I will outline briefly the basic holistic mathematical rationale by which the qualitative approach to measurement with respect to Special Relativity can occur.
Conventional Science is based qualitatively on a merely linear (i.e. 1-dimensional) interpretation of mathematical symbols. However corresponding to every number (as dimension) is a unique qualitative interpretation. So theoretically an infinite number of such interpretations is possible.
All interpretations (other than the default linear) entail a unique configuration of both linear and circular aspects of understanding.
In psychological terms this entails a complex mix of both conscious and unconscious (corresponding to rational and intuitive type appreciation).
Phenomenal quantitative measurements of space and time correspond merely to linear type understanding.
However when both linear and circular aspects are incorporated such linear measurements of space and time are seen as merely relative expressions of an underlying holistic basis of reality that exists simply as the continual present moment.
In holistic mathematical terms the precise configuration corresponding to each dimension (with respect to both linear and circular aspects of understanding) is obtained with reference to the corresponding roots of that number.
So for example to establish the qualitative nature of 2-dimensional understanding, we translate its two roots in a corresponding qualitative manner!
In this illustration we will confine ourselves to a comparison as between the (default) 1-dimensional and 2-dimensional interpretations respectively.
The key feature of 1-dimensional (linear) understanding is that it is unambiguous (relating to one positive direction of movement). So from this perspective objects move forward i.e. a positive distance in space; likewise time moves in a solely forward (positive) direction.
However 2-dimensional interpretation is much subtler in nature. Its holistic mathematical nature is obtained with reference to the two roots of unity i.e. + 1 and - 1. So from a 2-dimensional qualitative perspective, there is a valid sense in which space and time move in both a positive and negative direction.
Correct psychological appreciation of this requires recognising that actual phenomena do not exist independently (as merely external objects) but actually entail a dynamic interaction of subjective and objective aspects of understanding that are - relatively - external and internal with respect to each other.
Now if we try to treat these aspects as independent, unambiguous linear interpretation will be possible. So if we identify understanding with the external aspect of understanding (as "objects) one ambiguous direction of movement will result. Likewise if we understand understanding with the internal aspect of understanding (as "mental perceptions") an alternative ambiguous direction will result.
However if we now treat these opposite reference frames as interdependent (as befits integral appreciation) then they will move in both positive and negative directions with respect to each other. Furthermore the understanding of what is positive and negative is purely arbitrary depending on the initial reference frame chosen.
Fro example what is a left or right turn on a road depends crucially on what direction I take (i.e. "up" or "down") on the road.
Thus the analytic linear aspect of (2-dimensional) understanding corresponds to the treatment of either reference frame i.e. external or internal as independent .
The holistic circular aspect corresponds in turn to the treatment of both frames as interdependent (where space and time movements in rational terms are understood as paradoxical). Then in direct intuitive terms, this corresponds to a spiritual awareness of the continual present moment.
For example standard linear interpretation would tell us that the it takes about 8 seconds for the light of the Sun to reach Earth (travelling some 93 ml. miles in the process). So both of these measurements (with respect to space and time) are considered as positive.
However 2-dimensional interpretation would yield a more refined interpretation giving rise to two frames of reference. Now within each frame (treated as separate) both measurements will again appear as positive. However relative to each other (treated as complementary) movement is now paradoxical with both positive and negative directions of movement.
Then the intuitive realisation of such paradox is an awareness of the continual present moment as the primary basis from which the relative secondary phenomenal measurements of space and time have but an arbitrary relative meaning.
Thus the 2-dimensional interpretation is of a qualitatively distinct nature compared to the standard linear (1-dimensional) version.
This has far reaching consequences.
For example - largely as a result of Einstein's work - it is now conventionally understood that the Universe began with a Big Bang some 13 bl. years ago.
From the two-dimensional perspective this is strictly meaningless. The basic confusion here is a gross reductionism whereby interpretation with respect to the whole is not properly distinguished from interpretation with respect to the part.
Linear measurements of space and time are only possible by separating opposite polarities (such as external and internal). However clearly for the whole Universe this is not possible. We seem to forget that such linear measurements themselves crucially depend on the assumption that we can somehow separate ourselves as external psychological observers of the Universe from its original nature (which clearly is not possible).
Thus the correct starting point for a 2-dimensional interpretation is the continual present moment from which all phenomenal interpretations with respect to space and time have but a secondary - merely relative - expression.
In a primary sense the Universe is simply always now. Entering into such realisation we truly experience both its Alpha and Omega (i.e. as the present moment).
In this illustration I have dealt with the simplest possible case of integral understanding (i.e. conforming to the qualitative number dimension "2"). However all other dimensional interpretations (though much more intricate and refined) entail the same basic relationship whereby varying directions of movement (with respect to space and time) are seen as but relative phenomenal expressions of the present moment.