powers and people

27 02 2010

I just couldn’t find this on the blog, or any blog, and took me a while to find it one of my note folders… Just want to stick it in here before I lose it. It’s a bit messy, but there you have it…

maths: why powers are related to fractions? eg 2^-2 is 1/4… what does 2×2 in a negative sense mean?

i’d relate this to p is true, p is false, p is neither true nor false, p is both true and false

  • ?? 2 is true, -2 is the false version of 2, 2-2 is neither true nor false, 2+2 is both true and false
  • ??? 2 is true, -2 is false, 2^-1 is neither true and false, 2^1 is both true and false
  • ? 2 is just 2, -2 is not 2, 2^-1 is neither 2 and not 2, 2^1 is both 2 and not 2
  • ?? 2 is exactly 2, -2 is exactly not 2, how do we signify everything but the 2? ie ∞-2, neither 2 and not 2, neither 2-2; so what is both 2 and not 2, both 2-2
  • ? orange exists, not orange is imaginary, orange^-1 is neither orange nor imaginary orange, orange^1 is both orange and imaginary orange
  • ! 2^-1 is division ie recursive division, 2^1 is recursive multiplication, ie 2^2 is 2×2, whereas 2^-2 is /2/2, which actually leads to /4 oooooo

keep thinking of 2 as a point on a number line, ie a point in relation to other points spatially… tut

seems to be two ways of taking it: both 2 and not 2 seems empty and neither 2 and not 2 seems like infinity without that bit;

  • ? 2^0 is 1 is everything…
  • ?? 2^-1 is the imaginary, one dimension removed from actuality (what we have been thinking so far as not 2)
  • ?? 2^1 is the actual thing

gotta remember what x2 means… recurring pattern

  • 2^2 means 2 perceptions of…
  • 2^-2 means perception of perception
  • ! orange^2 means two perceptions of orange
  • ! orange^-2 means what i am thinking of your imaginary orange

so we have

  • 2^1 perception of the number 2… 2… i see two oranges
  • -2^1 perception of not 2… not 2… i imagine two oranges (and there aren’t any)
  • 2^-1 imaginary perception of number 2… ? both 2 and not 2… i imagine seeing two oranges and there are two oranges!
  • -2^-1 imaginary perception of not 2… ? neither 2 and not 2… i neither imagine nor are there two oranges

then we get

  • 2^2 two people see two oranges
  • -2^2 two people imagine two oranges (and there aren’t any)
  • 2^-2 a person imagines another person seeing two oranges (ie has heard there are two oranges… rumour, second order)
  • -2^-2 a person imagines another person who is imagining two oranges… but no oranges actually exist

is this approaching a subjective derivation/proof/evolution of numbers…?

  • 2^2 the two people could be looking at two different pairs of oranges, ie 4 in total, or the same 2…
  • it is repetition, seeing the same thing, that makes something more true in terms of reality, ie a million people believe in the pharoah/king/god/democracy/maths…
  • we may need a third thing here to determine whether it is the same 2… we can’t do that, since both are imaginary
  • but if they both refer to the same item of actuality, eg two orange-shaped things, there is an alignment, a trick, such that there is ‘agreement’ in terms of perception/word/value
  • maths is the purest mental form, the first abstraction as it were
  • actually 2×2 is two people seeing two oranges each, is 4 oranges…

the whole conflation of positive and negative with opposites, and true and false… that is, the mind’s capacity to see in opposites versus reality just is… imagine a maths that is not based on the mind’s capacity to think in opposites, a totally positive maths as it were… a maths based on actuality v reality

a maths based on actuality v reality… the multiplicity of realities creates popper’s third world of imaginary objective thoughts

  • 2^-7 a real chinese whisper chain… the further we go the more we don’t know if the 2 actually exist, could be -2^-7
  • traditionally -2^x output alternates +/-… morally, two wrongs don’t make a right, and yet in maths it does…
  • 2^7 are seven people looking at the same 2 oranges… (compare to 2×7)

this maths might be useful for computing eg re-tweets

is π neither an exact number nor a not-exact number… or is π both an exact number and a not-exact number?

all looks a bit crazy, but i am questioning the conventions of maths which have been adopted throughout history, deriving different conventions, different systems… just like non-euclidean geometry

that is, adopting non-duality mathematics, mathematics that is not based on opposites OMG





projected planes and vanishing points

27 02 2010

I dabbled a little with projected plane geometry, namely in the deep end with Reimann sphere (p80 XQ solution). Recently thinking about reflecting the social body (p83 Pulse), how to represent intentions and projections. So, two things: the social, the internal projections. But we need to think a little about projections; an image might help.

Some observations. The real world, here represented by the triangle ABC on the ground, but this could be a building. The plane of representation, A’B’C’. And the illusion of a singularity of the eye. Things get a little more complex if we add into the mix the non-self of buddhism, or that the eyes combine both images and composes a model of the universe, or matches it somehow.

Consider the point of convergence in perspective paintings, the illusion of parallel lines meeting at the vanishing point. What does this mean socially? Or mathematically, from an XQ interpretation.

So, first, how do you represent what we are doing socially? Talking with Tav with his new version of Tent, and it seems we concur on some form of visual representation, rather than just lists of words. The thing we are representing is social dynamic, and in a virtual dimension. Just read this today, which is a real eye-opener: human_flourishing. I liked the three coupled differential equations on the three virtual dimensions of self-other, positive-negative, advocacy-inquiry. So, how do we represent this rich psycho-social dynamic on the plane of representation, graphically? There is no physical model in the real world, hence the representation is not a visually linear projection, but rather a virtual projection. As we project into the future, such as 2020worldpeace, we can represent this as a point in a time-slice of 2020; any intention of mention of it, like in this blog post, is a plotted point in the time-slice today. There is a vector projection from the point on time-slice-today, to time-slice-2020. And there are intermediary objectives, such as takingthestand.org.

The point is, the projected field is imaginary, so it is a mistake to think we need to specify a point. There is no “point” out there, just a projection. So, just like the way we avoid argument about specificity in the future with the confluence model, so we don’t need to know where the point is, literally, in the time-slice-2020. There are several ways actually plotting this. Leave it up to people to plot the location, eg using tent/ampify script

/pointer #2020 (2,3)

/pointer #2020worldpeace (zero-carbon, olympics)

The first defines it on a map with an absolute point, relative to 0,0 at the centre. The second is defined relative to other projections, and the computer can calculate some local point between them. Three observations. One, only some people will want to point at the location, so once it has been set, generally, people will refer to that location. Two, if there are several pointers to the same projection, then the system supports both; like the way different ascriptions to a single projection, what you think or I think about 2020worldpeace for example. Three, any intention or projection relating to it, locates the co-ordinates of the point on the current plane in relationship to the co-ordinates of the projection; eg my intention in writing this blog post will be given co-ordinates close to (2,3) automatically.

Therefore, there is no fixed future projected field, but something getting close to probabilistic space, with a projection consisting of a set of points, as many as there are pointers, which might correspond to the set of different ascription of the projection. The benefit of using this system, is that it allows us, human beings, to translate our verbal concepts into spatial co-ordinates, rather than appealing to some kind of ideal mathematically spaced algorithm. It should allow a continuity of image so that a video of time-slices will show a smooth progression. And, the only precision we are looking for is the interface of future/past in the present; that is, how the time-slice-today turns intentions into done tasks. The multiple projections, definitions/ascriptions/points, become singular events/fact/point; the multiple views we have are braided in the present into the fact of the past.

Second, the maths plane. I have already suggested that XQ posits there is another side to maths. When explaining to people, I came up with the metaphor of suggesting that mathematics is the intermediary plane, like a window, through which we make sense of the real world. So, if objective reality is outside, ABC, then mathematics is the projected plane, A’B’C’. This goes for all poetry, etc. A book just happens to be a particularly high-virtual dimension object, that allows a reading eye to imagine/project a world. XQ posits that mathematics is just a minimal language set.

Now combine this with another thought, that of the mirror: maths as a mirror of our internal processing. So, A’B’C’ is a projection of some internal processing, A”B”C”, which we can not set as the object of our thinking. OR, they are the rules of projection, perhaps.

So, the illusion of convergence on the vanishing point on a projected plane, is the illusion of convergence of eg 2020worldpeace. It doesn’t exist. It is an illusion. But a useful one.

And, the illusion of convergence on the vanishing point on a projected plane, is the illusion of “self”, a point that interprets mathematics, or anything for that matter. It doesn’t exist. It is an illusion. A useful one.

Interesting…?








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