Remarks: This postulate has a strong physicalist (and thereforeanti-dualist) position. One should note, however, the apparent physicalist reductionist stance does not have to be naive physicalist (materialist) reductionism. This is because the underlying world view of modern physics is not classical physics but quantum mechanics.
We have to refer to language in a very broad sense here. Language includes the public or pragmatic language (mostly verbal) with which individuals communicate with each other in a community to achieve various goals; it also includes the private language (mostly non-verbal) of an individual, with which she represents and thinks about various subject matter. In this sense, pictures of animals, spears, or fire which were drawn in a cave must also be considered as a sort of language.
Remarks: Since classical physics can be regarded as a limiting case of quantum mechanics, the brain can be conveniently treated as a classical measuring device which is coupled with other quantum computational systems in the brain. The articulated language (remember this includes sounds as well as all kinds of signs in a patterned system) takes a classical manifestation and can be treated largely as a classical object.
Memory is crucial in this postulate. Since our sensorial data ``right on the spot'' is so ephemeral, we have to resort to memory in order to have access to reality in the world and to be able to reason upon the information. Because memory is aggregate quantum phenomena with a very large number of quanta, it is very stable. In fact, the probability may approach one, which is the absolute objectivity advocated in classical physics.
Remarks: Our impression of stable and invariant ``substance''and modern neurology indicate that our memory may be largely classical properties embodied in the specific orientation of nerves or synapse strengths, etc. According to modern physics, these classical properties are quantum properties in the limiting case. Nevertheless, there is also ``reality'' in our mind which is not stable and seems to be very evasive -- for example when we reflect on aesthetic or ethic judgments in some cases. This fact indicates that the proper quantum effects in our brain are probably playing a crucial part.
According to this view, thought in the brain is largely the interaction of the brain with its own memory and occasionally external sensorial data. Moreover, there must be something active in our mental process which can be accounted for only in quantum theory. In quantum mechanics, measurement results generally depend on the experimental arrangement. In the mental realm this active arrangement is participation instead of mere interaction. A corollary is that mental ``reality'' is something actively constructed instead of something passively given.
Remarks: Language understanding is a process of grasping meaning. Only after a measurement is performed, can meaning be given to a particular physical situation. As noted in the remarks of Postulate 1, language is used here in a very broad sense. Therefore, a mental image of a flower or a person standing up, when a particular memory composition is actively identified as such, is a kind of understanding. An image of a bunch of red spots on a colorful background is, however, meaningless. So is the pronunciation of ``rose'' (/ro:z/). It does not mean anything until it is actively identified as rose (the flower) or past tense of the verb ``rise.'' Since a quantum measurement can render only one of the eigenstates, a mental image can be either a flower or not a flower, but not both. Before the measurement is performed, on the other hand, a physical state is generally a superposition of eigenstates, so all utterances are basically ambiguous.
Quantum measurement is inherently participatory and active. In the same way all meaningful language understanding has to be participatory and active.
In a communication scenario, an individual grasps the meaning of the utterance of his/her partner by measuring his/her own quantum system coupling with the external physical environment. The external environment is influenced by his/her partner. For example, a speaker participating in a conversation may pronounce a series of sounds, draw pictures on a black board, pointing at something, or wink. All these activities alter the neighboring environment. The resulting physical quantity change is largely classical, the air pressure, the chalk residue, and the reflection of light are all classical properties. However, the final understanding is a quantum measurement, for the classical signals are coupled to something inside the brain, which is a quantum mechanical phenomenon according to Postulate 2.
The listener does not have to perform measurement on her/his eidetic experience resulting from his own memory and immediate external utterances. However, a not-measured eidetic experience, roughly speaking, does not enter consciousness and is not really of any value for a sophisticated linguistic activity, although it may result in coordinated behavior.
Remarks: A language formulation (short: formulation) or representationing is an utterance which is supposed to convey meaning. Gibberish may be interpreted by the listener to mean something. However, it is very likely not what the speaker means. On the other hand, a cough from a person, if purposefully made, may mean that she needs attention. If this is correctly interpreted by the listener, it is a formulation. Usually an utterance can mean something to others only if it first means something to the speaker herself. This is why a quantum measurement has to be performed before a state of affair is uttered.
A formulation is a description (incidentally, the etymology of describe is Latinde-scribe: to write down) or representationing of the internal physical state of the speaker made by writing down some kind of orthographic notations. The process of ``writing down'' is generally classicizing a quantum state, where something4.3 is doomed to be lost. A formulation can therefore be conceived as a projection from quantum state to classical state. Nevertheless, it is possible to rebuild the original quantum state to considerable accuracy by conveying more information. For instance, personal conversation may be a more complete form of reconstructing the original state of affairs than video teleconferencing; the latter, in turn, is a more complete form than a telephone conversation, etc.
Remarks: The fact that language understanding and language formulation do not commute can be demonstrated in the following example: suppose someone is given an arbitrary utterance. He reads it aloud to himself, takes a breath, and tries to grasp its meaning without speaking a word. Then he formulates the same subject matter again. If the subject matter is moderately complicated, with great chance he will end up with a different formulation (in the narrower sense, viz. orthographically). We have to understand the subject matter before we can re-formulate it. In fact, we are not mechanistic copycats. Once we understand something, we can formulate the matter quite freely (the only constraint, so to speak, is its meaning).
Apparently, if we take a verbatim audio or video record of our uttering the same sentence twice, in succession, the two utterances are definitely different in some minor temporal (frequency) and spatial (amplitude) aspects. But this is not the only source of non-commuteness. Non-commuteness of language has a deeper source: the collapse of a wave function. Collapse of a wave-function puts a quantum system into an irreversible state. In other words, the superposed wave-function of a quantum system is gone forever; only the eigenstate is left out and remains accessible.
Non-commuteness of formulation and understanding does not only manifest itself in colloquial language, it does in rigorous mathematical language as well. Try proving Pythagoras Theorem yourself, very likely you will end up with different formulations every time, especially if the interval between two proofs is long enough. Why? It is because you understand Pythagoras Theorem. A computer automatic theorem proving system built on a deterministic algorithm, on the other hand, yields the same proof every time. Few people will believe that such a program can come anywhere close to the understanding of a mathematician.