I will elaborate here on the holistic mathematical significance of the symbols 2iπ, which play a central role with respect to the (fundamental) Euler Identity.
Now 2π represents the circumference of the (real) unit circle (i.e. with radius 1). Therefore, 2iπ can be expressed as the circumference of the corresponding "imaginary" circle (with radius i). However what does one holistically mean by "imaginary" in this context?
Well, the holistic meaning of "imaginary" represents the indirect attempt to express the dynamic complementary notion of the union of opposites (i.e. + 1 and – 1) in the standard rational manner.
What this in effect means is that when the pure intuitive notion (represented by the complementarity of opposites) is fully realised in experience, any remaining linear notion of + 1 and – 1 as representing separate notions of distance are dissolved.
This can be easily seen through drawing the unit circle with its line diameter horizontally through its centre. Therefore the distance to the right of the mid-point is + 1 and the distance to the left – 1 respectively.
Now when the pure fusion of these opposite poles takes place in an intuitive manner, any remaining linear identification of + 1 and – 1 as being separate is thereby dissolved. So the situation is akin to a circle that now has shrunk to its midpoint (where its circular circumference is indistinguishable from its line diameter).
Therefore, quite literally, in a precise holistic mathematical manner, 2iπ represents now the important notion of a dimension as a single point (without quantitative characteristics).
Interestingly in Christian spiritual mystical literature this stage of contemplative realisation is likewise often represented by a point (as the point or apex of one's being). In Hindu literature the word "bindu" is used, which likewise carries the same connotation of "a point" , though now given a more impersonal meaning as the "seed", as it were, that potentially contains all of creation.
Indeed in more modern physical terms, we could refer to this point as a singularity (which likewise carries the potential sense of containing all creation).
However if the transcendent is later to be united with the corresponding immanent direction, it is important to appreciate this notion of point in both a personal and impersonal manner i.e. as the pure centre of one's personal being and likewise as the pure cosmic centre of the impersonal universe. And of course ultimately both meanings should be united in the same undivided experience!
I will also comment here briefly on the holistic mathematical significance of e (which as base number is raised to the dimensional power of 2iπ).
In conventional mathematical terms, e is unique in the sense that when we raise e to a power x, its differential (and of course corresponding integral) expression) remains unchanged.
So if y = ex , dy/dx = ex .
The holistic mathematical significance is likewise remarkable and revealing, for it implies the state where differentiation in psychological experience becomes dynamically indistinguishable from corresponding integration. In other words, when contemplative experience becomes highly refined, it no longer becomes possible to distinguish distinct phenomena of form (as differentiated) from the continuous experience of spiritual emptiness (as integrated).
Not surprisingly, this coincides with the arrival at that still point as the centre of being. And when both of these are simultaneously related, we have the pure notion of oneness as the transcendent holistic spiritual experience of the interdependence of everything (which is beyond all form).
However certain limitations with respect to this initial experience of pure transcendence are likely to remain.
The fact is that a point or dot (though without distinct physical characteristics) must still be given a specific location to have meaning.
Likewise in psycho spiritual terms, the arrival at the pure point of being implies that a certain attachment must still necessarily pertain to the volitional aspect of the will (which this point represents).
This means in effect that a certain conscious attachment will still exist at the "higher" aspect of personality with respect to the very desire to do what spiritually is deemed most appropriate in experience.
This likewise entails that a corresponding compensatory attachment will remain at the "lower" physical level of personality, that necessarily remains of an (unrecognised) unconscious nature.
In other words primitive physical projections of an involuntary nature therefore will still be emitted into consciousness.
In this way during Level 1 (Band 4) the "higher" spiritual self still attempts to exercise - to a degree - undue dominance over the "lower" instinctive self.
So this unfortunate tendency then needs to be addressed at the next stage.
Now 2π represents the circumference of the (real) unit circle (i.e. with radius 1). Therefore, 2iπ can be expressed as the circumference of the corresponding "imaginary" circle (with radius i). However what does one holistically mean by "imaginary" in this context?
Well, the holistic meaning of "imaginary" represents the indirect attempt to express the dynamic complementary notion of the union of opposites (i.e. + 1 and – 1) in the standard rational manner.
What this in effect means is that when the pure intuitive notion (represented by the complementarity of opposites) is fully realised in experience, any remaining linear notion of + 1 and – 1 as representing separate notions of distance are dissolved.
This can be easily seen through drawing the unit circle with its line diameter horizontally through its centre. Therefore the distance to the right of the mid-point is + 1 and the distance to the left – 1 respectively.
Now when the pure fusion of these opposite poles takes place in an intuitive manner, any remaining linear identification of + 1 and – 1 as being separate is thereby dissolved. So the situation is akin to a circle that now has shrunk to its midpoint (where its circular circumference is indistinguishable from its line diameter).
Therefore, quite literally, in a precise holistic mathematical manner, 2iπ represents now the important notion of a dimension as a single point (without quantitative characteristics).
Interestingly in Christian spiritual mystical literature this stage of contemplative realisation is likewise often represented by a point (as the point or apex of one's being). In Hindu literature the word "bindu" is used, which likewise carries the same connotation of "a point" , though now given a more impersonal meaning as the "seed", as it were, that potentially contains all of creation.
Indeed in more modern physical terms, we could refer to this point as a singularity (which likewise carries the potential sense of containing all creation).
However if the transcendent is later to be united with the corresponding immanent direction, it is important to appreciate this notion of point in both a personal and impersonal manner i.e. as the pure centre of one's personal being and likewise as the pure cosmic centre of the impersonal universe. And of course ultimately both meanings should be united in the same undivided experience!
I will also comment here briefly on the holistic mathematical significance of e (which as base number is raised to the dimensional power of 2iπ).
In conventional mathematical terms, e is unique in the sense that when we raise e to a power x, its differential (and of course corresponding integral) expression) remains unchanged.
So if y = ex , dy/dx = ex .
The holistic mathematical significance is likewise remarkable and revealing, for it implies the state where differentiation in psychological experience becomes dynamically indistinguishable from corresponding integration. In other words, when contemplative experience becomes highly refined, it no longer becomes possible to distinguish distinct phenomena of form (as differentiated) from the continuous experience of spiritual emptiness (as integrated).
Not surprisingly, this coincides with the arrival at that still point as the centre of being. And when both of these are simultaneously related, we have the pure notion of oneness as the transcendent holistic spiritual experience of the interdependence of everything (which is beyond all form).
However certain limitations with respect to this initial experience of pure transcendence are likely to remain.
The fact is that a point or dot (though without distinct physical characteristics) must still be given a specific location to have meaning.
Likewise in psycho spiritual terms, the arrival at the pure point of being implies that a certain attachment must still necessarily pertain to the volitional aspect of the will (which this point represents).
This means in effect that a certain conscious attachment will still exist at the "higher" aspect of personality with respect to the very desire to do what spiritually is deemed most appropriate in experience.
This likewise entails that a corresponding compensatory attachment will remain at the "lower" physical level of personality, that necessarily remains of an (unrecognised) unconscious nature.
In other words primitive physical projections of an involuntary nature therefore will still be emitted into consciousness.
In this way during Level 1 (Band 4) the "higher" spiritual self still attempts to exercise - to a degree - undue dominance over the "lower" instinctive self.
So this unfortunate tendency then needs to be addressed at the next stage.
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