Some mathematicians delude themselves into believing that, in order to be rigorous, a definition must include a bunch
of mathematical symbols:
- “ A line is the set of all points with coordinates (x,y) which satisfy an equation
of degree 1 in x and y, that is, a linear equation.” [1]
- Is this WHAT a line IS? Will an ET recognize this as a line?
The problems with the equation version of the line become insurmountable from the start. No one lacking a priori
knowledge would remotely equate a group of abstract mathematical symbols with a line. A geometric figure is
something you visualize with your eyes. An equation is a shorthand that allows you to calculate something if you
understand the language. Let's quickly run through other show stoppers.
• An equation has to be solved; a line need only be visualized. The group of artificial
- symbols mathematicians call an equation is not a geometric figure, but a method to
calculate a location.
- • Just as ludicrous, this calculation is applicable for a single location. The mathematician
- must repeat the procedure if he wants to visualize a series of points. He must replace
the variable with different numbers in order to produce a trace. If his calculator breaks
down after plotting the first point, the ET returns to his planet without ever having
understood what a mathematical line is or worse: mistaking it for a point.
- • The equation ax + by + c = 0 requires two inputs – x and y – to give us one location on
- a graph, but each of the components of this ordered pair (x, y) already embodies motion.
The symbol depicted as (5, 4) means that we first hop to the number 5 and then turn
northwards and look for a number 4. Only then can we mark the location with a dot.
Hence, the mathematician is feeding the computer 2 dynamic concepts to calculate one
static one. Then he plots all the static ones and again constructs a dynamic concept: an
itinerary. The equation line is conceptually circular and dynamic.
- • The equation line is a never-ending work-in-progress. We have no idea where we are
- supposed to stop calculating. The equation itself does not hold this kind of information.
Therefore, until the mathematician is through with his calculations, the ET has no idea
what the mathematician is attempting to do. Meanwhile, the ET is deprived of visualizing
one of the simplest geometric figures known to man pending ENIAC’s number-crunching.
The ET can't see the end of the mathematical line or determine whether it is finite or infinite
because the computer has yet to spit out the next point or location.
- • The set of solutions do not represent a standalone object, but rather a movie which the
- ET is required to watch from beginning to end. Each number comprising a number line
is unique and happily escorted by two guards. For any two adjacent numbers we can
conceive of another one in between. Hence, even after sitting through the entire movie
the ET must fill in most of the blanks -- the missing frames -- on his own.
The equation line of Mathematics is not a line. It is a movie of a line being built one point (meaning location)at a time
(Fig. 1). The equation line is a prescription to calculate the location of something with respect to something else. The
fact that our misguided mathematicians replace each location with a dot and call the result a line only shows that the
mathematicians don't speak for Physics. The number line is not a noun, but rather a verb. Unlike the line of Physics,
it is a segmented concept and an eternal work in progress.
| The equation line |
| Adapted for the Internet from: Why God Doesn't Exist |
- 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. The hinge
4. Hilbert's two bit line
5. Weyl's shortest distance
6. Hawking's geodesic
7. Anderson's footprints
8. Weyl's idiotic all-in-one line
9. This page: The equation line
10. So then, what is a line?
On our planet it's not that simple. We must first
calculate each point with a computer and
determine its exact coordinates. Then we take
a photograph of each location and make a film.
Finally, we show the movie to our students.
calculate each point with a computer and
determine its exact coordinates. Then we take
a photograph of each location and make a film.
Finally, we show the movie to our students.
| Man, that's the weirdest thing I ever... All that just to see a line? |
Fig. 1 |
| Is the equation line constructed with dots or locations? |
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- Copyright © by Nila Gaede 2008