consolidating not-addition

23 10 2009

Last night, came upon the rather nice and neat set of not-addition thinking along the lines of p, not-p, both p and not-p, neither p and not-p.

2, the whole positive number, eg the point on the number line at 2. The number which refers to the two-like thing of conceptual reality, which happens to correspond to two items out there in reality. TWO

-2, negative two, the not-two number, eg the point on the number line at 2, not that :) The number which refers to the imaginary quality of two, purely held in the mind, eg as 2 oranges.  NOT TWO

– 2, subtract two, less two, ignore two, eg the vector retraced from two back to zero. With three held up fingers, ignore the two turned down. BOTH TWO AND NOT TWO.

the difference between eg 5 and 3. Holding up five fingers on one hand, three in the other, what’s the difference? NEITHER TWO AND NOT TWO.

I get the last two confused. Can’t tell what is operating in my head. When holding up two hands, I ignore the two fingers turned down on the hand with three fingers, but I become aware of the extra two in the other hand with five fingers. Perhaps that’s BOTH TWO AND NOT TWO.

Hmmm… add two and subtract two are verbs, we do something, and normally we think of this as things physical. If we consider this to be project two and ignore two respectively, that is the mental equivalents, this makes some kind of sense. This is akin to vectors. Positive and negative two, then, are the static forms, 2 and -2 on the number line as it were. The two things in actuality that give rise to sensation, and the imaginary two things in my mind. The difference question is a comparative question, almost along the lines of ratio, of fraction… perhaps it is a completely different order of question, or a compound one?

Hmm, and I thought I had come up with something simple.





archimedes, viete and fermat

23 10 2009

Seems like the Greeks were limited in their appreciation of ∞. Without algebra, and dependent on pragmatics of geometry, Archimedes used Eudoxus method of exhaustion to work out the area circles and parabolas. Eg, inscribing and circumscribing circles with polygons, each being calculable as a set of triangles, getting a degree of accuracy as required.

Viete was the first european to create a series in 16th century, namely

infinite productSeems it is the dot dot dot which is significant, breaking some kind of psychological barrier, the idea of an infinite series.

Then came Descartes with his geometry, one of three appendixes to his philosophical work, and Fermat and Pascal. Then Newton and Leibnitz, of course. The book I am reading refers to ‘indivisibles’ whereas I am more familiar with the term ‘infinitesimals’. Zeno/s paradox, of an infinite number a formof steps, 1/2 + 1/4 + 1/8 + 1/16 etc will never reach one… the notion of an infinite series tending to a finite amount, in this case the limit is one.

The fact that it took so long for people in the west to approach this idea. I think it was accepted earlier, as it were, in the east. Not so much numerically, objectively with geometry, but rather the other applies side of maths, subjectively. As time tends to zero, subjectively experienced, strange things start to happen. Awareness of how one thought follows another. Uncovering the mechanism of preconscious thought, fiddling around with the projector such that the thoughts that arise are wholesome.

The strange thing is, by performing some clever tricks, transforming the shape of the expression, Fermat came round to defining a formula for the area beneath a parabola y=x^n by thinking of rectangles who bases form a geometric progression of a, ar, ar^2…

parabola

parabola1…which reduces to this when r  -> 1

parabola2…which happens to be the integration formula 0∫a x^n dx = a^n+1 / (n+1), thirty years before Newton and Leibniz.

That is, there is something about a technique used which the ancient greeks could not grasp that enabled the infinite to become comprehensible, or well behaved, manipulateable. What it makes me think of, in terms of the mind-drop solution, is that the dissolution of consciousness downwards into the preconscious processes, which is effectively infinite, somehow tends to a limit. The same for the other direction, upward to higher states of consciousness, perhaps. Allowing for thoughts that come to me while I write this, seems to be related to approaching the speed of light. That is, there is a barrier, which can not be broken if one continues with that line of thinking, but if one conceives of it, or becomes aware of it, at a higher/lower level, the barrier is simultaneously overcome, or perhaps conceived of, or perhaps there is a phase change of state of consciousness.

I am interested in the technique. The revolution of mind that enables the calculus to be derived.

Hmmm… upon editing, other things pop into my head. The conic sections wrt space-time…

Constudcone





five aspects from barnaby

21 10 2009

Spoke with Barnaby yesterday, told him a little about XQ and my recent thoughts about indices. In our engagement, Barnaby came up with five different directions of thought.

  1. resolving past traumas
  2. comparison between two people
  3. comparison within one person
  4. pre-cognition and surprise
  5. statistics
  6. (2 as vector or point)

First, most therapies nowadays attempt to create the right frame for a person to revisit their traumatic experience in such a way that it is resolved. Mostly through storytelling, and with NLP changing the modalities. We started to think of the mathematical equivalent. That is, by using mathematical values and letters to aspects of traumatic experience, manipulating the unknowns, might alter the values or solve the unknown, thus resolving the trauma. Think super minimal therapy. By performing the maths, one performs the transformation of the psychological entities. It’s like untying knot of entangled energy. In my terms, the bunches of negatives in the mind that just circulate needlessly.

Second, when two people come together they share their experiences, for example we both had been bitten by dogs. What are the modalities of the experiences? We came up with:

  • intensity i, a value between 0 and 10
  • how long ago, time t
  • replay factor, how often we relive it, talk about it, rate r
  • how often did the experience occur?

The last one is actually the fifth point, but I think it comes in here. It is related to whether it is chronic. Getting bitten by two rockweillers at night on a beach alone is one thing, constantly engaging people on london’s streets without positive emotional feedback is another. There must be other factors, of course.

Third, when someone compares two different experiences in their own head. Not sure how useful this is, but I guess it creates some kind of scale. If we consider an internalised experience as an equation, or a program let’s say, a recursive equation, then we have different scales of magnitude, or periodicity. This defines, in some way, our behaviour… which is related to our individual as well as shared ecology of memes. Fair enough.

Leading to fourth, getting hit by a bus. Barney was hit by a bus, he didn’t see it coming. This is quite different from the experience I had where I saw the dogs coming at me. This is like in tango where one is going to do a performance, or if one just happens to be dancing and other people leave the floor so that you end up being the only couple. Or doing a presentation, or just ending up people listening. That is, being aware of the experience before it happens, the period of which can be filled with unsettling mental processes, versus it just happens. Actually, I can relate this to the stages before a dive: checking feasibility, putting yourself on the edge, and then the actual dive. The second period is about calming the mind. Pre-cognition, versus it just happening by surprise or you are just doing it.

Very interesting stuff. When making notes on an envelope, I started with an equation:

reality parity

where r is reality, b is barney and d is david… so the values of a person’s reality is the sum of various experiences… what we are suggesting is that we can do local relative comparisons between subjectivities. We do this all the time, of course, but we do so clumsily. By applying a little more accuracy, we come to realise how… biased… we are. It’s like the sense-map of our bodies proportional to the number of nerve cells. (The following image is not quite the one I remember, but hey…)sense map





first post

21 10 2009

A shared place for further exploration of XQ.

There are other bits and bobs, such as the minimal pythagorean visual proof or the relationship between times tables and fractions, the shape of numbers wrt primes and square numbers etc, and the edges bleed into the confluence model et al, however I’d like to keep this blog focusing on exploring alternative interpretations of simple maths conventions as and when they arise.

Remember, XQ is about using maths as a reflective surface. Standard maths has been used as a tool for monkey to measure, model and thus control the external world of objects. It is also a pure field in itself, as it were. XQ is about exploring the subjective correlates within the mind represented by arithmetic and mathematical procedures.

A slight variation, XQ+, is when we actually alter the mathematical conventions, for example by replacing the notion that negative means oppositive positive with negative as not. Perhaps a new system might be generated, like non-euclidean maths… which we might call non-dual maths.

Finally, applying this type of maths comes in two ways. First, simply contemplating the subjective correlates is a tool for self-exploration. Second, we might be able to derive formula, like newton did with his physics, such that performing the maths actually resolves internal subjective disorders. That is, my manipulating the symbols we simultaneously manipulate the pre-conscious subjective aspects of out mind, ideally with the objective of releasing, solving, dissipating various forms of antagonisms and knots that interfere with a clean engagement with actuality and with one another. A slightly modified maths, XQ+, might be better suited for this, and the first post is an example of this.








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