1.0 The mathematical hinge
Some mathematicians define a line as an axis of rotation:
“ axis: a straight line through the center of a plane or a solid figure...” [1]
“ we regard the straight line as an axis of rotation.” (p. 12) [2]
“ An axis is a line” [3]
An axis, for its part, is the meeting of two planes:
“ If two planes cut one another, then their intersection is a straight line.” (Bk. XI,
Prop. 3) [4]
“ If a body has two mutually perpendicular planes of symmetry, their line of inter-
section is an axis.” [5]
“ To define a line, you need to intersect two planes.” [6]
“ Two planes are either parallel or they intersect in a line.” [7]
“ Axis: The term is also used to refer to a line through a sheaf of planes.” [8]
There are at least two problems with the 'axis' definition of line.
- • it is circular
• it is a proof and not a definition
2.0 Circular definition
The mathematicians define a plane as a series of contiguous lines or as lines that intersect:
- “ A plane surface is a surface which lies evenly with the straight lines on itself.”
(Bk. I, Def. 7) [9]
“ plane: two different lines which intersect… two different lines which are
parallel” [10]
“ Lines are used to construct all other figures in plane geometry, including angles,
triangles, squares, trapezoids, circles, and so on.” [11]
In other words, the mathematicians use the word line to define a plane and the word plane to define a
line! Again, the mathematicians give lip service to definitions and routinely rely on circular definitions,
synonyms, and proofs to present their theories. This is ironic because it is exactly the situation they
wanted to avoid by not defining what they regard as 'primitive' terms.
3.0 Proving a definition
The hinge version of Mathematics is an attempt to prove what a line or axis is. The mathematicians are
saying that if you want to know what a line is you must revolve a door 360 degrees.
In Science, however, we do not prove definitions. We do not run a test or carry out an experiment to
certify whether a definition is true. A definition is a set of limitations that a prosecutor places on a word.
The role of the juror is to check the definition for logic and consistency.
| The hinge |
| Adapted for the Internet from: Why God Doesn't Exist |
| Everything is rotating round and, hic, round. |
- Module main page: A line is NOT the shortest distance between two points
Pages in this module:
- 1. The primitive line
2. Endless breath: Euclid's breadthless length
3. This page: The hinge
4. Hilbert's two bit line
5. Is a line continuous or segmented?
6. Weyl's shortest distance
7. Hawking's geodesic
8. Anderson's footprints
9. Weyl's idiotic all-in-one line
10. The equation line
11. So then, what is a line?
- ________________________________________________________________________________________
- Copyright © by Nila Gaede 2008