As we have seen, Conventional Science is based on rational understanding of a linear logical kind which directly conforms with the qualitative interpretation of 1 (as a number dimension). And of course it is the very nature of such interpretation that qualitative notions are thereby reduced (for any relevant context) in a merely quantitative manner!
Also, as we have seen, directly associated with this approach is the interpretation of time also as 1-dimensional (where it moves in a single positive direction).
However, once we recognise that associated with all numbers is a corresponding qualitative - as well as recognised - quantitative interpretation, then potentially we can have an unlimited number of mathematical interpretations (all of which assume a certain limited validity within their appropriate relative context). This likewise entails that time (and space) itself - when appropriately understood - possesses a potentially unlimited number of possible directions (associated with varying configurations of real and imaginary aspects).
Later, we shall explore the enormous significance of this finding, in providing a fundamental explanation for the distinctive qualitative attributes that all phenomena inherently possess!
However, in this entry I wish to explore the significance of the first of the negative dimensions i.e. where time and space move in a single backward direction (both physically and psychologically) and how this dimension, though formally unrecognised, is intimately involved in all scientific understanding, especially of a creative kind.
Once again the basis of 1-dimensional interpretation (as the paradigm of what we conventionally call "science") is that polar reference frames are clearly separated with respect to formal interpretation of reality.
So typically the scientist, as for example in the case of Einstein, attempts to understand the physical world as objective (and thereby separate from subjective interaction). Even when this assumption is no longer strictly tenable as with the findings of Quantum Mechanics, the conventional paradigm fundamentally remains unchallenged. So physicists, while admitting that the findings of Quantum Mechanics appear deeply paradoxical, do not thereby accept that this exposes a fundamental problem with the existing paradigm. So, for all practical purposes, they just carry on, regardless of its non-intuitive findings.
The other key separation takes place with respect to the quantitative and qualitative poles, relating in turn to the whole and part aspects of reality. So science is understand in terms of precise quantitative type measurement (which thereby excludes interaction with its related qualitative aspects).
However momentary reflection on the matter will indicate that actual experience requires that these poles - which are formally separated in conventional scientific terms - must necessarily interact with each other. So in a richer scientific appreciation of reality, we must seek to understand the dynamic nature of such interaction in experience.
In this way, we can perhaps begin to appreciate that the conventional paradigm - whereby interaction is completely ignored in formal terms - represents but an extreme limiting case. Once again this corresponds directly with 1-dimensional interpretation. However in exploring the full range of possible dynamic interactions that can take place between poles, all the other natural numbers (and number types) as dimensions ultimately become involved.
So how does the 1st negative dimension arise?
A more refined interpretation of scientific reality entails the interaction of both external and internal aspects. So for example scientists' understanding of objective phenomena as external, cannot be ultimately divorced from their corresponding mental perceptions - which - relatively are of an internal nature. So a ceaseless dialogue therefore takes place in experience as between both objects and perceptions and at an even deeper level as between object classes and more generalised internal concepts.
The crucial point is that the actual switch from external to internal in experience always requires, to some degree, the temporary negation of what has already been posited phenomenally in an external manner. Likewise, in reverse, the corresponding switch from internal to external requires the temporary negation of what has been posited in an internal mental manner.
Put another way actual experience entails the ceaseless interaction as between both conscious and unconscious with the primary role of the unconscious in this regard to facilitate ready switching as between both poles.
Now when this takes place to a marked extent, a substantial amount of intuitive energy becomes available in experience (due to the successful fusion of both positive and negative polarities).
However when the role of the unconscious is not properly recognised, though a certain degree of switching must still implicitly be involved, little intuitive energy will be generated. Thus, rigid understanding of a conscious nature will result. Here, interpretation of objective phenomena will tend to confirm, in a somewhat absolute manner, corresponding perceptions and concepts (of these objects).
And indeed this is one great unrecognised limitation of the conventional paradigm, in that by formally ignoring altogether the role of the unconscious in scientific experience, it directly fosters such rigidity!
Therefore, though informally it may well be recognised that high levels of intuition are indeed required for truly creative scientific research, from a formal perspective its important role is completely screened out of interpretation. Not surprisingly, this leads ultimately to a somewhat distorted perspective on scientific truth.
Thus we can now perhaps better appreciate the nature of negative linear understanding (corresponding to the qualitative interpretation of - 1).
So first one posits objective phenomena externally in a rational linear fashion. This corresponds + 1 as qualitative dimension. However to posit corresponding mental constructs in a - relatively - internal manner, one must negate to a degree these objective phenomena. And then to posit phenomena once more in an external fashion, one must likewise negate the internal constructs (perceptions and concepts).
Thus, in dynamic terms, a continual process of positing and negating occurs, which enables the generation of holistic intuition. Thus in healthy scientific understanding, rational understanding is continually fuelled by holistic intuition of an unconscious kind. And such intuition can only be properly explained in a dynamic context (where opposite polarities continually interact).
So, we now see that in a true experiential context, the negative (as well as positive) 1st dimension must necessarily be involved.
This likewise entails that insofar as the negation of phenomena is concerned that time (and space) move in a - relatively - backward direction.
We can perhaps understand this better through looking psychologically at the process involved in great scientific breakthroughs.
For example, following his initial key insight regarding the equivalence of gravity and acceleration, Einstein laboured for many years in considerable darkness. Truly original work requires the development of radical new insights (of a holistic intuitive nature). However before these can shine through into consciousness, a long painful process may be required, whereby one is gradually weaned off customary rational understanding.
So quite literally, a considerable negation with respect to conventional understanding of reality takes place. and while this process is underway, it does genuinely feel as if one is, somehow, psychologically moving backwards in space and time.
Normally, from the positive linear perspective, when one works at a project, one expects a gradual accumulation of knowledge to take place. So as time and space move forward in a positive direction, one's knowledge thereby increases in a similar manner.
However where truly original insight is required to enable a decisive new breakthrough, the opposite can occur, whereby one's customary knowledge is gradually eroded with the forward movement of time (and space). One seems therefore to be going back to an earlier stage in one's development when one's knowledge was considerably less and this can thereby be associated with the experience of time (and space) moving - relatively - in a backward direction. This seemingly negative progress typically therefore leads to a feeling of disillusionment, tempting one to abandon the problem altogether.
However, it is through this process of negation (of what was formerly rationally posited in experience) that holistic intuition of a deep kind gradually incubates in the unconscious. Then when sufficiently developed in relation to the problem considered, it can then burst forth into consciousness in a new Eureka moment of wonderful discovery.
However such a key moment of enlightenment tends to be much more intuitive than rational (though later may indeed be used to support a new rational framework of understanding).
And once again in formal terms, though vital to the new discovery, such intuition is then screened entirely out of formal interpretation, which is presented misleadingly in a - solely - rational manner.
However an important observation needs to be made here. Though the process of scientific discovery in many ways is broadly similar to the process by which spiritual enlightenment is attained, one key distinction needs to be made.
The case of Einstein is in fact highly instructive in this regard. Though his General Theory of Relativity represents perhaps the single greatest breakthrough ever in physical understanding, it did not however lessen Einstein's commitment to the conventional scientific paradigm. So he basically maintained the dualistic view that objective reality could be successfully understood as independent of the enquiring mind.
However where authentic spiritual enlightenment of an advanced level is involved, the negation that takes place (with respect to former posited understanding) is so profound that one's very belief in the dualistic nature of reality becomes seriously undermined.
In other words, when applied to scientific and mathematical understanding, this entails that one can no longer accept its dualistic assumptions, for such assumptions misrepresent the nature of reality in a fundamental manner.
Thus, in normal scientific (and mathematical) discovery, both negative (allowing for the deepening of intuition) and positive linear understanding (of a rational kind) are involved. However here the (nondual) intuition involved is insufficient to undermine commitment to the overall (dualistic) paradigm of interpretation employed.
However with authentic spiritual development (leading to contemplative enlightenment) the negative aspect can be of such a profound nature that it seriously undermines commitment to this universal paradigm.
In other words, the clear implication is that one must now (explicitly) go beyond mere 1-dimensional understanding with respect to scientific (and mathematical) interpretation.
As always the psychological and physical aspects of reality are complementary in dynamic terms . This therefore employs that the negative 1-dimensional nature of time (and space) that we have just illustrated in a psychological context, equally applies to all phenomenal interactions in nature. Of course when we apply conventional 1-dimensional interpretation (of a merely positive kind) to such interactions, time (and space) will indeed appear to move in a solely forward direction!
However when we accept that physical interactions are governed by the same polarities (such as external/internal and whole/part) then the negative 1st dimension necessarily arises in the dynamic switching as between these opposite poles. Then in the extreme case, where the interaction is so dynamic that independent particles can scarcely exist, positive and negative aspects will fuse immediately in pure energy (as the physical counterpart to pure intuition).
We can see this most clearly in relation to the very nature of physical light where each photon - by definition - corresponds to its own anti-photon. So in terms of a beam of light, the positive movement in time (and space) of a photon is cancelled out entirely by the corresponding negative movement as its own anti-photon, so that light "travels" in the continual present moment! In fact within its own reference frame, both particles and waves of light have no phenomenal meaning and only - literally - appear through interaction with phenomena travelling at less than light speed!
However though the conventional paradigm preserves to a considerable degree the myth that movement in time (and space) takes place solely in a positive direction, in truth in dynamic relative terms, both positive and negative movement is necessarily involved with respect to all processes (physical and psychological).