# Structural and Symbolic Information in the Context of the General Theory of Information
## 5 Symbolic Information
Looking at symbols from the structural side, the code symmetry _impedes conclusions_ to be drawn from the structure of the symbols on the meaning of the symbolic message. \"Information and computation reside in patterns of data and in relations of logic that are independent of the physical medium that carries them\" ([45] p. 24). This means, _symbolic information is an emergent property_. The same message may be expressed by different symbols, tokens or languages; a sequence of symbols may be reversibly compressed or redundantly inflated without affecting the meaning of the message. In order to produce a cup of coffee, a single on/off bit may be sent to a coffee machine, or a long instruction may be given to an unexperienced cook to prepare an equivalent result. The same mathematical problem may be solved by very different program codes whose mutual equivalence remains elusive without knowledge about the receiver, namely the rules how to compile and execute the code and to convert the message back into structural information. This position differs from opinions like that of the sharp thinker [PERSON] ([46] p. 50) that \"we may say... without any dogmatic assumption that psychical effects can all be _reduced_ to physical motion\". 9. Added redundancy, such as partial repetition or embedded grammatical rules combined with orthographic vocabularies, leaves the meaning of symbolic information immediately unaffected but allows additional information-protection tools to evolve for _error-detection_ and _-correction_ of random perturbations. During later stages after the ritualization, such tools partially counteract the neutral drift of symbols and construct the set of available Goldstone modes. About half of written English text represents syntactic redundancy [47]. 10. Information processing of discrete symbols is performed by digital computers of any physical kind. Although [PERSON] asserted, \"This special property of digital computers, that they can mimic any discrete state machine, is described by saying that they are _universal_ machines\" ([48] p. 441), this is not true because digital computers cannot simulate (mimic) discrete state machines with an infinite number of states. Some think that computational universality suggests the possibility of simulating the human brain on an electronic computer [49]. However, this is also incorrect because nobody proved that the human brain is a discrete state machine. Moreover, it was demonstrated that even universal Turing machines are not _universal_ in the realm of algorithms and automata because there are super-recursive algorithms, which are more powerful than any Turing machine [50; 51]. Code symmetry, or coding invariance, is a key property of symbolic information that can be established after a complete ritualization transition. The physical carriers of symbols possess structural information apart from their symbolic meaning. Their physical structures maintain percessions of the symbols' evolution history over a certain characteristic relaxation time until random noise in the language development erases those traces. Symbolic information has a number of general properties ([PERSON] and [PERSON], 2011):  
1. Symbolic information systems possess a kind a partial symmetry, the carrier invariance In many situations, it is possible to copy information without loss to other carriers or to multiply it in the form of an unlimited number of physical instances. The information content seems independent of the physical carrier used. However, many linguists doubt a possibility of exact translation of the text from one natural language to another one (cf. for example, [52; 53]). This problem is also apparent as the absence of automatic translators between high-level programming languages, such as Fortran, Pascal, or C, demonstrates. 2. Symbolic information systems possess a new symmetry, the coding invariance. The functionality of the processing system is unaffected by substitution of symbols by other symbols as long as unambiguous bidirectional conversion remains possible.