understanding of the mechanisms involved, as was the practice prior to Dr.
Einstein's work. (In the case of GTR, one of the errors was the fact that
the definition of a straight line currently in use is inadequate even for
Euclidean geometry. A straight line is more properly defined as the
distance between two points WHICH REMAINS WITHIN THE GEOMETRY IN QUESTION.
I respect your work, and it appears that you are making valid scholarly
and scientific constructive criticisms of the matters that are so
popular in modern science.
You may want to check one definition.
I am an architect and student of geometry, and I found that the
definition of a straight line that you state is not exactly correct. I
realize that the context of physics is not the same as that of the
hierarchical science of geometry, however, here is the point that I wish
Euclid did not define the straight line as,
"A straight line is more properly defined as the shortest
distance between two points."
Euclid's definition given in "The ELements", Book 1, is,
Defn. 4: A straight line is a line which lies evenly with the points on
The prior three definitions that are essential due to the Aristotelian
system of hierarchical definitions that Euclid uses are,
Defn. 1 A point is that which has not part.
Defn. 2 A line is breadthless length.
Defn. 3 The extremities of a line are points.
Re. Defn 4, of the straight line, the principle of even-ness is the
differentia of the definition, or essential defining characteristic. The
genus of the definition, or wider class of ideas for the concept, is the
line that is the magnitude [meaning 'scientific concept' the the Ancient
Greek geometers] of length, and of course, the differentia of the
concept line is that it is breadthless.
The definition of a postulate is in order, here.
* A postulate is a demonstration of an axiom or axiomatic concept [the
latter meaning scientific concept or principle] either in logic or in
That's my definition, and it is consistent with Euclid's usage of the
term, postulate, in every instance. A Postulate to Euclid is NOT an
axiom or assumption. Those are incorrect modernist uses of terms that
greatly modify the hierarchy of the concepts of geometry, and probably
Euclid's Postulates regarding this matter of a straight line are,
Post. 1 Let the following be postulated: to draw a straight line from
every point to every point.
Post. 2 To produce a finite straight line continuously in a straight line.
Note that Postulate 1. demonstrates the universality of the concepts,
e.g., that one can demonstrate finite straight lines as a matter of
principle and as a matter of actuality.
Note, also, that Postulate 2 demonstrates the principle of the
universality of the concept, e.g., that it is both finite [meaning it is
an epistemological concept, or idea, as in mathematical concepts given
number], and that its principle is everywhere the same.
That a line or straight line may be extended a selected or chance length
is a matter that is a proposition, and because extension is a
non-essential non-defining characteristic, in "The Elements" it is given
status as a proposition to be proved later.
The concept of some length is the genus of the concept of a straight
line, however, to say that the entity is the shortest length possible
that connects two end points is to reduce the definition to a single
particular instance. In Euclid the principle of length is all that is
necessary, and that may be the length of a curled strand of thread, for
example. The concept of even-ness is the essential defining concept, and
that means that for every length one may conceive of a length that has a
type of order or organization such that it is everywhere consistent
according to its principle.
A lemma for the concept of a point that is given by Euclid, and that may
have been in use prior to Euclid, is that a point is that which has
location only. Selected or chance location is one of the characteristics
of a point, and if that idea were transliterated into a postulate one
would demonstrate in ideas a coordinate location or draw a point at a
specific location with a dot.
To define a straight line as the shortest length between two such points
is to say that only one such line between such points is possible. That
means that the universal defining principle of the straight line of
even-ness has been dropped from the definition, while at the same time
it has been assumed in the two-point concept. That is the fallacy of the
stolen concept, and additionally, it is an example of the fallacy of
post hoc ergo propter hoc, in that the thing proved is in the proof of
the thing being defined.
That's what I have to say regarding a straight line.
Where the use of the modern two-point definition causes troubles in
physics is in the creationist-expansionist's hypothesis of the expansion
of the Big Bang, for example. A star is seen to have red shifted light.
Ignoring for the time being that there may be causes for the energy
reduction of light that do not necessarily involve the star moving away
from the observer, e.g., that photons loose some of their energy in
interactions with hydrogen atoms or molecules in space. The BB advocates
assume the star is moving away claiming the Doppler Effect as the cause
while simultaneously ignoring the evidence of energy loss in
photon-hydrogen interactions. The hydrogen evidence would allow that the
star may not be moving with respect to the observer. The star, for the
time being is considered motionless as a point. Point A, that is. The
second point of the straight line is claimed to be the location of the
star having moved. That is point B. A straight line is drawn as an idea
from point A to point B, and the straight line is additionally extended
a selected distance. The distance selected is the extension of the
straight line to the intersection of the straight line extended from
another star that is also red shifted. That involves a lot of Euclidean
geometry, and that Euclidean mental drawing work is kept out of
discussion, e.g., kept secret or out of science, due to the popular
consensus that only Non-Euclidean geometry is correct. That's another
example of the fallacy of the stolen concept. The intersection, of
course, say the [religionist] creationist-expansionists, is the origin
point of dimensional motion of all physical, and also, mathematical,
existents in the universe. There is no physical evidence that the
claimed point of origin exists or ever did exist. Continuing that
explanation a little further, one may find that the religionists want to
deny that the universe is a continuing plurality of physical existents.
[My definition of the concept of the universe, that is, everything that
I will welcome your evaluations of the matter of the concept of the