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?


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.


positive and negative infinity

5 10 2011

Just noticed, perhaps for the first time, I can’t remember, that Reimann’s trick was to conflate positive and negative infinity to the same point. This is quite remarkable. This actually connects in my head to the higher-dimensional twist, the mobius loop in time, that I intuit is going on with consciousness. Ho hum, but there you have it.

It is strange. Start with zero, then the number line going off to infinity to the right along the positive axis, and going off to infinity to the left along the negative axis. And strangely, these two opposite directions meet at the same point.

OMG, as I write this, I am amazed I haven’t seen this. No I am amazed that Reimann saw this. I think this is what he saw.

It’s actually pretty simple. In terms of fairly standard human, enlightenment thinking, we are standing on the planet, let’s say at the equator. You point off east with your right hand, and west with your left hand, and sure enough, if you follow your pointing around the globe, you are actually pointing to a thing at the opposite side of the planet. And indeed, you could point through this and continue until you are pointing back along the opposite direction: your right finger pointing eventually meets the end of your left finger pointing in the opposite direction. In a way, you are pointing at yourself.

But this is predicated on the curvature of the earth. Now imagine this pointing is not bending. So you are standing in space. You point off in one direction, and you point in the other. You point off to infinity. The only way this could possibly make sense, is if you think there is a similar thing going on with the universe. That your right pointing eventually ends up coming back to meet your left pointing. This may or may not be the case with the universe. But what Reimann does, is suggest that it is, in effect. That is, be bends infinity. That is, infinity is not this endless thing, but converges. That is, he captures our ability to conceive of infinity. Or, more prosaically, our ability to label it, “infinity”.

We have taken a step from received understanding, I suspect. We are definitely performing within XQ space here now.

It is not so much that the infinity used in the reimann sphere has anything to do with existence, with the physical universe. It is to do with our human immersion in it. But not so much our physical embodiment, but our subjective orientation within it. Eg, left and right.

Returning to the math of Reimann, the strange thing is, positive and negative infinity meet at the same point. If you visualise this, it is a simple circle, as we have circumscribing the equator as in our initial thought experiment. This is ok if we are thinking of planets which are curved. This is a bit stranger if we are talking about subjective qualities, eg good things and bad things. A super extreme bad thing ends up meeting a super extreme good thing. The more they are apart, the more they converge on the same point.

It may be a mistake to think of this as a point, but it is definitely done with the Reimann sphere. Anyhoo, however you think about it, the reimann sphere is useful because it allowed mathematicians to map arithmetical functions to geometric functions. Multiplying by 1 and -1 and i and -i result in rotations of the Reimann sphere.

What I was trying to get around my head is how this is related to my notion of o being the centre of the individual and 1 representing the individual. I sometimes play with 1 as being the human, and in the Reimann sphere, that would be the equator delineated by 1, i, -1, and -i. I’d like to square this (might have to be careful with my language here;) with notions of internal states, which would be represented by fractions as aspects of being approach zero, or negative numbers as the mind’s reflection of what is, which takes zero as the centre point of the individual.

There’s something like a torus floating around here somewhere, but I can’t find it. Three dimensions of circularity, versus the two of a circle. Not sure if this is correct. Torus can be created from rotations of two circles of different scale. A sphere can be created by a single circle rotated around one axis. That is, a two dimensional shape rotate through the third dimension. A torus can be created by created by rotating a circle through a disconnected axis through the third dimension. So they are the same, except for the connection/intersection with the axis. That is, whether the zero is inside (circle, sphere) or outside (circle, torus). Interestingly, as far as I can conduct the transformations in my head, the first transformation can be conducted with a 180˚ turn, while the second requires a complete 360˚ rotation to complete the torus. But these are artificial means of producing torus, whereas I am more interested in how they form in smoke, for example, or dolphins producing air rings in water.

This was all sparked when I started to thinking of the mathematics of emergence. First spread consisted of systems, circularity, fractal in time, simultaneously iterative, Second spread has one equation/function/expression that simultaneously operates on several different processes which have different periods in time; which also may map to presence, mental, emotional, physical as basic levels of being. Third spread jumped to 0 = 1 – 1, which could be translated as

0 as the centre of the equation/function/expression, if it is to represent consciousness

0 or 1 and -1, if we wish to explode 0 into duality of mind

0 or 1 and not 1, which is kind of a description of the duality of mind

which leads to

e^iπ -1 = 0, euler’s equation

which means that

e^iπ = 1

and this has something to do with period, if i remember correctly, and the Reimann sphere.

There’s a lot in here. A lot. The revelation for today remains, that the positive and negative infinities meet at the same point, at least can in terms of maths. And if we are to take an XQ interpretation, this means the Reimann sphere is more a description of how we bend subjective thought space, eg the notion of infinity, to a well behaved point, eg the word “infinity”.

Somewhere along here is the math of emergent systems. It is do with nested systems in time.

And interestingly, I noted as I started out that my mind approached this from consciousness outwards. I started with zero, and then attempted to derive the other numbers, and found myself with euler’s rule, and thereby to Reimann’s sphere. That is, it is not about trying to work it out from the details, and integrating some kind of theoretical sense, but it is deriving details from some simple starting point. Kinda like the buddhist methodology, and like einsteinian physicists working it out from insight, first principles, and so on. This is quite promising. It suggests, that it is about appreciating simplicity, and from this derive all kinds of complexity. Can we intuit the field equations for consciousness?

Another thing to note, is that I am making progress, albeit slowly, on the notion that we may need a different form of maths. I am not sure about this at all, but it is simply a hunch when appreciating the invention of calculus by newton. A new maths had to be invented to capture the mapping of physical objects, that of functions. A new maths may be necessary to capture the mapping of mental objects. My mind might also have met with some encouragement when I read somewhere recently that the whole path of functions, the entire realm of maths, is limited in some way. Sadly, I can’t remember where I read this, heh. I shall have to wait until it pops up on the radar again, and again almost by random. Still, it will give me plenty of time to explore/prepare other areas.

ADDENDUM: after going back to include the image of the  Reimann sphere

What if the infinity point was the asymptote I keep thinking that mind is, not zero? And zero is the touching point with existence, the flat plane? I know this doesn’t make any sense, but all the numbers are contained in the sphere, and the plane below the sphere is just an illusion. Well, it is all an illusion. No, that’s not quite it. I keep getting fooled into thinking the  Reimann sphere is an object in space, heh, and I have thought about what is inside the Reimann sphere, for example, or outside it. Nope, the extra thought wasn’t this.

It was something about rotating the sphere through one of the axes, eg the real axis. Not the axis that is wrapped around the Reimann sphere, but the axis of the plane surface below. This should create a torus, which touches at zero, or rather does not touch at zero. But all mind is capable of is not really rotating the sphere but the great circle, marked by o, -i, infinity, i, 0, if we are rotating around the real axis. To rotate a whole sphere through space leaves what exactly? And an empty sphere at that?

Ho hum.

zero simplified metaphor

20 09 2011

So, it can get a little too much. But the simple version, which can be used as a field to metaphorise, is what follows. Useful for explaining where buddhists are, and perhaps help people who are a little… confused. After all, this is simple maths, it is true, and we have experience of it. Powerful stuff.

Zero has several … uses of it… or approaches to it.

First, the obvious, zero as a digit, used in place value with the other digits to signify numbers. eg 302 is the number three hundred and two, indicating three hundred and two things. The 3 stands for three hundreds, the 0 for no tens, and 2 for two units. A useful shorthand.

Second, the subtle, zero even as a digit, does not behave like the other digits. In eg 3003, the 3 stands for three thousand and the other 3 for three, and three thousand is quite different from three. You can’t confuse them. Whereas, the 0 stands for no hundreds, the other for no tens, that is the same number, none.

Third, the obvious, zero as a marker for the number zero. And what is the number zero? This gets tricky. No anything. Nothing. Is it even a number? Well, whatever it is, we have a symbol for it.

Fourth, the subtle, zero. Nothing. Not even the symbol to represent it. Beyond thought or thing. Void.

So, to map it to subjective experience. Fourth, the subjectivity exists as null-state, beyond conception, the void. Third, we can call this buddha. We can call it anything, as it happens, because it is just a symbol, “buddha” or “0” or “void”. Second, subjectivity as defined by context, a socially derived self. There is no meaning to the person beyond the engagement they have with others. And first, subjectivity as I, a specific person, here and now, thinking and reading this and believing they have a personality or perhaps beliefs independent of others, an essential self.

As pure as that. What number are you?

I have had some experience like 0 as place value, and I have met a lot of people who know about the marker “0”. They talk a lot, they know a lot, they know how it fits into the number system and all that. But they are a million miles from the actual experience of 0, the void. And I’d rather engage other numbers, than those who talk about and signify 0.

hehehe, that’s actually funny.

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