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The text below has been painstakingly typed in from A Thinker's Note Book. Through typing it in and proof reading I hoped to come to a good understanding of this text. I am intrigued by the curious application of mathematics to describe the relation in observing. The subject has never been finished, reason why in the heading it says "fragment".

The use of characters in bold has been reproduced to the best of my ability. There is some variation in how bold characters are printed. Because of this it is difficult to distinguish the 'observed' from the 'unobserved'. I wonder if I, in reproducing the text, have made any changes. If I have, while observing, is it still true that the observer is 'nothing'?

Confused by there ramblings? Read on and enjoy!

The essential relation in observing



The assertion is made that here the event of observing at its simplest must of necessity be complex. Without comparison (confrontation) no observation could be said to have been made at all. For (a) without simultaneous (as it were 'spatial') confrontation of difference in the observed ("This - not that") no observation could be said to happen at all since there would be no way of distinguishing the alleged observation from non-observation; and (b) without difference between the observed and the observer (observable by, successive as it were, 'temporal' comparison as "difference in the new observed") no observation could be happening either, since the alleged observer could not be distinguished from the observed. An "observed that is indistinguishable from the non-observed" will be regarded as unconstitutable as likewise an "observer with no observed" an "observed with no observers" and an "observer and observed indistinguishable inter se".

A The Division

1. Unless there is division between the observer and the observed, no difference can be compared and no observation can take place.

2. Unless what is observed by the observer is itself divided (from what is not observed), no comparison can be made (and without comparison in the observed, no difference can be found between the observed and the non-observed).

3. The simplest, minimum, elementary division in the observed can be called "affirmed/denied", the "this/not that", "yes/no". Since each counterpart excludes the other, (so regarded), they can be symbolized by the signs + and -. The two elements of the observed, so divided I shall call adjacent (to each other), and observed as such.

4. Division thus appears as a necessary factor (sine qua non) of observation: (a) between observer and observed and (b) in the observed. The observer, so divided from the observed, I shall call also adjacent (to the observed) but unobserved. Since observer and observed are mutually exclusive, (but not in the same way as the two divisions of the observed) they can be respectively symbolized 0 and 1. Each is, in fact, '0' in terms of the other - the 'divided' and the 'undivided' and my equating '0' with the observer is an arbitrary, if convenient, decision of a choice, which cannot be escaped if a statement to be made - (it could be made conversely).

5. The observed, therefore, in order to be observable at all, must appear to the potential observer at least as a duality. (N.B.: a "potential observer without any observed" and an "as-yet-unobserved observable" are convenient fictions at this stage, but will vanish). The two divisions of the observed I shall call the elements of the observable, and these together with the potential observer I shall call the elements of observation.

6. The division of the observable allows the differentiation in the observable allows the differentiation of "this/not that" = +/-. The division between the observer and he observable is expressible either as the difference of nature, namely undividedness/dividedness, or as the observability of the observable and the unobservability of the observer: the observer can observe the observable but cannot observe himself. (The objection will be made that all this 'observer-cum-observed' is being observed by some other observer, e.g. the writer of this paragraph. This is legitimate but must wait for treatment till later (§20).)

Here only a mental note need be made that in symbolizing the observer by '0' I have intended to signify also an essential incompleteness, which the unavoidable introduction of the observer (with his comparing) brings automatically with him. The description of the situation is thus structurally (skeletally) "completed" by the addition of "nothing" (the observer = 0), but is nevertheless still incomplete since it still "lacks nothing" (an observer of the observer = 0x0x .....); the mere ramification by division/confrontation in the observed 'completes nothing' in this sense. The apposition 0:1 is asymmetrical. Observation is originally asymmetrical.

B. The Constitution of the Observed as a field or Unity

7. The observable (+1; -1) which, to be so, must be divided (§2), is only constituted as a unity when the confrontation of the divisions is constituted by the presence of the observer ('0') in the Event of Observation (in which Event also the potential observer is constituted qua observer). This divided unity thus constituted I shall call the observed field (+1x-1).

8. But for this constitution to be effective, it is necessary (sine qua non,) that the observer should be unmistakably different by nature from the observed (i.e. unobserved) and that the two divisions of the observed should be unmistakably different by nature from each other and, in a different way from the observer (+1x-1, 0). This can be stated, for convenience, spatially as follows the constituted duality + <-> - cannot be so constituted as a line (of two points) except from a standpoint not in the same line (expressible as '0' in terms of that line). This "linearity" of the observed field constituted from outside I shall call Rectangularity (the "Rectangularity of a straight line").

9. But in order that what is essentially different in the Event of Observation may not absolutely fly apart, it is also equally necessary (sine qua non) that all three constituents of the Event have something in common to bind them. That, in fact, is 'nothing'. The 'nothing' that the divisions of the observed have in common is their not being the observer ('0'), who while observing that they have 'nothing' in common with each other, has 'nothing' in common with them. This state of being bound together (.......?) in the divided observed field as a unity I shall call Conjunctive Adjacency.

10. The constitutive power of the observer in binding the observed from a (rectangular) standpoint outside it (in virtue of which he is 'nothing' in terms of it) I shall call Disjunctive Adjacency.

11. The Event of Observation, with its three elements, so minimally constituted (by divisions and binding) I shall call the Relation. (There is no relation unless the two observed elements are constituted as a unity by the third element, the observer, who is 'nothing to them'. Therefore Relation has a minimum of three elements sine qua non).

12. That the three elements of the Relation 'have nothing in common' makes it incorrect to say that any one has an 'absolute opposite' within the Relation.

13. At this point I shall note that there are four possible confrontations (neither less nor more) to be made by the observer in the observed field. They can be symbolized as follows:

+x+, +x-, -x+, -x-.

These can be regarded as four unoriented pairs, four "states of the observed field" (spatially simultaneous). Their stated order - an order of simultaneous pattern not in succession - is arbitrary (being only one of the possible permutations). But without this arbitrariness no order can be stated. It is not possible to invert any of them since they (as yet) lack the orientation between themselves that would make any inversion observable by comparison (+x+ inverted is indistinguishable from +x+, not inverted). "Change" and "alternative" have not so far emerged; only "and" and "difference " have emerged (space is implied, but not time). Observation, as the Event (but not an event), has now been constituted.

(The balance of the manuscript page has been left blank (for addition?), with the following penciled note:)

Asymmetrical observer and observed are not "equal and opposite".

C. Change in the Constituted Observed Field

14. But a calamity occurs. If this Event, so carefully constituted is expressed symbolically in the terms I took care to choose, it must appear as follows (+1x-1)x0. (But, as everyone knows, the result of that is '0'! How absurd! My sums must be wrong or else there is No Event).

15. The sums are not wrong, and there is an Event. But the act of the constitution of the Event is also the act of its annihilation. While there is, it seems, no constituting it otherwise, the constitution automatically reduces it (the Event) again to nothing. Now 'nothing' is '0' and '0' is the observer. But the observer cannot be an observer without an observed field. Consequently the act of annihilation must be, cannot help being, an act of reconstitution. And so on..... (in retrospect as, it seems also, in prospect). (This "reconstitution " from '0' cannot be expressed in mathematical terms; for mathematically a specific proposition, once reduced to zero by multiplication with '0' cannot be resurrected). This "...constitution/annihilation/reconstitution..." (can it be conceived as a flow?) I shall call Successive Adjacency. (Time as well as space is now implied: and what cannot happen in time x space?).

16. This is another way of saying that "space without time is impossible", since, by its being observed, is simultaneously asserted and denied. Another decision is necessary. And, consequently, it follows that time has no nature of its own beyond that of the division between and succession of adjacent space.

17. With simple constitution (up to §13 end) the observational Relation I have described was only a generality as The Event and no alternative comparison was possible. This could only be effected by another division, namely, by the introduction of succession (§14) expressible as 'change or difference in time'. By this means, the four pairs (see §13) become oriented with regard to each other. This has rectangularity to the 'conjunctive adjacency' (§9) since it is expressible as 0 in terms of them.

18. The introduction of succession transforms the generality of The Event into a plurality of events, and adds to 'simultaneity' also alternativity, adds 'or' to 'and'. Consequently, while (in §§7-12) only simultaneity was possible as, for instance "yes/no" (yes and no), now the alternative "yes"," no" (yes or no) is possible.

19. At this point the four confrontations earlier stated as unoriented pairs (§12) can be stated as successively oriented pairs as follows:

(The 'pairs' are now oriented, or, as it were, 'charged'.) But whereas earlier (§12) the event was 'fixed' arbitrarily as to the as to the order of the four pairs though inversion made no difference, now, while the order can be changed, inversion makes a difference.

Consequently any statement of an event must, further, be an arbitrary instance of (one the permutations of) the Event. This arbitrary element which enters in as soon as the division comes about (§4) I shall call the dialectic.

20. However, conversely, whenever any arbitrary expression of the event is stated, the structure of the Event necessitates certain consequents and excludes others. This I shall call the logic.

The Dialectic and the Logic imply one another (they 'coincide' and are 'at war', but they are never 'congruent' and so no 'final peace' is possible.). The Dialectic is the 'if' (if this statement of the Event is made) while the Logic is the 'then' (then it follows that the pattern of orientation will be this, not that); but the 'if' is arbitrary and 'precedes' the 'then'.


arbitrariness (of mode)


the particular expression (which automatically excludes the alternative)



the two parts of the observed, and the observer



conjunctive adjacency of the two parts of the observed, and the disjunctive adjacency of the observer and the observed



the triple relation between the duality of the observed-field and the observer

Event of Observation


the mutual interconstitution of the observer and the observed





D. The Bracketing of the Observer '0'

21. The four alternatives (§19) can be interchanged, and being oriented, can also be turned upside down. With the constitution of the observed field (§§7-13) the confrontation of "and" takes place, while with the annihilation and reconstitution (§14) the succession of "or" becomes possible. With the possibility of alternative confrontations in Successive Observations the question arises, 'What of Successive Observers?' Now, while the basic division in the observed field as +:- leads to its ramification in the presence of the observer ('0'), no such ramification takes place in the observer, who is 'nothing' and whatever is 'done to' nothing may be -0, remains '0'. (I shall leave aside for the moment the proposition 1/0 = Infinite). The consequence of this is that, in order to multiply the observer I must describe him in terms of his observed, since no other way is possible, and this would seem to be a fiction.

22. The observer does not appear in his observed field in any way at all, which lacks 'nothing' (§7), which is why he is symbolized with '0'. While he is everywhere, while he is absolutely essential, he 'does not count' at all. Whether he is one or many it is impossible to tell except from the field or fields that are being observed. But this anticipates. Consequently, while his singularity or plurality may be a matter for consideration in an inquiry into his nature, an inquiry into the nature of the observed can be disregarded (so long as I remember that I learn nothing about him). I shall therefore, for the moment at least, but him in brackets ('0') and forget him (remembering of course that I have forgotten him).

This is what all Objective Science claims to do (and often forgets to do) and for which admiration is commonly expected. (The results of this I shall call 'Solalterism' or the 'Science of the Subject leaving himself out of his calculations'). Since He counts for zero in the observed, which is not observed without him, he can easily be reintroduced. It is, of course the converse of the opposite procedure, where results are usually condemned without trial as detestable and are commonly called 'Solipsism' or that of the 'madman who has shut himself up in an impenetrable blockhouse'. [See aphorism 373]

Here the manuscript ends with a blank page carrying only the chapter heading:

E. The Ramification of the Observed

(The following text, obviously belonging to the preceding treatise was found in a different file among the late Author's posthumous papers. The sheet was not paginated and had no paragraphing linking it with the above treatise.)

Existence is an operation. Operation comes into being with a leap and at once extends back to infinity and forward to infinity, yet with the personal horizon that conceals both infinities.

The necessity for the observed duality (+1,-1) to be in relation with an observer (0), in order to exist implies:

(i) that the observer (0) has perpendicularity to the observed (+1,-1),

(ii) that spatially the observer has no status (=0) in terms of the observed (+1,-1),

(iii) that temporally the observer (=0) is structurally related to (= multiplied with = added to) the observed and so spatially annihilates it by introducing change as temporalization,

(iv) that existentially (consciously) that observer (=0), having annihilated the observed (=+1, -1) must reconstitute it (he, the observer cannot exist as 0 - cannot 'non-exist' - except against the observed), immediately reconstitutes the observed (as thus reconstitutable = ±1 or 1),

(v) that in the reconstitution of the observable (±1 or 1) by the observer (0) a choice must be exercised whether the observable is to be constituted as is or that alternative (i.e. + or -). N.B. the term "observable" refers to the just-annihilated observed, neither more nor less,

(vi) this unavoidable choice in the reconstitution is arbitrary. Once exercised the world is determined logically, but subject to immediate annihilation.


Motion is spatial (change is temporal)

Motion existentially establishes space. Change existentially establishes time. In space-time, when no motion is observed there is no time, and where no change is observed there is no space.

Just as motion is relative i.e. it is impossible (purely existentially) to ascribe absolute motion (or stationariness) to any body (acceleration introduces features other than motion), so too change is relative, i.e. it is impossible to ascribe absolute change or stability to any state. The "absolutely motionless" and the "absolutely unchanging" (whether temporary or 'eternal') depend as such on consciousness functioning with the unique "I". (The consequence seems to be that all are relative.)