visualisations of e

22 08 2016

Here are a few visualisations for e.

Remember, this is if we interpret number in standard mathematical way, eg -1 as opposite to 1 on a number line, eg root -1 =i mapped on cartesian y axis. That is, spatially.

The trick, if you can, is to interpret number in terms of time. There are several ways. I will explore a few in another post. Just wanted to post these images here for now.

2000px-Euler's_formula.svg

Basic complex plane.

2552133613835878061

A standard inclusion of time as function of angle, ie rotation.

Euler's_Formula_c

Bask in all its glory, folks. Check out animated version on wikipedia.

Circular.Polarization.Circularly.Polarized.Light_Left.Hand.Animation.305x190.255Colors.gif

This is approaching the model I intuited in my undergraduate paper decades ago, something I shall need to revisit it seems. Probably take me another decade or two. Imagine that, returning to a structure one first saw nearly three decades before, as a summation of social anthropology. Beggars belief.

an ancillary perceptual exercise

As an interactive experiment, try inverting the image. I can’t. Well, not easily. What I mean is, apply the following transformation to the above image.

cube-clipart-cube.gif

Change your perspective. Either a cube with where you are looking at it at an angle from above and left, or at an angle from below and right. Shift between these two.

Can you apply this mental movement to the animated gif above?

 

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yin-yang

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

 

 





non-zero origin and polar co-ordinates

2 07 2015

A rather untidy foray. There are some useful bits in here… but not well presented. Uncut precious stones, maybe just common garden stones, you decide. Bears little relation to what I am spending nearly all my time these days, working on the Ecosquared app. Only direct correspondence is with money as a vector in time, and between people, and the value attribution towards people, things and projections. I’ve developed equations that captured a phase change in social space making a decision, but that was with MTTP and I haven’t had a chance to approach that for nearly two years. There’s plenty of stuff to explore, but I’d like to have the money to do so — and that will be after the £60k beta version. For now, a rough and ready rambling expedition.

I returned to this graphic I produced a while back. A way to represent the self where the three physical dimensions are conflated into Actual (I should just call it Space), and all psychological and social aspects conflated into the vertical Virtual dimension.

3D TAV longitudinal

Sadly the original and the numbers which this graphic is based is lost. Roughly, the outer boundary is at 10^0, and each word on the axes increases by an order of three.

I did a quite review of articles written here, after I conducted yet another review of my own mind regarding the application of number to human existence. Namely, the application of positive and negative numbers, the root of negative one as simultaneously +1 and -1 (ie presence and non-presence); hoping that a nice pattern of mapping appears from the same pieces, namely how to attribute number to our experience.

This recent venture derives an obvious correlation of sense and projection as positive a negative. Again I am not sure which way it is best to attribute the numbers, but it seems natural to think of sense as positive and projection as negative. Fits into early intuitions that thoughts, the substance of the mind is effectively negative. It does not exists. And as usual, I was wondering if there was a sweet spot of configuration regarding words which signify things (light) and words that have no actual correlation to things in actuality (dark). All this is pretty straight forwards.

The only subtlety revealed is that +6 is not referring to an actual thing, but to the sense of the thing. It is a vector, if one accepts that negative is a direction. Of course, when there are two centres of the universe in the same room, then the application of positive and negative are relatively interchangeable. Positive now, intuitively, is the projective sense from self, and negative as coming towards self. But there are plenty of different levels of human existence by which we can colour this simplistic physical model. Point is, there are issues regarding a straighforward positive and negative with several interacting selves.

some numbers

In my recent mental review, I attempted once again to apply some numbers to power of 1, which is how I wish to capture human density, 1^n. And the notion of scale, which simplistically is 1^10^µ. Scale is a general sense I have attempted to correlate across various dimensions of our human existence. In my mental review, I came up with µ=3 for tribe, µ=8 for globe, µ=13 for solar system, µ=16 for galaxy, and µ=-3 for conscious, µ=-8 for mental, µ=-13 for bodily processes. And 1^-10^3 as volition like a dog, 1^-10^8 as perception such as an organ like an eye, or a flower, and 1^-10^13 as sense, cell-like.

Screen Shot 2015-07-01 at 23.56.55

Its a frightful mess, I can’t tell what is best or appropriate because there is no use to it. But use is a very scientifically laiden concept; buddhists sense of use is very different I suspect. Remember the tool itself, the mind, is the thing we are attempting to examine, in a methodologically different way than treating it as an object. So, I could say 1^n is social density, 1^-n mental architecture or complexes, and 1^n^-1 as introspection. But who knows? I don’t have clarity of mind currently to settle on one.

stay simple — stick those numbers on a graph

So, if this post is not about exploring some brilliant new observation on how to apply math to psycho-social dynamics, what is it for?

Well, if you apply those numbers in the spreadsheet to the 3d visualisation, it makes some sense. Especially if you use the second column of numbers. That is, 1 is the ‘outer boundary’ of ego, say, of the self. It goes into fractional parts internally, physically, mentally and in terms of time. It goes into greater orders of expansiveness outwards, again physically into the world and mentally into society and over wider periods of time. At the centre is zero.

However, what happens if you use the first column?

IMG_20150702_243136502

Yes, it is very messy, but I hope you get the idea. If we use the power µ=0 as the boundary of the sphere, or circle in this diagram, we get the centre as being -infinity. Which is somewhat reminiscent of Riemann Sphere. But of course, you can’t use the map above in a cartesian way, since (-1,-1) could be any number of 4 points. So, you have to use a polar co-ordinate system.

I’ve never used polar co-ordinates. I mean I did a tiny bit at school, but I never really saw the point to them, and thus I never managed to explore how it connects up a lot of maths, to do with multiplication by i and rotational geometry. But here it is, one provides a scalar and an angle. The scalar normally centres the zero at the origin, and negative scalar presumably transforms the angle by adding 180 degrees.

I tried to search for a better image, but don’t know how to phrase it. No luck on Google. Point is, the origin is not zero but negative infinity.

This may mean absolutely nothing. And I mean that literally, if one can mean that…

Zero as digit, an unusual digit because in terms of place value it does not hold its own like other digits; zero as a representative of a number like other digits, but again there is no corresponding thing out there which is counted. That is, 0 as absolute absence, void, not even that which can be named or signified.

Or, from another angle, the interpretation of negative as not, eg -6 as the specific absence of exactly 6, eg the absence of this apple, the one you can not see, that is only an image in your mind. We’ve covered this before. So, the collective sum of all not things, all negative numbers, not 6, not 5, not 5.5, not any number, not anything. And whatever is left is that which can not be named, or if it is minimally, we say zero, and the act of naming it vanquishes it.

observations regarding social dynamics

This is not philosophy. We are not playing with words. This is maths, and psychology, and using a buddhist methodology. Well, I’d like to, but lack the mindstate to do so. Point is, this way of representing the self, the one above, combined with scale as a power, derives an origin that is negative infinity. The absence of all thought. That’s wonderful.

And finally, I suspect there are physicists playing around with the maths of blackholes. I wouldn’t be surprised if the event horizon can be represented by zero.

And when we consider two people, and the simpler mental dynamics that allow a more… conducive exploration of mental objects. And three people and unstable complexity, and with seven or more a calmer social dynamic. Why? Because it is to do with the number of dimensions between individuals, and the preponderance of listeners. That is, with two, one can switch from relative mind conditions easily enough, or at least I can, from my own to theirs. I can do so when two people are dialoguing too — in fact we are all pretty good at that. I just don’t have much capacity when there are three or more, or even two, when they are not sharing attention well. But, once you get a group of people, because of the preponderance of listening, the sharing of attention means a calmer dynamic. Think lecture, perhaps, it returns more to following a specific singularities continuity of thought. That is, there are no changes of relative position — the origin remains the same — and all relative movements can be mapped relative to that origin, and one’s one, as if it were a conversation, though a little one-sided perhaps in terms of who is vocalising.

So, this polar co-ordinate business may be a useful way to explore psycho-social dynamics in terms of sharing attention. Ie, what we are thinking about, talking about, feeling.

Oh, and here’s another. Linking it to the fraca between me and Gunther a long while back, where we revealed the deep seated application of 1 or 0 to self. In the above model, self is 1^0, and you can choose which to identify with. The self-attribution of the centre as 0 (which was my original clumsy mapping) may need to be upgraded. Gunther’s self ascription of 1 for himself and everyone else as 0 — you had to earn his trust. Equality was not a given at the start. That’s the thing about the map of 1 for self, even if one ascribes the centre as zero. With this revision, 1^0 has both. The self-attribution remains, whether 1 or 0, and it still remains indicative of a state of mind, or… setting of mind, that provides some potentially rich path of exploration for psy-math and its therapeutic value.





re-visiting psymath

5 06 2015

This is the third post in a vertical chain. I started with this post at ecosquared, then this at 2020worldwalk, and now this here at XQ, a site I haven’t visited for a long time. Indeed, my mind has not been in the condition to explore this space much. So, what is written below may be… insensitive, or inaccurate. I can’t tell. It is the result of a mind in the act of commitment.

So, marry a personal engine with a concurrent God-belief system, and you get a very powerful individual. Why these two? Because the middle-state is dispassion. Without will, there is neither the personal engine nor the God-belief system. To acknowledge zero of self, is to acknowledge zero of self of other. Or indeed, the difference between self, at that level of appreciation is equal.

psymath

Let’s call this area of XQ Psymath. I started on this path with Leon’s encouragement to make XQ practical. It is a continuation of the original insight that math has a therapeutic dimension to it, written in the original XQ Condition exploration back in autumn 2008. The most significant exploration since the confrontation with Gunther in winter 2013 which revealed a correspondence of 0 and 1 to inter-subjective judgement, and how it was reflected in the SEA or what I cam calling the SQ-algorithm. Interesting stuff. I think the following connects to that. Does it? Retrospectively, or from another mind, it might.

the math of will

Translating the above paragraph about will. It is not 1 = 1, which is how we like to think of equality. One person is equal to another person. Like we are equating bodies, things. We have escaped from this with the mathematical construct 1^n. 1^2 = 1^3 is true arithmetically, but only if we reduce. So, to say 1 = 1 is a crude reductive mapping, both mathematically, and also in terms of human beings.

Not even 0 = 0, which is a ‘soft’ version of buddhism. This is where we recognise ourselves as empty, as not being of value. The corollary is that we place value in the other, or perhaps the relationship between. This is too baggy for me, intuitively. I associate it with ‘soft buddhists’, well meaning people like ‘soft christians’ or indeed ‘soft anybody’, where they are living comfortably enough to be generous. A little more depth than the platitude that we are equal, but not much better. If 1 = 1 is the christian or western version, 0 = 0 is the buddhist religion version, lay religious types. People who are well meaning, but not serious.

Return to the insight — ‘the acknowledgement of zero as self’. Remember also the insight that 0 is different from the other digits. 2 may represent two things in the world, it represents something, as well as being a placeholder; it can mean 20 things, or 2000 things depending on where the digit is. 0 does not represent anything, but it does perform the placeholder function. So, it is the placeholder function that mostly accounts for 0’s use. And as a representation of zero, of nothing, it fails. Something which Leon has gone into deeply with Spencer-Brown’s attempt to create his Laws of Form, to account for the first mark of distinction. I have taken a slightly different angle. Whereas Spencer-Brown is attempting to create the logic, the externalised form of it, I am happy with maintaining the operation within mind. That is, my mind now, and your reading this. It is not relying on a new ‘formality’, script, etc.

So, 0 as a place holder, as representation of nothing. 0, as a mark, whereas nothing has no mark. It is absent. Though if we start thinking of absence, we go into our secondary interpretation of negative — what is not there. ‘0 as the omission of a mark’ is more like -0, which is just as ‘useless’ as +0 in this regard. That is, we attempting to point at the null of it. We can do so in our minds, but we can not do so well with words.

Returning to our mapping, not 1 = 1 nor 0 = 0, but rather a simple 0. With the acknowledgement of zero of self, and thus the zero of self of other, there is no distinction. The 0, is not ‘my mark’ that I apply to this nothing here, eg in 2000, the first zero is different than the second zero because of its place. And so, my sense of emptiness is different than your sense of emptiness because we occupy different places. However, the emptiness of self is the same. It is identical. There is no ‘=’ sign involved because there is not difference, because there is literally nothing to compare.

orbiting the point

This level of appreciation, of acknowledgement, is tricky to reach, immerse, and then to actually enact with others. So, a tendency to it is good enough. In terms of Ecosquared, it is the +0, the 0 which is the absence of a self-score. In terms of inner psychology, it is -0, the approach to zero from an internal state. No markers required, the reduction of thought to its minimum.

So, anything that deviates from this intention, towards zero, that lingers around 1, is will. This outward projection is will, and the differential between stasis and action is enacted through will. Will-power.

Of course, even gentle buddhists have will power, but the attempt is to root it in zero. To disengage the engine that was built as a child. So that the will that is effected is because of the conditions. The cup is filled with water because the cup is there, the water is there. The person is cared for because they are in pain. A life of service. Even the extreme martial artists monks are responding to external conditions. A dangerous game, of course, to play with the engine of will, but we can understand the how and the why it has evolved historically. A buddhist’s will is less a ‘power’ thing. It is more a pulling.

hooking up will-power to god-belief

God belief is the psychological version of 1^n where n is infinite, or at least uncountable. Let’s not talk about infinite, because it has been explored by mathematicians before, and we have evolved a formalism for it which I have glanced at but have not seen cause to explore properly yet.

Hmm, when I think about it, I think more 0^n or maybe -0^n. I don’t know. I went through an exploration winter 2013 which brought up some representational forms. I suspect it will hook up there better. I will leave that for another day.

All that we are doing today, in a rather unravelling way, is that absolute dispassion, maintaining a state of 0, means that neither personal engines may operate nor god-beliefs. And, because of my limited experience with a personal will-engine, small psycho-social experimentation, my own interpretative experience of God, and the social evidence of social movements based on will-power and belief in God, means there is a mathematics here that can be articulated precisely. Again, it is not the expression of it, that bears any ‘power’, but that minimal identity of it in order for a human being to exercise it psychologically and socially. Potentially therapeutic, personally, and perhaps somewhat more dangerously given historic precedence, socially.





superposition of x^2 and euler’s identity

20 09 2014

I am meant to be thinking about economics for the construction of the ecosquared app. When I consider relationships of giving, I get sucked into math, and I end up gravitating towards Euler’s identity for some reason:

Screen Shot 2014-09-20 at 22.58.26

The identity is the one at the end. That’s the one I have in my head.

starting with spencer-brown’s curiosity

The last time I saw Leon, he pointed me at this funny little morsel which happens to be at the start of Spencer-Brown’s Laws of Form:

If we begin with x^2 + 1 = 0

Transpose to x^2 = -1

Divide both sides by x, we get x = -1/x

This is self-referential of course, which we normally don’t like in maths. I certainly have been trained to avoid this kind of pattern.

Try substituting 1 in the equation and we get 1 = -1/1 which gives us -1. So 1 = -1

Try substitution -1 in, we get -1 = -1/-1 which gives us 1. So -1 = 1

Both are absurd. Or rather, this is an alternative way of interpreting root -1, or √-1, or i.

my thought when i saw this

Instead of coming up with a geometric interpretation, where i is the y-axis, and hence all the subsequent interpretations of equations as rotations etc — in space — what if this is simultaneity in time? Or rather, we consider actual simultaneity in time of two states. In this case, then, i is now simultaneously 1 and -1 at the same time. It is in super-position, or dual, or whatever you want to call it. It is both 1 and -1.

Not that we are saying 1*-1, which is -1. We are saying both 1 and -1 as the same time. And I guess at some point, we might say neither 1 and -1, but that tends off to one of our interpretations of zero.

Oh, and remember we have the notion of negative as in ‘not’. So we have the rather interesting mathematical, or arithmetical, expression for 1 and ‘not 1’, or a thing and not a thing.

Extraordinary.

now think about euler’s identity

That is, e^(iπ) +1 = 0

Becomes e^-π = -1 and e^+π = -1.

This can be turned into e^π = -1 and the reciprocal 1/e^π = -1, or -e^π = 1 and its reciprocal -1/e^π = 1

So, what is ‘1’ and ‘not 1’ becomes a value and… it’s reciprocal?… at the same time. I have no idea what this means.

The normal way to interpret π is in radians around a point, or 180˚, or half-turn around a circle. If we think of it as 3.14, we get

Screen Shot 2014-09-20 at 23.14.18

And the inverse is:

Screen Shot 2014-09-20 at 23.16.55

Which means what exactly?

Well, in terms of simultaneity, they are both… true… at the same time.

And here we are allowed the function of multiplying them together to get 1. Which seems to be a way of translating ‘1’ and ‘not 1’ into two absolute values (-23.140 and -0.043) that normalise to… 1.

The simultaneity of 1 and -1, can be made equivalent to multiplying these two numbers — negative numbers at that!.

And of course, if we are allowed any number, not just π, then we get multiplying any two reciprocals.

Clearly I have got my wires crosses somewhere along here. I just don’t have the brain right now to deal with this…

so friggen what?

Well, I’ve had the intuition that the SEA is based on a summative basis. Which is fine for now. However, I do like the notion of 1^n, with n being the number of people. There’s something in that I would like to unpick. And it is related to the notion of numbers multiplying together to give 1. So when someone is at 0.5, another is at 2, one at 0.1, another is at 10. They are reciprocals. And I am thinking of reciprocals in a complex way. So, what are the reciprocals for three people, say? eg 0.5 and 0.5 and 4. Or 0.5 and 0.4 and 5. Interesting, no?

And consider Euler’s formula with sin and cos, something I never think about:

760px-Euler's_formula.svg

Since I am currently thinking about how values interact in the relative value algorithm, I can’t help but think there’s a relationship here which I haven’t brought out. Ratio of sides relative to the hypotenuse, which is 1; the ‘cos x’ and the ‘sin x multiplied by i’ gives us ‘e’ to the power of ‘i times x’. Relative to 1. Forget about the visual interpretation. Relative to the same value of 1.

It’s a relationship between addition and multiplication and powers. And what these mean temporally, I am guessing, not spatially.

Will take me years perhaps.





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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