9. Newton space


What has happened previously: 

Step Eight:

The standard reorderings come in two, 3D and two 2D groups. We construct the twin Descartes type spaces by using the rectangular axes depicting the additions’ linear positions on the aspects relating to the sum and the inequality of a and b. The unit reorder is interpreted as a unit of dealing with logical contradictions that arise from the fact that differing sorting orders place the same addition on a different places. The re-translation of the description of the properties of a point in 3D space into a description by means of 1D sequence statements happens by means of two triplets that refer to the same Sachverhalt.

Step Nine

Constructing Newtonian Space

The construction of one space with three rectangular axes brings forth the gain of having the idea of one, homogenous, indivisible space in which what is the case takes place. The loss is that of accounting precision. The Euclid spaces were in an accounting sense exact, now we enter a world of (inexact illusions) implications. We observe that the Euclid spaces’ Y axis was CA and CB, the X axis was KA and KQ, the Z axis was QK and QA. We fuse CA and CB into one axis C, and so forth. (Please see graph 9.g.1)

The transplantation of a point into Newton space from two Euclid spaces brings forth that one point’s description applies now to four variants of it. This is a complication – probably that one used by Nature for marking one of four. In step eight we needed nine coordinates for one point of a triplet. Now we see that in the unified space we need four alternatives for the idea of the position of a point, and this in three planes. In Euclid notation we had known if a1’s notation in C had been CA or CB, now we ignore this and have to count with both alternatives. The same is the case with Newton-axis K which had been Euclid axes KA and KQ. (Please see 9.g.2)

The position of the triangle in one unified Newton space remains the same, but we reframe the picture by giving the axes alternative names. If we know, which of CA,CB; KA,KQ; QK,QA is the case, we can look at it as if either the triangle is changing position as we highlight the correct variant; or (and this is what Nature appears to be doing) one triangle is in a fixed position and we change the legend of the axes to fit the facts (Please see 9.g.3). We turn ‘if order then position’ on its head and say ‘if position then order.’

Stating that the order has changed allows for tautological peace for the moment, as it implies that somewhere else someone else will do something; that elements in a different chain of the same, relevant, reordering will arrive at their correct places in their correct number of steps. The order is a prediction.


The fact that C is one of the Newton axes allows integrating the concepts of counting with disregard to the summands into the present concept. Axis C is aspect c=a+b. It is a basic concept that we have arrived at that the sum is relevant to the place of an addition. The positions CA and CB show the relative position of the addition, once related to a compared to other as, and then b. 

The human brain takes great pleasure from the sense of upright. The effects of gravitation are a very potent ordering force, of an axiomatic value, and build the backbone of culture. No wonder that culture hopes and imagines aspect c to be prevalent horizontally, too.

The horizontal axes K and Q are each other’s inside and outside, being k=b-2a, q=a-2b. (Please use 6.g). How a part relates to the other part’s double – relative to how the other part relates to this one’s double has the air of something very archaic in the process of perception of stimuli. The concept of octaves and harmonies can be pointed out on the interplay of KQ and QK. One may suggest to use the connotations of the words unbalance, inequality, eccentricity and mainstream for the oddity of these two being together, quelle mésalliance! The rule that a ≤ b is a restrictive introduction into the grammar of the logical language, allows on the other hand finding possible advantages from not using the rules of commutativity.


The empty unit of the fused space can be assigned a numeric value. Calculating that each addition states an average of 17, and having found that each point needs 4*3*9 statements to be expressed in a 1D way, we arrive at 1836 as the numeric value of a unit of a Newton space containing one logical statement, thata point has coordinates.

We have 45 standard reorderings that keep space together by their movements. These are triangles, with differing geometric properties. We distinguish now between the space-related and the other attributes of the corner points as additions in their own right. We are distinguishing between the chains that go through the addition and bind it with two others into a space-creating standard triangle, and those chains that go through, but bind into a differing collection of co-located members of the same convoy. Each element coexists in space-building chains and also in other kinds of chains. Which of its relationships are relevant is decided on a case by case basis.

Pointing out which of the four variants of point a1’s representation is what is valid, and allows the implication that order S_* is the case, inferring from the position (that is, properties) of the point. That order S_* is the case is not a simple Sachverhalt, but a wide reaching Zusammenhang. It allows calculating deviations between what can be the case, as the inventory shows, and what will be the case when S_* is fully implemented.


Working with two logical objects, a and b, the world we build up will of course be bipolar, dual, dialectic, partly symmetrical and partly unbalanced, as it is two half worlds that are deeply related. We distinguish three classes of logical sentences; those that are relevant in the a-space, those that are relevant in the b-space and those that are relevant in both.

The idea that fits well is that the logical sentence is built up of words that are triplets that each contain a description of a point that can have four varieties. That this sentence comes in two versions that are near identical reminds one of the DNA and RNA observations of Nature. Maybe the idea is permissible that Nature uses the splitting-fusing of half identities also in the form of sexes. Then, the intersection of the sets would be that what we call life, and would consist of the logical sentences that are relevant in both sub-spaces.

If physics deals with the relation of the two Euclid spaces and the two planes in light of their contradictions, then chemistry would deal with processes where the local overall total is given with respect to place and amount, which happens in a sub-section of the Newton space that is a stable sub-world in both sub-spaces, and biochemistry would work within that stable niche of space in which order exists. We discuss the sequential order and its effects in the next step.

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