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.


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.


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:


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.

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