XOR-ing update; how come it works?

[lightofdarkness]

I have been 'playing around' with other logic operators to see if I can identify any other form of *strong* 'meaning' generation using such operators on the I Ching and have found none to date. By *strong* I mean a derivation that leaps out at you as the X-ness derivations do as compared to using the other logic operators.
(the symmetric operators pair as in:

XOR/EQU(aka COIN)
AND/IOR

The asymmetric operator is IMP (implies) and needs consideration in the context of hexagram dynamics)

I could not find any *strong* expressions of EQU although there were some interesting 'vague' associations where the context is in sharing of space (integrating) rather than extraction from a complex space (XOR - differentiating).

As such the EQU mappings would be 'vague' anyway!

I therefore focused on what was 'special' about XOR when compared to the other operators other than its association with self-referencing. One point was the association of XOR with destructive interference patterns, and the other was in cryptography where XOR can play a major part in encrypt/decrypt of data.

The IDM material suggests that for any level of recursion of a dichotomy, the resulting categories in each row of the recursion are applicable in parallel for each moment (the row symbolic of the WHOLE). HOWEVER, the set of categories can be sorted into 'best-fit/worst-fit' order due to qualities/interferences from the LOCAL context. This is applicable to the I Ching where all hexagrams apply to the moment and local context does the sorting and so determining the 'best fit'.

Our consciousness is attracted to the 'best fit' but in fact the WHOLE set applies and so contains meaning. This level of 'wholeness' is manifest in such studies as those on foreground/background dynamics in vision (see refs/comments in my page http://members.iimetro.com.au/~lofting/myweb/wavedicho.html )

If we are dealing with the encryption of the categories in the form of a distortion (affine transformation?) then the XOR material reflects the use of a key to extract the data that 'fits' that key where the key is the 'ideal' form of a category and its use extracts the 'distorted' form by analogy to some other category in the set of possible categories.

The bit values I identified are ordered from general to particular and encode patterns of behaviour. For example, the sequence "010" represents "I integrate in general to then differentiate so I can integrate in particular" There is a category derived from this dynamic. Thus XOR-ing 010 with a category will elicit the 010 representation in that category; if the category is 000 then the XOR will elicit the category in its pure form. Any other category (100...111) will elicit a 'distortion' - the quality X described by analogy to quality Y.

When we focus on cellular dynamics for vision, so abstraction is present in the form of 'line' sensitive neurons (or line-orientation sensitive etc) and as such a pattern of behaviour that leads to a particular categorisation; in the Necker cube paradox this dynamic elicits 'meaning' where there is none in that it extracts from the 'complex line drawing' the particulars of the necker cube 'paradox'.

Overall the focus is on issues of encryption/decryption of information where XOR extracts a particular from the full set of particulars that make-up the whole. The 'hologram' link is to the association of XOR with destructive interference patterns and so the 'key' of XOR is representative of the 'reference beam' frequency for a hologram that is necessary to extract from a 'film' the information associated with that 'beam' used originally for encoding.

... something like this! ;-)

[martin]

Congratulations! You are awarded the prize for vaguest post of the month!

Me thinks you are much more of a mystic than you would like to admit. http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif

[lightofdarkness]

yo dudette - its all "Language of the Vague"! ;-) (and so generally cryptic)

try this, a quote from a text of cryptography (ignore the figures references, just cover the gist):

"10.2.1.2 The XOR Operation
A common transformation is the exclusive OR (XOR) operation, denoted by the symbols XOR, or ??. XOR is a bitwise function that maps an element of {0, 1} ?? {0, 1} onto the set {0, 1}, as shown in Figure 10.6. If we interpret the second operand as a key value, the XOR operation can be thought of as a bit-level substitution based on the bit values of the key. With such an assumption, XOR sends a 0 or 1 to itself when the corresponding key bit is 0 and inverts a 0 into a 1 and a 1 into a 0 when the corresponding key bit is 1. The last property implies that when using a fixed-key value, the XOR operation can be applied to encipher a plaintext, which can then be recovered by simply applying the XOR operation to the ciphertext with the same key value. This property has led to the proliferation of many variants of weak encryption methods that rely solely on the simple XOR operation and thus are easily breakable.
Figure 10.7 shows how to XOR blocks of some plaintext P with a fixed-length key K, leading to ciphertext P??. The figure also shows that if P?? is then XORed with K, the original plaintext P is produced. Knowing a block of plaintext and its XOR transformation directly leads to K, by way of XORing the plaintext with the corresponding ciphertext, as shown in Figure 10.8. Similarly, by knowing two ciphertext blocks P?? and Q?? alone, one can XOR them together to yield the XOR of the corresponding plaintext blocks P and Q, as in Figure 10.9."

This rings bells regarding what the XOR function I discovered in self-referencing is in fact manifesting - the encoding of sensory data, and so 'encryption' that is then 'decrypted' with a key. The key is the binary sequence of 010 etc. where the key represents the steps of the encoding from general to particular (e.g. 010 = integrate in general to then differentiate to then integrate in particular).

Our sensory processes interact with 'plaintext' (reality) and then are encrypted through Analogue-to-Digital processes to become 'ciphertext'. This is also reflective of the holographic process. Thus when we XOR with a bit sequence we extract the 'nature' of that sequence WITHIN the whole we are analysing.
(there is also the implication here also of data being stored as a negative)

This XOR-ing with a bit pattern is akin to XOR-ing with a key. The original pattern is of encoding method of perception (as in a map of left,right,left,left,right). That is encoded into a bit format together with all other possible choices in the whole. Recall that we move through a PARTICULAR thread consciously of a GENERAL 'carpet' of categories that contribute to the particular. The XOR bring out the particular bit patterns in the form of analogies to the particular focus.

Thus the reason I cannot find 'meaning' in using the other logic operators is that the XOR has nothing to do with 'logic operators' in general but in encryption dynamics uniquely associated with the use of XOR and only XOR.

This gets us into the paradox material where the XOR is extracting 'something' encoded in the 'complex line drawing' that is analogous to 'a cube' where the line configurations elicit neural responses to lines to give us an object that is in fact 'not there'.

..... I think this is all heading in the right direction since I have not been able to come up with anything of value re AND, IMP, EQU (COIN), IOR etc etc as yet but the encrypt/decrypt focus does seem to make sense.

The relationship of XOR with holograms is that the XOR is associated with interference dynamics (destructive). If we use two light sources as input to a logic gate so if both are off (00) then there is no output. If one XOR the other is on then there is output (01, 10), but if BOTH are on (11) then there is destructive interference and so no output.

This would elicit 'banding' in information but biases to 'normal' vs 'dark band' mappings - no constructive interference.

From the IDM/IChing focus on recursion, EACH row of the recursion contains N categories for a WHOLE. The LOCAL context will then sort those categories into 'best fit/worst fit' order. As such all of the categories apply to any moment (and so allows for personal differences in perceptions of a particular state that can include contradictions, one person interprets as "A" and the other and "NOT-A". the point with the dichotomies is that when self-referenced all of their POSSIBLE states are expressed to varying degrees. If we include input from our memory, that inclusion can swing a "NOT-A" interpretation to an "A" situation.

This sorting process will contain data from senses as well as memory and so encode all categories into a 'superposition'. The XOR allows one to extract the expression of each category by analogy using the categories themselves as analogies.

If the superposition forms into a 000000 category, this category reflects all POTENTIALS (an integrated 'whole' that appears 'flat', no highs, no lows - equilibrium or 'heat death') and as such XOR-ing any category will extract that category. If the superposition forms any other category, that formation will 'distort' expressions such that the XOR 'key' will extract the equivalent expression compensating for the distortion up to 111111 where the XOR will extract its opposite form.

toto (we are not in Kansas anymore)