Metaphoric Algebra vs. Classic Algebra


  • Greater Context
  • From Equation-like Statements to Metaphoric Algebra
  • Life’s Dynamic Systems require a Different Algebra
  • Metaphoric Algebra: Comparing System Logic
  • Primacy of the System
  • Islamic History & Meaning of Algebra
  • Classic vs. Metaphoric Algebra: Affinities & Differences
  • Metaphoric Algebra: Notation
  • Basic Equivalency Rules #1 & #2
  • Cultural Holism: Personal Writing Example
  • #3: Must specify Nature of Metaphoric relationships
  • #4 Subsystems may employ incompatible Logics
  • Molecules ≠ Building Blocks of Cells
  • Metaphoric Logic & Algebra built into Humans
  • Don edit entire chapter 5-30-21

    Greater Context

    Throughout this work, we have developed a singular theme. Life has a substantial material side and an insubstantial experiential side. Rather than isolated parallel dimensions, we can envision Life’s two components as belonging to intersecting orthogonal1 planes. However, this metaphor is still lacking as Life’s substantial and insubstantial sides don’t just intersect, but actually interact. Due to this interaction, we have called these realms of existence, rather than planes. The Material Realm is the name we have given to the physical side. Because Attention generates Life’s insubstantial side, we have called it the Realm of Attention.

    Over these many pages and in some to come, this work has identified many qualitative differences between the two realms of existence. Some of these are listed in the following table.

    Material Realms


    Atomistic System

    Holistic System


    Not Reductionist


    Not Set-based

    Regular Equations

    Reflexive Equations




    Monitor and Adjust





    Time’s Horizontal Dimension

    Time’s Vertical Dimension

    Reacts to Information

    Interacts with Information

    Consists of Elements

    Consists of Systems

    Fragile Deductive Logic

    Anti-fragile Metaphoric Logic

    Summarizing some salient points: The Material Realm consists of clearly defined elements, e.g. electrons and molecules. Due to this feature, this realm is subject to the rigid laws of Deduction, set logic and Regular Equations. Founded upon this same logic, Classic Algebra is the ideal mathematical language for the Realms of Matter.

     Rather than elements, Life’s Realm of Attention consists of dynamic systems. We understand these systems by a comparison with other systems. Rather than fragile Deduction, whose logic is invalidated by a single exception, Life employs anti-fragile Metaphoric Logic to compare systems. The conclusions of this stable form of logic actually get stronger with the stressors of time.

    To succinctly summarize and derive general conclusions, the Realm of Attention requires its own algebra to accompany Attention’s Metaphoric Logic. This article develops the symbolic notation and equivalency rules of Metaphoric Algebra.

    From Equation-like Statements to Metaphoric Algebra

    Don edit 5-21-21: 5-24-21

    Equation-like statements allow me to say more with less

    I frequently employ equation-like statements to summarize and highlight my conclusions. Don’t be misled by their form. My equation-like statements do not represent the deductive accuracy of traditional equations. However, the conciseness of the one-line propositions enables me to say more with less.

    The precision of these equation-like statements is between equations and statements. More general than one and more specific than the other. Despite their fuzziness, I find the brevity of these statements very useful in crystallizing conclusions and comparing statements.

    I employ this mode of communication in many contexts. This article will focus upon the use of equation-like statements to compare the logic of systems. Humans regularly employ this type of comparison to form abstract thought. Due to the importance of this type of logic in the following discussions, we have developed a specific notation and will even suggest some useful rules for what we call Metaphoric Algebra.

    Life’s Dynamic Systems require a Different Algebra

    The intrinsic logic of Matter and the intrinsic logic of Attention are incompatible in three ways: type of 1) system, 2) mathematics, and 3) logic. (Developed in previous articles). Because of these fundamental differences, Matter and Attention also require different types of algebra to describe their respective systems. Like the rest, these algebras are also incompatible (≠) – shown in the following equation-like statement.

    Matter Algebra ≠ Attention Algebra

    2 Algebras?

    I know what you are thinking. “How can there be two algebras? There is a mathematical discipline called algebra.”

    Broadening definition to facilitate communication of difficult topic

    Well as usual2, I’m broadening the definition of algebra to explain and justify my peculiar mode of communication.

    Hey I’m sorry. I’ve got a difficult topic to explain – took me at least separate 4 volumes composed over a lifetime to make my point. Plus, my Person is not gifted as a writer. Sometimes, he just thinks in symbols – algebraic-like equations or even diagrams. He leans on these to bring brevity and clarity to his confused verbiage. Summarizes key points in a simple form.

    What is algebra? Webster’s Collegiate Dictionary defines algebra as:

    “That branch of mathematics which treats of the relations and properties of numbers by means of letters, signs of operation, and other symbols, including solution of equations.”

    Expanded Definition: Symbols to succinctly express relationships

    My Expanded Definition of Algebra: The use of simplified notation and symbols to more succinctly express relationships between factors/components. No sentences, paragraphs, or chapters. Algebraic statements, i.e. equations, consist of just a single line. The equations can be grouped together to make comparisons and draw conclusions. (More on this topic later.)

    Difference between 2 algebras revolves around identity

    What’s the difference between my algebra, i.e. the symbolic statements I use to clarify my work, and the traditional algebra that many of us learned in school. It revolves around the concept of identity.

    Classic Algebra: Symbols precisely defined – must remove senses

    The symbols in traditional algebra have an identity that is precisely defined, no ambiguity whatsoever. In fact, one of the thrusts of modern algebra was to remove the senses, especially sight, from the evaluation of identity – due to its subjectivity. Under these criterion, Euclid’s Elements failed to make the cut – had to be rewritten in the modern unambiguous symbol laden form.

    Precision necessary due to reliance upon Deduction with Unassailable Assumptions

    This precision was considered necessary due to Classic Algebra’s absolute reliance upon Deduction. If assumptions are ambiguous or questionable, deductive conclusions are equally challenged.

    Questionable Assumptions -> Questionable Conclusions

    Popper: Fragility of Classic Logic. Only certainty Via Negativa

    Karl Popper spent his illustrious career illustrating the fragility of traditional logic. He eventually came to the conclusion that the only thing we can know for certain are propositions that we can disprove. Via Negativa. I don’t know what God is, but I know he’s not that. Buddhism: our Self is not what we think it to be; we know it is not that.

    Classic Algebra perfect for Material Realms where absolute essences à Unassailable Assumptions

    Deduction’s fragility is not a problem in the Material Realms. In both the Molecular and Subatomic Realms, it is possible to make unassailable assumptions due to the many absolute essences, e.g. electrons, hydrogen atoms, and water molecules. Because these so-called particles can be precisely defined and quantified, Classic Algebra is perfect for the material world. This symbolic language provided scientists, mathematicians and engineers with the logical certainty they craved.

    Unsuccessful application of Classic Algebra to Attention Realm

    Buoyed by their triumphs in the Material Realms, they attempted to apply this perfectly successful mathematical technique (algebra) to the living Realm of Attention. A dismal failure. A mismatch made in Heaven. Algebra’s mathematical language seemed to be incompatible (≠) with Attention – like using the language of Physics to describe cooking.

    Classic Algebra ≠ Attention

    Identity in Attention Realm is fuzzy

    If appropriate for Matter, why not Attention? Data streams are the stuff of the Attention Realm. Our information digestion system consumes data streams. Rather than the distinct identity of objects or particles like quarks or molecules, the identity of a data stream is filled with nebulous propensity. Although possessing a center, Data Stream Identity is more of a cloud and less of a thing. Everything in the Living Realm is based in the digestion of data streams – even ideas and concepts. As such, everything in this Realm has a fuzzy DS Identity, not a precise Material Identity.

    To complicate matters, the Attention Realm is a holistic system, where the meaning of the parts is determined by their contextual relationship to the whole. As such, a data stream’s fuzzy identify is not even independent of surroundings, as is, for instance, the eternal hydrogen atom. Rather a data stream’s meaning/value is assigned by Feelings. And as we all know, Feelings are dependent upon a constantly changing context.

    Fuzzy Identity à Fuzzy Assumptions: Classic Algebra inappropriate language

    This inherent fuzziness of identity in the Attention Realm makes it virtually impossible to make unassailable assumptions. Because of the necessity of absolutely precise assumptions, the conclusions of Deductive logic are highly fragile when it comes to Life’s Attention related phenomena. Due to this inability to deal with fuzziness of any sort, the language of Classic Algebra is inappropriate for Attention.

    Attention requires Fuzzy Algebra that compares Logic of Systems, not objects

    Because of this fundamental difference between Living Identity and Material Identity, Living and Material systems require different algebras. Rather than the precise algebra of Matter, Life requires a fuzzy algebra.

    Metaphoric Algebra: Comparing System Logic

    What will this fuzzy algebra look like? Rather than the quantifiable features of objects, this algebra compares the logic of systems. Why?

    Living systems are holistic, while material systems are atomistic. In holistic systems, the parts are defined by their relationship to the whole – perhaps their function in a process. In some ways, the parts have no meaning except in relationship to the system they belong to. As such, how the system operates, i.e. relationships between parts, is much more important than its elements. This is the implicit logic of the system.

    How do we understand the nature of this system’s logic?

    Humans employ the implicit logic of a known system to understand the implicit logic of an unknown system. When mathematical systems are involved, there is frequently a feedback loop of understanding with each informing the other. We call this type of reasoning Metaphoric Logic.

    Life has two types of digestive systems – one for physical food and the other for information. The information digestion system consists of interlocking processes rather than things. The mathematics of the LA is compatible (≈) with these systems; they have an affinity.

    Identifying the quality and nature of the metaphorical relationships between these systems, one living and the other mathematical, is more fruitful than examining the content of the components, as they don’t really exist. For this task, we have developed a notation modeled after Classic Algebra. Metaphoric Algebra is the name we have given to this mode of communication – this symbolic language.

    Let us be up front. Despite its name, Metaphoric Algebra is not mathematics. It is a succinct form of communication that is modeled after the mathematical language of algebra.

    Why is not mathematics? Each symbol in the equations of Classic Algebra has an exact and particular meaning. The definitions and equations are not debatable.

    In contrast, the equation-like statements of Metaphoric Algebra contain verbal concepts as well as symbols. The symbols refer to loosely defined operations and equivalency statements. They have an approximate and general meaning. Due to these many ambiguities, the statements of Metaphoric Algebra are debatable – not mathematical at all.

    Further, systems have many features. It is essential to identify which features of the systems are being compared. Some features of each system are compatible (≈) and some are incompatible (≠).

    Despite these limits, Metaphoric Algebra is still a useful form of communication. The brevity and clarity of this algebraic mode of expression both crystallizes positions and narrows the debate by identifying specific issues.

    Primacy of the System

    Before proceeding forth into history and notation, let us briefly discuss how the system dominates in a holistic system. This is in contrast to atomistic systems, where the parts dominate.

    In holistic systems, the system determines the outcome, not the participants. For instance when a conquering culture adopts the indigenous political system, they are gradually assimilated and the system remains the same – injustices and advantages. When the Mongols or Manchus conquered China, they adopted the Chinese bureaucracy and gradually became part of the traditional ruling class. Existence for the agricultural peasantry continued to be difficult. Despite a change of cultural leadership, life remained unchanged for the bulk of the population.

    In order to institute any real changes, the political system must change, not just the leadership. It was only after the Communist system was instituted in China and Cuba that the precarious plight of the peasantry was improved.

    Holistic systems have a purpose, even if just to survive. Conversely, atomistic systems have no innate purpose, only that which we assign. For example, the water molecule has no innate purpose in the Universe’s atomistic system. However, when water joins a holistic system, it is assigned meaning and purpose. This purpose is not innate to the water molecule, but is rather determined by its function in the system. The system determines the purpose.

    For instance, in the respiratory system, the purpose of water is to sweat and evaporate, thereby cooling the body. Its function is to assist in the regulation of our internal temperature – act as an air conditioner. When in our elimination system, the same water molecules are meant to flush waste products. When in our circulatory system, water is the vehicle that carries blood through our capillaries and veins.

    The holistic system determines the purpose, and this function determines the form.

    System -> Purpose/Function -> Form

    In contrast, Matter’s atomistic systems have no purpose, hence no innate form. Rather the innate qualities of the parts determine the types of structures and interactions that can occur. A problem occurs when the logic of atomistic systems, in this case purposeless and meaningless, is misapplied to holistic systems, which have innate purpose and meaning.

    Due to the crucial importance of systems in determining function and form, it is important to study holistic systems in their own right, independent of the parts. Metaphoric Logic and Algebra attempt to fulfill this role – a logic that compares systems accompanied by a simplified symbolic notation.

    Islamic History & Meaning of Algebra

    Don edit 5-23-21

    If Metaphoric Algebra is not mathematics, why do we call this mode of communication an ‘algebra’? To answer this question, let us examine the history of algebra to better understand the meaning of the term.

    In 820 AD, al-Kwarismi, a Persian living in Baghdad during the Golden Age of the Islamic Empire, wrote a book that is foundational for mathematics and, by extension, science. The English name of al-Kwarismi’s classic text is Compendium on Calculating by Completion and Balancing. ‘Al-gabor’, the Arabic word for ‘completion’ in the title eventually became ‘algebra’ in the mathematical/scientific community of Western European. This cultural spreading center disseminated this marvelous technique to the rest of the world.

    What was the primary contribution of al-Kwarismi’s famous work? The manipulation of equations consisting of abstract symbols that represent numbers and processes. ‘Balancing’ in the book’s title refers to a process that is known to every student who has taken algebra: ‘balancing the two sides of the equation’. Whatever is done to one side of the equation must also be done to the other.

    The term ‘completion’ referred to the inherent equivalence of the two halves of the aptly named equation, the equal = symbol.

    In the attempt to stay somewhat true to the original meaning of the word algebra, our Metaphorical Algebra also has some rules for equivalences of equations. However, there are a few differences between the two types of algebra that we must take into consideration.

    1) The symbols and words in our equation-like algebraic statements represent a system’s logic rather than numbers.

    2) An approximation sign (≈) replaces the equal sign (=) in our equations. Metaphoric relationships are never exact. Rather than equal, two systems can be compatible (≈). This means that the logic of the two systems has many similarities.

    3) Two systems can also be incompatible (≠). This means that the implicit logic of the two systems is dissimilar. The two systems are filled with discrepancies, sharing few if any similarities.

    Classic vs. Metaphoric Algebra: Affinities & Differences

    Don edit 5-23-21

    Despite these differences, al-Kwarismi’s Classic Algebra is compatible (≈) with Metaphoric Algebra in three fundamental ways.

    1) The two systems employ succinct abstract symbolic notation, rather than words, to stand for operations and relationships between general concepts.

    2) Both systems are based upon equivalencies/equations.

    3) In both systems, equivalency rules enable us to draw general conclusions that apply to the particular.

    These three fundamental compatibilities justify employing the term algebra to our symbolic treatment of Metaphoric Logic.

    The two algebraic systems have a strong metaphoric relationship in terms of the use of symbolic notation, equations and proofs. However, they have some distinct differences, as is expected in any metaphoric relationship. Some of these differences are listed below.

    1) Classic algebra deals primarily with numbers. Metaphoric algebra deals with systems.

    2) Classic algebra relies upon inviolable deduction to arrive at necessary conclusions. Metaphoric algebra relies upon deductive reasoning to arrive at pragmatic conclusions.

    3) The proofs of classic algebra are always true – forever and ever, Amen. The proofs of metaphoric algebra are suggestive and pragmatic.

    4) Classic algebra applies to exclusively material systems. Humans actually employ metaphoric logic along with the equivalency rules to form abstractions with which they can better understand and thereby anticipate reality. As such metaphoric algebra can assist in the understanding of how humans reason and make choices. For instance, the sloppy misapplication of the equivalency rules can lead to serious misconceptions.

    Rather than invalidating the compatible metaphoric relationship between the two algebras, these differences act to qualify/refine the metaphor. The metaphor is founded on symbolic notation, equivalencies, and proofs. Content, logical rigor and applications are not part of the ‘algebra’ metaphor.

    Metaphoric Algebra: Notation

    Don Edit 5-23-21

    To justify the conclusions regarding my ID model, I found it necessary to develop a fresh, anti-fragile logic. Metaphoric Logic is the name we gave to this fresh logic. In turn, we developed a new symbolic notation (equation-like statements) to characterize the new type of logic.

    Let us examine how these equation-like statements capture the relationships in Metaphoric Logic. Let us start with notation.

    A ≈ B: System A has a strong metaphoric relationship with System B.

    A strong Metaphoric relationship indicates that the components of two different systems interact with a similar logic. We employ the approximate symbol (≈) because metaphoric relationships are never exact.

    A ≠ B: System A has a weak metaphoric relationship with System B.

    Another way of stating the metaphoric relationship: Systems A and B are incompatible (≠) or compatible (≈). In this case (≠), the two systems have virtually nothing in common.

    A = B + C: System A consists of two systems, B and C.

    The addition symbol (+) indicates that the relationship is additive rather than interactive.

    A = B x C: System A consists of the interaction between systems B & C.

    The multiplication symbol (x) indicates an interaction between two systems.

    A = B: Two systems are equal.

    In terms of metaphoric logic, the only time this statement is true is when A and B are the same system, as metaphoric relationships are never exact. As such, it could be considered a tautology.

    A -> B: There is a one-way interaction between System A and System B.

    System A acts upon System B, but not vice-versa. The arrow of influence only points one way, as in an unhealthy partnership. The arrow symbol (à) could also indicate an If-Then statement. If A, then B.

    A <-> B: There is two-way interaction between System A and System B.

    Rather than a one-way relationship, the influence goes both directions, as in a healthy parent-child relationship.

    A = ƒ (B): System A is a function of System B.

    The function symbol (ƒ) indicates that the operation of System B is a factor in the operation of System A. It is not necessarily the only factor. Another meaning: the processes of System B influence System A.

    A = ƒ (B, C): System A is a function of both System B and C

    This representation just indicates that multiple factors from two systems, B and C, influence the third system, A.

    ? A: Phenomenon A is a scientific mystery.

    The question mark symbol indicates that the scientific community has yet to reach a universal consensus regarding causes of the phenomena in question. The phenomenon is not a mystery, but rather a well-established fact. For instance, the reason for sleep remains a mystery.

    ! A: Phenomenon A is a scientific fact.

    The explanation point symbol (!) indicates that there is widespread consensus in the scientific community regarding the existence of a specific phenomenon. A scientific fact can also be a scientific mystery.

    The brevity of these algebraic expressions has many advantages. After all, less is more, maybe even everything. A profusion of words can easily be distracting, even confusing. Abbreviating these many paragraphs and sentences into a single statement can more easily crystallize illumination. The precision enables the Reader to better understand my position. The algebraic brevity enhances clarity. With clarity, it is easier to agree with, refine or challenge my propositions.

    Basic Equivalency Rules #1 & #2

    Don edit 5-24-21

    Metaphoric Algebra succinct way of communicating to facilitate understanding

    Metaphoric Algebra is a concise/succinct way of communicating complex ideas without the excess verbiage that frequently confuses rather than clarifies. To this end we employ some symbols from traditional algebra to make our points. Our reduction aims at simplicity that says so much. Less is more, perhaps everything.

    Metaphoric Algebra compares systems, not quantifiable entities

    The deductive rigor of traditional Algebra cannot be applied to Metaphoric Algebra. Metaphoric Algebra compares the metaphoric relationship between systems, not quantifiable entities (numerical relationships). The metaphors are conceptual, rather than literary.

    Conceptual: not surface similarities, Rather the logic of systems

    Let us not confuse the ordinary literary metaphor with these conceptual metaphors. Rather than comparing surface similarities (blue eyes with the sky), conceptual metaphors compare and relate the logic of systems. Every system has its own logic, which may or may not be applicable to another system. For instance pack logic with its top dog and under dog might be applicable to human group logic, but probably not to insect or plant logic.

    ≈ useful metaphoric relation, ≠ no metaphoric relationship, metaphor no =

    Because metaphors are never exact, we rarely employ the equal sign (=). Rather we employ the approximate sign (≈) to indicate that two systems are compatible, i.e. the metaphoric relationship between the two systems is close enough (has enough parallels) to facilitate understanding. Conversely we employ the unequal sign (≠) to indicate that two systems are incompatible, i.e. there is no metaphoric relationship between the two systems, or it is so weak as to be misleading rather than facilitating.

    A distinct feature of Classic Algebra is the ability to draw conclusions based upon the manipulation of equivalencies. This ‘balancing and completing’ of equations is the essence of the mathematical proof. Metaphoric Algebra also enables proof-like conclusions. Although not as precise as her older brother, Metaphoric Algebra does have some equivalency rules that are useful when comparing the logic of two systems. These equivalency rules enable us to draw some practical, if not necessary conclusions.

    We will first delineate the main Equivalency rules and then will provide some examples.

    Rule #1: The first rule is straightforward. If two systems, A and B, are logically compatible (≈) and one of these systems (B) is incompatible with another system, C, then System A is also incompatible with System C.

    If A ≈ B

    And B ≠ C,

    Then A ≠ C

    Rule #2: If two systems, A and B, are logically compatible (≈) and one of these systems (B) is compatible with another system, C, then System A is also compatible with System C.

    If A ≈ B

    And A ≈ C,

    Then B ≈ C

    General Examples: Following are some relevant examples of the equivalency rules in action. These constructive applications employ a syllogistic-form. If the first few propositions are true, then the concluding propositions are also true.

    1) Atomistic ≠ Holistic

    2) Atomistic ≈ Matter,

    3) Then Holistic ≠ Matter


    4) If Holistic ≈ Attention,

    5) Then Atomistic ≠ Attention

    6) And Matter ≠ Attention.

    The first syllogistic series is incontrovertible. Atomistic and holistic systems are logically incompatible due the relationship between the parts and the whole. In the first, the nature of the parts determines the nature of the whole. In the second, the nature of the whole determines the nature of the parts.

    Reductionist atomistic logic is compatible with Matter, as witnessed by modern technology. Applying Rule #1, we can safely conclude that the logic of Matter is incompatible with the logic of Holistic Systems.

    The second syllogism requires some justification. First, let us summarize the logic. Proposition 4 supposes that Attention belongs to a holistic system. Applying Rule #1 to Propositions 1 and 4, we can safely conclude that Attention does not belong to an Atomistic system. Applying Rule #1 to Propositions 2 and 5, we can safely conclude that the implicit logic of Matter and Attention are incompatible.

    What is the significance? For a mathematical system to effectively model a system, they must have compatible logic. Because of the incompatibility of their logic, the two systems (Matter and Attention) require mathematical systems that are incompatible.

    Elsewhere, we have developed the notion that Matter is best served by mathematical systems that are based in Regular set-based Equations. In contrast, Attention is best served by mathematical systems that are based in Reflexive Equations, such as the Living Algorithm.

    Cultural Holism: Personal Writing Example

    Don edit 5-24-21

    What is our justification for supposing that Attention belongs to a holistic system?

    By Attention we mean the Attention Synergy of our ID System. This Synergy specializes in generating meaningful Experiences and weeding our extraneous noise. The meaning of each Experience, its significance, can only be determined, not by its physical content, but by its contextual relationship to the whole. Although based in a physical substrate, the meaning or value of Experiences is not physical.

    Personal Example: Today’s writing (Metaphoric Algebra) can only be understood via its contextual relation to my scientific opus (Metaphoric Logic is very important for my Science.) In turn, my Opus only has meaning in its relationship with the greater culture. The act of writing is actually meaningless without a greater cultural context. Further, this context is not merely determined by what’s happening currently in 2021. To understand the significance, one must understand the entirety of society as it extends millennia into the past when humans began writing down their thoughts/inspiration regarding the Nature of Reality, or reversed, the Reality of Nature.

    Babylonians, Egyptians, Greeks, Indians, Muslims, Europeans, and Americans have all laid the groundwork for my insights regarding the Info Digestion System. In this case, my holistic system extends from current human culture deep into our distant past. There is no way of understanding the significance of the words that I am composing via the atomistic reductionism that works so well with atoms, electrons and molecules. Rather a deep cultural context is necessary in order to understand the verbal content of this work.

    In fact, the prime obstacle to transmission is the lack of cultural depth – the prevalent short-sighted perspective. Ah well. Fame and fortune are false ego-based desires. Bless the Gods for my role.

    #3: Must specify Nature of Metaphoric relationships

    Don edit 5-24-21

    Rule #3: The metaphoric relationship must be qualified. Before ‘deriving any proofs’ from these rules, certain questions must be answered. Which features, both elements and processes, are compatible or incompatible? What is the significance? Due to the verbal component of our ‘algebra’, examples are a must. Numbers are sharp, while words are necessarily fuzzy.

    Example: Our discussion of the metaphoric relationship of the two algebras provides a good example. The two algebras are compatible with regards to symbolic notation, equivalencies, and proofs; but are incompatible with regards to content, rigor, and type of reasoning. Some might say that the incompatibilities outweigh the compatibilities, or vice versa. Regardless of the weight (the value) that is assigned to each factor, the conclusions are valid as long as the factors are clearly identified.

    For instance, it is important to make it clear that I employ the term ‘algebra’ to describe my unusual notational system, not because it is equivalent to Classic Algebra, but rather because the system is algebra-like in three significant ways: use of symbols, equation-like equivalencies, and syllogistic-like proofs. These features are significant to me, as I will rely upon them in my upcoming examples.

    Sorry for all the peculiar verbiage. I’m just attempting to communicate a little more precisely, so that it is easier to agree or disagree with my conclusions.

    #4 Subsystems may employ incompatible Logics

    Don edit 5-29-21

    Rule 4: The subsystems of the same system may employ incompatible logics. Suppose that System A consists of subsystems D and E.  It doesn’t necessarily follow that Subsystem D ≈ Subsystem E.

    For instance, Living systems consist of the interaction between Attention and Matter, i.e. two interacting subsystems. Matter belongs to an atomistic system, while Attention belongs to a holistic system. Holistic and atomistic systems are incompatible. Therefore, Life’s two subsystems, i.e. Matter and Attention, are also logically incompatible.

    Life’s (Matter) ≈ Atomistic

    Life’s (Attention) ≈ Holistic

    But Holistic ≠ Atomistic

    Matter ≠ Attention

    Due to this unusual feature, i.e. two incompatible (≠) subsystems (Matter and Attention), Life consists of a logical duality. Extreme caution must be taken when applying a conceptual metaphor to a logical duality. Frequently, if not usually, a metaphor can apply to one part of the duality or the other, but not both. To avoid this confusion/fallacy, extreme diligence must be exercised when identifying correspondences between systems (Rule 3). It is essential to clearly identify where the metaphor is instructive and where it breaks down.

    Molecules ≠ Building Blocks of Cells

    Don edit 5-29-21

    Brilliant people, both scientists and philosophers, regularly employ fallacious metaphorical reasoning to justify their position and investigation. In other words, a model/metaphor that is useful under one set of factors is employed indiscriminately and inappropriately to link systems that are incompatible.

    For example: the building block metaphor facilitates the understanding of great swatches of reality. Due to its usefulness in one context, intellectuals inappropriately apply it to other circumstances where the model is out of place. Rather than merely inappropriate, this metaphor obscures fundamental differences by creating a mental filter, an inviolable frame that muddies the mirror of the Mind.

     The basic building block metaphor: Fundamental elements are assembled to make grander structures that have emergent properties. The metaphor is a useful way of understanding the phenomenon of emergence, where an accumulation or combination of parts has qualities that the individual parts do not have. For instance, copper and tin, soft metals, are blended to create bronze, a hard metal.

    Under this model’s logic, atoms are definitely the building blocks of molecules, which are in turn the building blocks of the stuff of our material world, e.g. tables and food. Each level of the hierarchical structure has emergent properties that weren’t there in the preceding level. Combining a few hydrogen and oxygen atoms together makes water, which collects to form lakes and oceans. Each level has its own unique identity.

    The same metaphoric logic applies to cells. Cells are definitely the building blocks of life. Cells combine to form multi-cellular organisms. These organisms have emergent properties that are unimaginable in the lowly single celled bacterium, e.g. the ability to sense color and to feel emotions.

    However, just because atoms and cells are the building blocks of Matter and Life respectively, it doesn’t follow that atoms are the building blocks of cells. Atoms, as their name implies, belong to an atomistic system. Conversely, cells belong to a holistic system. Just because the building block metaphor works internally in each system doesn’t mean that it works between systems.

    In fact, it can’t, at least in this case. Atoms can build upon each other to build elaborate atomistic systems, but not to build holistic systems such as cells belong to. Some other factor must be at play that is independent of matter.

    Molecules ≈ Building Blocks of Matter

    Cells ≈ Building Blocks of Life

    Molecules ≈ Atomistic

    And Cell ≈ Holistic

    Atomistic ≠ Holistic.

    Therefore, Molecules ≠ Building Blocks of Cells

    The building block metaphor is based around the notion that the building blocks are made up of the same stuff as the elaborate structures that have emergent properties. Although the pyramids are taller and enclose space, they are still only made up of sandstone blocks. Tables consist only of atoms and molecules. There are no secret ingredients.

    While molecules and atoms consist of substance, cells are defined by their organic systems. Although cells consist in part of atomistic subsystems (Life’s material component), cells are essentially holistic. Even the atomistic subsystems only have meaning in relationship to the entire living system. While it is convenient to think of atoms and molecules adding up to create cells, the metaphor breaks down when considering that the survival of cells, while consisting of molecules, is dependent upon the healthy functioning of multiple holistic systems. (This topic is treated more thoroughly in the chapter on the building block metaphor.)

    Metaphoric Logic & Algebra built into Humans

    Don edit 5-30-21

    Let us summarize our position. Matter belongs to an atomistic system, while Attention belongs to a holistic system. The underlying logical structure of these system types is incompatible. Therefore, the two systems, Matter and Attention, require a different mathematical language.

    Matter consists of atomistic elements – the particles underlying substance. Attention consists of holistic systems – the processes that ensure survival as a collective unit. The mathematical language of Classic Algebra specializes in the relationships between atomistic elements. The mathematical language of Metaphoric Algebra specializes in the relationships between holistic systems.

    But let us be clear. Metaphoric Logic and Algebra are not new. In fact, they are built into our neurological substructure, and I imagine other life forms as well. But I’m not sure, as this type of logic is the basis of abstract thought, which seems to be somewhat unique to our human species.

    We regularly employ the underlying logic of a known system to understand the underlying logic of an unknown system. (Metaphoric Logic.) Sometimes this process even entails a type of feedback loop, where each informs the other. We intuitively know that if one system has affinities with two other systems, then these two systems probably have an affinity with each other. Conversely, if two systems are incompatible (enemies), we strongly suspect that they are incompatible with each other’s allies. (Metaphoric Equivalencies.)

    So all this talk of algebra, metaphors, and logic is just a rough formalization of logical processes that are already in place. The same logic holds true for the LA’s relationship with our ID system’s image overlay process. The LA is not new, but just a mathematical realization of an ongoing process.

    The algebra-like notation associated with Metaphoric Logic is just a simplified method for understanding the logical processes that we go through every day of our lives. The notation is a recognition – a symbolic realization of how we engage with and understand the logic of our world. This knowledge enables us to better anticipate, hence optimize our response to environmental stimuli. Else why would Nature (evolution) have endowed us with this special capability.


    1 Our terminology and metaphor are borrowed from mathematics.

    2 In previous writings, I have already expanded the definitions of physics, power, information, time, space and energy. Why not algebra?


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