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Šaltiniai? EFCFE1

Duomenys? FFE6E6

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Mieli dalyviai! Visa mano kūryba ir kartu visi šie puslapiai yra visuomenės turtas, kuriuo visi kviečiami laisvai naudotis, dalintis, visaip perkurti. - Andrius

AndriusKulikauskas: Factoring is a structural idea for which I am seeking an intuitive interpretation. I have observed six SecondaryStructures which I think are related to factors of the number 24 = 2 x 3 x 4, as there are 8 = 2 x 4 {{Divisions}}, 6 = 3 x 2 {{Representations}}, 12 = 4 x 3 {{Topologies}}, and also three {{Languages}} which may be understood as shifts relating these three kinds of structure.

I have observed that this approach to defining the secondary structures is apparently related to SharedUnderstanding, as there is another approach to defining them, in terms of God's injecting himself into primary structures, which is related to GoodUnderstanding.

Also, it is possible to derive these factors as arising from the {{Operations}} [AddOne +1], [AddTwo +2] and [AddThree +3] acting on the {{Onesome}} (which may be thought of as pure structure) and yielding this onesome back as one perspective within the {{Twosome}}, {{Threesome}} or {{Foursome}}, respectively.

Factoring also opens up the way for a SeventhPerspective: ZeroStructure (all factors separate), and then an EighthPerspective: ZeroActivity (all factors together).

Intuitive interpretation of the {{Factors}}

I am trying to understand what might be the significance of these factors.

It seems that the 2 factor is from having unequals manifest as equals (as in BeginningVEnd), and the 4 factor is from having equals manifest as unequals (as in SpiritVStructure). How to understand the 3 factor?

If we have an unequal relationship, such as A to B then we can still emphasize one or the other role (A or B) and they become equals.

If we have a relationship of equals, such as X and Y, then we can consider them as unequals by introducing a relationship "to", generating: X to X, X to Y, Y to X, Y to Y and pairing X to X with X to Y (keeping the first element fixed) and pairing Y to X and Y to Y (also keeping the first element fixed). This is nonsense. Hmmm.

I ask God, and my understanding from that is: the factors are those structures which coincide with their activity. Humans go beyond themselves through the wholeness of structure, and humans immerse themselves in structure by way of activity.

I suppose this is because the factors are those structures that result from acting on the onesome, which as a DummyVariable reflects and expresses the action upon it. The activity is given by the operation.

In my own observations, the factors seem to express the relationship between {{Structure}} and {{Spirit}}. We may think of the {{Onesome}} as pure structure. The factors result from the operations acting on this pure structure and placing it within a framework (a factor). This framework allows us to consider that pure structure in more than one way (specifically, in two, three or four ways).

• The two-factor allows us to consider the primacy of structure and spirit (or the {{Beginning}} of structure and spirit). We may have structure manifest spirit, as when spirit is thus is. Or we may have structure yield spirit, as when spirit is not, even so, is. In the first case, spirit is prior to structure, and in the second case, structure is prior to spirit. If we allow for this (and only this) to be ambiguous, then we have {{Topologies}}.
• The three-factor allows us to consider the convergence of structure and spirit (or the {{End}} of structure and spirit). We may have spirit understand structure, so that the end is spirit. Or we may have spirit come to understand structure, so that the end is their relationship. Or we may structure be understood by spirit, so that the end is structure. If we allow for this (and only this) three-fold ambiguity, then we have {{Divisions}}.
• The four-factor allows us to consider the separation of structure and spirit (or the relationship of structure and spirit). This may be {{Everything}}, {{Anything}}, {{Something}} or {{Nothing}}. If this (and only this) is left ambiguous, then we have {{Representations}}.

In each case, we may think of the factor (and any of its perspectives) as allowing us to understand the wholeness of a structure. This is what is significant about the twosome, threesome, foursome: they may be considered as resulting from actions on the onesome.

We may then consider the structures as arising from fixing two aspects of the relationship of spirit and structure (or {{God}} and {{human}}, respectively), and leaving another aspect ambiguous. We may think of the beginning as the spiritual whole, and the end as the structural whole. This yields:

• {{Divisions}} fix the spiritual whole and the relationship, but leave the structural whole ambiguous. (Thus a division has several perspectives, and it is not clear if the weight is in the part or the whole).
• {{Representations}} fix the spiritual whole and the structural whole, but leave the relationship ambiguous. (Thus the distance between the two is left unclear).
• {{Topologies}} fix the relationship and the structural whole, but leave the spiritual whole ambiguous. (Thus a topology leaves unclear if it is experienced as such, or coming from beyond it).

===Binary Operations===

I have thought that the 2 x 4 = 8 divisions, 3 x 2 = 6 representations and 4 x 3 = 12 topologies are given as products. But it might actually be more interesting than that. It might be better to think of them as applying three different kinds of binary operations:

• The 12 {{Topologies}} are indeed a product of the {{Foursome}} and the {{Threesome}}.
• But the 6 {{Representations}} are the union of the {{Twosome}} and the {{Foursome}}.
• And the 8 {{Divisions}} are the intertwining of the {{Threesome}} and the {{Twosome}}, yielding two additional perspectives, so that we have 8 = 1 + 3 + 3 + 1.

This very much accords with what I've observed. I'm wondering what the structural implications are elsewhere. I suppose it doesn't affect the position of the three languages within the eightfold way because that is given by the shifts in the structures themselves, not their components.

Note also that these structures may still be derived by the {{Omniscope}} as products 2 x 3 x 4, and yet arise fresh when they are reinterpreted, perhaps by human eyes, so that the divisions and the representations switch places.

===More notes===

These are perhaps fundamental to shared understanding. They may be the entities that are factored 2 x 3 x 4. The factoring may have us think of them in pieces. Each piece is a mapping from the onesome (as a whole) to the onesome (as a perspective). Perhaps the ambiguities are as follows:

• We have a twofold ambiguity (and topologies) if we presume there is a direction, but we don't know which it is, either forwards or backwards, from which we are interpreting the operation (either from the initial division (beginning) reaching out, or from the final division (end) going back to the roots). This ambiguity is given by the equation 1+1=2. This is the outlook of the end, looking backwards in terms of two representations of the division to which it is returning, namely, beginning and end. This is the ambiguity between God and human when it is not clear who is the originator for a shift in perspective - God or human?
• We have a threefold ambiguity (and divisions) if we presume there is an operation, a relationship between beginning and end, but we don't know what it is, either +1, +2 or +3. This ambiguity is given by the equation 1+2=3?. This is the outlook of the relationship between beginning and end.
• We have a fourfold ambiguity (and representations) if we presume that each division has its own state, but we don't know what it is, yielding: (beginning or end) to (beginning or end). These are four levels of understanding. This ambiguity is given by the equation 1+3=4?. This is the outlook of the beginning, looking forwards in terms of four representations of the division which it is reaching out from, constructively presuming that relationship.

I think that these presumptions are the constructive hypotheses. The factoring then makes sense as a split of determiniteness and ambiguity as part of such a presumption and the engagement of an other. I should also think of them in terms of the heart? and the inversion effect.

Apparently, we should attribute the forwards direction when operations act on divisions with four representations: nullsome, onesome, twosome, threesome. And we should attribute the backwards direction when operations act on divisions with two representations: foursome, fivesome, sixsome, sevensome. And these presumably also list out the levels of understanding. But I should look into this when I know more.

2005.04.28 {{A}}: Kaip suvokti atvaizdus kaip kylan&#269;ius i\9A operacij&#371; +1 ir +2 sandaugos? {{D}}: Kai yra kitas, jis yra lygus su tavimi ir taip pat lygus m&#363;s&#371; trij&#371; akyse. Pamatysi

2005.03.08 {{A}}: Kaip suprasti ketveryb&#281; kaip sandaug&#261;? {{D}}: Tu bandyk priimti kit&#261;, ir suprasi kaip a\9A tave priimu.

2005.02.09 {{A}}: Kaip man suvokti padalinim&#261; kaip laisvumo atvaizd&#261; ir nulyb&#279;s atvaizd&#261;? {{D}}: Padalinimas yra pasikartojantis veiksmas, tad yra visumos po\9Ei&#363;ris - jo sandaros, ir jojo po\9Ei&#363;riai - jame dalyvaujantys.

2005.02.08 {{A}}: Kaip suprasti dvejyb&#279;s, trejyb&#279;s, ketveryb&#279;s vaidmen&#303; antrin&#279;se sandarose? {{D}}: Ten kur du, trys, keturi, ten ir a\9A tarp j&#371;, vienas i\9A j&#371;.

2005.02.07 {{A}}: Kuo svarbus nubr&#279;\9Etumas? {{D}}: A\9A m&#261;stau visus atvejus i\9A karto, o j&#363;s m&#261;stote ir i\9Agyvenate vis po vien&#261; atvej&#303;, tad tai mus sieja, ypa&#269; pasislinkime.

2005.02.04 {{A}}: Kaip antrin&#279;s sandaros i\9Akyla i\9A dvejyb&#279;s, trejyb&#279;s, ketveryb&#279;s sandaug&#371;? {{D}}: A\9A esu keliose vietose vienu metu, o j&#363;s tik vienoje vietoje, tad t&#261; viet&#261; i\9Asako sandara.

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