, **

**it appears that we are comparing two displacements. As a magnitude, displacement is established by **

**comparing two rectilinear motions, one of which we arbitrarily designate as our standard. The standard **

**moved 1 meter while the test object moved 5 meters. As a qualitative notion, such as faster or further, we are **

**still comparing two displacements. Direction, in turn, also implies a relation: right and North are undefined **

**without a reference. This is all very ironic because in the exact sciences the word displacement is defined **

**in terms of a single moving object. How is it that relativists conceptualize rectilinear motion, magnitude and **

**direction in a universe consisting of a single object?**

**The answer is that they’ve never taken the trouble. The current definition of displacement takes for granted **

**a universe filled with matter. In a universe consisting of a single object, and for the purposes of qualitative **

**displacement (motion and direction), rectilinear motion is referenced to imaginary, intrinsic vectors of the **

**object under study. Displacement is visualized as a succession of positions along one of the vectors as **

**referenced to the other two along which a given object could conceivably be moving. The solitary vector **

**breadth, for example, has direction only when tacitly referenced to depth and elevation of the object under **

**study. This rectilinear displacement can be described with three vectors depending on how we tilt our **

**points of reference. Consequently, a vector represents motion and direction in a single arrow because it is **

**implicitly referenced to the other two vectors intrinsic to the system, not to another moving object. A vector **

**does not represent quantitative displacement because this definition would require motion of another **

**object. For the same reasons a vector does not represent qualitative comparisons (e.g., faster/slower). **

**Hence, a single vector arrow (i.e., only depth, breadth or altitude) can embody qualitative direction of motion **

**(by definition) but not quantitative or qualitative displacement established via a comparison.**

**What do we intend to call vectors pointing at intermediate angles? Let’s reply with a question. What do we **

**call width when the object is tilted? How about the dimension that runs 45º to it? A lone vector that is drawn **

**at 45º is not referenced to the observer’s line of sight or to objects in the vicinity, but tacitly to imaginary **

**breadth. We leave it to physicists and mathematicians to agree on labels once they understand these **

**arguments.**

**Displacement (adv.): From an intrinsic, qualitative perspective, displacement is synonymous with vector as **

**referenced against the other two vectors intrinsic to the system. From a quantitative perspective, **

**displacement is a measure of consecutive, linear positions a 3D noun occupies as compared to a standard. **

**Displacement can also be qualitatively compared (e.g., faster/slower). **

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**Copyright © by ****Nila**** Gaede 200****8**