Niam wrote:

[...]

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

shortest

distance between two points WHICH REMAINS WITHIN THE GEOMETRY IN QUESTION.

[...]

Niam:

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

to suggest.

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

itself.

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

actuality.

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

all mathematics.

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

exists.]

I will welcome your evaluations of the matter of the concept of the

straight line.

Ralph Hertle