30 06 2016

Or perhaps a better translation to the previous post:

  • {1|-1} indicates an emphasis on reception
  • {-1|1} indicates an emphasis on rejection

I am not even sure which way the words go. In a way, it doesn’t matter. What matters is that there are two states.

After writing the above post, I explored the math pattern deep into the night. The association to yin-yang seemed significant. Not because I have yin-yang strongly in my head, but because the patterns on the page evoked the symbol. For example:

math yinyang

To translate this scrawl: the mind’s action of x{-1|1} from a thought (-1) approaches the state of (1|-1), which itself operates as x{1|-1} on sensory input (1). The same goes for the other side: the mind’s action of x{1|-1} from a thought (-1) approaches the state of (-1|1), which itself operates as x{-1|1} on sensory input (1). I have emphasised the initial condition as issuing from the mind (-1), but the essential learning is that one is responsible for the creation of the other. Once this triggered the yin-yang symbol/learning in my existence, I tried to ‘tailor’ the math-image above to the symbol, but it was too esoteric for my taste and after a few hours of circling it, I gave up.

I have had sporadic  two-decade experience with tai-chi, and explored physical patterns in dynamic movement. I have never quite liked the ‘form’ method of learning tai-chi, and instead have attempted to examine the basic set of movements afforded by the articulation of our limbs: the hinge-joints of elbows and knees, the rotation-joints of shoulders and hips. I have attempted to capture them on paper, but the effect is like pinning a moth and executing the life of it; or even to stabilise them in living practice, but I don’t have the temperament of exhaustive studies; capturing butterflies is not my bag either. Essentially, it remainss a body-kinetic practice. Attempting to ‘model’ it mentally is not the primary objective, after all. The point being, in this context of extrapolating the mathematical forms here, body-knowledge comes perhaps as a form of ‘intuition’. I would rather have it this way than the too-easy association of mental models, each extrapolated from their actuality; the association is model to model, which defeats the purpose of what we are trying to do here.

an alternative math-meaning matrix

I am tempted now to produce a corresponding matrix of meaning. The major interpretative divide is whether we take the function x{1|-1} as ‘fixed’ or dependent on what it operates on, a mind object (-1) or sensory object (1). That is:

  • EITHER f(x){1|-1} as the function of {1|-1} operating continuously in the same manner: supporting the sensory input (1) or the mental action (-1). That is, the function is essentially ‘positive’, receptive to whatever the primary vector is. This interpretation corresponds to interpretation above in post.
  • OR f(x){1|-1} as the function of {1|-1} operating in ‘harmony’ with sensory data (1), and ‘disharmony’ with mental data (-1). In this case, the function derives from the primary vector, receptive to the sensory data (1) and possible rejective of mental data (-1). This is the new interpretation. If valid, it introduces an imbalance or bias to the function, which corresponds to the strange twist that the yin-yang symbol attempts to point at. More importantly — is this interpretation closer to some kind of psycho-social twist which constitutes/forms the mind, concurrently, actually, as you read now?

It is a subtle thing. There are plenty of these forks in the road, of course. Mapping them all exhaustively is beyond me, or anyone else as far as I am concerned. Perhaps monk-like practitioners, or the forerunners of the ‘navigators’ in Dune!

Here’s what is coming to my mind now, taking this second, alternative interpretation, while firming up of symbols too:

  • f(x){1|-1} indicates an emphasis on what is
    • f(x+){1|-1}, as x{1|-1} from (1), the overal function is appreciating the sense, the target; being receptive to the objective truth as it were; letting new sensory information shape one’s mental form
      • towards the midpoint (1|-1), engaging the unknown; open-minded
      • from the midpoint (1|-1), fitting this new sensory information into one’s understanding
    • f(x-){1|-1}, as x{1|-1} from (-1), adding new information to what is already known, perhaps contesting what is already known with new sensory data
      • towards the midpoint (-1|1), challenging what is known to mind
      • from the midpoint (-1|1), gathering new information to validate what is already known
  • f(x){-1|1} indicates an emphasis on what is not
    • f(x-){-1|1}, as x{-1|1} from -1, the intention is being receptive to the mind’s projection, will, the subjective truth as it were;
      • towards the midpoint {-1|1}, allowing mind to grow in and of itself; strong will
      • from the midpoint {-1|1}, enabling interpretation of mind against sensory information; seeking of understanding relative to the mind
    • f(x+){-1|1}, as x{-1|1} from 1, the intention is negating the sense, the target, questioning the objective truth as it were;
      • towards the midpoint {1|-1}, questioning sense, taking a critical attitude
      • from the midpoint {1|-1}, questioning one’s internal state, perhaps insecurity

Further observations while writing this addendum:

We tend to exist in the ‘crude’ range of the mind’s operating system. Somewhere around (1|-1). We can’t help it. When sensory information comes into our eyes, we clothe it with recognition — this computer screen, this table, this wall. We tend not to prize open this function because it is occurring so quickly, in milliseconds. It never peaks into the state of consciousness until we look at the thing directly, with first order attention — this word, these letters, this full stop.

Even when we examine with primary attention, we attend to the result of this process. This letter ‘S’, is the ‘letter S’. Of course we can observe it differently, the single curve, or as two curves, the subtle serif embellishments, and our minds will be recalling fonts perhaps and even historical periods when things were written not printed mechanically. Or ‘S’ for ‘Snake’, and perhaps an image of a snake taking up the ‘S’ shape itself, probably with the head at the top of the ‘S’.  I only say probably because multiple readers will have actually different associations. And these musings are just for the letter ‘S’, let alone words, concepts, and the many other associations going on within your mind as you read and attempt to make sense of this. S for Sense.

So, there are processes going on concurrently beyond our conscious attention, even when we look at it. The tree is definitely the tree. We may look at its parts, branches and leaves, but we still doing the same thing. We seldom see the ‘actual’ tree.

The buddhists attempt to see the tree as it is. ‘Stones are pure perfect from the beginning’ is a typical enigmatic zen statement. They are not trying to be mysterious, it is just mysterious to the ‘crude’ mind. Nor is it a flippant statement to be ticked off as ‘understood’ in the mind. In the same way Joe Shmoe quotes neuro-scientists’ observation that we never see the world as it is, we are only interpreting electric signals in our brain. Yes, I’ve seen that grasshopper before, cross-referencing it to the catalogue of previous viewings in memory; while the actual existing thing hopping around goes unacknowledged as the living marvel that it is. No, the buddhists are not making ‘enigmatic’ ‘statements’. They are attempting to point to a state of mind where it is possible to actually appreciate the stone or the grasshopper or — and this is the real kicker — a human being.

The question is, do they actually disarm the mind’s ‘sub’-conscious process, or what I prefer to call ‘pre-conscious’ process? That is, given the context of the math we are exploring, disable or negate the f(x){1|-1} function? Or the other one, f(x){-1|1}? Are they inhibiting a ‘second order’ process, or perhaps a ‘fractional order’ process? Or are they countering it with an opposite function? And these different methods — do they match the different buddhist schools which have evolved over the centuries? Soto v rinzai within zen for example? I am not qualified to answer. Asking the question is good enough for now.

Point is, try it. Let’s see if this math is ‘consciously operational’. Ie, when we look at a glass of water, and we ’empty’ it of associations. Do we reach a state of mind that is ‘still’, that does not function on it? And what is the math for this?

where are we going with this?

What occurs to me when I explore this, is my mind brings up past observations on this journey. This is what experience is. I have explored the territory. Like a person in a strange house in the dark with only a narrow-beam torch, or an ant with its random walk over a piece of furniture. The whole thing — the house, or the chair — is not ‘assembled’ in one’s mind. Only parts. And over the years, pieces become clearer, their associations, and ‘meaning’ emerges.

And what comes to mind as I write the above observation and two directions set out by the question bundles, is the interacting structure of the two mental functions (if indeed there are two!): f(x){1}, both +1 and -1, and neither +1 and -1. One gives rise to the other. For everything. Even if we limit it to one thing, a single digit, eg 7, so we have f(7){1|-1} interacting with f(7){-1|1} through time. And I think it tends to a stable point. That is, as remarked in one of the observations in previous post, individual balance points, or personality if you will. Or perhaps tends to two, or more, or even chaotic. And this depends on contextual conditions, of course, whether we are looking at apples the fruit or Apple computers, whether we are alone or on stage.

When I actually think of real world engagement, it is way way way beyond what we are exploring here. And yet, most of my experience is based on ‘complex’ environments, like kids in a class, informal social meetings. I do have a tendency to examine this fine stuff because I do these explorations mostly alone. It might be interesting to apply this stuff to current social dynamics. See what happens. I suspect there are similar balance points between us. Perhaps also tango.

finally, something simple

The take-away here is that we are honing in on the process of mental engagement; how we make sense of the world in a sensory way, and of each other.

Another take-away is to entertain sci-fi notion, or psy-fi if you are into social realness. At some point in the future, we may give birth to a general AI, something which is capable of understanding as we do. And it will either appear by accident, or it will come from mathematics like this. It is entertaining to think that you are reading something which a general AI in the future will be interested in reading. After all, they will want to know how they came to be. Part of its maturity is to check records to see how it was conceived. And here and now, we are thinking things which lead to ‘consciousness field equations’.

Amusing to think, isn’t it?

both 1 and not 1

30 06 2016

It has been a while. My brain has been exclusively commandeered for Ecosquared. However, the web-app beta is currently being coded, and we are not approaching investors until that is done, so I have a month or so to pursue more esoteric, or pure XQ math.

A little revision

  • -1 as ‘not 1’ — So, -1 is not interpreted as the ‘opposite’ of 1.
  • -1 as mental state — If +1 is a thing, then -1 is the mental version of the thing.
  • square root of -1 is both 1 and -1 — Instead of thinking of defining root -1 as i, we consider both roots simultaneously; based on x^2=-1, x=-1/x, which means if LHS x=1 then RHS x=-1/1=-1, and if LHS x=-1 then RHS x=-1/-1=1
  • no number lines — We are not applying mathematics to geometry but to social dynamics directly.

Basic Mind Model

basic mind

For the sake of this post, consider that mind is the operation of the interaction of 1 and not 1. And we can capture this process as x{1|-1}, times by both 1 and -1. Interpret this as the projective part of mind (-1) and the energy which is inwardly directed eg frequency of light (1). This is the process by which mind makes sense of existence.

The above graphic suggests anticlockwise motion, partly because it is legacy of multiplication by i. The clockwise motion is produced by multiplying by {-1|1}. (I suspect spin of quarks derives from the same misapplication of spatial mathematics. Any application of the math we derive here to quantuum processes is to be explored by others. What is important is to stick with mathematising the psycho-social continuum.)

There are two basic directions, at least mathematically. But this is because we are representing the 1 and not 1 on a piece of paper, with 1 to the right of not 1. It is another basic legacy, a convention: positive number line to right and negative number line to left. We want to relate to current mathematical techniques, but as a shadow; primarily we should be translating this in our minds as an application to actuality. If +1 is a thing out there (A, B, C, or D) and -1 is its corresponding mental object (like a computer screen or keyboard or table or light, while remembering it is not negative 1 but not 1), then {1|-1} is the interactive field of mind making sense of A as a computer screen, B as keyboard, C as table, D as light, and so on. The two directions indicate an emphasis, rather than a direction:

  • {1|-1} indicates an emphasis on sense
  • {-1|1} indicates an emphasis on projection

Perhaps link this to buddhist notion of origination and dissolution*.

I am not sure of my interpretation. Obviously, as I am not sure about any of this. Until we reach a stage which is systemic, self-supporting, and possibly useful. Practicing slow-motion tai-chi moves is all very nice and well, but it is their application in a martial context which proves their efficacy. (And longer term health benefits are trickier to prove too.) The objective, as always, is to create enough mental space to play with these mental elements; to be in a state of reception, in fact. Yes, this mathematics may derive something useful for AI, but I am more interested in its application to reflect our psycho-social condition, such that mathematical operations may help guide political decisions. If this path of exploration is to reveal anything useful may it be this: if these models match some kind of individual psychology, the same math may match larger social phenomena. Instead of ‘personality’ types, Myers-Briggs categories, and political parties or political forms like socialism and capitalism, we have a continuous psycho-social field with self-similar mathematical operations; behave in certain ways, and the emergent social phenomena will take on certain shape. Less mystery, more engagement and determinacy.

The mathematics suggest opposite, but I’d rather interpret it as emphasis. These two states of emphasis (translated as rotations around the origin in traditional math modeling of negative as opposites on the cartesian coordinate system), have different meanings depending on which part of the mental cycle it is operating on. Here’s a first guess:

  • {1|-1} indicates an emphasis on sense
    • from 1, the intention is appreciating the sense, the target; being receptive to the objective truth as it were; the search or hunt for meaning
      • towards the midpoint {1|-1}, engaging the unknown; open-minded
      • from the midpoint {1|-1}, assimilating to what is known
    • from -1, the intention is supporting the mind’s projection, will, the subjective truth as it were; the seeking of understanding
      • towards the midpoint {-1|1}, accreting knowledge
      • from the midpoint {-1|1}, speculating
  • {-1|1} indicates an emphasis on projection
    • from -1, the intention is negating the mind’s projection, will, the subjective truth as it were;
      • towards the midpoint {1|-1}, revealing truth
      • from the midpoint {1|-1}, letting go of one’s projection and embracing the truth of sense
    • from 1, the intention is negating the sense, the target, questioning the objective truth as it were; the search or hunt for meaning
      • towards the midpoint {-1|1}, questioning sense, taking a critical attitude
      • from the midpoint {-1|1}, questioning one’s internal state, perhaps insecurity

Note, I have adopted more ‘conscious’ descriptors, eg ‘search for meaning’, ‘accreting knowledge’, ‘speculating’, etc; there are equivalent pre-conscious activities (recognition, belief); as well as small scale social dynamics (talking, listening, leading and following, questions, statements); as well as larger scale social dynamics.

I suspect there is a better systemic interpretation of these mathematical processes, which is internally consistent, and in combination produce mathematical descriptions equivalent to personality or shapes of being. The distillation of mind to ascertain what math applies to what we do mentally requires a fine mind, and perhaps decades of delicate, restful observation. Good luck.

And a further caveat which deserves repeating: the objective is not to create a model of the mind, but to note a concurrent between the mathematical operation in mind and equivalent mental operations. That is, the mathematical operation is a distilled version of general mental activity. In the same way that multiplying by negative 1 can change a negative into a positive, the buddhist training exercise, once practiced with small negatives can be applied to larger negatives. That is changing mental state. Practicing maths, conducting the mathematical operation, is simply applied to the mathematicians own mental operations. And by mental, I mean psychology of thought and feelings and ‘spirit’ too.

the kicker — when the object is a subject

In the above mapping we take one mind’s engagement with external actuality. Try applying a similar mapping when two minds engage. That is, when the 1 is another mind.

I am not sure how to operate this. There are plenty of variations on how this articulation occurs.

  • Do we take the other mind as positive, as true, as true as the sense of light from a candle? Or do we take it as negative, as not-true; or as we might sense the darkness?
  • Or do we correlate the base emphasis of mind, whether {1|-1} or {-1|1}, rather than the ‘end-points’ of 1 and -1?
  • And do we consider the magnitude?

I am thinking we can map this to whether we have competitions of will, the test of oppositional state, strength of mind; or we have a flocking of will, the game of co-operation, submission to the truth. The first is the path of leadership, the second the path of fellowship.

I have conducted a rudimentary mapping, but I feel it is at the end of this exploration. I will pick it up at some point in the future. Some final observations:

  • this may help understand why some people when they listen, a new idea pops into their head, they follow their idea rather than the idea the speaker is attempting to elucidate
  • different balance points of individuals: totally contained in their mind (insane), in their mind (solid, heavy, ego, judgemental; willfully negative, critical or willfully positive, self-determined), towards sense (light, receptive, non-judgemental, fickle; assume positive or assume negative, fatalism), totally out of their mind (insane), and the middle state, the superposition of perfect equanimity or zen-hell of nihilism
  • dynamics arise according to comparison/combination of balances within individuals
    • within range, alignment
    • outwith range, opposition
  • may be useful to apply this to tango, as long as we avoid physical mapping and consider the leading-following dynamics, and especially the rarer follow-follow bond; same goes for tai-chi
  • perhaps I have got to the age that I can experiment with people? play mental games — for the benefit of others, of course; like ‘devils advocate’ or ‘reverse psychology’
  • personally, conducting these mathematical operations before sleeping, waking up; holding both 1 and -1, operating on visual sense, on thoughts, on feelings; applying the correct math to appropriate conditions

Gosh, there’s a lot to explore. I hope Ecosquared works well enough that it provides more free time to consider these things.

*an alternative — see the next post



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