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Posted by Alan on September 17, 2003 10:10:48 UTC

A sample from rough version of my paper:

ZENO'S ARROW

There's a so-called paradox that goes: An archer fires an arrow towards a distant wall. In the first moment (a) it travels half the distance to the wall. In the next moment (b) it travels half the remaining distance. In the next moment (c) it travels half the remaining distance. In the next moment (d) it travels half the remaining distance. So does it ever get there given the increasingly small distances it travels with each moment? Of course what happened here was that "moment" was not defined except in terms of the halving distances. The moments were being halved too. Moment (a) was defined as the period during which the arrow traveled half way to the wall. Moment (b) was defined as the period during which the arrow travelled HALF the remaining distance (or 1/4 of the distance to the wall). Time was being sliced in two along with distance.

Are our assumed equal-spaced numbering system, rulers, and clocks, also caught in a self-referential imaginary number matrix that may generate "Zeno's Arrow" type illusions? Suppose I draw a diagram of Zeno's arrow: I draw a line and call it 2 which is half-way to the target. I draw another line following on from that which is half as long, and call it 4. Then I follow with increasingly shorter lines of 8, 16, 32, 64. These are my halving distances as fractions of 1 ("2" as 1/2, "4" as "1/4", "8" as "1/8", "16" as "1/16", "32" as "1/32", "64" as "1/64".)To show the neutralising of this effect by the halving times; I can write "64" over the "2" distance; "32" over the "4" distance; "16" over the "8" distance; "8" over the "16" distance; "4" over the "32" distance; and "2" over the "64" distance. (So 1/2 distance to wall took 64 units of time, 1/64 distance to wall just a 32nd of that or 2 units of time).

I can draw an arrow pointing right under the line-segments to represent the length contraction of my halving lengths going right; and I can draw an arrow pointing left above the line-segments to represent the time dilation of my increasingly longer moments noted while going BACK in time along the Zeno arrow path. (Time and distance contract or expand together if both going same way). Suppose I do not know how far the arrow goes in the first "moment". And suppose I do not know how far the arrow goes in the next "moment". Suppose I do not know how far the moment lasts for the first arrow distance. And suppose I do not know how far the moment lasts for the next arrow distance. If the arrow is free to travel any distance in any moment, and again travel any distance in any size moment, with these things not defined, then what?

If I just count them, and define them only by counting, surely I am making a Zeno scenario here by imposing math-defined alleged equal sizes on the arrow distances and times.What if I just defined each distance as "half the sum of the two from my perspective" and suppose I just defined each moment in terms of the distances, Zeno-style? Isn't that what we do with our mathematics when we define numbers as equally spaced? When we compare numbers it might be like we are defining a math 'clock' by a math 'arrow'? That's not necessarily a problem so long as we realise the limitations of making one-to-one correspondences between numbers here and numbers there. Physics involves making comparisons between numbers. If our defining of numbers as equally spaced gives them a self-referential Zeno aspect, any comparison of numbers would be like Zeno's time-dicing clock? Our physics might by default be a 4-D projection of our math.

Maybe we are dealing with many worlds of mathematics. To define numbers as equal-spaced makes math a self-referential system deeply layered. How can you compare one person's math to another's? To compare the two or more self-referential math systems might be a case of DEFINING them as in-step: and doing that may define whatever we map with that defined-in-step-math as trapped in a rigid grid or matrix? Maybe what happens in high-energy physics experiments is Zeno-like? Dicing our math finer and finer in lock-step with dicing distance finer and finer and dicing time finer and finer?The definition of equal divisions in mathematics seems to give that math a Zeno-type character. Math seems to be self-referential through and through. Dr. Stafford seems to have found what I might call a "Sorting Hat" (hat from Harry Potter books) perspective to modern physics. Does it involve a 2x2 Matrix-Hat of self-referential imposed-equal-space-assuming mathematics sorting physics into four houses?

To what extent might the physics laws be reflected as four sorting systems that sort each other? This seems to be the Dr. Stafford model. In the CTMU, Chris Langan talks of question + answer appearing together. This seems like "as you judge, so you are judged" or the mote you see in your brother's eye involves the beam in your eye. Our freedom in freedom means we do not have to judge the universe but can create in harmony with it. In physics we talk of "space-time". In practice "time" involves a self-referent (via retraced pendulum path or fixed origin clock hand) reference space (2 pendulum tracks or 2 fixed-origin different positions of clock-hand). So "space-time" becomes a unit of: space-SPACE/ space x 2.

OPTIONAL COUNTING

If distance is a category to be divided (counted), and time is a category to be divided (counted) then we have a distance-math and a time-math. Each math is defined as equal-spaced numbers; both maths are defined as one-to-one corresponding so together the two math systems are like Zeno's arrow and Zeno's clock? Each division of units in one math is defined as one-to-one in step with the other math. Is it reasonable to regard our measuring-rod of math as inherently split into two assumed identical rods coupled in a "virtual" Zeno coupling? (When we "split" the math to measure distance and time). We do not specify which math (virtual Zeno-arrow-math or virtual Zeno-clock-math) couples to which item (distance or time). So we have a superposition of Zeno-scenarios? Dividing distance in step with math generates a new level of Zeno scenario?

With original Zeno's arrow: remaining distance to target was repeatedly halved; as a referent time-interval was also halved. In math number system: number-labels are generated and assumed to be equally divided; as you progress you travel smaller fractions of your journey's jump from initial to final conditions. To begin with your jump is your whole journey; next jump is 1/2 the journey history, later a jump is say 1/20th of the whole history of the journey. Zeno's arrow goes shorter and shorter distances, but each moment is also shorter and shorter. In math counting: Each step is a smaller and smaller fraction of the history of the total journey to date, but each sum-of-history is broken into smaller and smaller fractions.

May have:

Z-math arrow + distance = Zeno-Zeno
Z-math clock + time = Zeno-Zeno
Z-math arrow + time = Zeno-Zeno
Z-math clock + distance = Zeno-Zeno

If we collapse our two maths to one superposed math; and look at distance time: get 4 ways of dividing 4 ways of dividing. Thus: 4 sorting systems that sort each other! Beyond the voluntary constraints of our math-defined MATRIX ALGEBRA we see pure self-referencing in freedom of definition in the law of non-contradiction. An "impossible object": the Penrose triangle has an "impossible" twist on each side: how about: three sides: math; time; distance.Math side has a distance-twist near the time-end and has a time-twist near the distance-end (classic Zeno scenario does this?); Time side has a math twist near the distance-side and a time-twist near the math-side; Distance side has a time-twist near the math-end and has a math-twist near the time end.

Pi: PHYSICS AS CREATION AND GIVING OF GIFTS

Consider: Two potential participants in discussion meet; they are two so are counted already by Existence; they meet in freedom and give gifts of each other's perspective to create a new common overap region of view.

So started with: new creation possibility that 2 will meet and exchange gifts of perspective. They both give of themselves to create the 'brainchild' of their giving: the child might be called "minus a third" as is the third party, a new, mutual, perspective, that appears from the gifts to mutual ground given by the 'parents'. So in the meeting of 2, 2 gifts offered: pi/4 becomes 1 - 1/3 new creation.

Suppose this new "child of discussion" were to meet, in a new discussion, the parent-perspectives from whence it was born; and all three parties gave gifts of their own perspectives to a new common ground, giving birth to a new creation from their considerations. From the point of view of the 'parents' of the original 'brain-child' of their debate; this "minus 1/3" has given something of themselves back to them in any new creative discussions: there are now 5 perspectives: the 'brain-child's gift (i) to new common ground (d), the gifts (ii)(iii) to the 'parents'(a)(b) from the 'brain-child' (c), and the gifts (iii, iv) from the parents (a)(b) to the new common ground (d).

The newly created common ground (d) is 1 meeting of meeting, pi/4 = 1 -1/3 (from 'child' and 'parents' to this new creation( d)), + 1/5 as follows: looking backwards in time we see a 1/5 in the new creation, a 1/5 given back to the earlier created 'child of discussions', a 1/5 given back to first 'parent', a 1/5 given back to second 'parent', and a 1/5 given back from original 'child' to it's parents along original path that gave birth to original 'child' when 'parents' met. (Maybe this is what "Feynman path integral" is about.)

Now suppose a new conference: participants are the two original 'parents'(a)(b), the 'brain-child' (c) of their discussion, and the new common ground (d) from a debate all three attended. These four give gifts to create a new perspective. This 'new perspective' partially receives back the previous back-in-time +1/5 that comes due to the participation of the 'new common ground' (d); but is now 1 - 1/3 + 1/5 -1/7.

You have seven 1/7ths come from the +1/5 as you have partial minus (five + two) gifts:
-1/7th: original parents (a)(b) to first 'child' (c);
-1/7th, -1/7th: 'child' to the 2 parents;
-1/7th, -1/7th: 'first child'(c) to new common ground (d) via those gifts to two parents (so 2 gifts parents to new common ground);
-1/7th: new common ground (d) gift to new perspective (e);
-1/7th: and 'new perspective'.

I think it may be that Dr. Stafford's discovery of the mapping of physics laws via his 4-space and his partial differential equation; may be seen via the Leibnitz equation pi/4 = 1 - 1/3 + 1/5 -1/7 + 1/9 -1/11 and so on. Although a lot of chemistry and physics seems implicit here; the use of numbers like 1/7th in what I've done here is really just as "possibility shells"; which are potential paths but to what extent paths are filled (the size of the gifts) is optional. To some extent our very presence on this Earth means we are already gifts to each other, we are children of God. What is being described is the possibilities to listen/ communicate with others, and to create through mutual consideration. Beyond math where counting is voluntary and not imprisoning; a glimpse might be seen that God is love; being and letting be; creation by mutual agreement. QED, Feynman path integrals, sum-of-histories, virtual-particle exchanges associated with creation in a 4th dimension, seem implicit in these patterns. The pattern pi/4= 1 - 1/3 + 1/5 -1/7 +1/9 -1/11 and so on appears to map a situation where "every way agreement can happen" is considered, where every perspective is taken into consideration in producing an agreement; where everyone has their say on any proposed changes anyone makes at any level of the discussion. The whole "draft agreement" can be re-juggled at each level with the arival of a new participant; nothing is determined it seems until agreed to, it is all open to discussion with any voice free to be heard and how much each contributes is not restricted

-----------Regards Alan

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