projected planes and vanishing points

27 02 2010

I dabbled a little with projected plane geometry, namely in the deep end with Reimann sphere (p80 XQ solution). Recently thinking about reflecting the social body (p83 Pulse), how to represent intentions and projections. So, two things: the social, the internal projections. But we need to think a little about projections; an image might help.

Some observations. The real world, here represented by the triangle ABC on the ground, but this could be a building. The plane of representation, A’B’C’. And the illusion of a singularity of the eye. Things get a little more complex if we add into the mix the non-self of buddhism, or that the eyes combine both images and composes a model of the universe, or matches it somehow.

Consider the point of convergence in perspective paintings, the illusion of parallel lines meeting at the vanishing point. What does this mean socially? Or mathematically, from an XQ interpretation.

So, first, how do you represent what we are doing socially? Talking with Tav with his new version of Tent, and it seems we concur on some form of visual representation, rather than just lists of words. The thing we are representing is social dynamic, and in a virtual dimension. Just read this today, which is a real eye-opener: human_flourishing. I liked the three coupled differential equations on the three virtual dimensions of self-other, positive-negative, advocacy-inquiry. So, how do we represent this rich psycho-social dynamic on the plane of representation, graphically? There is no physical model in the real world, hence the representation is not a visually linear projection, but rather a virtual projection. As we project into the future, such as 2020worldpeace, we can represent this as a point in a time-slice of 2020; any intention of mention of it, like in this blog post, is a plotted point in the time-slice today. There is a vector projection from the point on time-slice-today, to time-slice-2020. And there are intermediary objectives, such as

The point is, the projected field is imaginary, so it is a mistake to think we need to specify a point. There is no “point” out there, just a projection. So, just like the way we avoid argument about specificity in the future with the confluence model, so we don’t need to know where the point is, literally, in the time-slice-2020. There are several ways actually plotting this. Leave it up to people to plot the location, eg using tent/ampify script

/pointer #2020 (2,3)

/pointer #2020worldpeace (zero-carbon, olympics)

The first defines it on a map with an absolute point, relative to 0,0 at the centre. The second is defined relative to other projections, and the computer can calculate some local point between them. Three observations. One, only some people will want to point at the location, so once it has been set, generally, people will refer to that location. Two, if there are several pointers to the same projection, then the system supports both; like the way different ascriptions to a single projection, what you think or I think about 2020worldpeace for example. Three, any intention or projection relating to it, locates the co-ordinates of the point on the current plane in relationship to the co-ordinates of the projection; eg my intention in writing this blog post will be given co-ordinates close to (2,3) automatically.

Therefore, there is no fixed future projected field, but something getting close to probabilistic space, with a projection consisting of a set of points, as many as there are pointers, which might correspond to the set of different ascription of the projection. The benefit of using this system, is that it allows us, human beings, to translate our verbal concepts into spatial co-ordinates, rather than appealing to some kind of ideal mathematically spaced algorithm. It should allow a continuity of image so that a video of time-slices will show a smooth progression. And, the only precision we are looking for is the interface of future/past in the present; that is, how the time-slice-today turns intentions into done tasks. The multiple projections, definitions/ascriptions/points, become singular events/fact/point; the multiple views we have are braided in the present into the fact of the past.

Second, the maths plane. I have already suggested that XQ posits there is another side to maths. When explaining to people, I came up with the metaphor of suggesting that mathematics is the intermediary plane, like a window, through which we make sense of the real world. So, if objective reality is outside, ABC, then mathematics is the projected plane, A’B’C’. This goes for all poetry, etc. A book just happens to be a particularly high-virtual dimension object, that allows a reading eye to imagine/project a world. XQ posits that mathematics is just a minimal language set.

Now combine this with another thought, that of the mirror: maths as a mirror of our internal processing. So, A’B’C’ is a projection of some internal processing, A”B”C”, which we can not set as the object of our thinking. OR, they are the rules of projection, perhaps.

So, the illusion of convergence on the vanishing point on a projected plane, is the illusion of convergence of eg 2020worldpeace. It doesn’t exist. It is an illusion. But a useful one.

And, the illusion of convergence on the vanishing point on a projected plane, is the illusion of “self”, a point that interprets mathematics, or anything for that matter. It doesn’t exist. It is an illusion. A useful one.





One response

4 10 2010
The Certainty Of ‘Self’… What Is ‘It’? Could This Be The Greatest Human Delusion Of All!? « Polynomial

[…] We erected our self slowly, using nerve cells and circuits as building blocks. First we linked them at deeper subcortical levels, then at superficial cortical levels. They were almost Tinkertoy configurations, and it would take us years to assemble all of them. Now, each of our adult selves resides inside immense, distributed nerve networks. Together they code for a sensate physical body, feel visceral imperatives, think and know and act in this world, remembering the past and projecting it into an imaginary tomorrow. […]

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