applied XQ — what a leap!

3 11 2013

I took a massive leap the other day, in terms of math and psycho-social dynamics. I followed it with a second dive yesterday related more with the direct application of number to actuality, and a third today, where I explored SEA and its various value vectors.

Cliff-Diving-Timelapse-Capture-800x533

the leap

I started off with the intention of being heavy on my coming death-day, to raise the stakes. Instead, I ended up applying number to language, and then developing a reflexive syntax, generating a fractal social algorithm Qunity, and creating a social contract with a viewer (or other person) that merges decision, hope, trust, power and all the good qualities that make is worthwhile to be human.

I recorded the leap, thankfully, as a textango, and have put it online, with the first 30 min of the first movement visible if one has the link. The second bit, as well as the second and third movement are private. The last movement is more of the ‘return’ from the dive, attempting to apply it to the real world, specifically to team Goose, Gunther, Sasha and Bernard, as well as genius Alex.

nervous second dive

I have shared this video now with 6 people, none of whom have replied. I don’t expect anyone to follow the line of thinking, but there is always hope.

So I conducted a second dive yesterday, with mixed results, attempting to apply the syntax to the application of number to actuality, and I got in a muddle with Bitcoin and Qubits. I have made the first part of the hour’s dive visible, and the rest is locked.

third dive and joy

I have been nervous because the territory explored is… not new exactly, but a conflation of a lot of thinking over the last decade and more. I have had very loose models of reality, minimal systems, and I was concerned that the leap I took with applying number to language and developing the syntax was into a territory that was… too large to explore.

Given time, given money flow, given relaxed conditions, I might be able to conduct this comfortably. Doing so under poor social, financial, material and temporal conditions, makes it all rather ‘pressured’, existentially. I got into this in a post I wrote yesterday on my main, more human blog.

I shall put up the initial track, and keep the other’s private. Although I conflate everything to something entirely meaningless, I feel that I have explored enough of the space to be assured that the task at hand is not impossible. It should be relatively easy to design an algorithm which combines people-money-time-resources using SEA value vectors and has touch-points with money and the current valuations of e.g. property. I do hope the guys, Gunther, Sasha, Doug and Brendan, get a sense of it, and manage to pull something practical from it.

in sum

So, I still don’t know if it has any meaning, actually. Which is why doing what I am doing… tricky, or even dangerous. Playing around with value equations, where one is uncertain of one’s value, is… a vulnerable thing to do. I hope one day you may appreciate this, whatever happens between us these days and over the coming months.
So, it’s not clear, and it’s not concrete, however, there is enough space to explore. I am not sure how useful it will be to concrete plans, but I am confident (to an extent, perhaps k=7) that we’ll be able to produce a simple enough equation for it to be useful in a first application. This may come more from your side (e.g. Sasha) than from mine, since I am approaching it from a generalised space, as usual. MTTP and SEA were penetrating results, but exploring the space around these, considering the variations, systemically, is a rather tricky task.
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mandelbrot set as addition squared

15 05 2013

I think this makes sense.

disappearing dimensionality

I’ve been staring at this for a while. Looking at how 1 has the same value as 1 squared and has the same value as 1 cubed, etc.

1^n = 1

At least in terms of integers. IF we ignore the dimensionality of it. But that’s what’s annoying me. Since, obviously, a line of length one is different from a square which is different from a cube. 1^billion is a pretty dense multidimensional space. But when we just look at the integer value, it is just one.

When we multiply it, even by a tiny amount, the power function takes our number to zero if lower than one, or infinity if higher than one — both at an incremental rate.

eg x2: 1, 2, 4, 8, 16…

eg x1/2: 0.5, 0.25, 0.125…

But look at what is happening. I can understand that if I double a length, I get four times the area, eight times the volume. When we half the length, we get a quarter of the area, and eight of the volume. But don’t you think that an eight of the volume of anything has got to be bigger than half a line? Surely half a line is smaller in some way than a quarter of a square?

When we pull the same trick of forgetting about the dimensionality, by reducing the multiplier, we simply get smaller integers.

I sit and stare at things like this for a while. I stay awake in bed, thinking about this.

mandelbrot set

The Mandelbrot set is defined by the following iterative function:

z -> z^2 + c

It should read z_subscript_n+1 = z_subscript_n_^2 + c. That is, the next value of z will be the last one squared with c added to it.

I re-examined this, because it is somehow related to the mystery of disappearing dimensionality.

Let’s take c to be 1 (on the complex plain, c = 1 +0i).

We assume that we start with z = 0, so our first z = 0 + 1. Actually I am not sure if this is the first, or not. But after this, it get’s easy.

first z = 0^2 + 1 = 1

second z = 1^1 + 1 = 2

third z = 2^2 + 1 = 5

fourth z = 5^2 + 1 = 26

And so on… rapidly escaping to infinity. Which is why we don’t see much around the point (1,0) on mandelbrot set.

what’s the function again?

What are we actually doing in the iterative function that generates the Mandelbrot set?

It looks like we square then add to get each new version of z. This is how the transformation is written. But is there another way of looking at it?

Well, we add c (the original number) to a square of the previous addition.

The original script emphasises the function of squaring then adding. But in iteration, it doesn’t really matter what order it is, since it is squaring and adding, squaring and adding, squaring and adding and so on.

We could just as easily say that we are adding and squaring, adding and squaring, and so on.

This gives a slightly different sense, and can be written as follows:

z_subscript_n+1 -> (z_subscript_n + c)^2

The numbers that come out of this transformation are:

first z = (0 + 1)^2 = 1

second z = (1 + 1)^2 = 4

third z = (4 + 1)^2 = 25

fourth z = (25 + 1)^2 = etc

Notice our answers from the other way of parsing the operation are hidden in our calculations within the brackets, ie 1, 2, 5, 26…

So what, you might say.

Well,  the Mandelbrot set is the set of complex numbers that do not escape to infinity, and gives us the nice shape on the complex plain. We focus on the static numbers. Does 1 escape? Yes, so it is not in the set. Does 1+i escape? Yes, and so on.

Mandel_zoom_00_mandelbrot_set

However, in our alternative way of parsing the iterative function, we see that it is not the static number which is iterated, but the addition. It is the operation of ‘addition’ that is being squared repeatedly. Without that little addition being iterated, we wouldn’t get the fractal quality.

This is how the fractal is created. Without the addition, we simply get a unit circle. I think.

conclusion

There isn’t much of a conclusion in these explorations. Perhaps only the pleasure of coming up with an alternative interpretation of something I have been looking at for the last twenty-five years. That’s a buzz in itself. And the fact I don’t think anyone else on the planet is poking around this material in this way. Applying XQ scrutiny to math.

The implications are… well I don’t know. We will see if there are any.

It’s like teasing apart a structure, and by doing so, a little at a time, over the years, we have enough flexibility, enough alternatives, that new associations are made that depart from a path that math has taken us historically.

What would I like to see?

Well, there is something about dimensionality appearing in the Mandelbrot set. The increased detail, with a Mandelbrot zoom, indicates something about dimension. And this zoom is performed by increasing the accuracy of the initial number, the number of decimal places. What appears to be in the Mandelbrot set at 0.5 + 0.3i or whatever, turns out to be actually not in it at 0.55 + 0.30i. The precision, gives us the interesting boundary.

This fractal boundary is in the depth of the number of decimal places. There is uncertainty there. We don’t know after 1,000 decimal points for some points, whether it will be in the Mandelbrot Set or not. This is remarkable. It is like saying there is depth between 0.5 and 0.6, and it is not regular. Peaks and troughs of depth. Between numbers.

I am more interested in the movement through a Mandelbrot Set, rather than a straight dive, which I shall cover in another post. Movement beyond arithmetic iteration, or scale. Movement ‘across’ the set. I am thinking about the bulbs on the set, and the ravines.

The Mandelbrot set is too… static. I think there is something that we may find that is dynamic in it. And I would like to tease this out.

Why?

Because I think it is related to the shape of consciousness.








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