As we have seen, the conventional linear notion of time i.e. 1-dimensional, is based on the clear separation of polar opposites (such as internal and external).
And as the conventional scientific paradigm is based on such separation using independent polar reference frames, it directly fosters the (absolute) linear notion of time i.e. where time unambiguously moves forward in one positive direction.
However when we consider polar opposites as interdependent, this then leads to a paradoxical, merely relative, notion of time. Thus in this context, if time - relatively - moves forward in a positive direction with respect to one arbitrarily chosen polar reference frame, then equally it thereby moves backward with respect to the opposite polar frame.
So this alternative view of relative time is based on the complementarity of opposite poles of reference that are positive and negative with respect to each other.
And just as the linear view is 1-dimensional, this alternative view (of complementary real opposites) is 2-dimensional in a precise mathematical manner.
Therefore, the qualitative nature of time (as 2-dimensional) is directly related to the corresponding quantitative notion of the two mathematical roots of 1.
So 1 has two roots in quantitative terms i.e. + 1 and - 1 respectively that are considered as independent. Thus the square root of 1 is either + 1 or - 1.
However what is not recognised in conventional mathematical terms is a corresponding notion of 2 (as dimension) that is also + 1 and - 1 (in qualitative terms). However from this latter qualitative perspective + 1 and - 1 are considered as interdependent poles. Therefore from this perspective, 2-dimensional implies both positive and negative (unitary) aspects. So with respect to time, 2-dimensional implies movement with respect to time that takes place equally in both positive and negative directions.
Therefore, if with respect to one polar reference frame as arbitrarily fixed e.g. external, the movement of time is in a positive direction, then equally with respect to the alternative reference frame, it thereby - relatively - takes place in a corresponding negative direction.
Thus in terms of human experience of reality, if the movement is time is positive with respect to the external world as observed (the arbitrarily fixed reference frame) then the movement - relatively - is negative with respect to the internal self as observer.
Likewise in complementary manner, if the movement of time is now positive with respect to the internal self as observer (now the arbitrarily fixed reference frame) then it is -relatively - negative with respect to the external world as observed.
When both frames are considered as fully interdependent, the movement of time is rendered completely paradoxical as both positive and negative simultaneously.
This implies in fact that time has now but a present identity i.e. as the present moment that is continually renewed.
The very basis of the contemplative experience in the most general sense is to unify polar reference frames that are understood as separate in conventional scientific terms. Not surprisingly therefore, contemplation leads to this paradoxical experience of time where dualistic notions gradually break down.
So the pure contemplative experience is therefore of a spiritual reality that continually exists in the present moment. Then phenomenal events, in the light of such experience, are understood in a merely relative fashion.
In other words from this enlightened perspective the movement of phenomenal time in linear terms is merely of an arbitrary nature (i.e. where what is forward from one polar frame is thereby backward from the opposite frame and vice versa).
Thus in a more comprehensive scientific approach, reason and the contemplative vision would be harmoniously integrated though a paradigm that incorporates both quantitative and qualitative aspects.
When properly appreciated - as I am attempting to illustrate here with the number 2 - all mathematical symbols can be given a distinctive qualitative as well as recognised quantitative meaning. So the more comprehensive scientific approach that I suggest is based on the dynamic interaction of both aspects of meaning.
In human experience, scientific understanding is necessarily conditioned by this fundamental dynamic interaction of internal and external. Not alone is this true however of human experience, it is equally true of all phenomena in nature. For example an atom cannot relate to other atoms without implicit recognition of external and internal (which is the very basis of such interaction).
Thus the 2-dimensional notion of time equally applies throughout nature to all phenomenal interactions.
Now once again, because of the very nature of the conventional scientific paradigm, we tend to look on phenomena as if they possess a merely external (objective) identity. However strictly speaking this is ludicrous as dynamic interaction (expressing the interdependent aspect) necessarily implies an internal as well as external aspect. And once we recognise this, then all dynamic interactions with respect to external and internal are necessarily governed by the paradoxical 2-dimensional notion of time.
At a deeper level the clear recognition of both external and internal aspects relates to the fact that nature is not just physical but rather psycho physical. So strictly, all phenomenal reactions in nature entail both psychic and physical aspects.
Conventional scientists might abhor such notions (as the very antithesis of science). However as I have stated such science is based on reduced assumptions that quite frankly are ultimately untenable. In any case no one but the grossest of reductionists can reasonably deny that as human beings we do indeed possess psychic as well physical capacities. And these clearly have emerged through the process of evolution from "lower" forms of matter. Therefore if we now as humans admit such psychic capacities, then these were always thereby somehow inherent in matter (as potential for future emergence).
Indeed the 2-dimensional notion of time can provide additional perspective as to why at a deep sub-atomic level, the lifetime of particles is extremely short-lived.
By definition, such particles have yet attained very little independence (for a separate objective existence). Therefore linear notions of time scarcely apply. In fact we can properly conceive of such particles as largely defined by the confused interdependence of both their external and internal aspects. Therefore they conform much more to an existence in merely circular relative, i.e 2-dimensional time (where linear notions are rendered paradoxical).
Indeed at the other extreme of pure contemplative experience, phenomena once again can enjoy but a temporary fleeting existence (where again linear notions scarcely apply). So the 2-dimensional circular notion of time is much more appropriate to the scientific interpretation of such experience.
Finally in this contribution I wish to comment on the corresponding nature of space that characterises the 2-dimensional view.
Now quite clearly it is very similar to time. Therefore from a 2-dimensional perspective movements in space are of a merely relative paradoxical nature. This realisation indeed has very practical consequences.
For example in conventional linear terms, the distance from the Earth to the Sun is about 93 million miles (in positive terms) from Earth. However we can only attempt such measurement through an arbitrary fixing of reference frames. So fixing the reference pole with the Earth this distance is unambiguous in linear terms. Then fixing the reference frame with the Sun, the distance is again unambiguous in linear terms. However if we now attempt to relate both reference points simultaneously, measurements become merely paradoxical with what is positive from one perspective negative from the other and vice versa.
So when we succeed in relating both reference frames as interdependent, linear notions of spatial distance lose their meaning.
Once again this is the very basis of contemplative type experience. A contemplative for example could start out by considering the distance between objects in linear terms. However then the realisation that this necessarily involves dualistic reference frames would grow through the process of contemplation. And ultimately when such dualistic notions are fully dissolved, a merely present moment would be experienced. So this present moment would then apply not just to time but to space also.
So if we look now at what we conventionally refer to as the 4 dimensions of spacetime, from a 2-dimensional perspective these are understood as symmetrical with respect to both space and time.
Thus from this perspective, space has now two dimensions that are complementary i.e. relatively positive and negative with respect to each other.
Time also has two dimensions that are complementary i.e. that again are positive and negative with respect to each other.
The conventional linear perspective (where time is considered as 1-dimensional) initially served as a basis for absolute quantitative type measurements with respect to the remaining 3 "dimensions" of space. So in this very approach, through the separation of time from space there is a confusion of qualitative with quantitative notions.
When we go beyond 1-dimensional interpretation, quantitative and qualitative notions inevitably interact.
So higher dimensional appreciation of time (that then equally applies to space) is concerned directly with the nature of interaction as between quantitative and qualitative aspects. And we have illustrated this at length in the 2-dimensional case (involving external and internal poles).
However just as there are many more numbers (other than 1 and 2), there are many furter notions of higher dimensions (all of which have a direct experiential basis).
We will return to this topic in future blog entries!