not good

31 05 2013

There’s good, there’s bad, and there’s not good.

When someone does something good, we may appreciate this. We can map it with the positive number +6 say.

When someone does something bad, intentionally, we may ascribe a negative value, -6 say.

There is, however, a grey space, when it is ‘not good’. We might represent this with ~6.

What does this mean? To do something which is ~6 intentionally. That is, they are doing something in ‘negative space’, in absence. It is not that they are doing anything to you directly, but there is a detrimental concurrent effect. Eg, giving a biscuit to one daughter and not the other. The kid who gets the biscuit is happy, the other is not. It is not that the parent did anything wrong, it is that they simply did not do something with the second daughter — did not give them a biscuit, in this case. Not bad, but certainly, undeniably, not good.

what’s the problem?

The chances are, most actions going on in the world, at the inter-personal level, are not meant badly. People do not set out with negative intent. Very often, they set out with positive intent. They start out with a +6 intention.

Same could be said for scientific solutions, and indeed most of social evolution. Most people mean well, and seldom is there negative intent.

What is characteristic in our social dynamics is that this ~6 is interpreted as -6. The ‘not good’ is interpreted as ‘bad’. This induces what I have called over the years, ‘oppositional state’. When two people seem to be on opposite sides of an argument, or a conflict, when there was no original intention of negativity on either side. And, sadly, it is oppositional state that grounds most of our institutions, from politics and law, to science and religion. And it is also at the basis of most of our internal mental problems.

So, this ~6 is interpreted as -6, and then this escalates until we have a breakup of our relationship, brothers estranged, fueds between families, and even international wars.

War, or inability to communicate, is not the problem. Obviously -100000 is not a good situation, but these explosions result from sparks. The problem is the mis-interpreting of ~6 as -6.

what’s the solution?

The obvious solution is multiply by -1.

This is a mental trick described in XQ elsewhere. Basically, it means reframe. A broken leg may enable a period of peace where you can get all that reading you’ve been postponing over the year. Raining? Good for the plants.

In terms of inter-personal dynamics, it is a matter of translating a negative intention towards one, into a positive one. The multiplication by -1 can occur when one is in rather aggravating circumstances, such as in math classes while doing supply.

The best place, however, is to convert the negative that arises in the mind. So, it is the interpretation of negativity that is multiplied by -1. So, when I got a feeling that my friend was doing well and there was the hint of jealousy, by thinking of the positive version of this, I managed to ascribe a positive result to this feeling.

So, when one perceives an apparent -6, simply multiply it by -1, think the opposite of it, and you are good to go. What was +6, initially interpreted as ~6 and then -6, gets converted back into +6.

Basically, it works.

the problem with the solution

Multiplying by -1 works with simple negatives. It doesn’t really work on ~6 directly. So, when faced with something that is ‘not good’ but we haven’t taken this to be ‘bad’, what is the appropriate conceptual/emotional response?

If we borrow from math again, we might consider multiply by i, the square root of -1. Something I have been hovering around for a few years now. But what does this mean?

So, when we have some situation where we don’t understand someone else’s behaviour, and it may appear to be ‘not good’, what is our response?

My basic response is to ask, in order for the other person to confirm that it is indeed +6. If I establish that actually there is an aspect of their behaviour which is detrimental, ie -6, to others in the classroom or myself, then we have an opportunity to think of something else that does not have these negative concurrencies. Ie something other than +6, perhaps +9 or +4.

If they insist on going ahead, then they are willfully perpetrating -6, knowingly.

Another response is humour, I guess, to play with the ~6. Or ignore it, and see what the result of the +6 activity is.

the subtle problem with the solution

This is the real problem, when someone insists on perpetrating what they think is +6, when they know there is danger of taking a -6 interpretation, ie it is ~6.

Now, the emotional response is to something that did not happen. It is not rightly -6, because there is no negative intention behind it.

When someone perpetrates -6, and they know it, then you have to suffer it. Someone means harm. They don’t care, they are going to continue. In a good world, it may be a surgeon making the required cut, or a parent who is aggressively pulling the child away from an on-coming car. The results will have to prove whether the action in the end is good or not, even if they are not perceived. In the first case, the abscess has been removed, health is restored; in the second, the car is gone and the child does resents the aggressive pull.

When someone insists on perpetrating ~6, knowing there is a good and a bad side to it, things get more complicated. The child observes the parent who is giving the biscuit to their sister. They balance on the knife-edge. They do not fall for -6, and they know it is not +6 at least with respect to themselves. Here is the opportunity for the mind to jump to an other level. And we have the response of suppression, ie resentment, or celebration, ie trust.

That’s all I’ve got at the moment. Still not clear. But definitely in the ballpark.

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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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