tag:blogger.com,1999:blog-77251478226472725422017-06-21T19:55:35.646-07:00Integral ScienceAn alternative qualitative appreciation of science based on the holistic interpretation of mathematical symbolsPeter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.comBlogger112125tag:blogger.com,1999:blog-7725147822647272542.post-22331968263181662322015-03-31T03:26:00.001-07:002017-04-17T04:15:19.761-07:00The Rainbow - Where Science meets ArtWe have been discussing the notion of rainbow gravity and how it challenges conventional notions of the Big Bang!<br /><br />In fact the deeper implications of what is involved here require the recognition that scientific reality properly contains both analytic (quantitative) and qualitative (holistic) aspects, in dynamic relationship with each other.<br /><br />Therefore conventional scientific understanding is continually limited by the attempt to reduce reality in a merely quantitative impersonal manner (as detached from the observing mind).<br /><br />So when we allow for both scientific aspects, this allows for the local independence of events (in analytic terms) combined with the universal interdependence of all events (in a holistic manner).<br /><br />When this is done it leads to a fundamental change in perspective, especially with relation to our understanding of space and time.<br /><br /><br />Following Newton, space and time were understood in neutral terms as simply constituting a pre-existing background where phenomenal activity takes place.<br /><br />Then because of Einstein, it was realised that these dimensions have strictly no physical meaning independent of material phenomena.<br /><br />However Einstein still believed that this relative nature of space and time could be precisely formulated in an objective fashion.<br /><br />However once we incorporate both the analytic and holistic aspects of scientific understanding an inescapable Uncertainty Principle now attaches to the very nature of space and time.<br /><br />Put another way, relativity is now seen - not alone physically as applying to the nature of space and time - but equally in psychological terms to the mental constructs we use to understand these very dimensions.<br /><br />This ultimately entails that every event takes place in a unique framework with respect to both space and time.<br /><br />Thus from the accepted analytic perspective, each phenomenal object (as scientifically investigated) has a unique location in space and time. And this location is only possible due to all objects sharing a common impersonal identity!<br /><br />However from the corresponding holistic (qualitative) perspective, each object now assumes a unique qualitative identity, with no means therefore for establishing a local identity (in space and time).<br /><br />So properly understood, the non local behaviour of quantum particles relates to their holistic rather than analytic aspect!<br /><br />However this cannot be appreciated within a scientific paradigm that recognises solely the analytic aspect of interpretation!<br /><br />Thus once again, the deeper conclusion that can be reached here is that, the qualitative aspects of phenomena (at both micro and macro levels) entail unique configurations with respect to space and time.<br /><br />In other words, phenomenal objects now enjoy their unique qualities precisely because they relate to space and time configurations that are themselves unique.<br /><br />Therefore once again, this truth cannot possibly be approached while we remain confined to the conventional scientific paradigm (based on mere analytic interpretation).<br /><br /><br />We have been speaking about the rainbow (i.e. in relation to rainbow gravity). In fact the rainbow serves as an excellent example of a phenomenon with both quantitative and qualitative attributes. <br /><br />The conventional scientist can indeed give a convincing explanation for the rainbow phenomenon (relating to the reflection and refraction of sunlight with respect to water droplets). This explanation therefore appeals primarily to the cognitive function of reason.<br /><br />However the artistic experience of the rainbow would be somewhat different. Who for example has not at some stage found oneself rapt in wonder at the beautiful sight of a vibrantly coloured rainbow!<br /><br />Such an aesthetic appreciation appeals now primarily to the affective function of emotion! <br /><br />And indeed in the end it is somewhat artificial to attempt to neatly divide both types of experience for they necessarily intermingle with each other to a significant degree.<br /><br />So the total experience of appreciating a rainbow thereby necessarily combines both reason and emotion in a quantitative and qualitative type manner.<br /><br />However what we call science, then attempts to represent the experience, as if the quantitative aspect somehow can exist in absolute abstraction from the qualitative. <br /><br />Thus the crucially important task, which has not yet been addressed, relates to how the qualitative aspect - which necessarily applies to all phenomena - can be successfully incorporated with the quantitative, in a new more comprehensive form of scientific understanding.<br /><br />Now, I would still accept that this still needs to be achieved in a refined cognitive manner, where the translation of the qualitative aspect is understood in an indirect rational manner.<br /><br />However I would firmly believe that the ultimate task of such understanding is to pave the way for the full reconciliation in experience of scientific (rational) and artistic (aesthetic) aspects.<br /><br /><br />If we go back to the time of the Renaissance, before the specialised development of Newtonian type science, we can witness a much greater integration with respect to both the scientific and artistic quests.<br /><br />Perhaps this exemplified more than anyone by the life of Leonardo da Vinci who displayed supreme scientific and artistic gifts. <br /><br />Now it can indeed be argued that science was - certainly in terms of modern developments - still in its infancy at the time. So the specialised development of analytic science was thereby necessary to differentiate it successfully from other activities, subsequently enabling unparalleled progress.<br /><br />However the cracks in the modern scientific edifice have been long apparent and cannot be solved within the present restricted approach.<br /><br />Thus we need to rediscover in a much more comprehensive fashion the notion of Holistic Science (relating to the global interdependence of all reality). Then, ultimately both the analytic and holistic aspects can be combined in an ever more creative and productive manner (i.e. Radial Science). Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-17194102594024053082015-03-30T03:37:00.000-07:002017-04-17T04:11:11.576-07:00The Big Bang and Rainbow Gravity (2)<span style="font-family: inherit;">I mentioned in the last blog entry how there are in fact two interacting aspects (physical and psychological) to the relative experience of the nature of time and space.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Thus from the physical perspective, if a car is travelling at 120 mph then with respect to measurement by a stationary observer it will take just 30 seconds to travel 1 mile.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">However, when measured from the perspective of a person travelling in the car, the measured time to travel the mile would be slightly less i.e. 29.99999999999952 seconds. </span><br /><span style="font-family: inherit;">Now of course this slight difference would not be detectable with present time measurement devices. However if it were possible to imagine the car travelling at say 87% of light speed, then the measured time to travel the mile (from an occupant within the car) would be just half of that as registered by a stationary observer.</span><br /><span style="font-family: inherit;"><br />So in this sense, measurements are relative to the speed of the observer estimating both the time and distance involved.</span><br /><span style="font-family: inherit;"><br /><br />However there is equally a important sense - not yet properly recognised - in which both time and space measurements are likewise relative with respect to the dimensional manner in which psychological interpretation take place. </span><br /><span style="font-family: inherit;"><br />Conventional interpretation from this qualitative perspective is strictly linear (i.e. 1-dimensional). This is enshrined in the very notion that the Big Bang had a definite beginning in time and space some 13.8 bl. years ago!</span><br /><span style="font-family: inherit;"><br />Now the very nature of 1 as a dimension is that it is unambiguous with respect to its corresponding inverse meaning i.e. as reciprocal.</span><br /><span style="font-family: inherit;"><br />However associated with the "higher" stages of refined contemplative type understanding, are corresponding "higher" dimensions of which the most accessible relates to 2-dimensional appreciation. </span><br /><span style="font-family: inherit;"><br />But the very nature of such understanding is that phenomenal reality is no longer interpreted in terms of just one absolute external direction of movement, but rather in terms of the dynamic interaction of two directions (external and internal) that are - relatively - opposite with respect to each other.</span><br /><span style="font-family: inherit;"><br />2-dimensional interpretation is given by the two roots of 1 that are + 1 and – 1 with respect to each other. So the two polar directions, that dynamically conditions all phenomenal experience are thereby - relatively - positive and negative with respect to each other. </span><br /><span style="font-family: inherit;"><br />The two roots (representing these two directions) are expressed by the simple equation x<sup>2 </sup>= 1, which equally can be denoted as x = 1/x.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Thus when we view time and space from this new 2-dimensional perspective (where reality is dynamically understood in terms of the interaction of twin opposite poles), we move from a linear (unambiguous) to a circular (paradoxical) appreciation of their direction.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">So from this perspective, as we approach ever closer to the supposed starting point of reality, its very meaning is rendered ever more paradoxical with each smaller duration (from one valid perspective) equally representing an ever longer duration (from an equally valid perspective). Thus in the limit, as we approach a zero point in time, this becomes inseparable from the corresponding notion of an infinite duration.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Therefore, when we attempt to understand the beginning of our Universe from this 2-dimensional (or indeed any other "higher" dimensional perspective) it is thereby clearly meaningless to attempt to give it a definite starting point in time (and space).</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Again the key problem with the conventional linear perspective is the attempt to keep the (internal) observer as somehow outside - and thereby detached - from what is observed (i.e. the beginning of the universe). However this is clearly untenable in terms of the original process itself, where the "parts" of the system are inseparable from the "whole".</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Indeed if one thinks about it for a moment, the very notion of a "Big Bang" represents a poor analogy with respect to any adequate attempt to grasp the beginnings of the the Universe.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">The "Big Bang" suggests some kind of massive initial explosion. However any conventional notion of an explosion presupposes an already existing environment of space and time in which such an event takes place. Therefore by its very nature, the "Big Bang" would represent an "explosion" of a very different kind, which strictly would remain unobservable!</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Now again, this represents the epistimological approach to understanding the "Big Bang" which is associated with the unrecognised aspect with respect to Einstein's Special Theory of Relativity.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">So from this psychological perspective, the very way one seeks to interpret the nature of space and time, varies with respect to the light "speed" (i.e. interaction of opposite polarities) of the personality.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Thus the standard rational scientific view (where no explicit interaction between opposite polarities is considered) is 1-dimensional in psychological terms is tantamount to measurement by an observer at rest.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">However the highly refined intuitive view corresponding to an advanced contemplative state, is now tantamount in psychological terms to an observer moving at a considerable fraction of light speed (with substantial two-way dynamic interaction between polarities taking place).</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">And as we have seen this leads to a substantially different interpretation of the very nature of space and time as inherently circular and paradoxical in nature.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">However because both physical and psychological aspects are intimately related, this would strongly suggest that this impossibility of a definite starting point in space and time for the Universe can also be approached from a physical perspective.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Indeed I have long viewed the psychological aspect of development in terms of a spectrum moving from "low" to "high" energy levels. So the scientific worldview arising from an advanced contemplative stance would thereby represent a "high" energy state. However the conventional rational perspective would be more akin to the "lower" energy state associated with natural light.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">In corresponding physical terms, we have the electromagnetic spectrum where the energy levels vary considerably depending on the location of the spectrum.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Now rainbow gravity would concentrate just on the band of natural light where different frequencies are associated with the various manifestations of light (as distinct colours). </span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">If one were then to accept that these different energies influence the manner in which gravity interacts with light, then this would entail that all travel - ultimately - at different speeds.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">So the constancy of the speed of light would thereby be an illusion arising from the fact that our measuring instruments are not yet sufficiently refined to detect the actual differences involved.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">However if these differences in speed were indeed demonstrated to exist, then it would open the way for a direct physical explanation as to why our Universe could not have a definite starting moment (in time and space).</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Indeed it would seem reasonable to me to additionally assume that the speed of all the various forms of electromagnetic energy (and not just the natural light bands) would ultimately vary due to their interaction with gravity.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Therefore the deeper physical implications of this would be to suggest that the very notion of objects (even at the macro level) possessing a definite location in space and time is quite untenable.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">So the uncertainty principle necessarily applies to all such measurements.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Therefore we can attempt to definitely fix the notion of an object's location; however then the corresponding qualitative notion of space and time becomes increasingly fuzzy (as I demonstrated with my epistimological approach to the "Big Bang).</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Alternatively we can attempt to fix the notion of space and time (as in conventional scientific interpretation); however then the corresponding quantitative notion of an object's location becomes increasingly fuzzy.</span><br /><div class="MsoNormal"><span lang="EN-IE" style="font-family: inherit;"><o:p></o:p></span><br /></div><span style="font-family: inherit;"><br />Thus the realisation that the Uncertainty Principle equally applie</span>s at both the (micro) quantum level and the (macro) relativistic level can thereby pave the way for the successful integration of both elements.<br /><br />However as this entails explicit recognition of both quantitative (analytic) and qualitative (holistic) aspects to reality, it cannot be achieved within the conventional scientific approach.Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-35158419065673731392015-03-26T10:10:00.001-07:002017-04-17T04:05:46.810-07:00The Big Bang and Rainbow Gravity (1)I have never been a big fan of the Big Bang Theory, which for me represents an - ultimately - untenable conclusion, arising from a reduced linear approach to scientific interpretation.<br /><br />Initially, I formed my general reservations in philosophical terms. However, following recent speculation on rainbow gravity and its implications for the Big Bang, I would now be able to speculate better as to the deeper physical implications of this philosophical position.<br /><br /><br />What seems to be missing entirely with respect to conventional scientific interpretation is the enormous difference as between analytic and holistic type appreciation of reality!<br /><br />Unfortunately as such scientific interpretation is synonymous with mere analytic appreciation (of a quantitative nature), the holistic aspect, which is of distinctive qualitative variety, is thereby inevitably reduced in mere quantitative terms.<br /><br />The analytic approach admittedly however has its great merits, as the wonderful achievements of modern science testify. However it operates best for partial explanations, where a wider holistic background can already be assumed.<br /><br />However when we attempt to formulate a Theory of Everything (which can explain the ultimate interaction of the parts with the whole system), the analytic approach begins to break down badly.<br /><br />This is exemplified by the intractable problem in current physics of successfully wedding Quantum Mechanics (relating to short-lived particles at the sub-atomic scale) with the corresponding Theory of Relativity (relating to space time behaviour on a global scale).<br /><br />And I certainly would not see the Theory of Strings as likely to provide the answer here, as the very postulation of these (partial) strings, already requires the assumption of the (holistic) dimensions of space and time for their meaningful definition!<br /><br /><br />The Newtonian worldview is based very much on the belief that physical objective phenomena can be successfully interpreted in an abstract impersonal manner (as strictly external to the observer).<br /><br />Despite the severe problems posed especially by Quantum Mechanics with respect to this approach, modern physics is still strongly motivated by the untenable quest to find a coherent explanation, in a merely detached objective manner, for the ultimate physical secrets of reality.<br /><br />However momentary reflection on the matter will show that one can never have objective knowledge of the world independent of the subjective mental constructs, that are necessarily used to interpret this reality.<br /><br />So strictly we can never know reality as it objectively exists (i.e. independent of the inquiring observer).<br /><br />Rather all such knowledge of reality necessarily reflects a dynamic interaction as between both physical and psychological aspects that are - relatively - external (objective) and internal (subjective) with respect to each other.<br /><br />Put another way, physical reality cannot be understood in a mere quantitative manner, for attempted understanding of such reality necessarily reflects the dynamic interaction of twin aspects that are - relatively - physical (quantitative) and psychological (qualitative) with respect to each other.<br /><br />So conventional science from this perspective, thereby represents the attempted reduction of a complex quantitative/qualitative relative interaction (comprising both analytic and holistic aspects) in an absolute quantitative (i.e. merely analytic) manner!<br /><br /><br />Thus when we attempt to give our Universe an absolute beginning (in space and time) we thereby reduce its operations in a merely quantitative manner.<br /><br />However, by definition this very approach, is properly suited for relative interpretation of the respective parts with respect to an overall existing system. However it is quite unsuited to providing any adequate interpretation of the overall nature of this system (with respect to its component parts).<br /><br />One cannot, as a human inquiring mind, form an independent interpretation of the Universe (in a physical sense) as the beginning of all evolution, for any attempt to interpret its nature already presumes the developed mental constructs, that intimately depend on the evolution of this Universe that has already taken place.<br /><br />Therefore inevitably inquiry about the origins of the Universe must always implicitly embrace the present moment.<br /><br />This inevitably implies that any meaningful notion of space and time is thereby of a strictly relative nature.<br /><br />So if we take the movement of time from an earlier stage of evolution up to the present moment, then this can represent a positive direction. However, we can equally trace this time starting from the present moment back to that earliest stage, which is - relatively - represents a negative direction. So rather that just one absolute direction in space and time with respect to evolution (based on sole recognition of the physical aspect) we now have two relative paradoxical directions in space and time (expressing the two-way interaction of both physical and psychological aspects). <br /><br />So therefore, as the great spiritual mystics of all traditions have recognised, the only permanent reality is the absolute present moment, with all experience of time and space necessarily of a relative nature.<br /><br />When we look at reality from this enhanced perspective (which is more authentic in terms of the dynamics of experience), all inquiry starts from the present moment, with phenomenal expressions in space and time of an arbitrary contingent nature.<br /><br />Therefore the Big Bang could not have started 13.8 bl. years ago (in an absolute linear sense), as properly understood all creation takes place now, in the present moment, with phenomenal interpretation with respect to space and time ultimately of a merely relative paradoxical nature.<br /><br />Now of course I appreciate why there is such strong belief out there in the scientific community with respect to this starting point in time (i.e. some 13.8 bl. years ago). However this comes from attempting to extend an analytic type interpretation to an original overall context, where a distinctive holistic appreciation is properly required!<br /><br /><br />So far I have couched my argument in epistemological terms, which serves to properly highlight the reduced nature of conventional scientific interpretation.<br /><br />However it is indeed possible to trace out further the implications of this philosophical position, so that we can eventually begin to appreciate in an enhanced physical manner, why the Big Bang can have had no absolute starting point in space and time.<br /><br />I have mentioned on many occasions how I formed a great interest in Einstein's Special Theory of Relativity in my late teens.<br /><br />However, I quickly began to sense that there was indeed an important limitation evident with Einstein's approach.<br /><br />In other words despite his revolutionary ideas as to the true nature of space and time, Einstein still attempted to understand space and time in a detached objective manner.<br /><br />However on reflection, I began to realise that corresponding to all the major physical concepts in his Special Relativity were corresponding complementary notions of a qualitative psychological nature.<br /><br />So not alone are space and time relative in a physical sense, but equally - and very importantly - the very mental concepts through which we attempt psychologically to understand the nature of space are themselves of a relative nature.<br /><br />Put another way, though Einstein showed that space and time are relative to the observer in physical terms, he firmly believed that the psychological acceptance of this explanation (as scientific interpretation) would be absolute.<br /><br />Therefore, he believed that universal agreement could be validly reached with respect to his interpretation.<br /><br />However, implicitly this assumed that only one type of scientific inquiry could be valid (and universally accepted by all). And of course for Einstein this was his strongly held classical belief in an objective form of determinism operating with respect to the physical world.<br /><br /><br />However, following my initial insight as regards a complementary psychological aspect, I gradually began to realise that there are in fact other valid forms of scientific inquiry, of a relative - rather than absolute - nature, where both physical and psychological understanding explicitly interact.<br /><br />So this led me to the notion of Holistic Science entailing the complementary interaction of quantitative and qualitative aspects.<br /><br />This form of science however only properly unfolds at the "higher" stages of psychological development, which in former times has been heavily associated with the spiritual contemplative traditions.<br /><br />Now, what is fascinating about these stages is that the psychological nature of space and time itself becomes of a strictly relative nature (in a multi-dimensional fashion).<br /><br />This of course implies that not only is physical space and time relative for each observer but also that the very understanding of such space and time is now also increasingly relative in psychological terms.<br /><br />This would therefore entail for example in relation to Einstein's Theory of Special Relativity that an important Uncertainty Principle would apply (mirroring that of Quantum Mechanics).<br /><br />So we now recognise that there are two distinct aspects to the understanding of space and time that are quantitative (analytic) and qualitative (holistic) with respect to each other!<br /><br />Therefore if we focus on the quantitative physical aspect (as Einstein did) this blots out recognition of the corresponding psychological aspect (in the manner that external and internal polarities increasingly interact at the "higher" stages).<br /><br />Equally if we focus on the qualitative psychological aspect (as with undue attention to advanced contemplative states), this tends to blot out recognition of the corresponding physical aspect.<br />This perhaps explains why in the past meaningful dialogue as to the nature of space and time has rarely been possible as between scientists and mystics!<br /><br />In particular, this would suggest that the phenomenal features of light are thereby relative, so that for example its speed can ultimately vary.<br /><br />I will deal with this further in the next entry!Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-83484723978476783822014-12-18T09:56:00.004-08:002017-04-17T03:58:53.176-07:00Quantum BiologyIn the second programme of his two-part series "The Secrets of Quantum Physics" on BBC 4, Jim Al-Khalili dealt with several interesting examples from biology, showing how modern interpretations have become intrinsically based on principles from quantum mechanics.<br /><br />For example he explained how the navigation of the robin is seemingly based on the quantum entanglement, or what Einstein famously referred to as "spooky action at a distance". This enables the robin to detect minute changes with respect to the Earth's magnetic field associated with distinctive types of quantum entanglement associated with paired electrons.<br /><br />He then went on to explain how the modern explanation of smell relates - in a manner akin to sound - to the vibrations of the chemical bonds holding molecules together. The previous explanation based on the structure of component molecules neatly locking into appropriate sense receptor molecules (associated with a characteristic scent) could not explain for example why the smell of marzipan and cyanide is so similar (despite marked variations in their molecular structures). However the vibrations of the molecular bonds in each case show much greater similarity!<br /><br />He then went on to explain, with respect to the transformation of a tadpole into a frog, how the process of metamorphosis in nature is greatly assisted by the principle of quantum tunneling where enzymes can easily penetrate rigid barriers through assuming "ghostly" wave patterns.<br /><br />With respect to the all-important principle of photosynthesis through sunlight in nature, he went on to show how the efficient transfer of energy within cells owes much to the "uncertainty principle".<br /><br />He also speculated on how quantum effects may be directly relevant to the process of evolution, indicating more precisely how mutations with respect to genetic characteristics take place.<br /><br /><br />In one way none of this should really be so surprising.<br /><br />If we accept that physical reality at its minute subatomic levels is governed by quantum mechanical interactions, then this should ultimately apply at a deeper level of investigation to all biological processes.<br /><br />This strongly suggests to me that many of the current accepted explanations represent in the main "half truths" that inevitably will raise fundamental questions at a deeper level of investigation.<br /><br />Indeed I have long felt this applies to the Darwinian theory of evolution, which always struck me as a somewhat tautological explanation, concealing many difficulties. It only appears convincing within the reduced limits of present scientific interpretation, as this formally excludes the holistic aspect of meaning. However a deeper philosophical understanding of the holistic implications of quantum interactions, which necessarily underlie all evolutionary processes, will I believe ultimately lead to a far more nuanced appreciation.<br /><br />Looking at these issues in more general terms, what is currently deemed as scientifically acceptable itself reflects but a particular point in time with respect to its on-going evolution.<br /><br />Before the rise of modern science, quantitative were not properly distinguished from qualitative type considerations (often expressed through mythological religious type beliefs).<br /><br />One could therefore accept that just as in psychological terms, mature understanding requires overcoming the magical and mythical beliefs associated with infant development, that likewise this is true of science. Therefore the sharp differentiation of rational from spiritual type considerations, which typifies the last 300 year so of science has proved both a welcome and necessary development,<br /><br />And this has led to unparalleled progress with respect to quantitative type understanding of our universe.<br /><br />However I would very much see this as representing but a stage of scientific development which in many ways is now coming face to face with its inevitable limitations.<br /><br />Despite the great success of quantum physics, the deeper philosophical implications of its rationale have not been adequately faced by the scientific community.<br /><br />In fact I have long been convinced that quantum mechanics now directly requires the re-inclusion of the qualitative holistic aspect (that science has so vigilantly attempted to exclude from the fold).<br /><br />In the last blog I mentioned for example that quantum entanglement entails the simultaneous interdependent communication of particles that inherently is of a qualitative rather than a quantitative nature.<br /><br />So now as well as the accepted analytic aspect of science, we need once again to recognise the neglected holistic aspect - not through mythological religious symbols of the past - but rather through an extension of the very meaning of scientific symbols (with twin interacting aspects of interpretation).<br /><br />Indeed at an even more fundamental level this is likewise through of Mathematics.<br /><br />In my own investigations of the Riemann Hypothesis, I have come to realise that the number system, which underlines all science, is itself strictly meaningless in the absence of an explicit qualitative dimension. Indeed at its very core, the number system is of a dynamically interacting synchronistic nature (entailing the bi-directional complementarity of both the primes and natural numbers).<br /><br />And this same synchronicity which is a central feature of the number system is likewise a central feature of physics and biology and indeed of all evolution.<br /><br />However we will never be able to properly grasp this key point while remaining rigidly committed to the limited analytic confines of conventional science.Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-78827308673394505552014-12-10T09:14:00.001-08:002017-04-17T03:54:25.022-07:00Einstein's NightmareI enjoyed watching Professor Jim Al-Khalili's account of the development of quantum physics "The Secrets of Quantum Physics"with the first episode "Einstein's Nightmare" shown last night on BBC 4.<br /><br />Though I had both read about and listened to the discussion of these ideas many times before, I always welcome a new imaginative way of presentation, which can lead one to seeing the issues involved in a new light. <br /><br />What was discussed last night culminated with the Einstein-Podolsky Paradox, which though formulated in 1935 could only be satisfactorily tested much later (largely due to the original theoretical contribution of John Bell). <br /><br />As we know, Einstein was deeply unhappy with the philosophical implications of quantum mechanics, where sub-atomic events seemingly were based on chance and probability. He believed that acceptance of non-local causation would imply communication between particles faster than the speed of light, which thereby would violate a key principle of his widely accepted theory of relativity. <br /><br />However the experiments used to test this paradox according to Al-Khalili (many times since conducted) have convincingly proved that Einstein was wrong!<br /><br /><br />However as always it is never quite that simple with debate still raging as to to precise significance of the results that have arisen.<br /><br />The true problem from my perspective is that the very mind-set of contemporary physicists is still based on the common-sense notion of a physical reality "out there" that can be successfully investigated in an objective impersonal manner.<br /><br />And this is precisely why quantum mechanics seems so paradoxical as it does not conform to the intuitions that fit in with this objective viewpoint.<br /><br />So the true problem with physics is fundamentally of a deeper level in that the scientific paradigm, which still informs the very way that physicists view reality, is quite inadequate in terms of understanding reality as it truly is!<br /><br />In other words, only when the scientific perspective we adopt enables us to intuitively resonate with the findings of quantum mechanics (thereby becoming the new accepted common sense), can we then say that we understand such issues in the appropriate manner.<br /><br />The findings of quantum mechanics lead to the break-down in the very notion of an independent physical reality. Indeed this is equally true with respect to everyday macro reality (though admittedly at this level physical findings approximate well with independent assumptions).<br /><br />To properly understood reality from the scientific perspective, we need to replace physical with psycho physical reality (where both physical and psychological aspects necessarily interact in dynamic fashion).<br /><br />At the quantum level, the (psychological) observer is intimately involved with what is (physically) observed so that the physical event resulting has no strict meaning in the absence of this complementary psychological contribution.<br /><br />However once we accept the necessary two-way interaction as between observer and what is observed, we move outside the realm of mere analytic interpretation.<br /><br />Such analytic interpretation is always based the independence of polar reference frames (e.g. objective and subjective).<br /><br />However once we accept a degree of interdependence with respect to both poles, we inevitably move from analytic to holistic type meaning.<br /><br />So when Einstein protested against faster than light communication, he adopted a strictly analytic perspective (which is especially inadequate at the quantum level).<br /><br />In fact Einstein himself had already profoundly reflected on this issue in wondering what it would be like to travel on a beam of light! And he acutely realised that time would have no meaning in this context! So within its own frame of reference time does not pass for light.<br /><br />The notion of the speed of light therefore only has reference with respect to a partial phenomenal reference point (where movement is taken in just one direction).<br /><br />Therefore for example when we say that it takes about 8 minutes for the light of the sun to reach Earth, we are measuring time from the Sun as origin in relation to a phenomenal object (Earth) with only one direction of movement considered.<br /><br />However if we now attempt to measure time with respect to the two-way movement of light as between Sun and Earth, it is rendered paradoxical. For what moves forward in time from one vantage point moves - relatively - backward with respect to the other and vice versa.<br /><br />Thus in terms of two-way simultaneous "movement" time - relatively - has both forward and backward directions (which cancel out).<br /><br />We could then accurately express this as representing an (absolute) present moment, of which paradoxical notions of time (and indeed space) represent but arbitrary relative expressions.<br /><br />Therefore strictly speaking, any notion of speed with respect to holistic communication between particles (i.e. entailing two-way interaction) has no meaning.<br /><br />So we can maintain - as I ardently believe is indeed the case - that holistic communication takes place with respect to quantum particles (and indeed physical reality at every level).<br /><br />However this strictly occurs outside space and time in the present moment. Therefore it does not contradict Einsteins's prohibition on nothing travelling faster than light, which only applies with respect to relatively independent frames of reference. However the communication dealt with here. clearly applies to frames that are relatively interdependent with each other (as for example in human exchanges).<br /><br />Thus the truly real massive problem which remains yet to be addressed by physicists (and indeed science and mathematics generally) is that the prevailing paradigm is built on mere analytic type interpretation (directly accessible to consciousness through linear reason).<br />This remains even true with respect to quantum physics, where findings create considerable paradox with respect to this approach!<br /><br />However holistic understanding by its very nature entails an utterly distinctive form of appreciation that is directly based on intuition (entailing the unconscious). Thus genuine communication of a synchronistic nature cannot be meaningfully interpreted in a rational analytic manner. However it can indeed be embraced in a directly intuitive manner (that lends itself indirectly to circular type rational explanations of a paradoxical nature).<br /><br />So what we are witnessing at present - especially at the quantum level - are the severe limitations of mere analytic type understanding.<br /><br />However the need for of an equally important holistic aspect (of an utterly distinctive nature) has not yet been recognised by the scientific community. In psychological terms this will require recognition of the potential scientific importance of the unconscious aspect of understanding leading to a direct qualitative - rather than quantitative - type emphasis.<br /><br />Even more, the ultimate need for a comprehensive paradigm that will properly integrate specialised analytic and holistic type understanding (in both quantitative and qualitative terms) is not yet remotely recognised.Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-73655772847148132382014-04-28T02:40:00.002-07:002014-05-29T14:50:19.878-07:00Interesting QuotationI was struck by this following quotation when looking through once more Marcus du Sautoy's very readable "Music of the Primes".<br /><br />"When we observe an event in the quantum world, it is though we are not seeing the event itself in its natural domain, but a shadow of the event projected into our 'real world' of ordinary numbers."<br /><br />From a Jungian perspective this lends itself to a direct complementary comparison with the nature of unconscious experience from a psychological perspective.<br /><br />In other words we cannot observe what pertains to the unconscious mind directly. Rather when we observe an event in the unconscious world, it is as though we are not seeing the event in its natural (i.e. unconscious domain) but a shadow of the event projected into our 'real world' of conscious experience.<br /><br />The implications here are highly important as it entails that we cannot hope to understand the sub-atomic quantum nature of reality within the current scientific paradigm (that is based on mere conscious notions of interpretation).<br /><br />In psychological terms we are now well accustomed to accepting the inevitable interaction in experience as between both conscious (analytic) and unconscious (holistic) aspects of experience.<br /><br />However when it comes to scientific understanding we still misleadingly attempt to view reality from a mere conscious perspective.<br /><br />However in truth physical reality itself has its own equivalent of the "unconscious" in what we could refer to as the holistic ground of reality.<br /><br />Therefore when we attempt to observe particles at a quantum level we are dealing with a highly dynamic interaction of objects with both analytic aspects (as independent) and holistic aspects (as interdependent with the rest of reality).<br /><br />Therefore if we are to successfully understand physical reality at this level (indeed ultimately at any level) we must adopt a new paradigm of understanding that explicitly incorporates both analytic and holistic dimensions of understanding.<br /><br />Such understanding of physical reality would then be directly complementary with corresponding psychological experience of this reality (incorporating both conscious and unconscious aspects).<br /><br />And ultimately of course this extends also to the fundamental nature of Mathematics.<br /><br />The very reason why increasing links have been discovered as between the primes and quantum reality in recent years is because the very nature of the primes likewise incorporates both analytic and holistic aspects in dynamic interaction with each other.<br /><br />However mathematicians still seem intent on attempting to understand the primes from an absolute interpretative framework based on mere analytic notions.<br /><br />Though informally, harmonic musical metaphors are used in explaining the nature of the primes the obvious implication has not been taken on board i.e. that mathematical reality itself has a distinctive holistic aspect (that cannot be properly addressed within its present limited paradigm).<br /><br />This paradigm is based firmly on the notion of absolute independently existing objects such as numbers.<br /><br />However if such objects were indeed truly independent (then it would be impossible to study the relationship between different numbers (which reveals their interdependence).<br /><br />So in truth, from a dynamic interactive perspective, all mathematical objects have a merely relative existence combining both notions of (analytic) independence with (holistic) interdependence. <br /><br />Thus the nature of the prime numbers is inherently dynamic. However this cannot be appreciated from within the conventional mathematical paradigm (based on an abstract absolute manner of interpretation).Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-73704571763671978642012-09-22T10:03:00.000-07:002017-06-14T11:20:59.494-07:00Number and TransformationThis latest contribution in many ways entails a summary of the points that I have made in recent blog entries and in discussion with Anthony Judge in relation to <a href="http://www.laetusinpraesens.org/musings/converse.php">“Transforming the Art of Conversation - conversing as the transformative science of development”</a> at his hugely impressive “Laetus in Praesens” site.<br /><br /><br />I have been long fascinated by the fact that the two binary digits (1 and 0)<br />when used in a quantitative manner can potentially encode all<br />information processes.<br /><br />I am therefore of the opinion that the same two digits when used in an<br />appropriate qualitative manner can likewise potentially encode all transformation processes. <br /><br />So transformation itself (in all its manifestations) is basically encoded in number when appreciated in a qualitative manner. <br /><br />Now as geometrical symbols, 1 can be identified with the straight line and 0 with a circular circumference. So the relationship of 1 and 0 in qualitative terms implies the relationship between (rational) linear and (intuitive) circular understanding. (In this context circular refers to the indirect rational attempt through paradox to portray the nature of intuitive understanding). <br /><br />From a physical perspective this would imply that all transformation processes entail the interaction of a visible phenomenal aspect together with an equally important invisible holistic dimension.<br /><br /><br />At a deeper level this circular aspect relates to the manner in which the<br />fundamental polarities - which necessarily underlie all phenomenal<br />relationships - are configured.<br /><br />For convenience, I would see that two key sets here are essential to all dynamic relationships i.e. external and internal and whole and part. In dynamic terms, external always implies internal (and internal external). Likewise wholes imply parts (and parts wholes). All phenomenal creation necessarily entails the two-way interaction of both sets of polarities.<br /><br />Conventional Science and Mathematics are decidedly linear (i.e. 1-dimensional) in the manner that these polarities are treated with isolated independent reference frames employed. So the external (objective) is abstracted from the internal (subjective) aspect; likewise wholes are typically viewed as composed of parts in a mere quantitative manner. Not surprisingly this leads to a highly reduced interpretation of truth!<br /><br /><br />However an unlimited number of higher dimensional perspectives are possible which all entail an authentic dynamic interaction as between polarities.<br /><br />The nature of each number, as qualitative dimension, is structurally related to the corresponding notion of quantitative roots of unity.<br /><br />So the nature of 2-dimensional understanding bears a close relationship<br />therefore with the two roots of 1, i.e. + 1 and - 1. However whereas with<br />standard quantitative appreciation, these two values are separated, in<br />holistic qualitative terms they are interdependent. Thus 2-dimensional<br />understanding can be therefore expressed as the complementarity of (real)<br />opposites in the dynamic interaction of poles which are positive and<br />negative with respect to each other.<br /><br />These dimensions can be given a geometrical representation (though we must remember that the interpretation is now of a holistic nature).<br /><br />For example 3-dimensional understanding can be geometrically represented in terms of the well-known Mercedes-Benz logo (which equally is a geometrical representation of the 3 roots of 1).<br /><br />So in short, each number as dimension, relates to a unique manner of<br />configuring the dynamic interaction of the two fundamental sets of<br />polarities. So rather like with a compass with four starting coordinates, we<br />can obtain ever more detailed notions of direction, likewise starting with<br />the two fundamental polarity sets we can give ever more refined expression<br />to the dynamic interaction between opposite coordinates through moving to<br />higher dimensional numbers! So once again each number in this qualitative<br />sense represents a unique manner of configuring the dynamic interaction as<br />between the essential polarities that necessarily underlie phenomenal experience.<br /><br />This key issue is avoided completely in conventional scientific (and<br />mathematical) terms through sole concentration on the special limiting case<br />where understanding in formal terms is 1-dimensional.<br /><br />Now, I believe that this qualitative holistic notion of dimension intimately<br />applies to the true nature of space and time. So if we were to map<br />space-time reality, we could validly say that it is truly multi-dimensional<br />where the ceaseless interweaving of these qualitative numbers are involved. Going even further, the distinctive qualitative features that phenomena possess, thereby represent multi-dimensional configurations with respect to space and time that are ultimately rooted in the qualitative notion of number.<br /><br /><br />I would go even further. In dynamic relative terms, phenomena represent but appearances (in continual transformation) of an ultimate reality that is ineffable.<br /><br />In fact, from this perspective, we can say that such phenomena (which<br />possess no ultimate substance) fundamentally represent but the dynamic<br />configurations of number (with respect to both their quantitative and<br />qualitative aspects).<br /><br />From a geometrical perspective the quantitative shape of all phenomena can<br />be understood in terms of the interplay of both linear and circular<br />properties in varying dimensions.<br /><br />The corresponding qualitative "shape" of these phenomena in their uniquely<br />distinctive features can likewise be understood in terms of both specific<br />and holistic features again with respect to the combined interplay of<br />multiple dimensional numbers (which again represent a distinctive manner in which the fundamental polarities are dynamically configured).<br /><br />In a direct sense I would see the quantitative aspect of understanding as<br />relating to form, with the qualitative relating to the mysterious<br />transformation of this form.<br /><br />So if we are to isolate what is common to all patterns of transformation, it<br />is the intersection of this holistic qualitative aspect with established<br />quantitative notions of form.<br /><br />However when one accepts that the very nature of the standard paradigm of<br />science and mathematics is to attempt to reduce this interaction in a merely quantitative manner, then one can perhaps appreciate why it is inimical to transformation.<br /><br />It is not that science as such is opposed to such transformation, but rather the present limited version that is wrongly accepted as solely synonymous with valid scientific interpretation!<br /><br /><br />Now there is much greater freedom for both the development and expression of the qualitative aspect within the arts.<br /><br />So in the quest to transform present conversation - even scientific conversation - it would be helpful to informally dialogue with artistic metaphors.<br /><br />Of course acceptance of the (neglected) qualitative aspect of science (and mathematics) would eventually pave the way towards better integration with the arts (with both seen as complementary expressions of the same truth).<br /><br />My key point again is this! <br /><br />There is not just one Mathematics (that is qualitatively 1-dimensional in nature) but potentially an infinite set, with each interpretation as the complex expression of a number dimension possessing a partial relative validity. And as phenomenal reality can be expressed as the dynamic interplay of all these dimensional systems in complex space and time (with quantitative and qualitative aspects), ultimately it is vital that we abandon the present total adherence to just one! Even with the best intentions, it therefore continually leads to a reduced form of understanding that eventually can serve as the enemy of true transformation.<br /><br />Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-46889068701540927372012-09-21T08:15:00.000-07:002012-09-21T08:57:15.353-07:00Connections to TaoismI have always felt a special affinity to Taoism where the basic nature of reality is explained in a manner that readily lends itself to holistic mathematical understanding.<br /><br />So the Tao represents the ineffable undivided unity (which equally is a nothingness in phenomenal terms).<br /><br /><br />Then phenomenal reality arises from the splitting of this unity into polar opposites that are understood as separate from each other. However a deeper understanding of the nature of these opposites leads to the realisation that they are complementary (and ultimately identical in nondual terms) as yin and yang. So it is this latter realisation that enables the process of harmonising phenomenal reality with the original absolute nature of Tao.<br /><br /><br /><br />Last night I was briefly reading the section on Taoism in that wonderful little book on "Mysticism" by F.C. Happold. There, I saw the seeds of an even closer relationship in its thought to my recent notions expressed in these blogs on the all important role of number.<br /><br />For example on P. 152 we have this statement<br /><br />"As soon as Tao creates order, it becomes nameable."<br /><br />Now the very basis of ordering is number, both in its recognised quantitative, and also in its much less recognised qualitative manner.<br /><br />So, number itself freely arises from the absolute ineffable nature of reality, which then becomes the very means of identification of phenomena. <br /><br /><br />Just a few sentences later on the same page we have a more graphic statement on the fundamental nature of number!<br /><br />"Tao produced Unity; Unity produced Duality: Duality produced Trinity; and Trinity produced all existing objects.<br />These myriad objects leave darkness behind them and embrace the light, being harmonised by contact with the Vital Force."<br /><br /><br />So Unity, Duality and Trinity simply represent the qualitative holistic notions of 1, 2 and 3 respectively from which all phenomenal objects arise. Now one might validly query the sole emphasis on the holistic notion of number here! However the key point is the direct connection then made as between number and the manifest identity of phenomenal objects!<br /><br />So these multiple objects then leave darkness behind. What is implied here is that in the original state of Tao, where - by definition - no differentiation (or integration) has yet taken place, such objects would enjoy a mere potential for existence. So in becoming differentiated as separate objects, evolution can begin the process of gradual actualisation of Tao. And it is in the recognition of the ultimate nondual nature of phenomena (through the complementary yin and yang aspects of nature) that the integrated state of all phenomena thereby arises (which is inseparable from their absolute identity in Tao).<br /><br /><br />My simple purpose in all these blogs is to understand the true nature of Mathematics and Science as fully consistent with the accumulated great wisdom of the various mystical traditions.<br /><br />And when one looks carefully, the seeds of such reconciliation are already evident in these traditions (as illustrated here in an emphatic manner in Taoist literature).<br />Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-40530331453906985752012-09-08T06:53:00.004-07:002014-01-21T12:23:15.336-08:00What is Number?We have to be careful here. It is very hard in practice to distinguish numbers from the symbols used for their representation.<br /><br />And the very nature of such representation is that we thereby give a distinct phenomenal identity to number (as represented by its symbol).<br /><br />So when I use the symbol "1" to represent the notion of one, it thereby assumes this phenomenal identity.<br /><br />Furthermore because understanding of number in our culture is dominated by its quantitative aspect, numbers thereby become misleadingly identified as abstract phenomenal objects (with an absolute identity).<br /><br /><br />However in truth the meaning of number is much more elusive.<br /><br />As I have been at pains to illustrate, every number has both a qualitative as well as recognised quantitative aspect. Basically, the quantitative aspect relates to the notion of number as independent (i.e. where phenomenal poles such as external and internal are separated). The corresponding qualitative aspect relates to the corresponding notion of number as interdependent (where these same poles are understood as inherently complementary and ultimately identical).<br /><br /><br />We can easily illustrate this with respect to 1.<br /><br />In conventional terms 1 is given a mere quantitative meaning i.e. as a separate number object. This notion is indeed extremely important and serves as the fundamental basis for discrimination of any phenomenal object. Therefore in order to recognise an object phenomenon as a distinctive unit, the quantitative notion of 1 must necessarily be already implicit in such understanding. <br /><br /><br />However 1 can equally be given a qualitative holistic meaning as "oneness". The best example of this relates to the ultimate experience of spiritual oneness (where the explicit notion of an object as a separate phenomenon no longer arises).<br /><br /><br />So the very notion of 1 in this alternative qualitative sense pertains to the notion of pure interdependent relatedness (based on the identity of opposite poles).<br /><br /><br />Put another way, the quantitative notion of number is based on either/or linear logic, where the positive poles excludes the negative..<br /><br />Therefore in the expression where 1 - 1 = 0, 1 ≠ 0.<br /><br /><br />However the qualitative notion of number is based by contrast on both/and circular logic, where the positive pole includes the negative.<br /><br /><br />Therefore from this perspective where 1 - 1 = 0, 1 (as oneness now defined in this complementary manner) = 0 (as nothingness). <br /><br /><br />However before we can understand the (common) interdependence of opposite poles, we must recognise their (separate) independence (and vice versa). <br /><br /><br /><br />So properly understood, both the quantitative and qualitative notions of number are inextricably linked in all experience.<br /><br /><br />Thus, the ultimate notion of number (though necessarily implicit in all phenomenal observation) is of an ineffable nature where both quantitative and qualitative aspects coincide. <br /><br /><br />In this sense, though we must necessarily represent numbers in phenomenal terms with symbols, they cannot be confused with physical phenomena (where number is already inherent in their recognition).<br /><br /><br />Put another way, physical phenomena themselves represent a certain rigid confusion with respect to the quantitative and qualitative aspects of number. In other words, we can only recognise such phenomena, through maintaining a certain imbalance with respect to the quantitative and qualitative aspects of number. <br /><br />Once we recognise a physical object for example, we thereby associate number with its merely quantitative aspect.<br /><br />In this sense the very quest for ultimate spiritual unity is the corresponding desire to reconcile both the quantitative and qualitative aspects of number in their original ineffable state.<br /><br />So 1, in the unity of all form (through circular understanding) as pure interdependence is inseparable from 0 (as the emptiness or nothingness with respect to separate phenomena). <br /><br /><br />Thus once again, 1 - 1 = 0.<br /><br />However when we switch to linear (quantitative) logic, both poles are now positive<br /><br />So we have 1 + 1 = 2.<br /><br /><br />Thus duality (as the qualitative meaning of 2) arises from application of the alternative logic.<br /><br />In dynamic terms, all phenomenal reality in its forms and transformations represents the dynamic interaction of both types of logic (representing the quantitative and qualitative aspects of number).<br /><br /><br />So from this perspective, we could say that the very goal of all evolution is to ultimately realise the true original state of number (where quantitative and qualitative aspects are indistinguishable).<br /><br />And all the fundamental mathematical operations can be validly seen as an extension as to what is implied through the notion of number.<br /><br />This thereby gives an extraordinary significance to the role of a more comprehensive mathematical understanding (where both its quantitative and qualitative aspects are explicitly recognised).Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-6092216279056793322012-09-07T02:05:00.008-07:002012-09-21T08:50:38.383-07:00Binary WonderWe are already well aware of the great significance of number from the conventional quantitative perspective. However what we have not yet recognised yet is the equal significance of number from the greatly neglected qualitative dimensional perspective.<br /><br /><br />And when we combine these two aspects of number in interactive terms, then it is but a short leap to the recognition that - at its most fundamental - phenomenal reality is but the dynamic representation of number configurations (in both quantitative and qualitative terms).<br /><br /><br />Now a widespread view in contemporary physics is that reality is fundamentally composed of tiny 1-dimensional strings, the unique vibrations of which give rise to all the particles from which more conventional material forms are composed.<br /><br />However the notion of "physical strings" in any meaningful philosophical sense is but a fiction arising from the reductionist quantitative viewpoint that matter must ultimately be composed of smaller constituent parts of matter with the "strings" thereby representing the most fundamental parts.<br /><br /><br />However from a more correct dynamic perspective all such matter particles must necessarily be of a merely relative nature, arising from dynamic interaction of quantitative and qualitative aspects. And as neither quantitative or qualitative aspects have meaning in the absence of such interaction we can thereby never ultimately isolate the basic constituents of matter in merely quantitative terms. <br /><br /><br />This then leads to the even more extraordinary realisation that - what we recognise as matter - represents but the dynamic configuration of what in phenomenal terms are recognised as numbers.<br /><br />Now a number has no physical identity in either quantitative or qualitative terms (in isolation). However it is the unique vibration of both the quantitative and qualitative aspects of number that give rise to the rigid physical appearances in nature that we recognise as matter. <br /><br /><br />The two most important numbers - what I refer to as the original numbers - are 1 and 0.<br /><br />We are now discovering in this digital age the great significance of these two numbers as a potential means of encoding all information.<br /><br />However again what is not equally recognised is the qualitative counterpart of this digital revolution, whereby the same two digits can be seen as a potential means of encoding all transformation processes.<br /><br />It has always impressed me how these two numbers play such a big role in representing the mystical experience of reality.<br /><br />In the Western religious traditions - based more heavily on linear notions of form - the peak experience of transformation is commonly expressed in terms of union (or oneness) which is the holistic qualitative notion of 1. <br /><br />In the Eastern traditions - based more on circular cyclical notions - the peak experience is by contrast expressed in terms of a void or emptiness (i.e. nothingness) which is the holistic qualitative notion of 0. <br /><br />And as phenomenal reality itself is an information system undergoing continual transformation, we can perhaps recognise that such reality represents but the dynamic interaction of a digital system (based on the numbers 1 and 0) with twin aspects that are quantitative and qualitative respectively.<br /><br />So the numbers 1 and 0 in this sense are sufficient to encode all reality with respect to (quantitative) information and (qualitative) transformation.<br /><br /><br />However before this system can operate in phenomenal terms, a precise requirement is necessary relating to the prime number code.<br /><br />Therefore though prime numbers can be represented in a binary manner, with respect to both quantitative and qualitative characteristics, only one configuration is possible (in the generation of the prime numbers) as - literally - the prime condition for the subsequent unfolding of the phenomenal universe. <br />Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-58336245377664876402012-09-05T03:06:00.003-07:002012-10-04T11:36:45.746-07:00Prime MoversWe now come back to highlighting the significance of the prime numbers.<br /><br />Just as the prime numbers are recognised in quantitative terms as the building blocks of the natural number system, likewise the prime numbers - though conventionally unrecognised - are equally the building blocks in qualitative terms of the natural number system.<br /><br />What this again implies is that all numbers (as dimensions) are built up from prime number constituents. <br /><br />Then, as the number dimensions directly relate to the dimensions of space and time (physically and psychologically) these likewise are built from prime numbers (in qualitative terms).<br /><br /><br />Furthermore, as the qualitative characteristics that are inherent in natural phenomena are but manifestations of such space and time configurations, the prime numbers can then be clearly seen - in literal terms - as the fundamental basis of all qualitative characteristics in nature.<br /><br /><br />Thus, looked at from these two distinct perspectives (in isolation) the prime numbers can be thereby seen as the basis for all natural characteristics (quantitative and qualitative) .<br /><br /><br /><br />But we now come back to a familiar paradox. What seems unambiguous within isolated reference frames, becomes deeply paradoxical when these frames are treated as interdependent.<br /><br />So one once again, when I walk up a road (understood in isolation) movement takes place positively in space and time.<br /><br />Then when I walk down the same road (in isolation) movement likewise takes place positively in space and time.<br /><br />However when we understood these two reference frames (i.e. "up" and "down") as interdependent, movement takes place - relatively - in both positive and negative directions in space and time.<br /><br /><br />It is the same with respect to the prime numbers.<br /><br />When we consider both the quantitative and qualitative aspects in isolation, the prime appear unambiguously as the building blocks of the natural numbers.<br /><br />However when we consider both quantitative and qualitative in dynamic relationship to each other (as interdependent) then this comforting picture breaks down with both prime and natural numbers simultaneously giving rise to each other.<br /><br />What this means in effect is that the mysterious connection, that links primes and natural numbers in such a synchronous manner, is of an ineffable nature (and already inherent in number processes when they phenomenally arise). <br /><br /><br />And once again it is this mysterious connection to which the Riemann Hypothesis directly applies!<br /><br />So, properly understood, the Riemann Hypothesis is a mathematical statement of the condition required to reconcile both the quantitative and qualitative behaviour of the primes. <br /><br />And as Conventional Mathematics is formally defined by a merely quantitative interpretation of its symbols, the Riemann Hypothesis not only cannot be proved (or disproved) in this manner; it cannot even be properly understood from this perspective.<br /><br /><br />However far from being a defeat, a proper realisation of this fact would then open the way for a much more comprehensive appreciation of the true nature of Mathematics.<br />Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-73327176549617113492012-09-04T04:18:00.003-07:002012-09-21T08:52:25.561-07:00Reality as NumberWe now come back to highlighting the significance of the prime numbers.<br /><br />Just as the prime numbers are recognised in quantitative terms as the building blocks of the natural number system, likewise the prime numbers - though conventionally unrecognised - are equally the building blocks in qualitative terms of the natural number system.<br /><br />What this again implies is that all numbers (as dimensions) are built up from prime number constituents. <br /><br />Then, as the number dimensions directly relate to the dimensions of space and time (physically and psychologically) these likewise are built from prime numbers (in qualitative terms).<br /><br /><br />Furthermore, as the qualitative characteristics that are inherent in natural phenomena are but manifestations of such space and time configurations, the prime numbers can then be clearly seen - in literal terms - as the fundamental basis of all qualitative characteristics in nature.<br /><br /><br />Thus, looked at from these two distinct perspectives (in isolation) the prime numbers can be thereby seen as the basis for all natural characteristics (quantitative and qualitative) .<br /><br /><br /><br />But we now come back to a familiar paradox. What seems unambiguous within isolated reference frames, becomes deeply paradoxical when these frames are treated as interdependent.<br /><br />So one once again, when I walk up a road (understood in isolation) movement takes place positively in space and time.<br /><br />Then when I walk down the same road (in isolation) movement likewise takes place positively in space and time.<br /><br />However when we understood these two reference frames (i.e. "up" and "down") as interdependent, movement takes place - relatively - in both positive and negative directions in space and time.<br /><br /><br />It is the same with respect to the prime numbers.<br /><br />When we consider both the quantitative and qualitative aspects in isolation, the prime appear unambiguously as the building blocks of the natural numbers.<br /><br />However when we consider both quantitative and qualitative in dynamic relationship to each other (as interdependent) then this comforting picture breaks down with both prime and natural numbers simultaneously giving rise to each other.<br /><br />What this means in effect is that the mysterious connection, that links primes and natural numbers in such a synchronous manner, is of an ineffable nature (and already inherent in number processes when they phenomenally arise). <br /><br /><br />And once again it is this mysterious connection to which the Riemann Hypothesis directly applies!<br /><br />So, properly understood, the Riemann Hypothesis is a mathematical statement of the condition required to reconcile both the quantitative and qualitative behaviour of the primes. <br /><br />And as Conventional Mathematics is formally defined by a merely quantitative interpretation of its symbols, the Riemann Hypothesis not only cannot be proved (or disproved) in this manner; it cannot even be properly understood from this perspective.<br /><br />However far from being a defeat, a proper realisation of this fact would then open the way for a much more comprehensive appreciation of the true nature of Mathematics.Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-61503891949665028222012-09-03T08:39:00.006-07:002014-01-21T12:20:55.110-08:00Multidimensional Nature of Time and Space (20)Yesterday, I briefly attempted to explain the qualitative significance of the Euler Identity which essentially represents a holistic mathematical description of the precise nature of spiritual transformation where emptiness and form (and form and emptiness) are united. Here the contemplative journey - literally - comes full circle with the transcendent goal (beyond all phenomenal form) finally revealed as identical with its immanent source (as already inherent within such form). <br /><br /><br />Last week I was looking at a fascinating programme on the mapping of the Universe. We are of course accustomed to the mapping of planet Earth and to a lesser extent our planetary system. But ambitious attempts have already been made to provide a map of the entire Milky Way galaxy. And even beyond that considerable progress has been made with respect to the mapping of the visible universe (made up of countless billions of galaxies). Even some are already attempting to know what lies beyond the visible universe, with the current view that it is infinite in extent (or as I would prefer to put finitely unlimited with respect to its size).<br /><br /><br />Also it is quite apparent that on the grand scale that we have to move well beyond conventional notions of matter and energy. Though only dimly understood the prevailing view now is that most of the Universe is comprised of dark matter and dark energy. Now this seems to complement my own finding that when we look at Mathematics on a grand scale that the unconscious aspect of interpretation thereby assumes great significance! <br /><br /><br />So there are strong parallels here to my attempts to map both the mathematical and scientific Universe with the prevailing paradigm akin to the mapping of planet Earth. However there is so, so much more out there waiting to be discovered that we have not yet even begun to consider.<br /><br /><br />It perhaps will provide more perspective on my approach by giving a little more information on the "map of development" that I have now been using for the past few years.<br /><br /><br />I break this down into seven major bands (with each band comprising three major stages of development).<br /><br />The first band is well recognised in Developmental Psychology and is concerned with the gradual differentiation of conscious type abilities (in what might be referred as the archaic, magical and mythic stages).<br /><br />The second band then is concerned with the specialisation of consciousness through (linear) reason. As we have seen such thinking defines the prevailing paradigm and has become long established in - what we know as - Mathematics and Science. This is the gross realm containing both conop (concrete operational), formop (formal operational) and vision logic understanding. The third stage refers to reason that is infused with intuition, and is especially important for creative work of an original kind!<br /><br />Now the second band - correctly understood - relates merely to specialisation with respect to the quantitative aspect of mathematical (and scientific) understanding i.e Type 1.<br /><br /><br />The third band is then concerned - from a scientific perspective - with the unfolding of higher dimensional understanding that is directly intuitive in nature, though indirectly can be logically expressed in a circular rational manner. The stages of this band are sometimes referred to as the psychic, subtle and causal realms and we have already looked at the nature of the higher dimensional numbers associated with these realms.<br /><br />The fourth band (nondual reality) relates to both an extremely refined intuitive and rational type understanding and is concerned with the consolidation of this circular type appreciation.<br /><br />So the fourth band - correctly interpreted - is concerned with complementary specialisation of the qualitative aspect of both mathematical (and scientific) understanding.<br /><br />And putting it bluntly this aspect (Type 2) still remains completely unrecognised from the conventional mathematical (and scientific) perspectives. <br /><br /><br />However I now recognise three further bands on the full Spectrum of Development which I customarily refer to as radial development.<br /><br />These would entail the growing mature interpenetration of reason (linear and circular) with contemplation.<br /><br />In relation to both Science and Mathematics it would lead to the increasing dynamic interplay of both the quantitative and qualitative aspects of understanding. Band 5 would relate to its initial unfolding whereas with Band 6, full specialised understanding would commence. In relation to all the number types therefore, one would now seek the combined understanding of both quantitative and qualitative appreciation in what I refer to as Type 3 Mathematics.<br /><br /><br />This would likewise be associated with a final advance with respect to the qualitative aspect of dimensional understanding.<br /><br />We have already looked at the distinction as between the real and imaginary notions of number with respect to dimension. However until both transcendent and immanent directions are fully harmonised in experience, these tend to be used separately.<br /><br /><br />However, with the unfolding of the radial stages, they can now increasingly be used in a simultaneous manner. So this means in effect that the qualitative aspect of dimensional numbers as complex can now be appropriately reflected in experience. This likewise entails a corresponding dynamic appreciation of the nature of time (and space) in likewise complex terms that once again applies in complementary physical and psychological terms.Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-20469055177468438122012-09-01T09:10:00.005-07:002014-07-27T11:34:33.829-07:00Multidimensional Nature of Time and Space (19) Yesterday we considered how number (as qualitative dimension) can be given an imaginary (as well as real) meaning and that this thereby also applies to time (and space) in both physical and psychological terms.<br /><br />Basically what this entails is that development can take two complementary directions that are transcendent and immanent with respect to each other. Therefore if we associate real numbers (as dimensions) with the transcendent aspect, then the corresponding imaginary numbers are then - relatively - associated with the immanent aspect.<br /><br /><br />Though all these numbers (as dimensions) are implicit in actual human experience, remarkably little progress has yet been made with respect to any coherent explicit appreciation. And as I have stated repeatedly the conventional paradigm of Science and Mathematics as we know is merely of a 1-dimensional nature (in qualitative terms).<br /><br /><br />Now, when appropriately interpreted, the other dimensional numbers do unfold in varying degrees through the process of (authentic) contemplative development.<br /><br />However as practitioners in the past were rarely directly concerned with the mathematical implications of their newly acquired spiritual vision, the important scientific consequences were never made (except in the most general terms).<br /><br />So my own special concern from the start has been to marry the contemplative vision with rational understanding through exploration of the amazing new mathematical (and associated scientific landscapes) that thereby emerge.<br /><br /><br />One significant clue as to the nature of the imaginary number (as dimension) can be given through raising 1 to the power of i.<br /><br />Now as we have seen when we raise 1 to a rational number (such as 1/3) we generate a new number in the circular number system (i.e. on the circle of unit radius in the complex plane). <br /><br />However when we now raise 1 to the imaginary number i, we generate a new number in the linear number system. So we can see here how real and imaginary numbers (as qualitative dimensions) are associated with circular and linear quantitative results respectively. <br /><br />So a key task with healthy contemplative development is the successful balancing of both transcendent and immanent directions. This implies likewise the successful balancing of appreciation of number (as qualitative dimension) in a - relatively - real and imaginary manner.<br /><br /><br />As we saw yesterday transcendental type understanding (in qualitative terms) is of the most refined manner possible in the phenomenal realm.<br /><br />So before moving directly into the subject of today's entry, I will briefly summarise on the various types of transcendental dimensions.<br /><br /><br />Real transcendental dimensions are of the most refined type whereby one understands all phenomenal relations - not in terms of (separate) linear or (circular) holistic notions - but rather as the relationship between both.<br />The positive refer to the subtle rational appreciation of this relationship; the negative then relate to direct intuitive realisation.<br /><br /><br />However the final step in the phenomenal realm is making the understanding associated with corresponding imaginary directions explicit. <br /><br />So the imaginary transcendental dimensions relate to understanding of projections (in the indirect conscious expression of unconscious meaning) as the relationship between both (separate) linear and (holistic) circular understanding. <br /><br />Indeed it is precisely in successfully being able to understand projections in terms of this necessary relationship of conscious and unconscious that the involuntary nature of such projection ceases. So involuntary projections always arises due to a certain failure in properly relating the unconscious desire for meaning (embodied in such projections) with the conscious phenomenal circumstances through which they are expressed.<br /><br /><br />Once again the positive expression of such imaginary transcendental dimensions relates to a highly refined form of rational understanding of their nature; the negative expression again relates to the more direct intuitive realisation of this nature.<br /><br /><br />Now, I have already likened the contemplative journey to a steep mountain climb. The real transcendent aspect of this journey - notice the close association here with the qualitative mathematical meaning of transcendental - relates to the ascent (that ultimately leads to a spiritual experience beyond all phenomena of form).<br /><br />The corresponding descent then relates to the immanent aspect of the journey resulting in a spiritual experience that is inherent within all phenomena.<br /><br /><br />Just as the Riemann Hypothesis is generally considered the most important unsolved problem in Mathematics, the Euler Identity is likewise considered its most remarkable equation (formula, relationship).<br /><br /><br />Now because every quantitative relationship equally has a qualitative significance (that is formally unrecognised in conventional mathematical terms), this suggests that an extremely important qualitative meaning is associated with the Euler Identity (that can only be decoded in the appropriate manner).<br /><br /><br />Now conventionally the Euler Identity is expressed by the equation, <br /><br />e^(πi) + 1 = 0;<br /><br />Therefore e^(πi) = - 1.<br /><br />Then by squaring both sides <br /><br />e^(2πi) = 1.<br /><br /><br />We now have e (which is itself a transcendental number) raised to a dimensional expression (that is of an imaginary transcendental nature).<br /><br />Notice how when we raised a rational number to a rational number the result was irrational; then when we raised an irrational number to an irrational number the result was transcendental. So we have continued to move in the direction of increasing transcendence (from a qualitative perspective).<br /><br />However now in this special case where the base transcendental number is e, we raise it to a special case of a transcendental number where the dimension is 2πi, we obtain the simplest of all rational numbers (which in qualitative terms is thereby of the most immanent nature).<br /><br /><br />So putting it simply, the Euler Identity, when understood in an appropriate qualitative manner, points to the mysterious transformation in contemplative development where both form and emptiness are perfectly reconciled.<br /><br /><br />We saw earlier how development entails both differentiation and integration (through the odd and even numbered dimensions respectively. So the ultimate task of transformation is to reach a state where differentiation and integration both coincide. <br /><br />Now e is the perfect numerical symbol of such transformation as both the differential and integral of e^x are uniquely the same!<br /><br />Now in the real unit circle, the circular circumference is 2π. However if we now consider the radius as imaginary - rather than real - then the circular circumference is 2πi. However imaginary in this qualitative sense combines both positive and negative directions. So the imaginary circle is better represented as a non-dimensional point. Here both line and circle are perfectly reconciled from a quantitative perspective; likewise both linear and circular understanding are perfectly reconciled in qualitative terms.<br /><br /><br />So e^(2πi) in qualitative terms is inseparable from e^0 in quantitative terms!<br /><br /><br />Therefore in qualitative terms - when finally experience becomes of a pure formless nature as transcendence - it thereby equally becomes immanent as inherent in all form (represented qualitatively as 1).<br /><br />In the various mystical traditions extensive attention has been given to the nature of this key transformation.<br /><br />Perhaps the most famous expression is given in the Buddhist sutra:<br /><br />"Form is nor other than Emptiness<br /><br />Emptiness is not other than Form."<br /><br />Well in a precise mathematical manner (where symbols are appropriately understand in the qualitative manner) the Euler Identity describes the same transformation.<br /><br />However even this is not the end of the mathematical story of numberPeter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-67782447949228803712012-08-30T02:17:00.004-07:002012-09-21T08:15:40.217-07:00Multidimensional Nature of Time and Space (18)We looked briefly at the qualitative nature of a transcendental number yesterday.<br /><br />Once again it requires the explicit recognition of both linear (discrete) and circular (continuous) notions, with the transcendental aspect relating directly to the necessary (irreducible) relationship as between both.<br /><br />Therefore to stress an important point, if we wish to avoid gross reductionism, we cannot deal with the nature of a transcendental number such as π or e in a merely rational manner!<br /><br />And of course Conventional Mathematics is defined by such reductionism!<br /><br />Thus the value of π properly relates therefore to a mysterious conjunction as between (finite) discrete and (infinite) continuous notions which - literally - transcends the linear interpretation of reason.<br /><br /><br />So the transcendental notion of time (and space) arises from this explicit recognition of the dynamic relationship as between analytic (rational) and holistic (intuitive) type aspects. In the most accurate sense, it reflects therefore an understanding of dimension that serves as the relationship of both finite and infinite meaning.<br /><br />Now as the very recognition of any phenomenon requires a certain degree of linear separation in experience, the implication is that the purest form of transcendental understanding ultimately is so refined that (separate) phenomena can no longer be explicitly recognised.<br /><br />However as actual experience represents but an approximation to this state, refined phenomenal recognition necessarily arises.<br /><br /><br />So the positive aspect of qualitative transcendental recognition is in in the refined rational understanding of its dynamic nature. The negative aspect then relates to its direct intuitive recognition. So as positive and negative aspects interact in experience, clearly phenomena that arise become of an ever transparent nature (as relative expressions of the continual present nature of reality that is absolute).<br /><br /><br />However there is even one more step to take here.<br /><br />As we know the importance of imaginary quantities is now well recognised. This implies therefore that this notion of imaginary has an equally important meaning in the qualitative sense of dimension.<br /><br />Just as the dimensions can be given real numbers (with a corresponding interpretation of the nature of space and time), equally they can be given an imaginary interpretation.<br /><br /><br />So to what do these imaginary dimensional numbers precisely relate?<br /><br /><br />Basically I would explain it like this!<br /><br />Progression with respect to the real numbers as dimensions, relates directly to an increasing transcendent experience of reality. Here - literally - its ultimate spiritual nature (at the ever present moment continually renewed) is gradually seen to transcend all its more limited phenomenal expressions. And as we have just demonstrated, if one has reached contemplative experience (corresponding to these transcendental numbers) these phenomenal expressions are necessarily of a highly refined transparent nature.<br /><br /><br />However there is an equally important immanent aspect to development, whereby the ultimate nature of reality (as the ever present spiritual moment) is understand to be already inherent in every phenomenal form that arises.<br /><br /><br />So to use an analogy, that may be of some assistance! The transcendent aspect of development is akin to the ascent in reaching the summit of the mountain. However having reached the summit, one is faced with the opposite problem of achieving the successful descent and getting back on familiar ground once more.<br /><br />Thus if contemplative development is to be properly grounded as it were, both the immanent and transcendent aspects must be equally emphasised.<br /><br /><br />And the key role of the imaginary numbers as dimensions is that - when appropriately understood - these are directly tied up with theses corresponding immanent dimension.<br /><br /><br />The basic idea is not too difficult to express! Basically what is imaginary in qualitative terms, relates to the unconscious. Now, as we have seen with the Olympics this Summer, many athletes at a young age form a dream of one day reaching the summit with respect to their own particular event in becoming the Olympic champion. <br /><br />Thus this dream thereby represents the potential for transcendence, in going completely beyond all obstacles standing in the way of fulfilling one's goal.<br /><br />However though this dream is very important, it is not sufficient in itself. So if for successfully realisation, it must become grounded in actual life, through all the practice and training required. So when the gold medal is eventually won, the dream thereby now becomes the reality (with both transcendent and immanent aspects successfully united).<br /><br />So the actual attempt to realise the dream, consists in transferring this great drive and energy emanating from the unconscious back into the conscious domain through long dedicated preparation. So in this very process of transference, the unconscious is gradually made conscious, and the imaginary becomes real.<br /><br /><br />In fact when properly understood, this is related directly to the imaginary dimensions of time (and space).<br /><br /><br />So the real dimensions lead to an increasing intensification in depth with respect to the unconscious (through transcendence); the imaginary dimensions lead to the transference of this unconscious energy back into the conscious domain of everyday life. <br /><br /><br />So if we are to look at the most advanced development possible in the qualitative (contemplative) domain, it would involve transcendental structures of an imaginary kind!<br /><br />In the next blog entry, we will see the truly remarkable culmination of such understanding with respect to the famed Euler Identity (where its inherent qualitative significance can be made manifest).Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-38434521465767923282012-08-29T01:34:00.005-07:002012-09-21T08:15:56.353-07:00Multidimensional Nature of Time and Space (17)Yesterday we looked briefly at the qualitative nature of time (and space) from an (algebraic) irrational perspective.<br /><br /><br />Now an (algebraic) irrational number arises as the solution to a polynomial equation with rational coefficients. The famed square root of 2 - which is the best known example of an irrational number - arises from the simple polynomial expression x^2 = 2!<br /><br />What this implies with respect to the nature of time (and space) is that a hybrid dynamic mix of the two logical systems (linear and circular) are involved, whereby relative notions are continually reduced in somewhat absolute terms and - in reverse - absolute notions quickly transformed in a relative manner.<br /><br /><br />Once again, we see this clearly in nature at the sub-atomic level where energy is continually reduced in terms of mass and mass once more transformed into energy.<br /><br />So in holistic mathematical terms, such interactions properly take place in an environment characterised by irrational notions of time (and space).<br /><br />In corresponding psychological terms, understanding of these dimensions typically unfolds through authentic contemplative development, where nondual notions of reality are continually reduced in a dualistic manner and then likewise such dualistic notions continually transformed again in a nondual manner.<br /><br />And this leads to a a more refined dynamic type of understanding whereby reason and intuition continually interact in experience.<br /><br /><br />We have already looked at the differentiated nature of experience that corresponds with the odd integers and the corresponding integrated nature of the even dimensions. So in a very accurate sense, irrational understanding arises when both odd and even dimensions are combined. So once the first two dimensions unfold in experience, then irrational type understanding (in this strict mathematical sense) will then arise through the process of attempting to relate both dimensions.<br /><br /><br />As with rational, all irrational numbers can be given both a positive and negative identity.<br /><br /><br />So this then raises the question as to what is implied by the nature of time (and space) in negative irrational dimensions.<br /><br />Now, perhaps initially this can be more easily approached from the psychological perspective. We have already seen how with the odd dimensions (as positive) i.e. where one attempts to understand in a direct rational manner, that the main problem relates to unrecognised projections (of an unconscious intuitive kind).<br /><br />By contrast with the even dimensions (as positive) i.e. where one attempts to understand in a directly intuitive manner, the main problem arising is that of (unrecognised) rational attachments.<br /><br /><br />Therefore negation with respect to the irrational number dimensions, implies the dual attempt to erode unwanted attachments of both an unconscious and conscious nature.<br /><br />When successful therefore, this leads to both a purer rational and intuitive appreciation of the dynamic nature of reality involved.<br /><br /><br />However an important limitation attaches to (algebraic) irrational understanding in that the (imaginary) unconscious nature of personality initially remains comparatively undeveloped. This then sets limitations to the extent to which dynamic negation can be successful in eroding all unnecessary confusion.<br /><br /><br />This is where we come to another remarkable holistic mathematical finding.<br /><br />When Hilbert in his famous address named his 23 important - and yet unsolved -mathematical problems one of these related to the status of a number such as 2^(square root of 2). It was believed to be of a transcendental nature but this had not yet been proved. Indeed Hilbert mistakenly believed that this problem would take longer to solve than the Riemann Hypothesis!<br /><br /><br />In fact it was proved within Hilbert's lifetime. However it demonstrates once more how the the very nature of a number is transformed in quantitative terms through relating a base expression to a dimensional number (as power).<br /><br />So we saw yesterday with respect to a^b, when both a and b are rational (with b a fraction, an (algebraic) irrational number arises.<br /><br /><br />We can take this one step further by showing how when b is now irrational (and a either rational or irrational) that a transcendental number arises.<br /><br />In conventional mathematical terms, a transcendental number is expressed as an irrational number that cannot arise as a solution to a polynomial equation with rational coefficients. The most famous examples of such numbers are π and e.<br /><br /><br />However as always we can give such a number a qualitative as well as quantitative meaning.<br /><br />As we have seen the earlier stages with respect to authentic contemplative development (in what is sometimes is referred to as the subtle realm) imply the irrational interpretation of dimensions (from the holistic qualitative perspective).<br /><br />Typically one's perceptions of reality are much more fluid where both dual (rational) and nondual (intuitive) aspects increasingly interpenetrate. Later in development more deep rooted concepts likewise unfold with again dual and nondual aspects interpenetrating.<br /><br />However, as one now begins to increasingly match both perceptions and concepts of this nature a further important transformation in development is required, whereby experience now becomes transcendental (in a precise qualitative mathematical manner)<br /><br /><br />Now it would be valuable to probe more closely here what such transcendental experience entails. <br /><br />Putting in bluntly, at the earlier irrational (subtle) stages, a certain mismatch of conscious and unconscious is in evidence. From one perspective, one is still too ready to reduce what is properly unconscious (and nondual) in rational terms. Likewise from the other perspective one is equally too ready to elevate what is properly conscious and nondual in an intuitive manner.<br /><br /><br />However because rational and intuitive aspects are complementary in nature, the proper balancing of both irrational perceptions and concepts requires that both conscious and unconscious aspects come into equal balance.<br /><br />Thus when the new transcendental type knowledge unfolds (in what - again - is sometimes in Eastern terms referred to as the causal realm) it is of a new even more refined nature. So with respect to the nature of reality, one does not emphasise either dual or nondual aspects (as separate) but rather as the relationship between both dual and nondual aspects. Attaining such a position requires that attention focus more directly on the harmonising nature of the will (as a means of reconciling both conscious and unconscious).<br /><br /><br />This also provides a fascinating qualitative insight into why a transcendental number cannot be the solution of a polynomial equation. <br /><br />Such a solution always entails a reduction of a higher dimensional value in 1-dimensional terms.<br /><br />So once again if we have x^2 = 2, the higher dimensional value here (corresponding to 2 as dimension) = 2. Then we obtain x = the square root of 2, it thereby corresponds to the reduced 1-dimensional value.<br /><br />However the very nature of transcendental is that reality essentially represents the relationship as between dual and nondual. Therefore we cannot attempt to either reduce or elevate one in terms of the other.<br /><br /><br />So the transcendental nature of time (and space) is now of an extremely subtle variety as representing the essential relationship as between actual (finite) and potential (infinite) aspects of understanding. This corresponds in experience with a highly refined and dynamic understanding where both reason and intuition interpenetrate in pretty equal measure.<br /><br /><br />In fact perhaps the best representation of the nature of such understanding is with respect to most famous transcendental number π.<br /><br />Now π in quantitative terms represents the (perfect) relationship as between the circular circumference and its line diameter.<br /><br />Equally in qualitative terms, π represents the (perfect) relationship as between both circular and linear type understanding. And what is common to both is the point at the centre of the circle which equally is at the centre of the line diameter. <br /><br />So pure transcendental understanding, therefore can be expressed as the ineffable midpoint (or singularity) where linear or circular understanding of a separate nature no longer remains. <br /><br /><br />Just one further observation is worth making here!<br /><br />I have mentioned before how from a higher dimensional perspective the very nature of mathematical proof is inherently subject to an Uncertainty Principle. <br />What this entails is that - properly understood - such proof represents an inevitable dynamic interaction as between two aspects which are quantitative and qualitative with respect to each other.<br /><br />As we have seen elsewhere, implicitly the Pythagoreans were searching for this type of proof. From a quantitative perspective they were indeed able to show why the square root of 2 is irrational! However what really troubled them was that they were unable to provide a satisfactory qualitative rationale as why this was the case!<br /><br />So now we have yet another example with respect to the nature of a transcendental number. From a quantitative perspective, it can be proved why any rational (or irrational number) other than 1 raised to an irrational dimensional power will result in a transcendental number.<br /><br />And from my own holistic mathematical investigation of the nature of the stages of contemplative development, I have been able to provide a corresponding qualitative explanation as why to this behaviour occurs.<br /><br />Therefore, a comprehensive understanding of this relationship entails both quantitative and qualitative aspects (with an inevitable uncertainty attaching to both). Thus current mathematical proof with respect to the merely quantitative nature of transcendental numbers, reveals a subtle confusion (for in quantitative terms we can never precisely determine the value of any transcendental number).<br /><br />So for example the wide held belief that π is a constant, strictly has no meaning in - merely - quantitative terms (as we can never precisely determine its value). <br /><br /><br />When we look at Mathematics in a more comprehensive manner we realise that the quantitative is always balanced by a corresponding (holistic) qualitative aspect.<br /><br />So a rational number therefore (in quantitative terms) corresponds to rational type understanding (from a holistic qualitative perspective).<br /><br />Equally however a transcendental number (in quantitative terms) corresponds to transcendental type understanding (from a holistic qualitative perspective) And as we have see transcendental in this qualitative sense relates to the the highly refined understanding where both linear (rational) and circular (intuitive) type understanding are both explicitly recognised and kept in a certain balance to each other. (And as we have seen with the purest development of such understanding they are kept in perfect balance!)<br /><br />Therefore one cannot properly attempt - without gross reductionism - a rational proof (in qualitative terms) of what is transcendental (from a quantitative perspective).<br /><br />So once again for example we cannot give a - merely - rational meaning to the notion that π is a constant because it is not a rational number (with it's value strictly indeterminate from a merely quantitative perspective!) Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-3452306507588501022012-08-28T01:47:00.005-07:002016-09-26T06:47:59.991-07:00Multidimensional Nature of Time and Space (16)As stated so often when properly understood as the very nature of experience, Mathematics has both quantitative and qualitative aspects in dynamic interaction with each other. So from this perspective one does not understand symbols in static terms as absolute forms, but rather in dynamic interactive terms as symbols of transformation!<br /><br /><br />I will now attempt to illustrate one extremely important example of this new understanding (with intimate parallels to the nature of psychological development).<br /><br /><br />As befits the dynamic approach, in a number expression such as a^b, if we designate the base number a in quantitative terms - the dimensional number b is - relatively of a qualitative nature.<br /><br />And it is this interaction as between quantitative and qualitative aspects that can then be used to explain how the nature of number itself evolves to "higher" forms.<br /><br /><br />So for example if we start with the simplest of prime numbers 2 and then raise this to 2 (i.e. 2^2), the result is a natural number integer (which is not prime).<br /><br />So we can se how the very nature of the number has now changed.<br /><br /><br />Now to obtain the appropriate corresponding situation in psychological terms, we must remember that all experience necessarily entails the dynamic interaction of perceptions and concepts which are - relatively - quantitative and qualitative with respect to each other.<br /><br />Therefore if we designate the perceptions as quantitative (which is the standard approach in Conventional Science) then corresponding concepts - are relatively - of a qualitative nature. (Of course in formal scientific and mathematical interpretation, concepts are misleadingly also treated as quantitative leading to a merely reduced interpretation of subsequent dynamics).<br /><br /><br />So in other words an infant at the primitive stage of development initially will develop primitive perceptions and later primitive concepts (both of a transient nature) . It is then in the successful fusion of such perceptions and concepts that development reaches the next natural stage (i.e. where natural objects with a greater degree of constancy emerge in experience).<br /><br /><br />So in this sense we see how psychological development - in line with the nature of number - evolves from a prime to a natural stage. So what we are really showing here is how number possesses both a qualitative and quantitative relationship to order (with the qualitative aspect of number directly relevant to ordering the various stages of development).<br /><br /><br />Now switching back to the quantitative nature of natural numbers, the next development is to recognise a negative as well as positive identity in the generation of all the integers.<br /><br /><br />Then when we raise - as for example the number 2 to - 1 i.e. 2^(- 1) a remarkable number transformation takes place whereby we generate a new type of rational number (i.e. a fraction).<br /><br /><br />Now again there are direct correspondents on the psychological side. The negative integers here refer to the increasing ability of the child to hold objects in memory even when temporarily absent (giving them a greater absolute constancy).<br /><br />This in turn enables the child to experience concepts in negative terms i.e. where they can be held in memory as a basis for organising experience when dealing with corresponding perceptions. <br /><br /><br />And this is the very basis of rational ability whereby both object perceptions and concepts can be repeatedly subdivided in analytical terms and rearranged into new aggregate wholes.<br /><br />And once again Conventional Science (and Mathematics) is defined by the specialisation to the nth degree of such ability.<br /><br /><br />However now we come to the interesting part! <br /><br />If we take again the simple number 2 and now raise it to its reciprocal fraction 1/2, we generate a new type of number that is (algebraically) irrational in nature. Indeed this is the famed square root of 2 that caused so much difficulty for the Pythagoreans many years ago!.<br /><br /><br />The psychological correspondent implies that if we now try to dynamically relate rational perceptions with rational concepts, which is the very nature of scientific and mathematical experience, we should generate a new (qualitative) form of irrational understanding in holistic terms! <br /><br /><br />The obvious question then arises as to why this does not typically happen and the answer is - as we have seen - due to the misleading manner in which both perceptions and concepts are interpreted in formal terms with respect merely to their quantitative aspect. Therefore qualitative understanding, in the form of supporting intuition, remains of a merely implicit nature that is quickly reduced in rational terms.<br /><br /><br />So here we are giving a demonstration using the simplest of numbers to highlight an extremely important limitation of standard scientific and mathematical practice.<br /><br /><br />Thus even from the quantitative perspective, we cannot properly understood the nature of an irrational number without likewise also explicitly recognising a qualitative aspect! Now the Pythagoreans recognised this and their consternation arose from the inability to properly explain this qualitative aspect. However such appreciation has subsequently become lost through a greatly reduced - merely quantitative - interpretation of mathematical symbols in Western culture. <br /><br /><br />Therefore once again, because the (qualitative) dimensional nature of number relates holistically to the nature of both the physical and psychological dimensions, we must thereby recognise that time (and space) can necessarily be given an (algebraic) irrational meaning.<br /><br />Now the square root of 2 has two irrational roots i.e. that are positive and negative with respect to each other.<br /><br />I have attempted before to explain the nature of the corresponding experience of time and space with respect to the appreciation of a flower such as a rose.<br /><br />Now formerly one would have largely experienced this object as largely separate and discrete in experience. Initially this would be of a linear (1-dimensional) nature where the rose is viewed as a separate object in space and time. Then later with 2-dimensional understanding, greater subtlety would pertain with an appreciation of both mental and object perception of the rose as - relatively - external and internal with respect to each other.<br /><br /><br />These two directions would equally apply with this new irrational appreciation. However in relation to both the external and internal directions, a mixture of rational and intuitive appreciation would now be involved. Thus from the rational perspective, one would still appreciate the rose as a finite discrete object; however from the holistic intuitive perspective, one would recognise its continuity with all creation (as an archetype) whereby it radiates an infinite quality.<br /><br /><br />So quite simply the irrational nature of time and space arises when both discrete (finite) and continuous (infinite) aspects are so intertwined.<br /><br />This category of irrational dimensions likewise has deep implications for the true nature of sub-atomic particles, where again total independence (from other particles) does not strictly pertain, but rather a hybrid existence combining both discrete and continuous aspects. Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-12595160620956320172012-08-27T09:27:00.003-07:002016-09-26T06:44:51.292-07:00Multidimensional Nature of Time and Space (15)I have commented before on - what I refer to as - the Pythagorean Dilemma.<br /><br /><br />In other words the significance of the discovery that the square root of 2 is an (algebraic) irrational number, was as much of a qualitative as a quantitative nature.<br /><br />As I have stated, the Pythagoreans recognised an important qualitative significance to number. Prior to their discovery of the irrational nature of 2, they had assumed that all number quantities were of a rational nature. Happily this complemented well the scientific paradigm they used to interpret this reality which qualitatively was also of a rational nature.<br /><br /><br />So the true significance of the irrational nature of 2, is that the Pythagoreans lacked the qualitative holistic means to explain how it could arise, thus shattering the harmonious balance they sougth to preserve with respect to mathematical activity.<br /><br />The rational paradigm which still dominates present scientific and mathematical thinking is basically suited to interpretation of meaning that is of a finite discrete nature.<br /><br />However an irrational number by its very nature combines both finite (discrete) and infinite (continuous) aspects. Thus its quantitative value can be approximated as a rational number to any required degree of accuracy. However its qualitative nature leads to a continuous unending decimal sequence (with no fixed pattern).<br /><br />Therefore though the very nature of an irrational number - literally - transcends the mere rational perspective, Conventional Mathematics can only attempt to deal with such a number in a reduced quantitative manner.<br /><br /><br />Now once again the (linear) rational paradigm is 1-dimensional in nature (where all number quantities are ultimately expressed in 1-dimensional terms). <br /><br /><br /><br />Over the past 14 blog entries however I have been at pains to point out that a complementary (circular) rational paradigm exists where every dimensional number is defined in items of the same base quantity of 1. And as we have seen these dimensions then bear an important inverse relationship with their corresponding roots (in quantitative terms).<br /><br />So in these contributions, I have shown how all rational numbers (positive and negative) possess a unique qualitative significance that intimately applies to the nature of time and space (in both physical and psychological terms).<br /><br /><br />However just as an irrational number properly combines both finite (discrete) and infinite (continuous) aspects in its very nature, the same equally applies to an irrational number when given its appropriate qualitative interpretation.<br /><br />So the upshot of this is that from both the quantitative and qualitative perspectives, irrational numbers are of a hybrid nature truly requiring both Type 1 (analytic) and Type 2 (holistic) mathematical interpretation.<br /><br />And when this is done we can then give meaning to the irrational nature of time and space (in physical and psychological terms).Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com1tag:blogger.com,1999:blog-7725147822647272542.post-15062279876822534272012-08-26T05:04:00.004-07:002012-12-07T02:49:24.233-08:00Multidimensional Nature of Time and Space (14) To follow the next section requires even subtler understanding of psychological and complementary physical dynamics.<br /><br />My basic starting point with respect to the dynamic understanding of number, is that in any context the base quantity and dimensional number are quantitative as to qualitative (and qualitative as to quantitative) with respect to each other.<br /><br />Thus in the simple expression 1^2, the base number here (1) is understood in quantitative, whereas the corresponding dimensional number (2) is understood - relatively - in a qualitative manner.<br /><br /><br />As we have seen Conventional Mathematics is interpreted in terms of the (default) dimensional number of 1 (as qualitative) whereby qualitative is necessarily reduced to quantitative meaning.<br /><br />Therefore if we take the expression 2^3 to illustrate, the result will be expressed, from this perspective, in reduced quantitative terms as 8 (i.e. 8^1). <br /><br /><br />Now to explore the qualitative nature of mathematical symbols in isolation, we then reverse interpretation, whereby every mathematical expression is defined in terms of a default base quantity of 1! <br /><br />And in our exploration of the nature of time (and space) we have illustrated the varying configurations that arise through changing the dimensional numbers as powers with respect to the fixed quantity of 1 (which have an inverse quantitative interpretation as corresponding roots of 1). Thus the first 2 dimensions (where only 2 are involved) - which intimately apply to the dynamic nature of time and space (+ 1 and - 1) - bear an inverse relationship to the corresponding 2 roots of 1 (in quantitative terms). <br /><br /><br />However we could equally adopt as our starting point the position whereby the base number is now understood in qualitative terms and the corresponding dimensional number - relatively - as quantity.<br /><br /><br />And in the actual dynamics of psychological experience (and the complementary physical reality corresponding to such experience) continual switching takes place whereby both base and dimensional numbers keep alternating as between quantitative and qualitative interpretation. With respect to psychological understanding this simply means that both perceptions and concepts likewise continually alternate between actual and potential meanings resulting in a continual transformation of experience.<br /><br /><br />And once again the actual aspect (with respect to both perceptions and concepts) is directly associated with (conscious) reason whereas the corresponding potential aspect is directly associated with (unconscious) intuition.<br /><br />This likewise means that with respect to the fractional nature of time (and space) that we briefly explored in the last blog entry, that understanding likewise continually alternates as between qualitative and quantitative interpretation. <br /><br /><br />This represents a generalisation, with respect to the nature of space and time, of what we take for granted on a more mundane level.<br /><br /><br />For example if a cake is divided into 4 slices one will naturally be able to view each slice as unit whole and also as a fractional part of the whole cake. Likewise one will be able to appreciate the cake itself as a whole unit that is composed of multiple unit parts. Implicitly the dynamics of such understanding requires that we are able to view both parts and wholes (in quantitative and qualitative terms) in order to make these connections. However the qualitative aspect remains merely implicit in customary understanding, with the results interpreted in reduced quantitative terms! <br /><br /><br />So for this reverse understanding with respect to the nature of dimensions, whereas the emphasis is now explicitly on qualitative type appreciation, implicitly it equally requires the ability to view these dimensions in quantitative terms.<br /><br /><br />Using the more spiritualised language, that customarily is associated with respect to multidimensional understanding, when the dimensional number is seen as qualitative - relative to a base number as quantitative - this will lead to a more transcendent appreciation of the nature of reality (where its holistic nature is gradually understood as beyond all form). <br /><br />However when the dimension is now seen as quantitative - relative to a base number as qualitative - it will lead to a more immanent appreciation of the nature of reality (where its holistic nature is gradually seen as inherent within all form).<br /><br /><br />Again for truly balanced appreciation of reality both aspects are required. Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-29326465461875098062012-08-25T07:21:00.005-07:002012-09-21T08:16:55.605-07:00Multidimensional Nature of Time and Space (13)As we know from a quantitative perspective rational numbers exist that are not integers i.e. fractions.<br /><br />This applies therefore that from a qualitative perspective, we equally can give meaning to rational numbers as fractions.<br /><br />And as the very nature of time (and space) when appropriately understood is intimately related to the qualitative dimensional notion of number, this likewise applies that we can give meaning to the fractional nature of time (and space) from both complementary physical and psychological perspectives. <br /><br />It perhaps will be easiest in this respect to start with the number 2 (as ordinal dimension). As we have seen this ordinal dimension (from a qualitative perspective) is intimately connected with its corresponding root (in quantitative terms).<br /><br />Thus the 2nd root of 1 can be written as 1^(1/2) = - 1 and in quantitative terms this result matches the corresponding 2nd dimension i.e. 1^2 = - 1 (which here relates to a qualitative interpretation).<br /><br />Thus as we have seen the 2nd dimension in qualitative terms relates to the - relative - negative direction of the nature of time (and space) in switching as between polar opposites in experience. And we already have seen how this dimension is implicitly involved in all scientific interpretation (though explicitly completely ignored).<br /><br />However because each whole number (as dimension) is intimately linked with its reciprocal (in quantitative terms) this implies that we can now give a meaning to 1/2 with respect to the nature of time (in quantitative terms).<br /><br />What this simply means is that because now one explicitly recognises the existence of two dimensions with respect to the qualitative nature of time (that are positive and negative with respect to each other) then if we isolate just one of these directions (in absolute terms) it thereby represents 1/2 of the total number of dimensions.<br /><br />Once again let us illustrate with the simple example of a straight road. So starting from a given point, I can move up or down the road. Now if I separate the two reference frames (considering movement with either "up" or "down" as independent), movement along the road will take place positively in space and time. So clearly because there are two possible directions, one of these in isolation represents 1/2 (of the total number of possible directions).<br /><br />However if I now consider the two directions as interdependent (befitting the qualitative approach) movement is of a merely relative nature. So positive movement up the road, thereby - relatively - implies negative movement with respect to the corresponding "down" direction. And it is this relatively negative movement that the 2nd dimension directly implies (in qualitative terms). <br /><br /><br />So an integer number (in qualitative terms) is necessarily associated with a corresponding fraction (from a quantitative perspective). So in this restricted quantitative sense, we can thereby give a fractional meaning to time (and space).<br /><br /><br />Let us further illustrate with respect to the especially important case of 4 dimensions. The 4 dimensions of 1 correspond in turn to the 4 roots of 1^1, 1^2, 1^3 and 1^4 respectively.<br /><br />Therefore the 4 roots of 1 in quantitative terms are 1^(1/4), 1^(2/4) = 1^(1/2), 1^(3/4) and 1^(4/4) = 1^1. <br /><br /><br />The corresponding dimensions in qualitative terms are provided through the reciprocals of these powers i.e. 4, 2, 4/3 and 1.<br /><br />Now three of these are integral dimensions relating to the 1st, 2nd and 4th dimensions respectively.<br /><br />However the 3rd dimension (in this context of 4 dimensions) is already expressed as a fractional number. And in this case the fractional number has a qualitative rather than quantitative meaning!<br /><br /><br />Underlying this is a very deep issue indeed with enormous consequences for the very nature of Mathematics which seems to me entirely overlooked in conventional understanding.<br /><br /><br />Putting it simply, an unavoidable ambiguity attaches to the ordinal notion of number.<br /><br />For example we might consider that 3 is an unambiguous number. However 3 can be given both a cardinal and ordinal meaning. <br />And when we look at 3 in an ordinal sense its meaning is entirely relative. In other words the 3rd of a group of 4 items is quite distinct from the 3rd of a group of 5.<br /><br />Equally the 3rd dimension (as the 3rd of 4) is quite distinct from the 3rd (as the 3rd of 5).<br /><br />In other words, properly understood, the ordinal nature of number is merely relative. And as the ordinal itself is inseparably linked with its corresponding cardinal meaning, this implies that the cardinal notion of number - when properly understood - is likewise of a merely relative nature.<br /><br />This is just another way of recognising that the number system itself represents - when appropriately understood - a dynamic interaction as between quantitative and qualitative aspects (which are - relatively - cardinal and ordinal with respect to each other).<br /><br /><br />Furthermore, Riemann's finding that a harmonic system of wavelike numbers (the non-trivial zeros) underlines the number system is simply evidence - again when correctly understood in dynamic terms - of the dual relative nature of number. <br /><br /><br />Therefore in considering higher numbered dimensions (in ordinal terms) we are inevitably led to the generation of fractional numbers for most of these dimensions. And the integer dimensions represent but a special case of these fractional dimensions.<br /><br />In other words, if we limit ourselves to n members (in cardinal terms) the nth member (as ordinal) can be given an unambiguous interpretation. Thus the 4th dimension (of 4 dimensions) can be written with the integer 4 (in qualitative terms). However the 4th member of any higher number of dimensions will be represented as a fraction (in qualitative terms).<br /><br /><br />Thus from this perspective, the dimensions of time (and space) can be given meaning in terms of rational fractions both directly in qualitative and indirectly in quantitative terms.<br /><br />Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-21227482991550367612012-08-24T03:39:00.007-07:002015-02-06T06:32:44.385-08:00Multidimensional Nature of Time and Space (12)We will now consider directly the nature of time (and space) associated with the negative integers (as qualitative dimensions). <br /><br /><br />The even integer dimensions (- 2, - 4, - 6, - 8,...) are easier to explain, for here in all cases - from the psychological perspective - time has no phenomenal meaning with experience relating directly a present moment continually renewed. This in turn would be consistent with a pure contemplative state.<br /><br />Of course, because in actual experience, all the varying dimensions co-exist (at least with the potential to exist) we cannot completely isolate the experience of any one dimension. However having said this, at any moment one or more can be especially prominent. <br /><br />So therefore for example if the experience of the negative 2nd dimension is predominant then indeed one will have little consciousness of time (or space) but rather the spiritual awareness of the (absolute) present moment. Once again such experience is of a purely intuitive nature resulting from the successful negation of any secondary rational attachment to the notion of reality as merely relative (based on the the complementarity of real opposite poles).<br /><br /><br />So the positive 2-dimensional experience relates to refined rational understanding of the relativity of opposite real poles, in which case one understands time (and space) as having both positive and negative linear directions.<br /><br />The negative 2-dimensional experience then relates to the direct intuitive realisation of the relativity of these same poles (which results in immediate experience of a present reality). <br /><br /><br />And again because physical and psychological aspects are themselves complementary, this equally implies that a physical correspondent exists for all negative even dimensions. Again the positive 2-dimensional structure would relate to the dynamic nature of matter particles resulting - relatively - from both positive and negative aspects (of time (and space) i.e. real matter and anti-matter particles. The negative 2-dimensional state would relate directly to the energy fusion (arising from the interaction) which again would exist in an immediate present moment. <br /><br /><br /><br />Once again, the negative odd dimensions are more difficult to describe, especially in relation to the dynamic nature of time and space involved.<br /><br />In one important respect they represent the reverse of what is involved with the even number dimensions.<br /><br />Perhaps again it may be initially easier to appreciate this from a psychological contemplative perspective (where explicit experiential knowledge of such dimensions unfolds).<br /><br /><br />Now all the mystical traditions speak of the dangers of possessive attachment (which essentially relate to a confused interpretation of the nature of reality). One such attachment is where rational understanding tends to dominate purer intuitive realisation of what is appropriate to the situation leading to an unfortunate form of reductionism. As we have seen such reductionism is endemic with respect to conventional (formal) interpretation in both Science and Mathematics. <br /><br />Therefore from the psychological perspective though (discriminating) reason and (holistic) intuition necessarily interact in all such understanding, formal interpretation completely excludes intuition - and thereby distorts - its true nature; equally from the complementary physical perspective though phenomenal reality entails the dynamic interaction of visible finite particles with an invisible holistic ground, again experience of reality formally is based on the direct reduction of the infinite aspect in finite terms.<br /><br /><br />Thus one important task in the development of an authentic contemplative vision is the erosion of (rigid) conscious attachments (of sense and reason) thereby freeing the intuitive light, with which is equally associated a new refined appreciation of the nature of physical reality.<br /><br />And essentially, it is this type of passive purgation (i.e. negation) that applies with the even numbered dimensions which - when successful - leads to the experience of ever more refined intuitive states.<br /><br /><br />However, there an equally important type of active detachment required (which to my mind is not sufficiently emphasised in the mystical literature). Thus, higher stages of development are not just concerned with the attainment of ever more refined intuitive states. Equally they are concerned with with the attainment of ever more refined rational structures, whereby one is enabled to think about reality in a much clearer manner (which should be one important goal of Science).<br /><br /><br />So, whereas purer intuition is developed through cleansing of the confusion of unnecessary rational attachment, purer reason, is developed - by contrast - through cleansing the confusion associated with unnecessary intuitive clutter. <br /><br />Such clutter typically arises through unrecognised projections of an unconscious nature that then can considerably interfere with conscious type activity.<br /><br />So much as we might profess the neutrality of science, based merely on objective rational assessment of truth, in practice this is but an illusion with scientists' judgement at every turn subtly - and sometimes not so subtly - influenced by all sorts of unconscious prejudices (of which they generally are not aware).<br /><br /><br />As I have stated before, the higher odd dimensions are always associated with the pursuit of linear activity. However the higher the dimension involved, the more aware one becomes of new unconscious projections that interfere with direct rational activity. <br /><br /><br />Putting it bluntly, all scientists and mathematicians inevitably fall victim to unconscious projections and prejudices that interfere with the neutral pursuit of rational truth. However at the 1-dimensional level, they are likely to remain largely unaware of these projections, whereas at the higher odd dimensions, there will be a growing realisation of their nature (and how they interfere with conscious reason).<br /><br /><br />Thus the negative odd dimensions are, in psychological terms, associated with the gradual erosion of involuntary projections. So when successful traversed, a purer form of rational activity results (largely free of involuntary projections).<br /><br />Once again there is a remarkable correspondent of this with the Riemann Zeta Function, whereby for all odd integers a rational number results.<br /><br /><br />So therefore with respect to time and space, the negative odd dimensions are associated with a purer experience of their linear nature (where both move in a forward direction). And this linear nature corresponds with the ability to actively involve oneself in a conscious rational manner (free of interference from involuntary projections).<br /><br />So strictly when one is the victim of phenomenal projections, all sorts of confusion arise. One may still interpret that one is operating within a framework of linear time (and space) but in truth this will be mingled also with unrecognised rigid forms of imaginary time (and space).<br /><br /><br />Most of my attention over the years has been to provide a truly scientific rationale (of a holistic mathematical nature) with respect to the higher stages of development. Though such stages have indeed been successfully traversed by the spiritual superstars of the varying mystical traditions, accounts are generally couched in the language of the various religions they represent. <br /><br />Unfortunately such accounts do not lend themselves readily to qualitative mathematical interpretation. So in some ways I would see myself as in the process of attempting to develop a new mathematical language that is consistent with the transformed understanding that unfolds with each of these stages.<br /><br /><br />And of paramount significance in this context is the holistic mathematical notion of dimension. So the stages of higher level development literally entail journeying through these varying dimensions (in their positive and negative form).<br /><br />And in this quest I would emphasise the importance of balance.<br /><br /><br />1. Higher level rational understanding of reality must be counterbalanced equally by higher level intuitive realisation, for in dynamic terms both mutually serve each other. Traditionally there has been far too much emphasis on mere reason within the scientific community and then too much emphasis on mere intuition within the esoteric mystical traditions. This has resulted in a considerable division as between the religious and scientific quests though in truth they should be seen as mutually complementary.<br /><br /><br />2. Even numbered dimensional stages are directly concerned with the integration of reality and the ultimate attainment of pure intuitive states as negative dimensions (which have an indirect rational interpretation as positive).<br /><br />Odd numbered stages - by contrast - are directly concerned with the differentiation of reality and the ultimate attainment of pure rational structures as negative dimensions (which have an indirect intuitive interpretation as positive).<br /><br /><br />3. For proper balance both odd and even numbered dimensions need to be emphasised; equally both positive and negative aspects likewise need to be emphasised.<br /><br />So contemplation (intuition) and reason are designed to mutually serve each other; Likewise differentiation (in active engagement with reality) and integration (in passive withdrawal) are equally complementary and likewise need to be kept in balance.<br /><br />Thus the contemplative quest is not designed just as a means of going beyond reality (as transcendent); equally it is designed as a means of more fully engaging with the world (as immanent). And the intuitive nature of both of these aspects needs to be always finely balanced with the complementary use of reason.Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-47732394514930054732012-08-23T01:53:00.009-07:002012-09-21T08:17:26.969-07:00Multidimensional Nature of Time and Space (11)We made the distinction yesterday as between implicit qualitative recognition of the 1st dimension as negative (where it remains completely ignored in formal mathematical interpretation), and full explicit recognition which inevitably leads to a redefinition of the nature of Mathematics (whereby both quantitative and qualitative aspects are recognised).<br /><br /><br />So once again, a mathematician may well recognise the important role of intuition with respect to important new discoveries. And this inherently requires to a degree - sometimes marked - the temporary negation of customary rational understanding. This then allows deeper holistic insight to incubate in the unconscious which is essential in enabling an important new breakthrough. But unfortunately such a mathematician will then formally interpret this new finding in a merely reduced rational manner (with the 1st dimension as positive solely recognised).<br /><br /><br />As I live in Dublin I can identify with the inscription on Brougham Bridge in honour of William Rowan Hamilton.<br /><br />"Here as he walked by on the 16th of October, 1843, Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication<br />i^2 = j^2 = k^2 = ijk = - 1"<br /><br />So this inscription indicates well how the "discovery" essentially relates to a sudden illumination (releasing holistic intuition into consciousness). Notice how this does not happen in the normal sequential manner of successive rational linkages spread out in linear time! Rather it represents the present moment thrust as it were into linear time (where the relationship of all aspects of the problem to each other are understood simultaneously). Indeed so fearful was Hamilton at losing such inspiration that he felt compelled to carve the equation immediately into the stone at the bridge (though alas no record of this now remains). <br /><br /><br />However in formal terms, Mathematics has nothing to say about the role of intuition in understanding, or its important dynamic interaction with rational type understanding. <br /><br /><br />So, in the most accurate sense, conventional mathematical interpretation thereby offers but a reduced and ultimately quite distorted account of the nature of mathematical truth.<br /><br />In other words, in the qualitative mathematical manner that I now use these terms, Conventional Mathematics is entirely defined within a merely (positive) 1-dimensional framework of interpretation, where qualitative is reduced to quantitative meaning. However proper incorporation of quantitative with qualitative requires recognition that all other numbers (as dimensions) have an important potential role to play in mathematical interpretation.<br /><br /><br />So once the negative 1st dimension - which remains merely implicit in conventional mathematical interpretation - is then explicitly recognised, the very nature of Mathematics changes from an absolute fixed to a relative dynamic approach, which necessarily entails the interaction of both quantitative and qualitative aspects. <br /><br /><br />Now, we have already looked at the nature of 2 as a dimensional number, which immediately arises through explicit dynamic recognition of the negative aspect of linear understanding. So 2-dimensional interpretation contains both positive and negative aspects, in dynamic relationship with each other (as the complementarity of real opposites).<br /><br />There is a remarkable evidence of this provided - when appropriately interpreted - by the Riemann Functional Equation. So s, representing a dimensional number (i.e. power) of the Function on the RHS, can be given a complementary expression on the LHS, now expressed with respect to the dimensional number 1 - s.<br /><br /><br />This suggest therefore that there are intimate connections as between 2 as dimensional number and - 1 (on opposite sides of the equation). What this means in effect is that we must keep switching as between quantitative and qualitative (and qualitative and quantitative) type understanding with respect to interpreting both sides of the equation.<br /><br /><br />Therefore when we explicitly recognise the holistic intuitive significance of the result for the Function, with - 1 as dimension on the LHS, this immediately leads to a corresponding recognition of the rational nature of the result for 2 (as dimension) on the RHS. In other words whereas the numerical result (π^2)/6 makes sense from a rational linear perspective on the RHS, this is not so with respect to the corresponding result (- 1/12) on the LHS! And the reason for this is that the LHS result does not conform directly to a linear quantitative, but rather a circular qualitative interpretation (of a holistic kind). <br /><br /><br />The deeper implication of this is that proper interpretation of the nature of the Riemann Zeta Function cannot be carried out from within the conventional mathematical perspective. As the real secret of the primes relates to this fundamental relationship as between its quantitative and qualitative aspects, clearly this is completely missed from a mere 1-dimensional perspective (where qualitative meaning is inevitably reduced in quantitative terms). <br /><br />So just as the Riemann Zeta Function is uniquely undefined in quantitative terms where s = 1, equally it remains uniquely undefined in qualitative terms (in terms of overall interpretation) likewise where s = 1. <br /><br /><br />We can now suggest a further important connection with the Riemann Zeta Function. <br /><br /><br />We have already defined 2 (as dimensional number) as the rational interpretation of the complementarity of opposite real poles.<br /><br /><br />However the very nature of reason is to separate poles. So we are attempting therefore to express with the number 2 (as positive dimension) what properly relates to the true nature of interdependence in an indirect rational manner (which tends to give it a somewhat independent identity).<br /><br />Therefore to move to the true intuitive meaning of what is implied by 2 (as dimension) we must negate such rational interpretation. <br /><br />Then when we successfully negate any lingering independent element we are left with the intuitive recognition of true interdependence (which is nothing in phenomenal terms).<br /><br /><br />Now this is deeply illuminating as the value of the Riemann Zeta Function (the first trivial zero) for which s is - 2, = 0.<br /><br />This strongly suggests that this numerical value corresponds directly to the holistic qualitative - rather than specific quantitative - meaning of 0. So once again, whereas we can interpret values on the RHS of the Functional Equation (> 1) in quantitative terms, corresponding values on the left are - relatively - of a qualitative nature.<br /><br /><br />In short whereas the positive sign with respect to any dimensional number, represents its rational interpretation, the corresponding negative sign represents its direct intuitive recognition (through negation of independent rational elements).<br /><br /><br />This explains therefore in qualitative terms, why the Riemann Zeta Function = 0 for the trivial zeros (i.e. negative even integer values of s). In all cases, these represent the complementarity of opposites where pure interdependence arises. And such interdependence is directly grasped through intuitive recognition (which implies negation of indirect rational understanding provided through the positive even number dimensions). And this recognition = 0 in phenomenal terms.<br /><br /><br />My own route to this understanding was based on a deep resonance with the work of St. John of the Cross, who deals very well with the negative dimensions (from a mystical contemplative perspective).<br /><br /><br />So the "dark nights" or purgations are directly concerned with the experience of negative dimensions (in qualitative mathematical terms).<br /><br />The active purgations relate to the odd numbered dimensions (especially 1). The passive purgations relate to the even numbered dimensions. And the direct goal of such passive purgation in St. John's terms is "nada" i.e. nothing (= 0 in qualitative terms). <br /><br /><br />Finally he talks of "nights of sense" and "nights of spirit". The former would relate in scientific terms to empirical perceptions whereas the latter would relate to more deep rooted theories and concepts. And we will later demonstrate a further startling holistic mathematical result that arises through the dynamic interaction of perceptions (as parts) and concepts (as wholes) respectively!<br /><br /><br />Thus once again we can see in the process of discovery of the greatest scientists and mathematicians (e.g. recently with Andrew Wiles) long periods spent in the intellectual wilderness. These implicitly in a mathematical context, constituted active nights of sense and spirit i.e. where attachment to former customary perceptions and concepts required considerable erosion before essential new insights could successfully develop.<br /><br /><br />Just to complete this section we return to the fact that what is true in psychological terms has - by definition - a complementary meaning from a physical perspective.<br /><br />Now just as interdependence in psychological terms leads to the generation of spiritual energy (in the form of holistic intuition) equally interdependence in physical terms leads to the generation of physical energy. However the mysterious feature of such energy as with light, is that it has no phenomenal existence in itself, but rather only indirectly through interaction with other phenomenal processes. <br /><br /><br />So if you look at the world through contemplative eyes, you will realise that because mass represents just another form of energy, that phenomena essentially do not exist! Rather what we term "physical reality" relates to arbitrary appearances of a merely relative nature that have no ultimate substance.<br /><br /><br />However the point that I am making is that such realisation is equally consistent with a more comprehensive mathematical interpretation of number, where quantitative and qualitative aspects are equally recognised (through the marriage of reason with the contemplative vision). Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-42522591538306888222012-08-22T02:54:00.011-07:002012-09-21T08:17:44.391-07:00Multidimensional Nature of Time and Space (10)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!<br /><br /><br />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).<br /><br /><br />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).<br /><br /><br />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!<br /><br /><br />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.<br /><br /><br />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. <br /><br />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.<br /><br /><br />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).<br /><br /><br />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. <br /><br /><br />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.<br /><br /><br />So how does the 1st negative dimension arise?<br /><br /><br />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.<br /><br /><br />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. <br /><br /><br />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. <br /><br />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). <br /><br />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).<br /><br /><br />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!<br /><br />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.<br /><br /><br />Thus we can now perhaps better appreciate the nature of negative linear understanding (corresponding to the qualitative interpretation of - 1).<br /><br />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).<br /><br />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).<br /><br /><br />So, we now see that in a true experiential context, the negative (as well as positive) 1st dimension must necessarily be involved.<br /><br /><br />This likewise entails that insofar as the negation of phenomena is concerned that time (and space) move in a - relatively - backward direction.<br /><br />We can perhaps understand this better through looking psychologically at the process involved in great scientific breakthroughs. <br /><br />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. <br /><br />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.<br /><br />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.<br /><br /><br />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.<br /><br /><br />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. <br /><br />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).<br /><br />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.<br /><br /><br />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.<br /><br /><br />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.<br /><br />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.<br /><br />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.<br /><br /><br />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.<br /><br /><br />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.<br /><br />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. <br /><br /><br />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!<br /><br /><br />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).<br /><br />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! <br /><br /><br />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). Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-75139834501129372012-08-21T02:27:00.005-07:002015-02-06T06:27:31.392-08:00Multidimensional Nature of Time and Space (9)So far we have investigated how a unique experience of time (and space) is associated with all the positive integers (representing dimensional numbers). <br /><br /><br />And as such an experience directly complements the nature of physical reality, this implies likewise that a corresponding structure of time (and space) likewise exists in the physical world with respect to all positive integers. <br /><br />And once again the very reason why this is not readily apparent is that the conventional scientific paradigm is based solely on the linear use of reason (with 1 as the default dimensional number). This then explains the customary interpretation of time as 1-dimensional (where it is believed to move in a single forward direction).<br /><br /><br />Likewise we have seen that a fundamental distinction divides, as it were, interpretation of time (and space) with respect to the even and corresponding interpretation with respect to the odd dimensional numbers. Basically - when understood appropriately in a dynamic relative manner - integration in nature (physical and psychological) always relates directly to even numbered, whereas differentiation is associated with the odd numbered dimensions.<br /><br /><br />So in this context Conventional Science - based on 1 as dimension - is properly suited merely as a means of differentiated interpretation of reality (and then only at the simplest unrefined level). Such science is therefore directly of an analytical rather than holistic variety.<br /><br /><br />However if we are to adopt a proper integral notion of science, it must be based on an even integer as dimensional number. Thus the simplest version of a holistic scientific approach, that is truly integral in nature, is 2-dimensional, allowing for direct complementarity with respect to the fundamental polar opposites underlying phenomenal reality (such as internal/external, quantitative/qualitative, form/emptiness etc.)<br /><br /><br />Of course the most comprehensive approach to science must necessarily combine differentiated and integrated aspects in a dynamic relative manner (allowing therefore for both odd and even numbered dimensional interpretations).<br /><br /><br />Using my own terminology. I refer to the differentiated (analytical) aspect of science as a Type 1 approach. However once again Conventional Science in fact represents but the simplest version of the Type 1 approach (where interpretation is of a basic 1-dimensional nature).<br /><br /><br />The corresponding integral (holistic) aspect of science represents the Type 2 approach. Once again the simplest integral approach is 2-dimensional in nature (using circular type reason based on the direct complementarity of "real" opposites)!<br /><br />Most of my own work in recent decades has been geared to exploration of the precise implications of the 2, 4 and 8-dimensional integral approaches for science respectively. <br /><br /><br />Finally the most comprehensive is the Type 3 approach (which I formerly referred to as "radial"). This attempts to combine both the differentiated (Type 1) and integral (Type 2) aspects of science in a coherent dynamic fashion. So this would entail use of both the odd and even number integers (as dimensions). And as we shall now begin to see, it involves much more besides! <br /><br /><br />Again to briefly recap, my basic starting point is that all numbers with a recognised existing quantitative interpretation can equally be given a coherent qualitative meaning.<br /><br /><br />So far we have investigated the nature of such qualitative meaning with respect to the positive integers (both positive and negative). Therefore a distinctive dimensional meaning is associated with every positive integer, which intimately applies to the nature of time (and space) in both physical and psychological terms.<br /><br /><br />However we can have negative as well positive integers (in quantitative terms). Likewise we can have rational (fractional) values that are not integers. Then we can also have irrational number quantities (both algebraic and transcendental) as well as imaginary and complex values.<br /><br /><br />Thus, in principle, each of these number notions (as quantities) can thereby be given a corresponding qualitative meaning (as dimensions) which again intimately apply to the nature of time (and space) in both physical and psychological terms.<br /><br /><br />Therefore we start with this ongoing investigation. by first attempting to clarify the notion of negative dimensions and the important manner in which they dynamically apply to all processes in nature!Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0tag:blogger.com,1999:blog-7725147822647272542.post-9579710340899448372012-08-09T02:51:00.008-07:002017-04-23T06:32:09.534-07:00Multidimensional Nature of Time and Space (8)In dealing with the nature of 2, 4 and 8 dimensions of time (and space) respectively, we saw how that in each case they are characterised by the complementarity of opposite poles. <br /><br />So 2-dimensional reality is characterised by the complementarity of the "real" poles (i.e. external and internal).<br /><br />4-dimensional is then characterised by the additional complementarity of the "imaginary" poles (i.e. whole and part).<br /><br />8-dimensional is finally chracterised by the additional complementarity of special complex poles where both real and imaginary parts are of equal magnitude. This can then be understood as relating to the ultimate interaction as between form and emptiness (i.e. where the dynamic interaction of phnomena are so refined that they do not even appear to arise). So in this sense the dynamic nature of form becomes inseparable from emptiness. <br /><br /><br />Now it must be understood that further distinct structures with respect to the nature of time (and space) are associated with all other even numbered integers.<br /><br />However they all possess one important common feature in that they are characterised - however intricately - by the complemenentarity of opposite poles.<br /><br />This can be simply appreciated with reference to the fact that the qualitative dimension entailed (for each even integer) is inversely related to its corresponding number of roots of 1 (in quantitative terms).<br /><br />And as all even numbered roots can be arranged in a complementary manner (with half of the roots expressed as the negative of the other half) this entails in turn that the dynamic dimensional structure for all even numbers applying to time (and space) is based directly on the complementarity of opposites.<br /><br /><br />However this principle clearly does not apply to the odd integer dimensions.<br /><br /><br />For example in the important case of 1 i.e. the linear mode, which again characterises conventional scientific understanding, time is not understand in dynamic complementary terms (where its ultimate nature is paradoxical).<br /><br /><br />And in an important more refined manner, this linear view likewise characterises all the odd integer dimensions.<br /><br /><br />For example, to examine the dimensional structure associated with 3, we need to look at the corresponding three roots of 1 i.e. 1, - .5 + .866i, and - .5 + .866i (expressed correct to 3 decimal places).<br /><br /><br />As we can see the first root here is 1, which in a sense stands out on its own (as independent of the other roots). The remaining roots - necessarily of an even number - always appear as pairings of complex conjugates (with the imaginary part arranged in a complementary manner).<br /><br /><br />So how do we explain the nature of such odd numbered dimensions? How do we, for example, attempt to describe the nature of time as experienced in 3 dimensions?<br /><br />Now this is an issue that I have given an enormous amount of thought to over the last 30 years or so. However suffice it to say that the odd numbered dimensions (apart from 1) are much more difficult to clearly explain than their even counterparts.<br /><br /><br />I would describe it this way. <br /><br />The standard dualistic rational approach - where phenomena are treated as independent - is of a linear (1-dimensional) nature. <br /><br />The standard nondual contemplative approach - where phenomena are treated in merely relative - and ultimately illusory - fashion is based on the complementarity of opposites. So associated with the ascending scale of even integers are ever more refined contemplative (nondual) experiences of reality. <br /><br /><br />However the odd integers (<span class="_Tgc">≥</span> 1) are associated with a hybrid of both approaches (and ultimately are incompatible with each other).<br /><br /><br />In this respect I can draw on my own experience of 3 dimensions. Indeed I remember suggesting a proposal for a thesis on a dynamic methodology for Economics (that I only realised many years later, was, in holistic mathematical terms, of a 3-dimensional nature). <br /><br />On the one hand I was here trying to preserve the validity of the standard conventional model (i.e. 1-dimensional). On the other hand I was trying to reconcile this with the 2-dimensional approach based on the complementarity of opposites. So I was attempting to balance the traditional linear with a new dynamic 2-dimensional approach (based on a circular logic). However from an experiential perspective this led to inevitable conflict. Commitment to the linear aspect fostered - what in spiritual terms is referred to as - dualistic attachment; meanwhile the 2-dimensional aspect experientially required the very erosion of such attachment. So in the end I abandoned that approach (though later was able to return to it from a more refined perspective).<br /><br /><br />So this led me to the view that it in experience odd dimensional structures are necessarily asymmetrical in nature and ultimately inconsistent with the nondual perspective.<br /><br />So in terms of psycho spiritual growth, one starts with dualistic 1-dimensional understanding, which is of a strongly differentiated nature. Then 2-dimensional understanding provides the "lowest" level with respect to integrated experience (of a nondual contemplative kind). However because both dual and nondual are dynamically related, to reach higher levels of integration represented by the even dimensions, one must equally embrace higher levels of differentiation represented by the odd dimensions (which inevitably are of an inconsistent temporary nature).<br /><br />So in terms of space and time the very nature of the odd numbered dimensions entails that space and time can no longer be experienced in a complementary manner. This means that new forms of phenomenal rigidity i.e. new forms of matter, necessarily arise with the odd numbered dimensions.<br /><br /><br />If we apply this understanding to the dynamic nature of "lower" physical reality, this implies that associated with each higher odd dimension are new matter particles, whereas with the appropriate even dimensions these quickly dissolve in the creation of energy. <br /><br />And as all dimensions in a sense co-exist simultaneously, there is an unending trail of matter as it were waiting to be discovered. In other words the higher the dimensions we can access (which in a sense is the task of particle accelerators) the more new forms of matter will arise.<br /><br /><br />Equally from a psycho spiritual perspective, the higher the dimensions one can access through advanced contemplation, the more refined one's experience can become so that one can actually now "see" such matter arising from a deep unconscious level of experience.<br /><br /><br />From a physical perspective, the interaction of odd with even integer dimensions relates to the continual transformation of matter into energy (and gravity). And there is no limit to this process with ever more dynamic short-lived transformations associated with the higher dimensions. <br /><br /><br />From a corresponding psychological perspective, the interaction of odd with even integer dimensions relates to the continual transformation of dualistic matter phenomena into (contemplative) spiritual energy. And again there is no strict limit to this process with ever more dynamic short-lived transformations associated with the higher number dimensions.Peter Collinshttp://www.blogger.com/profile/03702540376694818466noreply@blogger.com0