Compiled my life’s work as Fulcrum, which includes a ‘chapter’ on XQ.
It was tricky to decide which elements to include in a small introduction (twenty pages). I had hoped to consolidate something mathematically significant, but only got as far as exploring Euler’s identity. I’ve also projected Uni adoption leading to a collective development of the psycho-social XQ equivalent to Einstein’s field equations for 2033. If we manage it in the face of AI, this will help us self-organise for greater social cohesion globally.
I am writing this post because I’ve had a few explorations and not updated this site. I’ve only got notes in places. This will be brief.
Infinite Series
First, the oddity of the sum of infinite series of eg 1-1+1-1… can be equal to 1 or 0 depending on which pair we nullify, ie (1-1) or (-1+1), and depending on the initial condition. It is also interesting to note that the different between consecutive terms (an operation used in quadratic sequences) is -2,+2,-2,+2.., and whose differences in terms are +4,-4,+4… etc. This is interesting. Exponential differences. Something about words, multiplication of meaning, etc.
I tend to stay away from infinite maths because it can become detached from reality, the finiteness of experiential time. Asymptotes etc explore extreme psycho-social states.
This, Not That
Second, a nice observation that explains why oppositional state is useful for generalists. Explaining why eg regenerative folks or any diverse group, have conversations that fall apart. Education, specifically the adoption of a critical stance, is antithetical to collaborative enterprises. It all comes down to a simple pattern, the initial starting point of Spencer-Browne’s work. I’m not keen on SB because he takes into a formalist logic, his Laws of Form, ie symbolic logic. Whereas I’d like to reflect on what it means to our psycho-social experience, not as an objectivised representation.
So, here’s a thought experiment. This letter ‘s’ at the beginning of the last sentence. Not the ‘s’ in the quote marks in the previous sentence, nor in this one, nor any other s. ‘This’ letter s by contrast with other letter s’s.
One way to describe it is the positive: this ‘s’. Whatever one is drawing attention to. ‘This’.
Another way to describe is is in the negative: not that ‘s’ or any other s. ‘Not That’ or any other ‘that’.
Keeping it simple: this singular thing, versus not the many that’s out there.
As I describe in Fulcrum, I’ve been confused in general conversation or indeed academic, when people disagree. In the vast array of mental objects, the notion of a precise opposite is quite rare, so it is often misused. A person begins describing something, A then B then C. And then someone disagrees, what about M? Or P? Or X? Because of the limits of linear conversation, the pinhole communication of wording or linear letters on a page, it is easy for people to object to what is said, ‘this’, because they think of something other, ie ‘that’. And the power game ensues: which is more important, the this in my head or the that in yours? And of course there are many things not said when the person began with A, B then C.
So, when regenerative folks gather, and someone disagrees, it is a complete waste of time — unless the disagreement is sensitively, fundamentally put forwards. Not just another ‘that’ in the universe of all possible ‘that’s.
This is important.
For science, linear thinking, critical either-or exclusive logic, great for objects, the opposition state can be useful to exclude all possible variation, not ‘that’ or any ‘that’ until only ‘this’ is left. Isolation of control experiment and change of one variable. Proof by falsification, experimentation.
For social engagement, which is inherently ecological, ambient (as well as reflexive!), the number of variables are huge, and also unreachable (ie within psychology or as massive social objects). The methodology of science, and normal ‘rational’ discussion, doesn’t work. Or at least, can be useful within certain limited contexts. What is essential is the ‘togetherness’ before addressing differences and linear, object-of-mind discussion etc.
Ok, going back to the letter s. There are lots of letters on this page, not just s’s. If this is what is pointed out (the totality of letters), then the negative, ‘not this’, is…. interesting. Leaving everything else out, except for that specific S at the beginning of that paragraph. The ‘not this’ except for ‘that’.
So, we have the table of options between ‘this’ and ‘that’, positively or negatively (ie itself or its opposite).
The starting point is… we are midstream. Whatever object of thought you have in your mind, is part of a stream which was in flow before you began reading this and will continue afterwards, with good fortune. The true condition is that whatever ‘this’ is in our attention, is contrasted with whatever other ‘this’ happens before and after, or is concurrently held by simultaneous minds. Thus, to be oppositional is… absurd.
We begin with an environmental mindset, the ‘thisness’ of which we all part. And however must we manage to process with our minds over a lifetime, or hold in our minds at any moment, it is a mere fraction of what is. In this way, we are always presenting ourselves with humility, with respect.
I’m inviting the co-creation of an online practice which correlates to the inperson design of the Action Cycle, which appears to be third stage of the Invitation Protocol, an hour of first welcoming engagement at an Open Meeting.
Tesseract and Hypertetrahedron
Third, tesseracts and the tetrahedron version.
I’ve perhaps complicated the psycho-social model of the Open Business practices as a tesseract, a 4d version of a cube, or a hypercube. It came upon me while looking at the animated gif how the outside is folded into the inside, and this somehow captures something of our attention. Our mind focuses and brings into primary attention something. It also contains the notion of a lens, the intermediary cubes which frame the same inner cube; and how the frames themselves can become the focus on intention as the inner cube.
The tetrahedron version has somehow eluded me until now. One tetrahedron surrounded by four tetrahedra, one on each face. There is no outside. The outer tetrahedra fold along their faces and end up at the same point. Which is interesting, when compared to the cube tesseract: the entire volume that is outside gets contained within a cube. Volume to volume transposition. This doesn’t happen with the hyper-tetrahedron.
Questions remain. If the hypertetrahedron has a point in the centre of the inner tetrahedron, is this the same point at the outer points of the four framing tetrahedron? And, somehow, my mind brings a correlation between the internal visual proof of pythagoras theorem and the dynamic of the hypertetrahedron.
Ho-hum
Who knows? I’ve been drawn to the dimensionality of simple shapes since a child. And it has helped me exercise the feasibility of the dimensionality in our psycho-social reality and it peculiar reflexive quality. These dynamic animations help us shift perspective.
It would be useful to have some more minds contemplating a more sensitive way to match mathematics to our psychosocial reality, to help us self-organise as the ‘Regenerative Movement’ surges, especially in the face of the storm that AI is threatening over the next few years. You are more than welcome to co-create XQ math, a meeting structure that has the power to embody our trust unlike the board and managerial meetings of hierarchical organisations, financed of course through Ecosquared’s vector-money, or any other aspect of Fulcrum.
XQ+ 