a
    1.0   Distance vs. distance-traveled

    Hawking tells us that forces don't act upon planets to move them around the Sun. The planets are simply
    rolling or sliding around warped space:

    "Bodies like the earth are not made to move on curved orbits by a force called
      gravity; instead, they follow the nearest thing to a straight path in a curved space,
      which is called a geodesic. A geodesic is the shortest (or longest) path between
      two nearby points." (p. 29) [1]

    Thus, he introduces one of the weirdest versions of the word line known to Man. The geodesic is an
    unscientific concoction of Mathematical Physics and fails as a line for several reasons:

    •        it is alleged to be simultaneously a noun and a verb
    •        it is alleged to be both straight and curved, rectilinear and curvilinear
    •        the 'entity' doing the motion is a location
    •        it equates distance-traveled with a geometric figure


    2.0   Is a geodesic a physical object, motion, or both?

    The mathematician presents a geodesic as a geometric figure, specifically as a straight line, or insinuates
    that he is talking about architecture:

    " a geodesic is a generalization of the notion of a 'straight line' to 'curved spaces'." [2]

    " Geodesics are locally extremes of length... Take a strong cord and stretch it tight" [3]

    " The shortest distance between two points is the length of a so-called geodesic" [4]

    " The mass of the sun curves space-time in such a way that... the earth follows a
       straight path in four-dimensional space-time. " (p. 30) [5]

    So what are we talking about? Does the infamous geodesic refer to a highway or to an itinerary along a
    highway? A road is made of dirt and perhaps asphalt. A trajectory is not made of anything except a bunch
    of abstract locations. A trajectory is a movie of an object at different locations, one location per frame of
    the film.

    So what did the mathematicians do to answer this formidable question?

    The scholars found the strategic word path which ambiguously and self-servingly embodies both
    notions. A path can be both a street and the itinerary along a street. A path is both a highway and hiking
    along the highway. In the religion of Mathematical Physics, the word path is used simultaneously as a
    noun and as a verb. It is this handy duality that makes the mathematical geodesic so formidable.

    Therefore, unless we can settle whether the mathematician is referring to an object or to motion, the
    geodesic will remain a formidable and enigmatic 'entity'. The first problem we will encounter is when we
    attempt to qualify it. Should we use adjectives or adverbs?


    3.0   Is a geodesic straight or rectilinear?

    Scientific language is radically different than ordinary speech (i.e., religion, Mathematical Physics,
    astrology, etc.). In our vernacular, the word 'motion' is a noun, and the word 'rectilinear' is an adjective, for
    example, the phrase 'rectilinear motion.'  Here the word motion serves as a noun, perhaps the subject of
    the sentence. This converts the word rectilinear into an adjective, a qualifier of a noun.

    This convention is untenable in a scientific environment. For the purposes of Science, the word motion is
    always treated as a verb. Motion is what something does; not what something is. This summarily converts
    the word rectilinear into an adverb. In Science, rectilinear is always and without exception an adverb, a
    qualifier of motion. On the other hand, for the purposes of Science, a line is always a noun (a physical
    object, a geometric figure, something with shape). This notion summarily ensures that the word straight is
    always an adjective. In Science, an adjective may only be used in the context of a physical object.

    The mathematicians have never learned these fundamental notions of Physics in high school or college,
    and this is how they ended up introducing ordinary speech in scientific contexts. This is how contem-
    porary mathematicians end up qualifying verbs with adjectives: straight trajectory, continuous motion,  
    flat space-time, rigid vector  (p. 7).

    If the infamous geodesic is supposed to be a line, we can qualify it with the adjectives straight or curved. If
    a geodesic is supposed to be an itinerary, we can qualify it with what for the purposes of science are
    adverbs:  rectilinear  or curvilinear. Of course, if the geodesic is a 'path,' meaning that it is simultaneously
    a dirt road and a bunch of footprints, then the mathematicians can alternatively invoke adjectives and
    adverbs at will when it suits their arguments:

    " space-time is not flat, as had been previously assumed: it is curved or 'warped'...
       bodies like earth are not made to move on curved orbits...instead, they follow the
       nearest thing to a straight path in a curved space " (p. 29)  [6]

    Hawking is alluding to motion but uses adjectives -- flat, curved, warped, straight -- throughout his
    dissertation. He could have used the words trajectory or itinerary, but he chooses the more convenient
    and ambiguous path. The word path is magical in Mathematical Physics because you never know what a
    mathematician is talking about. Is Hawking's term 'straight path' a highway or the footprints you left in the
    sand?Therefore, although it is clear that a geodesic is a movie of a moving object, we don't find a single
    adverb to qualify this motion in Hawking's entire presentation.  

    The bad habit the mathematicians have of equating geodesics with ‘lines’ comes from the bad habit the
    mathematicians have of depicting the motion of objects on a graph with a trace. They don’t realize that
    they are using an object (a geometric line) to represent a movie (a series of locations of one object). By
    sketching a solid line, the mathematicians are stealthily converting the movie of an itinerary into a still
    image. The geodesic of Mathematics is a collage, a row of frames of a film pasted onto a photograph. The
    infamous 'path' of Mathematical Physics is a trace, and conveniently embodies both the long streak
    marked on the paper as well as the itinerary of the pen.


    4.0   Geodesic: a dynamic location?

    The distance of Physics is conceptually a photograph whereas the distance of Mathematics is
    conceptually a motion picture. The infamous geodesic of Mathematics is therefore neither a length nor a
    distance, but rather a distance-traveled:

    " geodesics...are infinite in the two directions: one can travel along their own
       length indefinitely." [7]

    " In relativistic physics, geodesics describe the motion of point particles... the
       path taken by a falling rock, an orbiting satellite" [8]

    One problem certainly arises when not a particle, not a dot, but a location does the traveling:

    "The crossing point, near -25 for g2p7 has moved in to near -2.4, on the slope
      of hill2. A fair guess is a critical geodesic may occur when u0 is slightly lower" [9]

    [The ordered pair (x, y) moved? Oh man, that's scary!]

    If the mathematicians insist so much that their points are actually locations, how is it that they visualize
    these abstract, static concepts to suddenly acquire speed? How do you move a location? Nevertheless,  
    if the mathematical geodesic is actually a moving point, the mathematicians cannot call it a straight line.
    They can at best talk about an incessantly  moving dot. And certainly it doesn't belong in Geometry!


    5.0   Does the word geodesic belong in Geometry?

    The mathematicians tell us in their own words what a geodesic means to them:

    " On a sphere we of course cannot draw a straight line between two points, but we can
       draw a shortest line, really an arc of a great circle of the sphere. Such a line is termed a
       geodesic, and would be marked out by a smooth thread tightly stretched along the
       surface from the one point to the other. To the Filmite a geodesic will play the part of a
       straight line… " [10]

    " geodesic: A straight line is the shortest distance between two points, a straight line may
       extend infinitely far in both directions." (p. 112)  [11]
    " Euclid in his work proved that the shortest distance between two points is a line; that
       was the triangle inequality for his geometry." [12]  …triangle inequality is the theorem
       stating that for any triangle, the measure of a given side must be less than the sum of
       the other two sides but greater than the difference between the two sides."  [13]

    [Of course, if we are going to discuss lines in terms of length, the mathematicians have no
    choice but to talk about segments (i.e., finite lines). (See Bk. I, Props. 15 and 20) [14] [15] ]

    Relativists extrapolated this notion 'shortest of distances' to the geodesic, an itinerary along the surface
    of a sphere:

    " The shortest path between two points in a curved space can be found by writing the
       equation for the length of a curve, and then minimizing this length using standard
       techniques of calculus and differential equations." [16]

    Hawking is a maverick when it comes to the infamous geodesic. He has a slightly different version,
    believing that a geodesic can also be the longest distance from one location to the other on a sphere:

    “ A geodesic is the shortest (or longest) path between two nearby points.” (p. 29) [17]
     
    [Clearly, the longest distance we can travel between two points, whether on a sphere
     or on a plane, would include an erratic itinerary that conforms neither to a straight line
     nor a geodesic. The only circumstance under which the shortest and longest distances
     are identical is when we refer to a static gap. Obviously, Hawking confuses ‘physical’
     direct distance between two points (shortest/longest separation/gap) with distance
     traveled (never the longest possible trajectory). Choose the longest distance you can
     think of. I bet you I can think of a longer one. Hawking is talking about motion of one
     object (Mathematics) and switches in the middle of the conversation to separation
     between two static objects (Physics). ]

    So let’s recap the main points to understand the problem. The mathematicians say that:

    •        A geodesic is infinite in two directions (i.e., incessant walking).
    •        A geodesic is the shortest distance between two points (i.e., at some point you
    stop walking).
    •        A geodesic is also the longest distance between two points. (You walk forever
    from one point to the other?)

    A geodesic seems like a very convenient word to explain anything. It sounds like this definition is about to
    lead us to another of those un-falsifiable propositions.  

    I conclude that the mathematicians want their cake and to eat it too. A geodesic is an itinerary along the
    surface of a sphere. It does not allow the traveler to go through the sphere, for example along its diameter.
    So Hawking is unwittingly invoking two distinct definitions of distance when he says that a geodesic may
    be both the shortest AND the longest. Relativists have developed these poor habits because they don't
    define strategic words such as dimension, length, distance, and point rigorously. Then they fail to use
    their lame definitions consistently throughout the dissertation anyways.

    For instance, relativists hold that a sphere is a hollow shell or balloon, you know... like their skulls. If so,
    there is no impediment to short-circuit the geodesic with a straight line running directly through the
    interior of the sphere (Fig. 1).

    Let me run that by again. The mathematician begins his presentation by telling you that a geodesic is the
    shortest distance between two locations on a sphere. He draws a curve along its surface and calls it a
    straight line. You tell the numskull that he can draw a shorter line if he cuts through the sphere. The idiot
    replies that you cannot travel through the Earth. You must go from Buenos Aires to Tokyo around it. This,
    he tells you, is the shortest path. However, the sphere of Mathematics is defined as a hollow shell 'made'
    of 0-D points (i.e., locations).

    " the term 'sphere' refers to the surface only, so the usual sphere is a two-dimensional
       surface. The colloquial practice of using the term "sphere" to refer to the interior of a
       sphere is therefore discouraged, with the interior of the sphere (i.e., the 'solid sphere')
       being more properly termed a 'ball.' " [18]

    Pursuant to their own definition, what impediment is there to travel through the interior of a balloon as
    opposed to around its surface? To win the debate, the morons of Mathematics borrow the geodesic of
    Math and the solid sphere of Physics. The mathematicians treat the sphere as a bowling ball when it suits
    their arguments. Nevertheless, if I dig a tunnel through the Earth to go from Mexico to the US, will the
    morons of Mathematics insist that the curve they call a geodesic running through Immigration is the
    shortest path? The mathematicians of the world are a bunch of idiots! That's what they are! We have too
    much respect for them. They throw this type of logic at you in their chats and forums and want you to
    think that you are the one who has to visit the psychologist.

    ________________________________________________________________________________________


     Home                    Book WGDE                    Glossary                    Extinction   

    Last modified 02/12/08


        Copyright © by Nila Gaede 2008

    6.0   Conclusions

    If the geodesic of Mathematics is a verb, it does not belong in Geometry. The definition of architecture
    cannot be predicated on motion. We are not looking at a still image of a static geometric figure we call a
    line. We are watching a video of a trajectory. The tracing of such line necessarily involves two or more
    locations of the pen, and viewing the construction of this line necessarily invokes two or more frames of
    the film. Without the film or memory, we cannot conceive of the mathematical geodesic.

    Because it is defined as a series of discrete locations, motion is a segmented concept. Therefore, if a
    geodesic is an itinerary, it also conceptually segmented, and if it is segmented, it cannot be straight. It can
    at best be rectilinear. Indeed, in Science, it is irrational to use adjectives such as straight to qualify motion.

Fig. 1   Hollow numbskulls
Look at the red ball,
Novice Bill. You see how
it goes back and forth
when I shake the tree?
That's what we call a
geodesic in relativity!
That's a straight line!
You and your friend depart from the same location
(A) on a balloon and walk towards B. You walk
through the hollow shell along the diameter (red
itinerary) and he goes around the circumference
(green itinerary). Who has the shortest route?
Relativists allege that the green path is the shortest
route. The reason they reach this conclusion is that
they insinuate that you can’t go through the sphere
because it is a solid ball. (Perhaps they have planet
Earth in mind?) However, the official definition of the
word sphere in Mathematics is the notion of a hollow
balloon. The only reason the mathematicians can get
away with their ridiculous explanation is that they
arbitrarily invoke the geodesic of Math and the
sphere of Physics when it suits their arguments. If
tomorrow we perforate through the core of the
planet, will the idiots of Mathematics continue to
insist that a geodesic (along the surface of Earth) is
the shortest length or distance between Tokyo and
Buenos Aires?

Adapted for the Internet from:

Why God Doesn't Exist
Hawking's geodesic