eureka

In a nutshell
seven steps to understanding natural science.

Numbers are Ratios
The word ‘one’ (1) refers to a specific pre-agreed definition of that which constitutes the type of object or event of current specific interest. All other ‘numbers’ are pure dimensionless ratios which represent some quantity (ie, number) of the specifically pre-defined object or event divided by one (1) predefined unit for that object or event. For example, the phrase 'five apples' is verbal code for the thought that there are five objects of that type of object which we have defined as one apple. In mathematical symbology the phrase should be presented as the ratio: 5 apples/1 apple.
All Numbers are void of dimensional characteristics
By standard mathematical procedure, the name assigned to the type of object of interest appears in both the numerator and denominator of the ratio, and is therefore self-canceling from both numerator and denominator. The result is a pure dimensionless ‘number’. The process of carrying the name of the type of units of interest forward with the number is a verbal shortcut, and that shortcut must be recognized when the thought is translated into mathematical symbology.
The only real time is now
Time is not a reality which flows like water in a river. Time is simply a 'placemarker' for one current real instantaneous state of relativity between all of the perceived ‘parts’ of our universe. All prior and future instantaneous states of relativity exist not in reality, but only in our mental thoughts or documented imagination (symbology).
Time is a convenient tool created by man to organize the sequence of changes in instantaneous states of existence. A tool similar to the page numbers which we use to note our current place within a book. Each instantaneous state of relativity is similar to one still frame of a movie film. As we observe a movie we mentally convert that sequence of separate still photographic frames into a concept of a continuous 'flow' of both time and change - but that mental conversion is not representative of the 'real' content on the strip of film.
Time duration is a dimensionless ratio of some quantity of unit values of time duration (such as seconds, hours, or days) to the pre-defined unit value itself. As such the concept of time duration is a purely imaginary factor whose mathematical value is totally dependent on any pre-definition of the 'unit' value of time duration.
The mathematics of motion
During two separate observations, the relative location between objects may change. We use the word 'motion' to report such a change. The observation of that change (motion) is indeed real, and a report that motion did occur is therefore true. However that simple truth contains no information about the direction or quantity of change which was perceived. More significantly, unless we assume that man has an ability to perceive motion instantaneously, rather than only during some real lapse of time, then it is impossible to be certain that motion continues to exist during the current instant of time.
To quantify the term 'motion', man first created the mathematical concept of 'speed' which enabled him to assign a magnitude for the motion. Speed is a mathematical ratio comparing two other ratios defined as the number of pre-defined units of distance of change which occurred during a corresponding number of pre-defined units of time lapse. Note that the resultant mathematical value of speed is totally dependent on the pre-definition of the unitary measure for both distance and time duration. And the pre-definition of those unitary measures was almost certainly totally irrelevant to the current observation of interest.
To further quantify the motion, man then created the mathematical concept of a coordinate system so that he could communicate about the corresponding 'direction' of the change in motion. But again, note that the choice of the imaginary coordinate system may be totally irrelevant to the observation of current interest, and may be defined in any of an infinite number of formats in Cartesian or polar systems which are may be based on either static or mobile base points.
While the concept that relative motion is (or was) occurring is a true statement of reality, the statements used by man to quantify that motion in terms of speed and direction are based on imaginary mathematics. And the mathematical values are totally dependent of arbitrary pre-defined unit values and coordinate systems.
It is also interesting to note that the process of dividing one type of dimension (distance) by another (time) is contradictory to the rules of ‘dimensional analysis’ - a process which all beginning students of science are told must be avoided. It is through the creation of the word 'speed' or 'velocity', and insertion of that word on the opposite side of the equality sign that the improper equation is rebalanced to satisfy the demands of dimensional analysis.
When the concept of speed is carefully analyzed it becomes evident that the creation of a ratio of distance-to-time is parallel to a creation of a ratio of apples-to-oranges and then justifying the existence of the ratio though creation of a new word (maybe apanges?). Given enough time and formal training, perhaps man would begin to believe that the concept of apanges was logical and that the mental division of a dozen apples divided by one orange produces a natural reality of 12 apanges?
While the existence of relative motion between any two objects is a natural phenomena, the associated numbers and equations have meaning only in man's own imagination. However, as a result of extensive reference to the concepts of numbers and mathematics, man currently tends to believe that those conveniences of words and numbers are the reality of nature. Due to long term conventions which are reinforced by the educational process, man currently tends to think of the concept of motion as being a characteristic which is 'owned' by a specific object of current interest. For example, we may refer to the speed (or velocity) of an automobile as being '60 miles per hour'. Such statements conceal the actual reality that the velocity is only true when related to a 'fixed' point on the surface of the Earth, and that imaginary value of velocity is totally dependent on an arbitrary choice of unit values for the dimensions of both time and space.
The Mathematics of Acceleration
When two observations (two perceived states of instantaneous relative separation distance) of two selected objects are known, man may manipulate that information to determine a ratio named motion, or average speed, or average velocity. Omission of the word 'average' may cause a major error in thought transmission because the actual path (and distance) through which the object moved between the two observations is unknown. If the path was non-linear, then there may be a great difference between the actual and calculated speeds and velocity.
If at least three observations are known, then man may calculate a value of speed and direction between the first two and the last two of the three observations in the manner discussed above. He may then compare the two values of velocity which he has derived.
If the velocity is perceived to be constant then the motion is called 'linear motion'. (Note that this may be a false assumption, because the actual path between any two consecutive observations may not have actually been linear.
If the motion is linear, and the mathematical values of speed assumed to have remained unchanged between the first and last pair of observations, then the concept named 'acceleration' is considered irrelevant and given a mathematical value of zero.
If however, the motion is linear, but the computed values of speed are not identical, then by definition, the term 'linear acceleration' is said to have occurred, and another mathematical equation was created to establish a value for the associated linear ‘acceleration’.
On the other hand, if the motion is non-linear, but the values of speed are identical, then by definition, the term 'radial acceleration' (or centripetal or centrifugal acceleration) is said to have occurred. In which case an assumption is made that the path of the object traced through a perfectly circular arc between all three of the observed locations. Mathematical techniques are then used to create a value for an imagined radius of that imagined perfectly circular path, and still another equation was created to express the mathematical value of the radial acceleration.
As a result of dogmatic education about the end equations pertaining to linear and radial acceleration, there has been a tendency for current scientific scholars to overlook all of the questionable assumptions which those terms include. And again, current scholars tend to assume that the equations represent the reality of nature, while the true reality of motion is thought of as simply an interesting 'owned characteristic' of one single object.
While the concepts of linear and radial acceleration seem at first to be completely different in basic nature, it can be easily shown that the same form of mathematics used to define the two terms can be used to show how the resultant mathematical values are interchangeable. Explain this
Radial and Linear Acceleration Values are interchangeable
Even though the concepts of linear and radial acceleration seem to be unrelated, it is not difficult to recognize that a simple means is available to show that the mathematical value associated with either form can be converted into a mathematical identity of the opposite form. This is possible by simply working through the mathematical assumptions in reverse order.
To convert the mathematical value for linear acceleration to equal value of radial acceleration, imagine a perfectly circular arc having both radius and arc length equal to the value of the change in 'linear velocity' which occurred during one pre-defined unit of time duration. Assign that mathematical value to an imaginary circle, and imagine that an object traces through one radian of angle along that imaginary circle during the same pre-defined unit of time duration. The resultant mathematical values for linear acceleration imagined to exist based on observation will be identical to the mathematical value of the imagined object which moves along the circular arc. In mathematical terms dV/dT = V^2/R.
To convert the mathematical value of a perceived radial acceleration to equal value of linear acceleration set the mathematical value of difference between the first and last linear velocities during one pre-defined unit of time lapse equal to the mathematical value for the length of the imagined radius on which the mathematical value for the radial acceleration was based. The resultant values of perceived radial and imagined linear acceleration are then identical. Explain this
Force and Mass are mathematical idenities
In a prior section of this document pertaining to the history of time and space, it was discussed how the concepts of a natural 'magic' inertial resistance force which is directly proportional to an applied force was demonstrated by Galileo's work. And that the ratio of the applied force to the inertial resistance force is a mathematical constant equal to the factor we currently call 'acceleration'. It was also discussed that these findings (in Galileo's experiments) were misconstrued by Newton when he created the concepts of 'mass' and variable 'acceleration'.
With that history in mind, and the recognition that it is impossible to apply a force to any object unless that object 'pushes back' or resists with an equal and opposite force, we can recognize that the factor we call 'inertial resistance' is that same factor of equal and opposite force.
The mathematical value of ‘force’ and ‘mass’ are identities simply because 'mass' is only a word which Newton's created to replace the 'magic' inertial resistance force which was proven by Galileo's experiments. 'Mass' is simply natures equal and opposite reaction to rebalance any force which is applied in an attempt to cause a change in the current instantaneous state of natural balance of forces (or state of motion) throughout the universe. Mass is not a constant factor attributable to individual objects - it is a variable factor better recognized in the form of that 'magic' force which is directly proportional to any applied force. When the force being applied to an object ceases to exist, the 'mass' of that object also ceases to exist.
The only reason that the mathematical value which man assigns to the 'mass' of an object differs from the mathematical value which man assigns to the 'force' which may be applied to that same object is that science has not yet recognized either the errors in Newton's definition of 'mass', nor the relative equivalency between time and space which is inherent in the word 'velocity'. If man had initially selected the unit value of 'distance' as 1/32.2 foot (rather than 1.0 foot) then perhaps it would have been more apparent to both Galileo and Newton that force, inertia, and 'mass' are identical mathematical values.
That same error has been carried forward in many other mathematical equations used to define the factors named momentum, work, and energy. And also into many currently accepted scientific concepts associated with potential versus kinetic energy and wave length versus frequency.
Impact of above
Upon recognition of the above, we arrive at the recognition that every known factor which man has imagined to exist pertaining to motion, and associated forces are simply different mathematical treatments of one true natural change which is the existence (or lack thereof) of current instantaneous state of motion.
While not detailed in the above, the currently accepted scientific-mathamatic concept referred to as 'dimensional analysis' is erroneous. The error is inherent in the belief that various factors of time, space, and force are separate natural occurrences, rather than separate mathematical perceptions of one single state of reality. During the history of our currently accepted state of science, the established rules for dimensional analysis were circumvented by simply creating a new word (such as velocity, acceleration, mass, etc) whenever those rules were violated. The creation of such words tended to obscure the reality of the equivalency of the dimensions of time, space, and force.
For example, the statement that 'velocity' is the rate of change of an object expressed in units of distance per unit of time, conceals the reality that any specified value of velocity is actually a statement of the equivalency of the quantity of pre-specified units of distance which is an identity to one pre-specified unit of time, and that identity applies only for the object said to possess the factor of 'velocity' relative to some other unstated - but assumed - reference coordinate system (such as the surface of the Earth).
The currently accepted concepts of physical science are not concepts about nature - they are concepts about words and mathematics which have been created by man himself.
EXAMPLES
Some QUICKIES
MOTION ('velocity' is meaningless)
ACCELERATION ('gravity' without mass)
OUR EYES ARE RIGHT (mental 'mutney')

RETURN TO INDEX
RETURN TO INTRODUCTION