No, neither intimidated nor unfamiliar with science but actively and intensively interested in exploring the source of limitations hidden in mathematical science. Goedel’s theorem tells us that we can’t trust finite systems of mathematics but it doesn’t tell us where to look to find the ‘holes’ or inconsistencies that arise. Others have probed that one, such as Poincaré who some claim developed an intuitive proof of Goedel’s theorem thirty years prior to Goedel doing it.
Be that as it may, a major hole in our logic (exposure to inconsistency) derives from our habit of using Euclidian space, one of the conventions that we use to frame our observations. We like it partly because it is “the simplest of all geometric spaces in the manner that a polynomial of degree one is simpler than a polynomial of degree two.” (Poincare). And we like it partly because it presents the things in it as local objects with their own local agency which is how we (western culture imprinted souls) like to think of ourselves.
Euclidian space is the space that accommodates Aristotelian either/or, black/white, good/evil linear thinking, so that when one imposes that logic on one’s observations, one is using that convention for space.
There are also non-euclidian space conventions wherein the general case is ‘gray’ and black and white are special cases of gray; i.e. ‘gray is the parent and black and white are two special needs children’. This arises in ‘strand-in-the-interdependent-web-of-life’ thinking where A and not.A are mutually inclusive. The me (A) that is is the spring in the matrix of springs is also, at the same time, the matrix of springs (not.A), as in a wave-dynamical space. The springiness (elasticity) is the primary thing and when you stretch it, opposite tensions (positive tension and negative tension) are born. These opposite tensions are the black and white children of the basically gray space.
This is the point that Heraclitus makes about opposites; i.e. they arise out of a unity by way of a hidden back-stretched connexion, as in the string and wooden arch of the bow (the bow is one thing, like a spring, that is capable of getting at odds with itself.
In our scientific default of the Euclidian space convention where A and not.A are mutually exclusive, there are two parents, ‘black’ and ‘white’ and the grays are their children.
Since we all use logic of one type or another, here we are talking about difference in how a person can think of themselves relative to the world they live in. This is how different cultures are born.
If you see yourself as a ‘strand-in-the-web-of-life’, in other words, as a ‘spring-in-a-matrix-of-springs’ (simultaneous mutual interdependence) then you are dealing with dynamics that are beyond the dynamics-rendering scope of Euclidian space. Euclidian space is constrained to accommodating EITHER local objects OR emptiness; i.e. ‘BEING’ or ‘non-BEING’ or, A that is mutually exclusive of not.A.
Science that uses the default of the Euclidian space convention thus forces everything into the categories of being and non-being (local objects with their own locally originating, internally directed behaviour, A, versus passive space, not.A). This is abstract idealization that is too restrictive for capturing the dynamics of nature that we actually experience. Motion is relative and to capture relativity, one has to switch to non-euclidian space conventions where we are not constrained by the black and white choice of ‘being’ and ‘non-being’. In non-euclidian space, for every assertive intrusion there is a simultaneous reciprocal, complementing accommodation (as in wave action). (imagine people populating the space on the surface of a sphere. when they scatter, they are at the same time gathering.)
How we think about our relationship with space plays a role in dividing us up into different cultures. For example, most of us believe that nature is more powerful than us, so how should we relate to and engage with nature. How would we engage with a very powerful force that arises such as Hitler? In Euclidian space based thinking there are three choices;
1. Capitulate and be submissive to the superior power. This will establish order in all the world which is good. This was advocated by King Edward VIII, the Duke of Windsor.
2. Fight against the other power and overcome it. This was advocated by Churchill.
3. Make a deal with them and like the Biblical lion and lamb, walk side-by-side into the future together, cooperating and in harmony. This was advocated by Chamberlain.
None of these make sense if one thinks in terms of non-Euclidian space where one sees oneself as a strand-in-the-interdependent-web; i.e. as a ‘spring-in-a-matrix-of-springs’ because there is no ‘mutual exclusivity’ in this view. It is a view where INTERDEPENDENCE or grayness predominates. One has to accept that strife is a constant companion in this geometry (when the US goes to war against Iraq, everyone else in the spring-matrix is shaken by it). So the ethic is to accept strife but move so as to cultivate harmony and balance. But to split the whole global population into two opposing factions A and not.A so as to try to achieve peace by absolute authority of A over not.A is insanity in the Amerindian cultural view (of course, Amerindian culture was not in vogue in Europe).
As historians of philosophy note, the natural primacy of gray where A = not.A that was maintained by Heraclitus, was missed by Aristotle (Aristotle didn’t even address it).
“Plato (‘Sophist’ 242D, DK 22 A.10) clearly distinguished between Heraclitus’ SIMULTANEOUS unity and plurality of the cosmos and Empedocles’ separate PERIODS of Love and Strife. At the same time, they are mentioned together as both alike in believing in the unity and plurality of the cosmos; and Aristotle’s coupling of the two might conceivably have been motivated by the Platonic comparison, the important distinction between them being overlooked. See also Guthrie, ‘History of Greek Philosophy’,HGP1, 455f, and 458, with further references, and D. WIggins, ‘Heraclitus’ conceptions of flux, etc.’ in Language and Logos, ed. Scholfield and Nussbaum (Cambridge, 1982), 1ff.”
Clearly, as the world headed for WWII people wanted to embrace the Germans and, at the same time, to kick them in the butt. And when Germany got its first taste of backlash, the German people wanted to kick the butt of the rest of the world and to embrace them at the same time (make allies, not slaves out of them. Hitler was deeply disappointed that he was rowing with his beloved English). If Germany were populated by Amerindians who would never subjugate themselves in a self-abnegating fashion to someone else’s authority, the rapid industrialization couldn’t have happened and neither could the widespread loyal submission to authority. These derived from Aristotelian logic.
Euclidian space can only bring order and organization to things by an approach that assumes that A and not.A are mutually exclusive; i.e. that ‘leader’ and ‘followers’ are mutually exclusive. In the non-euclidian space convention, everyone can be both leader and follower at the same time. If you are a spring in a matrix of springs, the A is in a conjugate relation with the not.A. As Mach’s principle which assumes space-matter relativity says; “The dynamics of the spring-matrix conditions the dynamic of the springs at the same time as the dynamics of the springs are conditioning the dynamics of the spring-matrix.”
If you consider yourself a spring in a spring matrix, you know that strife/conflict is going to be part of everyday life (you know that when your neighbour shakes up the dynamics of the milieu you both share inclusion in, you are inevitably be going to be shook up), but you would be nuts to think, in this space convention, that the way to peace and order was to try to take control of the world. That is a decidedly western Aristotelian notion that makes sense if you are using the Euclidian space convention.
Anarchists (some, at least) intuit that the relationship between self and other can benefit from getting out of the Aristotelian Euclidian space mind-trap.
emile
Frequency/Time
Negentropy1 Negentropy2 Negentropy3 Dogma Time/Freq RideOnTheWildSide Vibroseis Visualizations TimeTranslator Spectrum Great Mysterious MRI’s
Khaos on the mind 
