C. A. Hilgartner
Martha A. Bartter
Ronald V. Harrington



We assert that even the most rigorous of today’s scientific theories rest in part on already-discovered error. We propose a basis for theorizing, more general that its currently available rivals, which eliminates that body of error.

We regard Newtonian and non-newtonian physical theories as acceptably testable, within the acknowledged domain of applicability of each. But according to our chosen assumptions, self-reflexive topics form an intrinsic part of every theory, and the transacting of physicists with their experimental systems and with their theories forms an unavoidable part of the "subject-matter" of physics. Current physical theories do not explicitly include self-reflexive topics. This "blind spot" in these theories renders them non-testable in the domain of their self-reflexive assumptions.

In order to display a few of the advantages that our alternative frame of reference offers to practicing scientists, we examine some of the presuppositions encoded in the framework of the contemporary physical sciences, and contrast those presuppositions against the ones encoded in our own (more general) frame of reference. Procedurally, we select examples of breakthroughs in physics. With each historical example which we discuss, we acknowledge the profundity of the insights encoded therein and the ingenuity it took to reach them, as well as showing how our brand of non-standard reasoning accounts for these insights. We also bracket these insights, pointing to what remained not-known at the time, and to what relied on the portion of scientific reasoning of the period which scientists now see as non-valid.

We provide the fundamental basis for a physics that takes the observer — the physicist — into account. We assert that such a fully transactional way of doing physics will improve the predictability of contemporary methods and may lead to new breakthroughs.

C. A. Hilgartner
Ronald V. Harrington
Martha A. Bartter

In this paper, we outline a new way of taking the observer into account, and consider a few of its implications.

Starting around the turn of the twentieth century CE, physicists began to notice that when a worker measures — observes — a physical system, that alters the system observed. The revolutionary figures who devised quantum theory and relativity waxed ingenious indeed, and found ways to quantify some of the changes they induced.

However, these people did NOT explicitly point out that when a worker measures a physical system, that also alters the worker who made the observation. Instead, like Newton, these folks continued to regard themselves as UNMOVED MOVERS. 1  That stance amounts to a kind of self-annihilating — symbolically eliminating oneself from consideration. Today’s physicists still eliminate themselves from consideration in this way. The present authors regard this as signifying a primary and fundamental theoretical error.(1)

When asked to name the discipline that best models scientific rigor and high predictability, most people would name physics. People generally take the success of physics as tantamount to the success of the scientific method itself. To question the "scientific-ness" of physics shakes the foundations of the modern world. To question the success of physics seems even worse. In exploring this new way of taking the observer into account, we must do both.

Physicists of the Western Indo-European (WIE) tradition generally regard themselves as having nothing to do with organisms. The domain of living systems, they seem to believe, belongs to biologists. The present authors, however, regard that commonly-held attitude as a sign of fundamental theoretical error in the ways these physicists do physics. In holding that attitude, our physicists ignore three existential facts: (a) that the constructs of organism, of environment, and of a non-fixed, non-static boundary between them, mutually require each other; (b) that any organism relates to its environment by a process known as transacting, which we express as "two-way interchanging across the boundary, which leaves the participating parts fundamentally altered in some sense that affect(s) the further living of the living organism(s) involved"(2); and (c) that the physicists themselves function as organisms, and the physical systems they study fulfill the role of (a part of) their environment.

Thus we assert that even the most rigorous of our present scientific theories rests in part on already-discovered (but not yet widely recognized) error. We propose a basis for theorizing which eliminates that body of error by drawing on recent increases our knowledge of human knowledge.2,(3)

Both the historical and the logical beginnings for these gains in our knowledge of self-and-other came from the work of Alfred Korzybski (1879-1950). As perhaps his most important contribution, Korzybski framed, and proposed answers for, two perennial, troublesome, self-reflexive questions: a) What do we humans DO that distinguishes us from other living organisms? and b) How do we gain our living in the biosphere?

Korzybski provided a single generalization which answers both questions: We humans gain our living in the biosphere by cooperating to apply what we know, in the process coming to know more — a process which he called time-binding.(4) As time-binding organisms, we humans accumulate human knowledge (in the form, the present authors assert, of tested guesses), at rates that depend on how much knowledge we already have — in other words, at exponential rates. Thus each young human INHERITS the available body of knowledge, and in the process of growing to maturity, ASSIMILATES some portion of the heritage; each human CONTRIBUTES TO the heritage (whether or not s/he can name her/his contribution); and each human PASSES ON the resulting augmented body of knowledge to peers and progeny and to the generations yet unborn.

The present authors point out that in order to assimilate some fraction of the time-binding heritage, we have to TRUST OUR PREDECESSORS. In order to contribute to and enhance the heritage, we have to TRUST OURSELVES; and in order to pass the enhanced heritage on to peers, progeny and the unborn, we have to TRUST OUR SUCCESSORS.

Currently, doing science forms an important part of the process of time-binding. But like the rest of the human community, most of us scientists have not yet so much as heard of, much less assimilated, the construct of time-binding. Hence, we have not effectively focused on our own behaving-and-experiencing — not recognized that our trusting/not-trusting, and other aspects of how we relate to self-and-others, form intrinsic parts of how we practice science and integral parts of the scientific theories we generate. We can continue to ignore these self-reflexive aspects of our behaving-and-experiencing only at our peril — the peril of the entire human species (and perhaps that of all other kinds of organisms).

To display the error which we discern, we shall compare the fundamental presuppositions of traditional WIE frames of reference with the presuppositions of our alternative, non-traditional one. Instead of relying on a conventional one-level, straight-line rhetoric, in the present paper we use a spiral mode of argument to develop this comparison — we return to our key points again and again so as to penetrate ever deeper into their assumptions.

The presuppositions encoded in standard WIE frames of reference posit that any "thing" remains identical with itself. In other words, that setting posits a static world, in which the notion of "absolute certainty" appears both tenable and attainable. Speaking from within such a frame of reference, Bronowski asserts that

All science is the search for unity in hidden likenesses. (Ref. 5, p. 13) Other workers have used slightly different terminology, but virtually all agree in making notions like similarities or likenesses or identities somehow primary. Then, to put the matter in slightly humorous terms, the "punch-line" of a ‘proof’ in a WIE frame of reference characteristically says, "… And so, as any fool can plainly see, A º B (or A º A)."

We hold a different opinion. Our altered presuppositions require us to say that any organism whatsoever lives under conditions of radical uncertainty — no living organism knows for sure exactly what will happen next. (So far as we know, however, only humans can name this as "radical uncertainty".) Within this setting, our alternative (non-WIE) frame of reference utilizes a kind of holistic approach — we could call it a Gestalt approach (where the term Gestalt signifies "a whole-configuration composed of a figure of focal interest to the organism, against a (back)ground relatively empty of interest"). Instead of seeking "hidden likenesses" (similarities, identities, a basis for "absolute certainty"), our frame of reference intrinsically involves seeking differences — drawing contrasts. In English, we commonly express such contrasts as distinctions or discriminations: "This IS NOT that." In this frame of reference, we treat figure/ground formations, contrasts, distinctions, discriminations, differences as primary; and we create similarities and generalizations secondarily, as needed, by IGNORING DIFFERENCES. Again as caricature, the "punch-line" of a ‘proof’ in this alternative frame of reference says, "… And so, as any fool can plainly see, A B (or A A)."

In order to display a few of the advantages of our alternative frame of reference in the arena of practicing science, we shall examine some of the presuppositions encoded in the framework of the contemporary physical sciences, and contrast those presuppositions against the ones encoded in our own frame of reference. With each historical example which we discuss in detail, we shall acknowledge the profundity of the insights encoded therein and the ingenuity it took to reach them, as well as showing how our brand of non-standard reasoning accounts for these insights. We also shall bracket these insights, pointing to what remained not as yet known at the time, and to what relied on that portion of the scientific reasoning of the period which we now see as erroneous, non-valid.

Speaking from our non-traditional standpoint:

We assert that even the most rigorous of our present scientific theories rest in part on already-discovered (but not yet widely recognized) error. We propose a basis for theorizing which eliminates that body of error.

For a little over three hundred years our theories in physics have delivered quantitative results. Repeatedly, the quantitative findings from experiments in physics have matched the quantitative predictions from theory — the hypotheses — within acceptable limits. So the practitioners and most everyone else have regarded the explanations provided by physics as highly satisfactory. The scientific method provides the most devastating way of criticizing guesses — hypotheses or assumptions — yet devised. Physicists over the centuries have complied with its sine qua non: they have generated, tested, and judged their guesses and, at need, replaced or revised them; and a portion of these guesses have survived such testing.

When Newton's successors set about applying Newtonian mechanics to new tasks, e.g. accounting for how inventions, such as the steam engine, the Watts governor, etc., work, they kept extending physical theory into new and interesting areas. Toward the latter quarter of the nineteenth century, workers began probing into the arenas of the very small, the very large and the very fast; and there their results failed to match the predictions of the existing (Newtonian) physical theory. For the first time, physicists found the tenets of Newtonian theory repeatedly disconfirmed.

During the first two or three decades of this century, Planck, Einstein, Bohr, Heisenberg, and colleagues handled most of those anomalous findings, by creating theories — relativity and quantum theory — which diverged from the framework of Newtonian theory. These theories re-drew the boundaries of physics and accounted for the anomalies by fitting them into place within these modified boundaries. The theory of relativity, for example, dislodged Euclidean geometry from the privileged status it had held in physics, and eventually explicitly replaced it with a more general non-euclidean geometry, that of Minkowski. More recent studies have filled in details within the framework provided by these revolutionary theories. But most commentators hold that the premises of the revolutionary theories differ only in small ways from those of Newtonian physics. Then these newer studies have not further altered the fundamental assumptions of the field by much.

Meanwhile, greatly altered fundamental assumptions came into existence from another quarter, namely, from the work of Korzybski.

Above (ms. p. X4), we point out that Korzybski produced his discussion of time-binding by re-wording a perennial question of WIE philosophers. Instead of asking, "What ‘IS’ Man?", he made his question usefully answerable by re-framing his inquiry in what, today, we might call operational or functional terms: "What do we humans do that distinguishes us from other living organisms?"

In so doing, Korzybski takes a kind of Gestalt approach — he posits a multi-level whole-configuration, which today we might designate as a holistic theory of the transacting organism/environment field.3,(4) Further, Korzybski explicitly treats his Gestalt approach as self-referential — as generated by human organisms. Moreover, he considers this generating itself as transactional — it affects the human organisms who do the generating.

Thus, the way he dealt with this answerable question opened the way to an alternative ‘World-View’, based on alternative assumptions.

In the remainder of this section, we shall consider two main topics affected by these altered assumptions: a) Rejecting identity as valid; and b) Redefining "the observer."

a) Rejecting identity as valid:

Using his field-theory species definition — humans as time-binding organisms — as a frame of reference, Korzybski asks an unexpected question. After reminding us that the logical construct of identity (defined as "absolute sameness in all respects") plays a central role in the frame of reference common to the WIE languages and cultures, he asks: In a world which includes transacting human observers, when and where does this construct actually apply? Under what conditions may we regard identity as valid?

After giving his question due consideration, he answers it in the negative — NOWHERE-NOWHEN does identity actually apply (in a world which includes human observers).(7) And having taken identity, even in the guise of self-identity, as never valid, Korzybski suggests that we reject it — refuse to rely on it. He proposes that we rely instead on non-identity, the rejecting of identity.

Although we — like Korzybski — define the term identity in a fashion similar to common usage, the fact that we too declare it non-valid means that we handle the term in a novel fashion. Our own Gestalt approach requires us to treat identity as half of a pair of opposing or polar terms — namely, identity/non-identity. And in doing so, we provide a choice, previously unnoticed, as to how to HOLD this term-pair. We can express this choice in terms of constructs such as "like" or "prefer" vs. "dislike": One can (i) "like" or "prefer" identity and "dislike" (or ignore) non-identity (as our ancestors do); or one can (ii) "like" or "prefer" non-identity and "dislike" identity. Thus our way of building on Korzybski's work makes the term identity (or the term-pair identity/non-identity) into a kind of "blank check," which becomes unambiguous only after the person using it has declared how s/he HOLDS it.4 

In the process, we define two groups of humans — "assumption communities" — and declare ourselves members, and Korzybski the first member, of group (ii), the "explicitly prefers non-identity" group.

b) Redefining the observer:

In a non-identity based system, we posit a setting with transacting human observers in it. Under such conditions, we hold, any "physical happenings" that we humans observe, or can observe, occur in the possible presence, not the absence, of at least one transacting observer. Further, in generating a 'map' of such happenings, a transacting observer engages in a self-reflexive activity — any 'map' or theory generated under such conditions will contain some kind of representation of the map-maker or theorist, the transacting observer (perhaps in the form of some kind of representation of how the theorist (organism) generates the theory). After all, a 'map' or 'picture', in the sense in which we use these terms here, occurs solely and exclusively through the 'map-making' or contacting or abstracting of an organism. Otherwise stated, the "existence" of a 'map', e.g. a theory, stands as evidence for the "existence" of a transacting observer (theorist); and the map or theory eventually refers back in part to the transactional organism/environment field of which this human forms a part. This, then, describes the domain of discourse of "physical theory" in a non-identity based frame of reference.

In the identity-based WIE frame of reference, in contrast, we describe the domain of discourse of "theories of physics" as dualistic and as not-self-reflexive (or, as we term it, metaphysically linear): Within the dualism of physical/mental — "theory of physics" vs. "physical reality" — "theory of physics" belongs to the domain of "the mental," which already "exists," independent of any observer. Such theory describes "physical reality" or "the physical," which also already "exists" "out there," independent of any observer. Operating within this persisting symbolic structure, exponents of WIE physics have focused mainly on the topic of non-living, "physical" happenings — the motion of planets, or points, or sub-atomic particles, or whatever, initially without referring to an observer. Yet the thrust of their on-going collective accomplishments — the process of progressively generating, testing and judging explicit hypotheses — has led them progressively to modify this persisting structure and to produce ever more elaborate discussions of "the observer" and "how s/he generates physical theory." We can trace this progression historically:

i) Newton (along with his followers for about two hundred years) does not explicitly mention or use the constructs of "observer" or of any "picture" of "physical reality" which an "observer" might generate — much less consider HOW an "observer" might generate such a "picture." Instead, his theoretical system tacitly eliminates from consideration any representation, any notion whatsoever, of a transacting observer. In not taking the transacting observer/organism into account, Newton also effectively eliminates from consideration the environment of said observer/organism, and any transacting between them. Since it cannot handle these kinds of holistic, transactional "doings" or "happenings", the resulting theory provides the symbolic means to represent only the "objective", the "physical" — the trajectories of points, etc. — and represents such matters as if "That's the way things REALLY ARE."

ii) Einstein discusses the constructs of observer and picture of a pre-existing physical reality, and in fact allows for multiple observers. Further, he shows that the non-infinite velocity of light, along with the position of an observer in space-time, produces certain observable discrepancies between the observations of observers located at different points in space-time; and he implies that light has some kind of further influence on the process of generating such a picture. For example, if Paul occupies location (x1,y1,z1,t1) and Jim occupies location (x2,y2,z2,t1) as event1 occurs, their observations will differ — and someone can reconcile the difference between their observations by means of a set of deterministic transformation rules, the Lorentz-Einstein transformations. But Einstein's theories eliminate from consideration any differences between different observers. He assumes a kind of "Immaculate Perception" — he assumes that if Paul, or else Jim, or else Kathy, or else Denise had occupied location (x1,y1,z1,t1) as event1 occurred, they would all have made the SAME observations. That means that Einstein posits multiple copies of the SAME "observer", and no matter which version of "the observer" occupies (x1,y1,z1,t1) as event1 occurs, s/he finds the SAME environment. As Eddington puts it, a relativistic "observer" consists of a collection of pointer readings, rather than a person.(8) And as a final point, Einstein's theories neither mention nor use the construct of a (non-static) boundary or interface between organism and environment — another way of saying that his theories do not deal with a transacting observer.

iii) Quantum theorists define their "physical system" so as to take into account the effect of a quantum theoretic observer or experimenter on the experimental system. When s/he makes an observation, that process alters the system. Furthermore, they treat different observers as different. Transformation from the frame of reference of one observer/experimenter to another becomes not deterministic but statistical. If Jim measures position, and Paul measures momentum, we cannot predict Jim's findings from knowing Paul's. We cannot unite their observations. Furthermore, although the quantum theorists do take into account the effect which making an observation has on the system, they neither postulate nor describe any effect that making an observation has on the observer/experimenter. In other words, a quantum theoretic observer still functions as an unmoved mover. Therefore the quantum theorists too do not deal with a transacting observer.5,(9)

Below, we discuss in detail Popper's assertion that the scientific method does one thing only: to disclose and allow us to eliminate error.(10) In the physical sciences, the use of the scientific method has led to the disclosure of more and more aspects of those presuppositions which have the effect of eliminating the transacting observer from consideration. In other words, our science has progressively eliminated the eliminating of the transacting observer. Above, we display the "end-point" of this progression, as we now visualize it — the stance of taking the transacting observer into account — and lay out the progression within WIE science which has approached but still not reached that "end-point."

In order to show the relation between our presuppositions and those of WIE physics, and so back up our first assertion, we will now consider the topic of central cores of general principles.

Does physics itself have a central core of general principles?

Newton, having devised what we now call the calculus, put physics on a mathematical basis — he conducted his explorations in a rigorous, quantitative notation. After Newton's time physicists showed agreement on the content, on the methods of study and standards of rigor, on the boundaries (what to include as "part of physics" and what to exclude as "not part of physics"), etc. So Newtonian physics appears to have a central core of general principles.

Although Newtonian theory enjoyed two hundred years of expanding experimental-and-theoretical success, the physicists eventually showed dramatically that they did in fact hold it provisionally. (When C. S. Peirce first described scientific method in about 1895, he prescribed just that attitude.) In the period between approximately 1880 and 1905, experiments began yielding anomalous results. One observer after another found that his observations and the related observations of one or more of his colleagues failed to agree in some important respect (or the observations of one observer, done on different dates and in slightly different ways, failed to agree); and one or both of the observations contradicted tenets of Newtonian theory.6,(11) By 1905, perhaps one to two hundred of these anomalies had accumulated.

In principle, it took two observers cooperating in a new way to discover one of these anomalies. At an earlier period in the development of physics, an exponent of the Newtonian way of doing things would have assumed that there exists only one Right Answer to a question. Thus, he would have no problems accepting supportive findings; but when facing findings which contradicted his own, he probably would have sought to discredit, dismiss or ignore those findings (and perhaps discredit the worker who "obstinately" set them forth). But in the last fifth of the 19th century, at least a significant fraction of the community of physicists managed not to behave in that fashion. Instead, without fanfare or explicit discussion, they began to develop a new way of dealing with each other's work. When faced with incompatible results, these workers managed to overcome the temptation to discredit the observations which directly contradicted their own. That left them free to experience the dissonance between the two, to take both sides seriously, and to set out to find a way to reconcile them so as to show both sets of observations as possibly correct. This cooperative manner of operating did not form an explicit part of any physical measurement or discussion. Instead, it amounted to a new floor of trust for scientific endeavors — and proved utterly crucial to the further development of physics.

By his age 16 (1895), Einstein had started speculating about physics in self-reflexive terms which consistently contained the term observer: concerning what findings an observer would obtain in a laboratory traveling at the speed of light, concerning what a cat — or a physicist — would experience in free fall, etc. In presenting the conclusions he reached, Einstein reasoned about what the various idealized observers involved have to DO in order to observe the physical "events" in question; and in that discussion, he introduced two new assumptions into the previously-existing core of general principles of physics:

a) that light has a non-infinite velocity 7

b) which remains constant for all observers, regardless of their motion relative to each other or relative to the light source.

By starting from these premises, which yield the special theory of relativity, Einstein rejected the privileged status of Euclidean geometry (and of related constructs such as an independent and absolute space, time, matter, etc.) in physics. Later, he replaced Euclidean geometry with the generalized Riemannian geometry of Minkowski. And since the bulk of the language of physics consists of explicit statements in a mathematical notation of more or less known structure, the exponents of the new theory had the means to handle these revisions of theory, these aspects of the theory of relativity.

This approach to physics turns the term observer from an occasional vocabulary item into the center of a self-reflexive principle: "Take the observer into account." But no one had the means to examine this principle beyond using it immediately, in a practical fashion, to build up a theory of relativistic mechanics and to account for the anomalies, and so to restore adequate predictability to the discipline of physics. Thus the relativity theorists ignored some of the broader implications of the relativistic approach. For example, the principle of "taking the observer into account" calls into question not just the privileged position of Euclidean geometry but also the acceptability of granting any unquestioned, privileged position within scientific theory — even the one Whorf focuses on when he remarks that

What we call scientific thought is a specialization of the western Indo-European type of language....(12) As a trenchant way of illustrating Whorf's 1942 insight, we suggest that WIE logic, mathematics, and science in general — and WIE mathematical physics in particular — grant a privileged position to the grammar shared by the WIE languages. This way of saying it, we insist, amounts to a 1999 insight, unavailable to physicists active in the heyday of the theory of relativity, e.g. between 1905 and 1920.

Until very recently, no one had spelled out in detail the relations between grammar and assumptions.(13) Hence, no one had had the means to make explicit the theory encoded in a traditional grammar such as the WIE one. The most creative of physicists devised ad hoc ways to deviate from that encoded, traditional "theory," but have lacked the means to spell out just how their novel theories actually deviate from it.

Thus it appears that physics has a central core of general principles; and that this core has evolved and changed over the years. Some of the most recent alterations to it have centered about the self-reflexive principle of taking the observer into account.

What does one assume in order to take the transacting observer into account, as compared to what one assumes to eliminate her/him from consideration?

The authors know only one route to taking the transacting observer into account. First, one assumes that humans assume, that they cannot not-assume. Then what humans DO (including what brand of physical theory and of other shared or sharable views or maps they elaborate/subscribe to) follows from what they ASSUME — in roughly the way that, in a formal deductive theory such as Euclidean geometry, a theorem follows from the premises. And second, one assumes that humans can change what they DO by changing what they ASSUME and so assuming something else instead; they can NOT assume nothing-at-all. (Under certain circumstances, humans can change what they ASSUME by changing what they DO; they cannot do nothing-at-all.)

The constructs of assuming and of changing what one assumes hinge on an analogy which compares the construct of living to the process of map-making: To say that an organism lives means that it generates maps of that territory composed of what goes on in and around the organism, and then it guides its doings and choosings by its maps, in the process putting them to test.8 

When one uses a map to guide one's behavior, one can in principle explicitly distinguish or, by default, neglect to distinguish, between map and what the map refers to (‘territory’). Where one neglects to distinguish between them, we regard this neglecting as undiscriminating, and refer to this form of undiscriminating as postulating map-territory identity. Such neglecting manifests itself in treating the map as if it yielded some kind of "absolute certainty," and in holding oneself unwilling even to consider questioning, testing or revising it. Such neglecting sets the stage for "eliminating the transacting observer from consideration." At the other extreme, one can remain conscious of the distinction between map and what the map refers to. We regard this as discriminating, and refer to this form of discriminating as postulating map-territory non-identity. This discriminating manifests itself in remembering (a) to treat the map as more or less tentative and approximate, as incomplete, and as created from one's own point of view for one's own purposes; (b) in remaining willing to test it for accuracy; and (c) in holding oneself in readiness to revise it at need. Such remembering sets the stage for "taking the transacting observer into account."

Using this terminology, we can make explicit what one assumes in order to take the observer into account — namely, the three postulates set forth by Korzybski in 1941, and stated in a set theory notation by Hilgartner & Randolph in 1969:

The cautionary principles expressed by postulating map-territory non-identity, non-allness and self-reflexiveness underlie the scientific method and form the basis for its power. According to at least one version of the logic of science, the scientific method accomplishes one and only one thing: To provide a principled basis for selecting between guesses. In a fully specific setting (e.g., with reference to such and such kind of happenings, as tested by these specific methods, as judged by this criterion), it either shows one's hypotheses, assumptions or other guesses as in error; or else, this time, finds nothing wrong with them. It does not "confirm" them, for now or forever.

Whenever one violates the tenets of non-identity, non-allness, and self-reflexiveness, one thereby allows the possibility of starting from already-discovered error, and thereby predictably reduces the predictability of one's guesses (maps).

It becomes clearer that these postulates underlie taking the observer into account when we notice what it takes to eliminate the observer from consideration. To do that (or, equivalently, to eliminate the construct of self-reflexiveness from consideration), one assumes the converse of these three postulates — one neglects to distinguish between map and territory. However, no one would state these counter-premises explicitly, nor even willingly admit to holding them:

If, indeed, one's map should qualify as identical with the territory which it represents, that would make it perfect, a matter of "absolute certainty". To believe this, one must hold that the map contains all the necessary information in perfect order, and that it reflects no bias or contamination from the map-maker. Possessed of such a perfect instrument, one dispels any misgivings about the territory merely by consulting one's map, and need not bother to survey the territory itself.

Thus when one assumes (explicitly or tacitly) that one's map qualifies as identical with its territory, one's procedures profoundly violate the scientific method. This assuming also suffices to eliminate from one's consideration the construct of the transacting observer. A map qualifies as identical with its territory if and only if three conditions hold: (a) every point of the map represents one and only one point of the territory; (b) no point of the map represents anything extrinsic to the territory; and (c) no point of the territory goes un-represented. But a transacting observer remains distinguishable from, extrinsic to, her/his environment. Thus a map identical with its territory has no "room" in it for any kind of representation of the observer. Further, with the construct of transacting observer eliminated from consideration, one has no way to define observing, nor happenings to observe. That leaves one knowingly or unknowingly holding the attitude that one "just knows what really happened" — the insupportable claim to "absolute certainty".

Conversely, we may take the finding that a map fails to take the transacting observer into consideration as suggesting that it includes among its premises the postulate of tacit identity.

These considerations suggest that we amend the sine qua non of the scientific method by incorporating the new standard implied by the revolutionary physicists: Consider no theory as fully scientific if it eliminates the transacting observer from consideration (or shows any other hint or sign of relying on tacit identity).

To illustrate these constructs in action, we trace the development of increasing reliance on non-identity from the work of Newton through that of Einstein. We begin by examining three aspects of Newton's work —

and two aspects of Einstein's work — In each instance, we bracket the historical insight by reminding readers of what the innovator in question did not know at that time, which we now do know.


A. Universal gravitation

Today, having had over 300 years to assimilate Newton's great discoveries and imbed them as almost-tacit cultural agreements, we have difficulty imagining the shared viewpoints of Westerners prior to, in the absence of, these agreements. An individual may have a particular view or an insight, but in the absence of a shared agreement, discussing the view with other humans proves difficult at best.

Prior to 1665, the commonly held, unquestioned view or map maintained that "Things like balls or apples just naturally fall, while the Moon naturally stays up there — that's the way things are."

Unquestioned here means that those who held the view did not treat it as a provisional construct, but rather, tacitly treated this map as somehow certain, identical with the territory. Galileo and others had done earlier work dealing with topics in mechanics, including problems involving falling objects. But in 1665-6, no one besides Newton had discussed the possibility that the moon could fall, much less asked how come it didn't.

Bronowski(17) relates the familiar story of apple and moon as Newton told it in his old age; and quotes the conclusion that Newton drew from the calculations he performed. (18,19)

In effect, in developing the construct of universal gravitation, Newton changed what he assumed. In place of tacitly assuming map-territory identity on this topic, like everybody else, he came to distinguish between map and territory: What if the commonly held view comprises only a surmise, instead of expressing 'the way things really are'? This sentence expresses only the background of the Gestalt encoded in his insight9,(20,21). To express its figure, Newton devised an alternative map: What if the ball (or apple) and the moon BOTH fall — and the apple reaches the surface of earth whereas the Moon doesn't. How would I account for that?

As Bronowski indicates, Newton immediately sought some test which would give him convincing grounds for selecting between the two views — he resorted to astronomical facts and to computations, using his brand-new theory of fluxions (or as we now call it, the calculus), to choose between the traditional view and his alternative. From data he had on hand, he computed the centripetal force on the moon (the force drawing it toward the center of its orbit) produced as a function of the gravitational attraction to the earth. His first rough calculation gave the period of the moon close to its true value, about 27.25 days.(22)

Thus, to use the language of assumptions, Newton made his advance by replacing (at that point of his theory, at least) one usage of the tacit assumption of map-territory identity with a usage of the assumption of map-territory non-identity.

The resulting distinction between map (or hypothesis) and territory (or results of testing) forms the center of the scientific method. In 1665-6, testing on logical grounds, for consistency with one's starting premises, already had a history that went back some two thousand years. Newton's original work provides one of the early examples of what we now might call testing on empirical grounds, for a match between the map composed of an explicit hypothesis and the territory composed of the results of a careful and deliberate study (designed so that it could in principle show the hypothesis as wrong).

This procedure, within the setting Newton provides for it, allows its users to generate maps or hypotheses concerning the domain of physical happenings — especially those of an extent that lies within a few orders of magnitude of the size of a human's body — where the hypotheses, when tested, may turn out not-disconfirmed.

B. Absolute space and time

Newton explicitly posits the constructs of absolute time and absolute space, separable from one another, as fundamentals of his theoretical system.

In the critical appendix to his new translation of Newton's Principia, Cajori designates these as postulates of Newtonian mechanics, and states that

... they are not based on experimental evidence and may therefore be said to be metaphysical.(23) From another point of view, however, these constructs form a part of the background of experience of every native speaker/writer of even one of the WIE languages (and we know that Newton used at least two, English and Latin). For these constructs make up part of the linguistic or grammatical structure of those tongues. In any WIE language, most of the vocabulary belongs to two main groups of terms (which in English we call nouns and verbs); there exist also several much smaller groups (such as adjectives, adverbs, prepositions, etc.). In WIE grammars, we encode the construct of "time" in certain adverbs or prepositional phrases (such as when, then, at that point, etc.) and in the way we inflect our verbs for so-called "tense", "aspect", "mode", etc. — past, present, future, perfect, etc.; and we encode the construct of "space" — concerns centering about where, about location or place — in certain adverbs or other prepositional phrases (such as where, there, at my house, etc.) and in noun-forms (such as garden, kitchen, seashore, etc.). (24)

Thus, in the language of assumptions, when Newton made "space" and "time" fundamentals of his theoretical system, he tacitly treated these arbitrary categories of WIE grammars as basic features of the Cosmos.

By so doing, he subscribed to the tacit assumption of map-territory identity, and thereby ruled the transacting observer out of his theoretical system.

Since the separable categories of space and time came from the grammatical structure of the WIE languages, they had already undergone extensive refinement via informal testing against the experience of countless generations of native speakers of these languages. That makes them fairly reliable, within the domain of common experience. Hence, even within the setting of logical-and-empirical testing which makes up scientific physics, the indiscriminateness which these constructs encode remained undetected as long as physicists continued studying more or less human-sized happenings. But more than that, the tacit map-territory identity which they entail bestowed an aura of "absolute certainty" that served to protect the constructs from scrutiny. Only after physicists began dealing with the domains of the very large, the very small, and the very rapid did these constructs ultimately lead to hypotheses which did get disconfirmed. And in this domain, it takes two observers working together (or one observer whose viewpoint, experimental setup, etc., has grown and changed) to see the crucial "happenings" clearly.(25)

C. The social theory implicit in Newtonian physics

According to the Postulate of Self-reflexiveness, any theory includes some kind of representation of the map-maker, whether we had noticed or not. Let us briefly focus on the "shape" of the hidden social and self-reflexive component of Newton's theory. To infer it, let us look at the setting for Newton's life and work, and at a few biographical details.

In Newton's day, contributions to experimental and theoretical science came mostly from the activities of gifted "amateurs." They conducted studies, generated new viewpoints and constructs and then shared their findings and ideas in organizations such as the Royal Society. These men (almost without exception) came from a privileged class and had the advantages of financial resources, education, and free time. No one "employed" them to work in science (or as they called it, natural philosophy) — they volunteered. The Royal Society, and similar organizations in other countries, provided fertile ground for burgeoning science, as members developed, tested and shared ideas.

In this relatively open social setting, Newton lived as a profoundly closed, private and mistrustful person. As Bronowski puts it,

... All his life he makes the impression of an unloved man. He never married. He never seems to have been able to flow out in that warmth which makes achievement a natural outcome of thought honed in the company of other people. On the contrary, Newton's achievements were solitary, and he always feared that others would steal them from him....(26) He devised his theory of "fluxions" (the calculus) in 1665-66, but did not publish until many years later. Meanwhile, he used it to show up his colleagues — in letters to London scientists which outlined results he had obtained by the use of his innovation, he wrote out his findings in the standard mathematics of the day, so as to preserve his advantage. In 1676, Gottfried Wilhelm Leibniz independently developed the calculus. Modern scholars regard this as an authenticated instance of independent co-discovery; but Newton claimed that Leibniz stole it.

Similarly, Newton made the basis for his contributions in astronomy and mechanics public only in 1687, some twenty years after his first spectacularly successful results. He might not have published at all had not the young astronomer Edmund Halley camped on his tail for the preceding three years, spending his own time in concentrated urging, wheedling and nursing of Newton's moods. He provided Newton with financial assistance, and perhaps even did some ghost-writing on the Principia.

In 1703, after the death of the previous President, Robert Hooke, the Royal Society elected Newton, then aged 60 years, its President; and thereafter annually re-elected him until his death in March 1727. According to Bronowski, Newton ran the Royal Society as an absolute monarch. He tolerated no dissent, and put down his rivals and their work effectively and ruthlessly. And under his domination, the Royal Society ceased doing any real scientific work10,(27)

These details give some indications of the "shape" of the hidden social and self-reflexive implications of Newton's theory. We can generalize the assumptions he seems to have worked from in his inter-personal relations as follows: "I know what really goes on; I possess "absolute certainty"."

When operating from "absolute certainty", one finds any views which differ from one's own offensive and threatening — an affront to one's Rightness. After all (in this frame of reference), there exists only one Right Answer to a question. The mere existence of any view which deviates from one's own suffices to elicit rage and outrage. Under such duress, one might succumb to the temptation to try to invalidate or otherwise put down such views, and perhaps even to attempt to invalidate the holder of such views. If one's "opponent" should seek to defend himself from the attacks, and in the process should similarly succumb to these temptations, then the transacting engaged in would look to others like a full-fledged, old-fashioned power-struggle. Further, in the milieu of power-struggle, one might grow to enjoy Being Right, and seek to achieve that desired state by Making Others Wrong.

We have already established some of the ways in which Newton relied on non-identity in his theory; and have likewise established some of the ways he also relied on the postulate of tacit identity. Newtonian mechanics knowingly or unknowingly makes the insupportable claim to "absolute certainty". By overtly relying on distinctions, and the underlying postulate of map-territory non-identity, in the area of "external" physical happenings, Newton made his mechanics able to account for the behavior of (posited) non-living (and more or less human-sized) "external" material "things" which enter into transient relations. Concurrently, by relying on the postulate of tacit identity concerning the "internal" topics of what he assumed and the process by which he changed what he assumed, Newton tacitly made his mechanics blind to those happenings with an "internal" component, such as what we call living systems (including transacting observers). Consequently, the theory of human behavior and of social systems which Newtonian theory "secretly" encodes remains fixated on power-struggle and other social manifestations of the pretense to "absolute certainty".

Under these assumptions, Newtonian physical scientists build up the basis for a superbly effective mechanical theory and technology. But Newtonian theory does not discuss how one arrives at a "picture" of "physical reality" — does not allow for even one observer. Thus physicists tacitly ignored the social relations among scientists. This failure to include themselves and their interrelations in the system of physics, we maintain, functioned in a self-defending fashion, making it more difficult to discover the kinds of mismatches between different observers' results that we call anomalies — the findings which ended up disconfirming Newtonian theory and pointing the way to relativity and quantum theory.


A) Relative space-time

In the latter part of the nineteenth century, physicists assumed that an "ether," a medium through which radio and light waves propagate, fills space. Various observations concerning aberrations in the propagation of light persuaded them that the ether does not travel with the earth as it orbits the sun. In 1887, Michelson and Morley attempted to measure the "ether wind" generated by the passage of the earth through this ether; they found no evidence for such an ether wind. In 1895, H. A. Lorentz (and, earlier, G. F. Fitzgerald) suggested that matter, due to its electrical structure, shrinks when in motion, and that this contracture occurs only in the direction of motion. The amount of shrinkage comes to 1/b where b = c/(c2 - v2)**1/2. When applied to the results of the Michelson-Morley experiment, this correction factor gives the correct answer. Poincaré objected that an explanation invented for the express purpose of smoothing out a certain difficulty, which assumes a correction of just the right amount, seems excessively artificial and unsatisfying. Lorentz (1904) examined his contraction hypothesis against other data, and again found his correction factor fit these facts also. However, he ended up dismissing these equations as a mere mathematical fiction, without physical meaning.(28) Einstein, however, took the Lorentz transformations seriously, positing that they reveal something fundamental about the universe, something more basic than do the traditional constructs of space and time themselves.

In discussing these views, Einstein introduced his two assumptions ((a) and (b) above, ms p. X7) into the core of general principles of physics. When he did so, in effect he questioned, and abandoned, the usage of the assumption of tacit identity encoded in Newton's postulates of separable, absolute time and space. He replaced it with a usage of the postulate of map-territory non-identity, as encoded in the construct of a relative (non-absolute) space-time, and expressed in the Lorentz-Einstein transformations (among other places).

In presenting his arguments concerning the Lorentz-Einstein transformations, Einstein used phrases which posited characters named "the observer at coordinate system A, B, etc.," or mentioned "observer B's clock," etc. His mathematical arguments, however, dealt with coordinate systems or pointer-readings, not observers.

B. "Absolute certainty" again

As we do with Newton, we infer that Einstein eliminated (at one point of his theory, at least) a usage of the postulate of tacit identity. But he also subscribed to the assumption of tacit identity in other ways or places, by uncritically accepting certain of the assumptions encoded in the grammar of the WIE languages. For, grammatically, our logical and mathematical languages (such as symbolic logic, set theory, algebra, differential and integral calculus, the calculus of tensors, etc.) and our discursive languages (such as German and English) do follow approximately the same rules.

As noted above, we WIE provincials have ways, built into the grammar of WIE languages, to indicate and handle the constructs of "space" and "time." (And as noted above, Einstein found ways to modify these traditional constructs). However, we have no built-in grammatical means for explicitly handling the distinction between map and territory.11,(29) No affixes, no special words or special class of words, etc., REQUIRE us to make that distinction. Instead, at the level of grammar, we do not and cannot do so. But if we provincials do not explicitly distinguish between map and territory and so explicitly posit their non-identity, then by default we tacitly fail to distinguish them and so TREAT them as identical. At the level of grammar, then, we posit map-territory identity and make the pretense to "absolute certainty". This fundamental error functions as a hidden assumption encoded in our grammar, and operates in our logical and mathematical languages as unavoidably as it does in our common speech.(30)

In what respects does modern (1999) physics fail to live up to standards for fully scientific?

The revolutionary physicists of the first decade of this century employed the construct of "taking the observer into account" as a principle. Today, most people, physicists and non-physicists alike, seem to believe that contemporary physicists handle this construct as well as anyone does.

But our contemporary physical theories do not explicitly include any discussion of the kind of living systems we call physicists, theorists, transacting observers. For example, in the theory of relativity, the discussions of "the observer" hinge only on a linguistic metaphor, not on mathematical developments. Relativity theorists use mathematics which deals only with pointer-readings, or differences in the position and velocity of coordinate systems; they have no way of dealing with "the observer" in any other sense. Similar constraints hold for quantum theorists.

According to our chosen postulates, no map exists free of some kind of representation of the map-maker. If an expression signifying the physicist or the theorist or the transacting observer does not explicitly appear among the terms of a theory, that does not mean that the theory in question eludes the constraints on the relations between map and territory. Instead, we suggest, it means that in that theory, the transacting observer gets represented only implicitly, in a concealed fashion. In other words, this situation provides evidence of a hidden assumption included among the premises of the theory, which eliminates the transacting observer from consideration. In such a theory, that portion of its premises which DOES deal with the transacting observer remains undisclosed, unstated, unquestioned — framed so as to remain untested and untestable.12,(31)

Judged against even the unmodified sine qua non of the scientific method — the demand that a scientist generate, test and judge hypotheses derived from his theory (or assumptions encoded in his theory), and, at need, replace or revise them so as to avoid relying on any hypothesis or view already disconfirmed — no theory which includes an untested and untestable hidden assumption of this type among its premises makes muster as fully scientific.

Judged by this criterion, Newtonian physics appears acceptably testable with respect to the motions of bodies or points; and utterly unexamined concerning the transacting observer and other self-reflexive topics.

Similarly, relativity physics appears acceptably testable concerning motions and concerning spatio-temporally ordered happenings (happenings centering about the distinctions here/there and before/after); and entirely unexamined concerning the topics of self and the social and other self-reflexive topics. Likewise, quantum theory has its strengths, but shares this weakness.

Then the theorists who write the current versions of the theory of relativity (and quantum theory) have not completed their job; and to whatever degree their theories and hypotheses may appear similar in structure to the external happenings which they explicitly aimed to deal with, in the arena of self-reflexiveness their theories remain unexamined.

Crucial self-reflexive topics ignored in contemporary physical theory include

These four topics bracket the process by which (in our analysis) the community of physicists made the transition from Newtonian theory to the theory of relativity (and, by extension, to quantum theory). But the exponents of neither contemporary relativity nor contemporary quantum theory have anything at all to say about these or most other self-reflexive topics. Hence, in these areas, they end up knowingly or unknowingly holding the attitude that they "just know what really happened" in their physical experiments — the insupportable claim to "absolute certainty". Concurrently, they also eliminate the relevant aspects of the process of observing, and of happenings to observe. No wonder no one had noticed!

Any physical happenings that we humans can observe take place in the presence, not the absence, of possible transacting observers. Trying to elaborate objective (observer-free) theory appears from this point of view as elaborately misguided: It sets up the accounting so that it cannot account for crucial aspects of ANY observation.

Physicists seem to prefer to focus mainly on the topic of non-living happenings — the motions of planets or points, or sub-atomic particles, or whatever. When physicists discuss "the observer" in the mathematics of relativity theory, they represent this construct in terms of static-and-unchanging things — coordinate systems — which enter into transient relations — expressed in terms of the position, velocity, etc., with respect to these coordinate systems. Regardless of their preferences, however, their findings deal not only with their chosen non-living subject-matter, but also, self-reflexively, with the kind of living systems we call physicists.

The WIE languages — including symbolic logic, set theory, analysis, recursive group theory, etc. — cannot readily handle such self-reflexive relations. Consequently, as long as we continue to grant a privileged position to the grammar common to these languages, we WIE provincials in principle cannot adequately represent anything living. And that inability prevents us from adequately accounting for anything non-living.

We need to generate a common core of general principles for our sciences, human psycho-social, biological, and mathematical as well as physical — principles sufficiently rigorous and general so that our physical theory articulates seamlessly with the rest of human knowledge. Finding ways systematically to take into account the transacting observer looks like a necessary first step. Our way of doing this accounting (generating and accepting a system based on presuppositions that include the construct of time-binding and the postulates of Non-identity, Non-allness and Self-reflexiveness, which rejects identity as valid, redefines the construct of observer, rejects the privileged position which the WIE grammar enjoys in our sciences, etc.) looks acceptable, in light of the evidence available so far.

1. Frederick S. Perls, Ralph Hefferline & Paul Goodman, Gestalt Therapy: Excitement and Growth in the Human Personality. Julian Press (1951), pp. 243-4.

2. John Dewey & Arthur F. Bentley, Knowing and the Known. Boston: Beacon Press (1949). Paperback edition, 1960.

3. D. David Bourland, Jr. "A Linguistic Note: Writing in E-Prime". General Semantics Bulletin Nos. 32/33, pp. 111-4. Also, E. W. Kellogg, III "Speaking in E-Prime: An Experimental Method for Integrating General Semantics into Daily Life". ETC.: A Review of General Semantics 44:118-128 (1987). ]

4. Alfred Korzybski, Manhood of Humanity: The Science and Art of Human Engineering. Dutton (1921). 2nd Ed., M. Kendig, ed., Institute of General Semantics (1950)

5. Jacob Bronowski. Science and Human Values. Harper Torchbook (1956), revised (1965), p. 13.

6. Ref. 1.

7. Alfred Korzybski, Science and Sanity: An Introduction to Non-aristotelian Systems and General Semantics (1933). Non-Aristotelian Library Publishing Co., Chicago (1933). 5th edition, Institute of General Semantics, Englewood, NJ 07631 (1994).

8. A. S. Eddington, (1928). The Nature of the Physical World. Cambridge University Press.

9. David Finkelstein, personal communication, 1 May 1991.

10. Karl Popper, The Logic of Scientific Discovery. Hutchinson (1959).

11. Walter Kaufmann, "Die magnetische und electrische Ablenbarkeit der Bequerelstrahlen und die scheinbare Masse der Elektronen" ("Magnetic and electric deflectability of the Becquerel rays and the apparent mass of the electron"). Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen, Math.-phys Kl.,2, 143-155 (1901).

12. B. L. Whorf, Language, Thought, and Reality: Selected Writings of Benjamin Lee Whorf. John B. Carroll (Ed.) MIT/Wiley, (1956) p. 246.

13. C. A. Hilgartner, "Some Traditional Assumings Underlying Indo-European Languages: Unstated, Unexamined, and Untenable." General Semantics Bulletin Nos. 44/45, pp. 132-154 (1977/78).

14. Alfred Korzybski, "General semantics, psychiatry, psychotherapy, and prevention." American Journal of Psychiatry 98(2):203-14 (1941). Reprinted in Alfred Korzybski Collected Writings 1920-1950. M. Kendig, ed., Institute of General Semantics (1990), pp. 295-308.

15. C. A. Hilgartner & John F. Randolph, "Psycho-Logics: An Axiomatic System Describing Human Behavior. A. A Logical Calculus of Behavior." Journal of Theoretical Biology 23:285-338 (1969a), pp. 295-7.

16. C. A. Hilgartner & John F. Randolph, "B. The Structure of 'Unimpaired' Human Behavior." Journal of Theoretical Biology 23:347-374 (1969b), pp. 353-6.

17. Ref. 5, p. 15.

18. Sir Isaac Newton, Philosophiae Naturalis Principia Mathematica, London (1687). Alexandre Koyré & I. Bernard Cohen, 2 vols, Cambridge University Press, 3rd ed., 1972. Quoted in ref. 19, p. 142.

19. Jacob Bronowski, The Ascent of Man. British Broadcasting Corporation (1973) Paperback edition, London: Macdonald Futura (1981), p. 142.

20. Ref. 1.

21. Michael Polanyi, Personal Knowledge: Toward a Post-Critical Philosophy University of Chicago Press, (1958). Second edition, Harper Torchbook, (1964), pp. 57-60.

22. Ref. 19, p. 142.

23. Florian Cajori, "An Historical and Explanatory Appendix." In Newton’s Principia, third edition (1726). Translated into English by Andrew Motte (1729) Revised by Florian Cajori. Berkeley: University of California Press (1934) pp. 627-80.

24. Ref. 13.

25. Ref. 11

26. Ref. 19, p. 141.

27. Ref. 19, pp. 140-155.

28. Lillian R. Lieber & Hugh Gray Lieber The Einstein Theory of Relativity. New York: Rinehart & Co. (1936; second edition, 1945), pp. 3-20.

29. Ref. 13.

30. Ref. 13.

31.C. A. Hilgartner & Joseph DiRienzi, "A Non-aristotelian View of Quantum Theory." Physics Essays 8(4): 472-505 (1995)

1  Aristotle used the Greek equivalent of the phrase unmoved mover as a synonym for his term for God. To state our point baldly, we find that, where even the best of our scientists (along with other exponents of Western Indo-European (WIE) frames of reference) eliminate from consideration the ways that making an observation alters the observer, they subscribe to untenable assumptions (or assumptions so restricted and restrictive as to apply under no circumstances whatsoever). Below, we discuss in some detail this body of untenable assumptions. We have disclosed and stated at least some members of this collection of assumptions, and have found ways to eliminate them from the premises of our alternative frame of reference. From our standpoint, then, what WIE scientists DO when they act, and/or theorize, from these restrictive assumptions amounts to making at least two insupportable claims: that they alter their experimental systems (the world) without getting altered themselves (which amounts to omnipotence), and that they have access to “absolute certainty” (which amounts to omniscience). Or succinctly put, they “play God.”

2  Among other things, in the course of developing the altered frame of reference we came to an altered way of using English. For example, we write in a dialect known as E-prime, which consists of a scientific English, minus all forms of to be (e.g. am, are, be, been, being, is, was, were, ain't, aren't, I'm, isn't, wasn't, weren't, etc.) By itself, to use E-prime does not satisfy the demands of the alternative viewpoint; but it helps to maintain awareness of that viewpoint. See ref. 4a & b.

3  Thirty years after Korzybski’s 1921 book (ref. 2), Perls, Hefferline & Goodman explicitly proposed a physico-bio-psycho-social field theory that fits this description. See ref. 6.

4  The issues here seem quite similar to the issues surrounding Euclid's Fifth Postulate and the construct of geodesic (“the shortest distance between two points”). From Euclid's day (fl. ca. 300 BCE) until approximately 1825-1860 CE, geometers had only one version of the Fifth Postulate. Stated in its usual form, the Fifth Postulate reads, “Through a point lying external to a given line, one and only one line parallel to the given line may pass.”
For classical geometers, then, a straight line (nowadays described as a line-segment of zero curvature) gives the shortest distance between two points, and Euclid's comprises THE geometry. After 1860, geometers had at least three versions of the Fifth Postulate, and the term geodesic had become ambiguous, a “blank check” which they could specify in at least three different ways. By then Euclid's plane geometry (“one and only one parallel”) had become A geometry rather than THE geometry, which stood next to spherical (“no parallels”) and pseudo-spherical (“as many parallels as you like”) geometries.

5  See ref. (10). Finkelstein neatly summarizes some of these points. He characterizes four kinds of invariance under transformation — four kinds of relativity — and discusses three parameters for each. Relativity0, which he calls “physics-totalitarianism,” refers to physics from Aristotle, to Newton, to the Newtonians of about 1899 or 1904; Relativity1 refers to Einstein's theories; Relativity2 refers to quantum theory; and Relativity3 refers to Finkelstein’s ideas of how physics develops in the 1990’s. I don’t know exactly how he has framed this alternative; from my point of view, something like the present suggestions concerning the construct of transacting observer fits well here.
Relativity0: Everyone

Relativity1 (Einsteinian): We give up “same language”. You might say here while I say there.
Relativity2 (Quantum theoretic): We give up “same experiment”. You might measure position, while I measure  momentum. You might do your measurement yesterday, I do mine today.
Relativity3 We give up “same system”. The transacting observer forms a part of the system; so your “system”  differs existentially from mine. Further, to make an observation alters both the system  (environment) and the transacting observer.

6  As an example of the one-person variant of this pattern, consider Walter Kaufmann. Working in 1901, before anyone had measured either the mass or the charge of an electron, Kaufmann measured the charge-to-mass ratio of electrons. In a high vacuum chamber, he fired electrons through both an electric field and a magnetic field set at right angles to one another, onto a photographic plate. From the displacement induced by the fields, he calculated the charge-to-mass ratio. In his first series of experiments, he used a cathode ray tube as the source of electrons. Then the Curies gave him some samples of radium chloride, which emit electrons (beta particles) at velocities near that of light. For his second series of experiments, he used the radioactive element as his source of electrons. The charge-to-mass ratios he measured indicated that the high-velocity electrons had a mass three to four times that of the lower-velocity electrons. This comparison of results yields an anomaly of the type we describe above — Newtonian theory predicts no effect of velocity on mass. See ref. 12.

7  Consider the difference between the velocity of light as an empirically measured quantity and as a construct with theoretical significance. In 1676, Olaf Roemer & G. D. Cassini first measured the speed of light empirically, giving it a value of about 2.2 ? 10**8 m/sec. (Modern workers estimate it at about 3.0 ? 10**8 m/sec.) Surely Newton knew this work; but the foundations of his work date from 1665-6. The velocity of light played and could play no explicit theoretical role in his mechanics.
Early in the twentieth century, someone noticed that the Lorentz-Einstein transformations collapse into a structure equivalent to the Galileo transformations, provided that one assumes that light has an infinite velocity. This mathematical relation gives a way of bridging between the presuppositions of Newtonian and relativistic mechanics, via the following criterion:

The criterion of generality:
Given: A body of concerted observations, and at least two theories,  C  and  D , which purport to account for (at least some of) these observations. Then we can show  D  as more general than  C  if and only if the following circumstances hold:

Specifically, Here the restricted and restrictive assumption consists of the notion that light has an 'infinite velocity.' As Korzybski points out, we define velocity as distance divided by time, where the rules of arithmetic forbid dividing by zero. The phrase “infinite velocity,” however, signifies the “result” obtained by setting time to zero and then calculating the quotient — dividing by zero. Hence, strictly speaking, that phrase amounts to a meaningless noise — or, as we would phrase it, a manifestation of assuming tacit (map-territory) identity. Therefore: We may regard the theory of relativity as more general than Newtonian mechanics; and regardless of the fact that Newton does not discuss the velocity of light as a construct with theoretical significance, we may infer that (at the level of theory) he tacitly assumes that light has an 'infinite velocity'.

8  Any living organism, we say, remains in contact with its environment, and lives according to a kind of self-correcting logic: Thus organisms create 'maps0' or 'pictures' of “what goes on in and around themselves” in general. And (as we said), in particular, by a process of ignoring differences, they create whatever similarities and generalizations (maps1 of a higher order) they may need to guide themselves toward survival. These maps1 they use to make predictions (maps2) concerning how to maintain themselves, to satisfy their needs, etc. — for humans, for example, these predictions deal with how to obtain suitable air, water, food, shelter, clothing, companionship and friendship, the physiological aspects of sex, etc. When we humans act on such predictions or guesses, in effect we put them to test, and then we can judge them against how the situation “turns out.” Where the outcome does not match what we expected, we can treat the prediction we started with as disconfirmed, and discard and replace it. Where things do turn out roughly as we expected, we treat the prediction as not-disconfirmed, assimilating it and bringing it up in the next relevant situation, as an expectation (maps3) — and so test it again. In doing science as well as in more informal living, where a prediction turns out not-disconfirmed, we may say that it appears similar in structure to whatever “territory” (“doings” or “happenings”) it supposedly represents or refers to.

Instead of functioning like a self-correcting system, we humans can also maintain the (usually unspoken) attitude that “I don’t make any guesses — I see only what ‘is’ REALLY THERE.” Then when things turn out other than as we expected, we do not proceed to reject and replace any guesses. Instead, we ‘rationalize’ the outcome, e.g. by blaming: “It’s MY fault!!” or : “It’s YOUR fault!” or: “It’s ITS fault!” Then we go out of the situation still clinging to the guesses we came into it with, even though now we have evidence that these guesses don’t work. Such self-defending behaving-and-experiencing invites diagnostic terms: it appears rigid, or fixated, or neurotic, or psychotic, or whatever diagnostic terms the viewer prefers.

Please focus clearly on what self-defending “defends”: It does not protect the skin, nor the organism’s “face” or “feelings”, nor the inter-personal relations, etc. Self-defending behaving-and-experiencing “protects” only THE GUESSES.

9  Exponents of Gestalt psychology maintain that we can analyze any sensing, any feeling or any moving into a Gestalt, composed of a figure of focal interest to the organism, against a (back)ground relatively empty of interest. For further elaborations, see refs. 21 and 22.

10  See ref. 27. Newton lived a very complex life, in which what he said publicly and what he did privately did not match. Bronowski gives some clue of this where he writes,

 Now if Newton had been a very plain, very dull, very matter-of-fact man, all that would be easily explicable. But I must make you see that he was not. He was really a most extraordinary, wild character. He practiced alchemy. In secret, he wrote immense tomes about the Book of Revelations. He was convinced that the law of inverse squares was really already to be found in Pythagoras. And for such a man, who in private was full of these wild metaphysical and mystical speculations, to hold this public face and say, “I make no hypotheses” — that is an extraordinary expression of his secret character. William Wordsworth in The Prelude has a vivid phrase, which sees and says it exactly.

 Well, the public face was very successful. Of course, Newton could not get promotion in the University, because he was a Unitarian — he did not accept the doctrine of the Trinity, with which scientists in his time were temperamentally ill at ease. Therefore he could not become a parson, therefore he could not possibly become the Master of a College. So, in 1669, Newton went to London to the Mint. In time he became Master of the Mint. After Hooke’s death he accepted the Presidency of the Royal Society in 1703. He was knighted by Queen Anne in 1705. And to his death in 1727 he dominated the intellectual landscape of London. The village boy had made good. (p. 149)

11  The grammar of the WIE languages (e.g. English) requires its speakers/writers explicitly to make large numbers of distinctions. Nothing in that grammar, however, REQUIRES any speaker/writer to distinguish between the words s/he generates and that which the words designate (if anything). Let us put this in terms of the map-territory analogy, which holds that to say an organism lives signifies that it generates some kind of map(s) of that territory composed of “what goes on in and around our organism”: nothing in the grammar of the WIE languages requires language users to distinguish between map and territory. We have no specially named parts of speech, no reserved prepositions, adverbs, etc., no prefix, suffix or infix — no grammatical arrangement whatsoever — that makes the map-territory distinction and that every speaker HAS to use in every sentence. That amounts to saying that the grammar of the WIE languages tacitly equates — identifies — map with territory. By tacitly regarding the match between our languaging and the territory it refers to as “perfect,” we WIE speakers/writers display — at levels we rarely even notice, much less question — the assumption that our maps provide “perfect knowledge” of the territory. But — at least on the levels we remain aware of — we recognize that no human legitimately has access to “absolute certainty” or “perfect knowledge.” For further discussion, see ref. 31, especially pp. 476a-b.

12  In principle, no one can explicitly test an assumptions which s/he does not explicitly state.