Now we come to our main concern -- language. Mathematical expressions are themselves language. Moreover, it is in language (partly artificial and partly natural) that the logical relation between mathematical objects is explained. Language is also something with which Equation 2.1 is presented. And of course, physicists talk about electrons or quarks, their energy, momenta, charge, mass, and even colors. All these are discourses in language.
A striking insight is that our memory itself is a patterned system, so it can be seen as a language as well. This must be the case, otherwise our memory would have to consist of verbatim records of experiences, and this is very unlikely. I know how roses smell, because I have the memory of how roses smell, although I don't have access to the sensorial data now. And indeed, I have a memory of roses so that I know there are things which are roses. In my thought, I can see roses, experience how they smell, how they sound, and how it feels to touch them. This leads me to conclude that there is something which is a rose.
We have to use the term language in a very broad sense. For the purpose of discussion, any compact system capable of generating images -- all kinds of sensorial environment -- is entitled to be called a language.
In fact, when I think of roses, I think of things which are called ``roses.'' If something pops up in my mind and I cannot tell whether they are roses, I call them ``something that I cannot identify as either roses or not roses.'' Every time I think of something, it has a name. Whether the color of a rose is red, or not red, or I can not tell if it is red, has to be called ``red,'' ``not red,'' or ``something that is undetermined if it is red.'' Whether a rosebud falls, floats, or neither, has to be called ``falls,'' ``floats,'' or ``neither.'' Even the higher level categorical images such as movements or attributes have to be called ``movements'' or ``attributes.'' Thus we name everything, including those which can not be named.
It turns out that this habit of giving everything a name is typical in many languages, especially in Western Indo-European (WIE) languages. In German, for example, nouns are even called Hauptwörter (head-words or main-words). We have reason to believe that this habit of objectification predisposes one to think of everything as ``objects,'' and there is no other way to think about reality other than crystallizing. Its ultimate form may be information theory, in which information is reduced to well-defined objects (bits) and the structure thereof. There are many prejudices of this kind, for example in [22], Dretske stated:
... there is something in nature (not merely in the minds that struggle to comprehend nature), some objective, observer-independent fact or set of facts, that forms the basis of one thing's meaning or indicating something about another.
Indeed, whenever we talk, something is spoken out. It is a description (Latin: write-down) of a state of affairs. A spoken or written utterance consists of sounds or words, which take the form of symbols. In this sense, symbols are objects, or rather, symbols are something being objectified. However, it is a fallacy to confuse the necessary objectification of words with the objectification of reality. It seems that many have over-generalized the subjective naming to the (conjured) objective information. It is even more erroneous to equate information to meaning. In fact, we should not forget that meaning is a dynamic process which brings forth the world. As Whorf stated:
Sense or meaning does not result from words or morphemes but from patterned relations between words or morphemes. (P.67 [23])
Indeed, this observation has caused some linguists to question the adequacy of the discrete symbolic approach to language. For example, Kenneth Pike [24] has proposed a view of language as ``particle, wave and field.'' He has also proposed the difference between emics and etics (e.g. phonemics vs. phonetics). In a sense, these insights reveal a similarity between wave-particle duality in quantum mechanics and word-sense relation in language2.11. In quantum theory, a particle is localized and exclusive -- it is either there or not there. It is about static structure. On the other hand, a wave is always holistic and synergistic. In waves, what is important is the patterned relation. It is about dynamic process.
This shift from structure to process is in a way similar to David Bohm's thought experiment with language and thought in [1]. He calls it the rheomode of language by putting the verb at the center of language usage. The purpose is to emphasize the effect of ``participation'' instead of ``interaction'' in understanding what the world is.
If this is an adequate account of language, language usage deserves to be called rheomode computation. It is a sort of quantum computation, except that the activeness of the quantum system should be emphasized. In light of this, the memory in Figure 2.1 should not be taken as a classical object but a quantum object, which is represented by a superposition of eigenstates (for a summary of quantum mechanics see Chapter 3). Each eigenstate is a monadic entity (a name in a language -- manifested as a symbol.) Following the tradition of cognitive science, this superposition is called a state of affairs. If a particular memory happens to be a ``pure'' state (an eigenstate) such as in the case of an invariant mathematical symbol (e.g. 
), a measurement will not distort the sensorial data generated by the memory. In day-to-day language, the state of affairs is mostly impure (i.e. with multiple components of mutual orthonormal eigenstates).
Within this framework, mathematics can be regarded as a quantum computation done on pure states (so it is always reversible); while everyday reasoning is a quantum computation done on superposed states (so it seems to be random and irreversible). Moreover, the Newtonian view is also a quantum computation on the expectation value of superpositions. Since most macroscopic objects have a huge number of quanta, the expectation values of physical properties approach that predicted by classical physics.
There can be a crucial impact on the interpretation of quantum mechanics. A closer look at the formalism of quantum mechanics reveals that the paradox of quantum mechanics lies in the unavoidable objectification of mathematics. When we realize this, the paradoxical question in quantum mechanics dissolves. Quantum mechanics, and indeed any science, consists of pictures or utterances that are speakable.
Now we can make a picture of the physical and mental world comprising all that what is speakable (according to the very broad sense of language). This is shown in Figure 2.2. In this view, language and mathematics play a pivoting role in bringing forth the physical and mental world and bridging them. Nevertheless, this is the case only if language (or mathematics) is being used to describe the world (labeled with Particle-like view of world in the figure). However, there is another way of understanding the world (labeled with Wave-like view of world in the figure). In this view, the subject matter cannot be spoken and everything becomes blurred. The formalism of quantum theory is speakable, this is the case only if we see it at a more subtle level (that is, if it is brought forth this way). If this picture is taken as the subtle reality, physical and mental reality can be seen as two aspects of the underlying reality.
To conclude, an intelligible naturalist account of meaning consists of a formalism based on a strong analogy between the physical and the mental world.
