Terminology: Communication needs meeting of Languages. Communication is a base for Languages. Communication as a base itself forms a Language. Thus, Communication is Language. Thus the program may be renamed as LangLang Program. I am interested in a broader category of Languages than those currently seen as Language. I would like to use the word Language to be any structure used to represent knowledge. As in usual usage, when both language and knowledge are specified, a particular language will be used to represent the specific knowledge. To clarify again: whenever I use the word ‘Language’ with a capital L, I mean anything that we use to represent knowledge. I loosely refer to anything specific (already represened in some Language) that we would like to represent (in another Language) as ‘knowledge’, with a small k.

Language

Language is seen in different forms. Language and representations of knowledge using Language are to be identified. Language is structure, structure is Language. Structure and its inherent Duality are seen as fundamental to Language.

Program

Unify (Identify) various Languages by creating connections from one Language to another. Once the unification is done, reverse mapping one form of a Language to another to see the diversity in expression of forms through various Languages.

Currently the Fundamental Base Language is that of Identity. Identity takes froms as Dualities, the simplest example of which is \((-x)(x+)=0\) or \(x=x\). In the language of Symmetry, the simplest form is Reflection. In the language of Groups, the simplest form is \(S^0\) or \(\mathbb{Z}_2\).

How to map other Languages back to Identity? That is the program: to provide a base (form closest to identity) for each Language and then connecting back all the basis to Identity. These are relative and can change depending on circumstances, which means, the base for different people may be different. A high school student may have a different base than an expert in a specialized area. It is one’s own responsibility to choose the base with which one is most comfortable. The most commonly recognized base for each Language is mentioned below so that the mapping is quick. For visualization look at Language of Nature (Physics), for concrete communication, start from Language of Mathematics.

There are many examples of Identification which each person does at several levels. I highlight those which are well known to many people so that most people can identify with the process.

  • Reading : We identify several alphabets together into a single word. The word is unification of letters. Similarly, a sentence is another level of unification which identifies several words together as a whole. The Paragraph is identification of Sentences.

  • Friends : Identifying people is a unification. We form groups by Identification. We form Networks by identification.

  • Balance : Balancing two different objects on either side requires connecting them by a common support.

  • Waves : Identifying droplets of water together to see a wave is a unification.

  • Algebra : The symbol \(x\) identifies various values. For instance, various Numbers such as 1,2,3,.. are identified as a single symbol \(x\) in Algebra. This is process is unification or Identification. In Calculus, the word “Integration” is used for the same. In Group Theory, symmetry or simply group is the word used. Groups can be differentiated to give Fields. Looking at it the other way round, Fields connect two groups. Commutative Algebra can be differentiated to give Non-Commutative Algebra. Looking at it the other way round, Non-commutative algebra connects two sides that are individually commutative to produce a new non-commutative algebra.

  • Calculus : Integration connects various forms. Differentiation is the separation of Identity into various forms. Looking at it the other way round, various identities are connected by differentiation to give a New Identity.

The Base in the Language of:

  • Mathematics : Symmetry (Groups). Classifying Simple Groups (Calculus being the simplest one). Complete list of finite simple groups.

    • Reflection: Groups are identified by their symmetry and symmetries can be seen as composition of reflections.

    • Simple Calculus (Differentiation and Integration) is mapped to Groups in previous post Calculus Group Language. Category Theory is to be mapped to Representation Theory. Harmonic Analysis and Fourier Analysis are connected.

    • Langlands Program is an integral part of this.

    • Geometry: Euclidean Geometry, Hyperbolic, Riemannian Geometry are to be identified.

    • Algebraic Geometry : Algebra and Geometry are identified.

    • Combinatorics : Counting is identified with geometry, algebra and representations. Measure is to be identified as counting.

  • Nature (Physics) : Mass Balance.

    • In this Language, mass takes various forms such as Energy, Temperature, Frequency, and so on.

    • Thermodynamics, which is seen as a Mass Balance in a previous post Intensive-Extensive Duality in Thermodynamics as Mass Balance. Phase Transformations is Thermodynamics.

    • I will update a post on how to identify Quantum Mechanics as Thermodynamics. This involves reinterpreting Quantum Mechanics without probability. Every Quantum Mechanical wave is identified as a composition of Eigenfunctions with appropriate amplitudes and a “Phase Mixture percentage” is the amplitude correspoding to each Eigenfunction as a Phase. The Reflection (dual) to the Wavefunction is its Adjoint.

    • General Relativity is identified as Space-time Duality composed with Energy-mass Duality. This reduces the Metric to Energy functional and the equilibrium condition as the Light Cone. Hence General Relativity is Identified with Thermodynamics to be seen as a Mass Balance. Gravity is identified as the fabric of Space-time itself.

    • String Theory : Gravity is the fabric. Strings are threaded together to form the fabric. Space-time is identified as the Fabric and strings as the units from which the fabric is made. Strings represent Duality. Hence String Theory can be identified as a Mass Balance.

  • Materials Science : Phase Diagrams (Phase Transformations)

    • Materials can be classified into their Phases. Phase Transformations is Thermodynamics. Hence Materials Science can be identified as Mass Balance through Thermodynamics.

  • Art: Composition (Symmetry)

  • Psychology : Balancing Subconscious and Conscious.

  • Story : Script.

    • Director is the base to compose everone together. Recognizes the characters as parts which compose together to tell a common story.

    • Actors see the Script through the Director’s vision. They identify themself with the character.

  • Symbolic Language : Binary.

    • Symbols can be identified as duals to reduce them to binary.

  • Natural Language: Vowels

    • Sanskrit, English, Marathi, Hindi and so on reduced to vowels.

Physics

Nature is Symmetry. Language of Physics is aware of the Language of Symmetry and displays it in various forms. We may reinterpret all Physics in terms of symmetry. This is best done by connecting Theories of Physics to Thermodynamics. Further, I have shown Thermodynamics to be a mass balance Equilibrium Themrodynamics.

Group theory in Mathematics captures the same concept: Symmetry which translates to “same measure” is really about how to balance measure (which is mass). In thermodynamics Energy (E) is the identity which gets partitioned into various forms and in Group theory “e” is the identity which gets divided (form of partitioning) into various forms (seen in Calculus Group Language).

The respective Language Masters and Translators may use these basis to thread together groups. The comments section is open and the tags for every post are useful to navigate.