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 Be the first pioneers to continue the Astronomy Discussions at our new Astronomy meeting place...The Space and Astronomy Agora What Is "counting"? Forum List | Follow Ups | Post Message | Back to Thread Topics | In Response ToPosted by Alan on September 17, 2003 10:18:09 UTC

Hi, another sample from rough draft of document I've been writing:

WHAT IS "COUNTING" ABOUT? WHY EQUAL GAPS?

Anton was talking of the idea of a "perfect framework". Dr. Stafford had apparently found a circularity in physics, and he mentioned the idea of a dictionary where you keep going around in circles looking up the meanings of words and finding more words.

John Hospers in "An Introduction To Philosophical Analysis" notes that in real life one escapes the circularity of the word dictionary. Words are "ostensively" defined by practical circumstances when we are children. Karl Popper gives the idea of humans as "jumping to conclusions", making guesses. Einstein said "God does not play dice with the universe". Is man playing dice with the universe? "Uh-oh" the telletubbies might say.

Here is an idea what I found:

Consider a clock pendulum: it swings this way along a path from A to B; then retraces its path back to.................. back to where? Usual answer is "back to B" but........can one ask how do you know that? What is going on here? On what grounds does one claim equal spacing of each subsequent swing of the clock pendulum?

In mathematics: on what grounds does one claim that the gap between "1" and "2" is the same as the gap between "5" and "6"? Seems reasonable to assume our rulers and our clocks and our math contain internal equal spaces? Or does it? From a particular point of view the spacings might be regarded as equal: but that is a CHOSEN perpective? Not compulsory? Do we use imaginary rulers? Imaginary clocks even? Imaginary mathematics?

It seems to me that the basis for regarding the divisions between marks on a ruler, marks on a clock, or unit gaps betwen numbers; as EQUAL spaced; relies on a self-referential layering. And the more self-referential layers that are added (e.g. by counting "1, 2, 3, 4, 5..." in math), the more possibilities there are that the next gap could be defined in a variety of ways by self-referencing throughout the gaps collected so far. Sounds a bit fishy? When you count; what happens?

Consider say: "1". "1 what?" "2". "2?" What does "2" mean? To exist is to be (different); if "A" were the same as "B' in every way, it would have same place, same time, same name, same ... you would just have "B" and no "A". So what does "2" mean? SAME difference? A categorising of "this one" and "that one" that groups them together in a common ground. The ones seem to be partially differentiated from the perspective of "two"; this does not require that they be equal ones (they could be one apple and one orange). A new "imaginary one" is generated by regarding the ones as "two"; "two" is "the new group, the new one".

But count to three; and you have lots of ways that this "three group", this new grouping, can happen. No equality required between the ones? Math allows "3" to include any sub-grouping? (e.g. two oranges and one apple; or three cars; or one bus, one plane, one boat). I saw a picture that showed that a primitive way of counting in a tribe involved placing sticks in a one-to-one correspondence with the counted items. Our math numbers seem to imply, by their assumption of equal spacing, a one-to-one approach. If I look at a row of items and count "1,2,3,4,5,6,7,8,9,10" what am I doing? Am I not effectively still matching one bunch of items (or sticks) with another bunch, one-to-one?

But the first bunch of items are already counted; if they were not already noticeably different from each other how would I count them? Isn't everything we count already counted? If the divisions in 10 provided by our math say that they are equally spaced; then this implies the ten ones can swap places? Is quantum physics (calculating every way an event can happen) the ghost in the "machine" of equal-spaced mathematics? Looking at all the ways "10" can happen with different orders of "ones"; perhaps these "ones" can be regarded like light-photons in physics. Going from one way "ten" can happen with an order of "twos" to another ordering of "twos", would involve it seems a rejuggling of the ways (different) "ones" could make those "twos" happen. Counting from 1 to 100 gives a rapidly expanding variety of choice as to how a number is constructed. Yet we assume equal unit spacings between adjacent numbers?

In real life when we count 1 to 100 we count SOMETHING. A category is chosen and we count that
item. There seems to be an alternative to counting? Just interacting directly with reality; no labelling, no double-defining, just freedom counting and all other counting being voluntary? I guess: to count is to "wear category-vision glasses"; to count SOMETHING. As you categorise, so you categorise; if you wear "sheep glasses" and count sheep; you will get so-many sheep. But you could have counted say goats. The idea of voluntary counting seems to be that you do not have to put a particular "counting beam" in your eye at all. Suppose the category is always optional; you can JUMP to another category and get quite a different perspective? Like, counting cars; jump from "cars" to "wheels" and the numbers look different.

But what about the "equal divisions" in the number system? The SAMENESS in the same-differences that make up 50 cars is provided by the ONE sameness group: "car". But within that SAME division "car" you could have small cars, red cars, fast cars, big cars, blue cars, vintage cars......... So the assumed EQUAL divisions in numbering seem to involve an implied "definition black hole"? A singularity of definition that is vague in that it applies a generalisation "car". A "damped oscillation" (borrowing the phrase from Russ) right here?

Counting cars seems to involve re-asserting the choice of category "car:"car. car. car. not car. car. not car. car. car......" ? All that freedom of "ways "car" could happen (red, blue, fast, slow, old, new, etc.") seems to get collapsed into the generalisation "car" each count of "car". One could expand the category of what "car" is by allowing each possible car to construct the definition of what "car" is as the current form of the category "car" addresses the question of whether to include this new item (this candidate for car-ness.)

Every encounter with a possible "car" perhaps does partially refine what "car" is as a group. Perhaps every "car" in that group is slightly "rotated" or refined, as a definition about the new encounter with "car, not car" choice?Are our clocks really made of equal-spaced divisions? Seems reasonable from a certain perspective. But is this circular reasoning? Equal-spaced with respect to......? A ruler? And its divisions are equal spaced with respect to? And are numbers even equally spaced? What is going on here? Maybe our equal-spaced math numbers implies the "many worlds" physics interpretation. To regard a series of items as equal is to acknowledge they are all different (they are plural) in a manner unspecified? Or rather, each number-name, that we tag the items with, is a new category, so a new world, allocated to each item? A series of one-on-one meetings each in its own "universe"? When we conclude with "ten items", we group in one "ten world" the many worlds and the many ways "ten world" can happen?

LOOKING AT CHEMISTRY AND UNDERLYING PHYSICS AS "MEETINGS AND
DISCUSSIONS"

A way of looking with help from the periodic table of the elements: Here is an idea: Suppose a dictionary was such that the meanings of its words were defined by relations with other words in the dictionary. If the dictionary comprises one word: the word is the dictionary. If the dictioary comprises two words; I might call them "almost anything A" and "almost anything B". Why "almost"? Because A and B are different, they can be anything except the other word. The dictionary is divided into A and B. If it was divided into A, B, and C, there are different relation options appearing. It could be divided into separate A, B, C; or one of A, B, or C may be a subset of B, C, or A. (example: A, B with a subset of B being C). More possible arrangements of grouping the divisions in the dictionary occur if it comprises more words, say A,B,C,D. But once you choose a particular definition grouping; the law of non-contradiction insures the remaining groups are logically consistent with your choice. If A and B are defined as fully accounting for the group D; C must not be made of A and B except via C's mutual defining of itself with respect to D.

One can look at this as meetings, and shells (group boundaries). There are many ways A, B, C, D could meet. Example: A meets B; C arrives; D arrives. A meets D; C arrives; B arrives. Suppose one considers every possible order of meeting of A, B, C, D, E.

Example: suppose A met B; then they meet C; after that D says hello; then E arrives.

In this example A and B have a discusion. They then take the point of view of C in to consideration. A and B might modify their views with C's input. A meets B. They exchange opinions.

There are two possible spins on the outcome: A might modify their views thanks to B's input to the discussion; or B might modify their views with A's input. Both may partially modify their views. I could call this A:B meeting "Shape 1" of the meeting, containing two spins (two orders): A meets B (call: "electron" or "modification" with clockwise spin); B meets A (call electron or modification with anti-clockwise spin).

What I'm saying is that what we call "quantum" can be regarded as "meeting where discussion and exchange of views can take place". The basic shape (shape 1) of a meeting is A meets B. This gives the "principal quantum number", the energy level (the alternatives level) of the meeting.

According to "Modern Chemistry" (Metcalfe, Williams, Castka)(1970 Holt, Rinehart, Winston) p. 64 "the principal quantum number indicates the average distance of the electron from the nucleus of the atom". If "atom" refers to a "conference"; and "electron" refers to "possible modification of a conference-participant's opinion" (and "charge" would be the bias of their current opinion); in a meeting of two the average distance in opinion from the nucleus of the discussion will be 2 divided by 2 = 1.

Now consider C turns up at the conference. The Modern Chemistry 1970 text says: "The orbital quantum number indicates the shape of the orbital in which the electron moves. The number of possible shapes is equal to the value of the principal quantum number."

There are three ways this A,B,C conference could happen:

First shape: consider 2 electrons or spins or "orders in which debate can be modified by C's arrival as a third party": spin-l: A meets B, C arrives; spin-r: B meets A, C arrives;

Second shape: spin-l: A meets C, B arrives; spin-r: C meets A, B arrives

Third shape: spin-l: B meets C, A arrives; spin-r: C meets B, A arrives.

The average distance from the nucleus of the discussion involving A, B and C is simply the number of basic meetings: A meets B, meet C gives principal quantum number (meeting number) 2 meetings or debates. These two debates can have 3 shapes.

There are two sublevels here:

First sub-level: We have the generalized shape: 2 meet. (e.g 2 participants reach agreement and talk to a third; so 1 group meets 1 participant)(participants can take turns in forming an initial discussion group of two)

Second sub-level: participants take turns in being the third party:
shape-1 (A meets B) meets C (other "electron" of this pair is (B-A)-C;
shape-2 (A meets C) meet B (other electron of pair: (C-A)-B
shape-3 (B-C)-A (other electron or spin on modifying participants' views: (C-B)-A.

It seems possible to describe the detailed structure of the periodic table and quantum physics in terms of: a discussion where every voice gets a hearing, every perspective is considered, a discussion where participants take turns, swap perspectives, look at the debate from each others' point of view and from each grouping potential point of view. Every avenue is explored, no one is left out. Christianity teaches: God is Love. Here the infrastructure of chemistry and physics looks like all is made from, in, with love. Being and letting be.

The 1970 Chemistry text says: "The magnetic quantum number indicates the orientation about the three axes in space of the orbital whose shape is given by the orbital quantum number." It puzzled me as to why the number of orbitals per sub-level went up in twos: 1 for the s sublevel in 1 meeting; 3 for the p sublevel from the s,p in 2 meetings; 5 for the d sublevel from the s,p,d in 3 meetings; 7 for the f sublevel from the s,p,d,f in 4 meetings.

WHY DO NUMBER OF ORBITALS PER SUB-LEVEL INCREASE IN TWOS?

I had 3 shapes for two meetings (A meet B) meet C. But why should another meeting with D give only 5 shapes to meetings involving D in the d sub-level? It seems the reason may be that there are only two really NEW shapes that are different from basic grouping-frameworks already covered. The two new shapes are: A,B,C conference consider D's point of view. D swaps with any of the perspectives in the A,B,C conference to consider their points of view.

The "three axes of space" could it seems be translated into the more general idea of: "pattern, pattern, comparison". There are 3 orientations of "compare 2 patterns" in (A meets B) meets C. Each of A, B, C can take turns being the third party at the conference. Each of these three possibilities comprises two orders (spins)(modifications, electrons) each so 6 electrons in the p sublevel (plus two in the s sublevel, 2 spins on a one-one view of the conference (group meets newcomer, newcomer meets group). So total of 8 electrons in the energy (alternatives) level asociated with principal quantum number 2 (2 meetings).

Why with three meetings: ((A-B)-C)-D are there, as I asked before, just 5 orientations for a d orbital in "compare and match two patterns)(otherwise known as in "3 axes in space")? Well: how many ways can this conference take shape as "compare and match" TWO patterns from the perspective of D, the fourth arrival? That is: how many ways can the layers of meetings here be viewed as a single meeting of two perspectives (two potential groups)?

One: ((A-B)-C) pattern with -D (electrons: with A-B order, with B-A order) D last to arrive, C third; A,B first or second.

Two: ((A-B)-D) pattern with -C (electrons: with A-B order, with B-A order) D third to arrive, C last; A,B first or second.

Three: (A-(B-C)) pattern with -D (new order, electrons here B-C; C-B) D last, A B,C first or second or third.

Four: (D-(B-C)) pattern with -A (new order, electrons here B-C; C-B) D third; A,B,C first or second or last.

Five: ((A-D)-B) pattern with -C (new order, electrons here A-D; D-A) D first or second; A,B,C first or second or third or last.

I'm not sure I got that right. Here is an idea: "Trying on different thinking hats". We seem to be looking at templates for ways meeting can happen. D turns up at the A,B,C conference and tries on different "thinking hats"; looking at the debate from other perspectives.

The patterns are curious as they involve "what COULD happen" in a musical chairs game with what does happen.

HOW PI MAY BE IMPLICIT HERE

It seems that chemistry and quantum physics can be mapped out of the Leibnitz equation for pi. Consider "pi" as the whole conference (or universe). Dividing pi by 4 would be "mapping from the perspective of compare two patterns, make a new comparison. That is: (1) meets another (2) gives comparison (3) which is met by another (4).

That is: group meets newcomer. Or a "time"( self-referent reference space) view of space (meeting). The Leibnitz equation for "pi" is regarded as elegant, but not very useful for calculating pi as it converges very slowly on pi. However, this humble pi appears to provide an astonishing map of modern physics? The equation is: Pi/4 = 1- 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 + 1/17-1/19 +1/21 and so on. Curious that the number of orbitals per sublevel in the periodic table goes: 1, 3, 5, 7.

Here is a way of looking at the situation: Two perspectives MEET. This can be drawn as two circles that overlap. One meeting shape.
These two can now be regarded as ONE circle of new agreement, which now meets a newcomer perspective.

There are now three ways of looking at this new discussion. A agrees with B; discusses with C. Or A agrees with C; discusses with B. Or B agrees with C; discusses with A. Each of these has two possible spins; e.g. A agrees with B, may be biased (charged) in favour of the opinion of A or of B giving two possible modifications of viewpoint (can call these modifications: electrons)

So we have 6 possible electrons (view modifications) in the p sub-level; of course we also have two possible biases in the s sub-level (A meets B gives possible bias towards A or towards B).

From a meeting of meeting (pi/4) point of view, the first ONE meeting is now minus a third (to accomodate the ideas of the newcomer C, A and B have divided the meeting consciousness by three (the consciousness of the meeting, the ways of looking at it, are now three). A and B have each given up a third of their ONE consciousness to accomodate the new shape of the meeting involving a newcomer.

Drawing so far: A meets B: two overlapping circles.
A meets B; meet C: the two overlapping circles' two centers form the foci of an elipse, from an outside perspective the centers collapse to a point of agreement and the two circles become an elipse that collapses to a new circle. This new circle AB overlaps newcomer circle C. A and B had considered each other's point of view (orbited each other); now as one they acknowledge C, consider C's point of view (orbit C and vice versa).

Now along comes D. The AB circle centre and the C circle centre become foci of an ellipse that collapses to a new circle of acknowledging the newcomer D. There are 5 new templates (if this is going to fit chemistry and the Leibnitz equation for pi!), or new frameworks, for looking at this conference of ((A-B)-C)-D.

There are 5 new templates (if this is going to fit chemistry and the Leibnitz equation for pi!), or new frameworks, for looking at this conference of ((A-B)-C)-D. ½RELATIVE to having given up a third of their meeting of meeting consciousness when C was acknowledged; A and B now recover some of that earlier framework in this game of give and take (PLUS a fifth). (I'm hoping I can get this logic to work out as I go along!)

A and B considered C's point of view; but now the "minus a third" that represents the common ground gifted to each other by the first two participants, is (from a shell or discussion-potential point of view) re-distributed by the arrival of D: the framework of MUTUAL consciousness of the overall meeting has moved plus a fifth RELATIVE to the previous minus a third.

A way of modelling this:
Two perspectives meet. Can represent this as two circles comprising two halves each, where the circles are overlapped so as to give a superposition of halves where each circle gives one of its halves to the common ground. So the diagram shows three "halves", a Venn diagram of two overlapping circles containing a left region (one "half"), a shared region (another "half" that is a superposition of halves given by each circle), a right region ('third' "half"). The common ground superposition can be regarded it seems as "minus a third" of the perspectives on this ONE conference; as there are three perspectives in the Venn diagram: left, middle-superposition, and right.

Now another perspective arrives: so one may draw another circle overlapping the other two and the earlier overlap. Suppose that the new circle simply gives up half its perpective to sharing in the middle ground between the other two; so you have the middle ground now becoming a superposition of the old superposed half wth a newly given half. Seems there are now five perspectives on the conference? The independent halves of each of three participants, the old two-meeting middle-ground superposed half, and from the necomer meets the two-meeting, we have the new middle ground superposition half?

Why go from minus a third to plus a fifth? If these patterns are to fit the Leibnitz equation for pi/4 the question is why the alternating -,+,-,+,-,+? Not sure but could try various ideas. Perhaps the shared middle region, the superposition region, is continually modified by the re-aligning of the framework of the possibilities for common ground at this expanding conference as newcomers arrive. Modifications on previous descriptions of the middle-ground framework would be RELATIVE to the previous modification, so if the previous was "minus", a modification on the "minus" would be "plus"; and a modification to a previous "plus" would be to adjust things via a "minus". You may have a kind of margin refinement process reminiscent of fractals and of the Mandelbrot set. Maybe this fits Chris Langan's idea of "cospansive duality", and of "a self-swallowing set", in his CTMU paper. What we call "relativity" in physics may be all about "same-difference" or"+,-"; and electro-magnetic may reflect the concept "+,-". One might say that to modify an addition you subtract a little from it; to modify a subtraction you add a little to it?

Modification of the middle ground where perspectives overlap (superpose) at the expanding conference: I guess you could say if the middle ground represents local-to-global relations, that might be represented by diameter to circumference of a circle, or pi. A view of local-global relations from the perspective of two patterns compared with a new comparison, might give a 4-view of pi, or pi/4? So you start with 1 meeting of two (global view) who swap views giving a 4 halves scenario where two of the halves are superposed as middle ground between the two who are meeting? To the expanded conference resulting from a new arrival; that previous middle ground has given up a third of the previous conference to the new discussion?

The new person has that previous agreement as a starting point? And maybe the newcomer modifies the historic sum of this conference by a fifth; as any modification is one of five perspectives now (the 3 participants, the old agreement, the new agreement). A fifth added to minus a third? The sum of history of this expanding conference is now further modified by another newcomer. RELATIVELY the new modification to the previous fifth added would be minus a seventh? As there are now seven perspectives: 4 participants, and 3 superposition states or levels of common ground.

After that you have plus a ninth and so on. I'm not sure if this works properly but it would be curious if you could map quantum physics and chemistry from the Leibnitz equation for pi/4. Maybe we are blinded by maths; as beyond number we really seem to be talking here about freedom, consciousnes, and taking every view into consideration, and the idea of being and letting be and of finding common ground.

TRYING TO FIGURE OUT THE 5 ORIENTATIONS OF d (Third) ORBITAL SHAPE

The arrival of D brings 10 new electrons (two spins or biases on each of 5 orientations of orbitals for the d orbital shape. Exactly how this works out is not so clear but could be: Since magnetic quantum number refers to orientation about three axes in space of the orbital whose shape is given by orbital quantum number: Translate "orientation about three axes in space" into "orientation about ways of comparing (1 axis) and matching two patterns (2 axis, 3 axis).

A-B type meeting: one to one (1 orbital)

(A-B)-C type meeting includes one to one type: pair meet one (1 orbital). And brings two other variations on one-to-one as pair-meet-one giving 3 shapes: AB meet C; AC meet B; BC meet A (3 orbitals)

((A-B)-C)-D type meeting includes one-to-one type: pair meet pair (1 orbital). And it includes "pair meet one" type: (AB,C) meet D, with variations (AB,D) meet C, and (C,D) meet AB. Note AB are held together as one here to give a broad pattern template. (3 orbitals). Also have "three meet one" type: (ABC) meet D. (1 orbital) (total 5 orbitals for d sub-level. It seems very strange but the idea seems to be "partial differentiation"; only basic new pattern templates seem to be considered, with the other detailed variations relegated to lower energy levels (lower choice of alternative permutations). So the five orbitals templates involving D are given as broad frameworks containing high energy, high internal permutations possibilities. Obviously the "three meets one" template contains many possible orderings. The d orbital orientation for one-to-one is pair-to-pair; so high energy (many possible permutations because of it being pair to pair). The d orbital template for pair-to-one had three possible frameworks but with high energy (many possible permutations e.g. AB could have been AC etc.)It all seems a bit contrived but that seems to be how the periodic table can be seen to work.

How does the Leibnitz equation for pi map this? Two meet: one meeting. Another arrives: 3 ways of looking as consciousness templates? So 1 minus 1/3 giving room for newcomer perspective? Another arrives; 5 broadly speaking new frameworks of consiousness that dilute the previous impact of minus a third so you get RELATIVE to the previous conference, a plus a fifth? Another arrives; maybe 7 even more broadly-speaking new frameworks of consciousness that dilute the previous gain of plus a fifth so you get RELATIVELY minus a seventh?

Perhaps it works like this:

Basic meeting: one meets one (1 orbital in s level)

Basic complex meeting: group meets newcomer, exchange views; group swaps places between a group member and the newcomer; a group member swaps the remainder of the group with the newcomer. (3 orbitals in p level)

Basic pattern with each additional newcomer added to group: 2 orbitals added for each newcomer covering: group swaps places between a member and the newcomer; a member of the group swaps remainder of the group with the newcomer. (So the pattern templates that cover the permutations and combinations of meeting with all options open, give 2 extra orbitals plus the previous ones for each new orbital shape (each new addition to the conference).

What we have is three related games of musical chairs:

Group, newcomer: swap perspectives (game 1)
member of group, newcomer: swap perspectives (game 2)
member of group swaps rest-of-group perspective with newcomer perspective.(game 3)

Game 3 is the difference between games 1 and 2.

DRAWING PAIRS OF CIRCLES THAT OVERLAP, AND SUPERPOSE TO ORBIT A NEW CIRCLE

About the drawing: drawing this idea of an expanding discussion where views come together and are orbited by new views: on drawing this it quickly looks reminiscent of a Mandelbrot set structure. Given the ever-changing "yardstick' as one meeting of two perspectives is held as a unit-perspective in mutual rotation about a newly arriving point-of-view; it looks very much like fractals. It also looks very much like DNA: with two spins on every meeting; looking at the patterns of overlaps through many meetings it seems that there is a double helix spiralling away with structure at every level in the form of exchanges of views.

The drawing is: two overlapping circles; they come together as one bigger circle and overlap a similar-size single new circle; these two now come together as one bigger circle and overlap a new similar-sized single circle, these now come together as a fresh large circle and meet another single large circle and so on.

The Leibnitz equation for pi: Consider a dot. One point of view. Consider two points of view: two dots, form a line, a category containing two. This line can be "diameter" of a bigger dot that results from spinning this line to form a circle that gives the line freedom to look at all surrounding possible viewpoints. Diameter times pi gives circumference (2 points of view meeting in freedom (if pi represents freedom?) give many possible perspectives of that meeting. Diameter x 3 gives slightly less than circumference; like if you took two similar circles and superposd them with a slight overlap: the superposition of diameters could be slightly less than a single circle's diameter. Take the extended diameter from crossing both overlapping circles and you have a bit more than a circle diameter- enough more to times by 3 and get a circle's circumference say. This fuzzy circle of slightly overlapping circles could be seen as an ellipse with two focci. One could collapse the two focci together to get a circle whose new centre becomes a new focci for a new ellipse formed by a close overlap with another circle at right angles. And so on. It seems that the Leibnitz equation for pi can be modelled by a series of meetings of slightly overlapping circle pairs that become ellipse then new circle, then pair with a new slight overlapping circle etc. with a pattern of fine overlap structure consistent with the -,+,-,+,-,+,-,+,-,+ of pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 and so on.

SELF-REFERENCING

About the way our clocks, rulers, and math works: I asked on what grounds can we assume equal divisions? What if was self-referential? Two is made of this one and that one, but does not seem to specify anything about the size of the ones, just that there are two of them. A pendulum seems to travel on path A to B, then return to A; but the feature here may be self-reference: it self refers to A via B. Then constructs a yardstick of self-reference? By the sequence A-B, B-A, A-B dividing A-B-A B. It seems like we have a "4-wheel drive" system for our clocks, our rulers, and our math. A jump, another jump, these regarded as equal dvisions of a big jump comprising them both, another jump calibrated by these. Compare and match two patterns, make a new comparison: 4-wheel drive, 4 types of jump.Physicists call their 4-wheel drive "space-time"; but that collapses the role of the big JUMP.

IMAGINARY MATRIX?

Seems our math system could be trapped in a 2x2 matrix; increasingly vaguely defined as you count beyond 4 (thus Heisenberg's matrix algebra of physics reflects our system of assuming equal divisions in our math number system?) If our math is pinned down by an imaginary 2x2 lattice or grid structure; then the pi of interest may well be pi/4, the Leibnitz equation for pi. It is curious that argument can be made that an absolutely breath-taking pattern of pure freedom of meeting can be seen implicit in pi, when we take the math-beam out of our eyes and divide pi by the 4-wheel-drive of our math. Beyond the constraints of blind-number we find all perspectives taken into consideration, from which the structure of DNA, of quantum physics, of our math, can be seen implicit in the pi/4 = 1 -1/3 + 1/5 -1/7 +1/9 -1/11 and so on?

Seems that in this Leibnitz perspective we have -,+,-,+,+,-,+,-+,-.... give and take? Swings and roundabouts? Every voice gets a hearing........A particular "+" is RELATIVE the previous "-", a particular "-" is RELATIVE to a pevious "+". The pattern of -,+,-,+,-,+,... seems to be like electro-magnetic radiation (electro and magnetic are RELATIVE views of a "4-wheel-drive" phenomenon (space-time). The force of plus, minus in math seems reflected as electro, magnetic force in physics. The structure of modern math-physics may fall right out of the Leibnitz equation for pi: pi/4 gives you your 4 of space-time (more generally of: 2 patterns compared, meet new comparison); the periodic table seems to map from "every way a meeting can happen", modifications to viewpoints (electrons) have charge (bias) and emit or absorb photons (comparisons) of electro-magnetic (+,-) radiation.....? Somehow it seems plausible. Dr. Stafford seems to have aready uncovered the structure of physics as a minimal tautological framework; this idea about pi seems consistent with his discovery. It seems one can say: God is all in all; the freedom of freedom. A baby has the ability to know anything, it knows knowing. Knowledge is voluntary, a conversation inside consciousness?

HISTORY OF THE UNIVERSE?

It is possible to model the history of the universe with the Leibniz equation for pi as follows:
1 (single point) - 1/3 (comparison of two patterns gives many possible overlaps of two perspectives on the universe, 1, 2 perspectives with 3 the overlap so three parts with the third given up to be overlap, to common ground, to communication, to light) so high energy (many alternatives) photons (comparisons) of light (of +,- or same-difference or mutual agreement) + 1/5 birth of the 5 forces: the five forces seem to be obtainable once you go from -1/3 to relatively + 1/5: you have "coming together" (gravity) multiplication and division (weak/strong and strong/weak) and electro-magneticŪ½(plus minus). If God made the Heaens and the Earth in 6 divisions and rested in the 7th; perhaps the idea that the framework is in place by -1/7 has something to do with this? God however seems to rest in our conscience, our inner sense of honesty, of being and let be.

(needs work)

-------Alan