C-154. Introducing math, II: The V-transform
The ahistorical, mathematical Valuation of particulars departs from the very CEM-historical (App. XI) Course (C-139) of the human condition – i.e., life. For good reason: It’s enormously helpful. For matters of ADOPT (e.g., decision making: comparative value) and of ADEPT (e.g. constructing solutions to situational problems [I:Psit]) if not so much for matters of ADAPT (e.g., how far, how avidly).
Because Valuation departs from that Course, it should be helpful to see math as a transform technology: a V-transform, with V-protocols to parallel the R-protocols (C-151) that we introduce to help improve the productivity of Realization processes. Like the R-transform (C-111) it’s a way to introduce useful changes in the Course of human lives by introducing, following and attaching a tangent path forward. Like the R-transform, it must answer to the test of consequentiality. Thus, for example, getting the amounts, V, of ingredients right in a solution is criterial along with getting them righted sequentially, R. (See the two relevance questions of content and timing [C-103].)
V-protocols are many. The most basic are those of addition, subtraction, division and multiplication. How long should students – and the rest of us (!) – wait for this further V-transform introduction to math? To see that these “tools” were themselves inventions in consequence of Realized needed functionality, strengthened and exercised capabilities (Involving cognition, communication and composition) in order to become “tools that”? To begin to see more of the potential interdependence of the R- and V-transforms for problem solving?
We have developed Valuation technology much, much better than we have Realization technology. These technologies need to be brought together interdependently – once both are established independently, and for interdependence to come about most effectively they need to be balanced strengths (XI; C-71). Which now they are not.
Natural languages struggle to give expression to the Course of the human condition, somewhat better aided by the V-transform (e.g., the first factor derived in Osgood, Suci and Tannenbaum’s measurement of meaning – and the first three when the derived factors are rotated [Carter, Chaffee and Ruggles]). Even so, special languages in the Valuation domain have become necessary inventions (e.g., calculus as a V-protocol). With notable success … so much so that V-transform compositions have yielded models which (only then) can be used to express heretofore inexplicable observed conditions (Boltzmann; Heisenberg).
Realization has lacked a commensurate linguistic technology, mired as it is in a conceptual technology (0:S-P; C-81,85,114,124,155) predicated on, and biased by, an emphasis on bodies, particulars and an assumed order of things. (See C-153 footnote; also C-155.)
We can Grasp the Course of a planet in relationship to the sun via the V-transform’s technology. But we have a very weak Grasp of the human Course if that is the only transform technology available to us. This makes some sciences harder and some the hardest (C-152). “Know thyself” makes a point TO … where consequentiality, general as well as particular (III), most flourishes in quality and quantity (C-3).
***
Why is application of the R-transform so urgently needed? It may help if we see this as the necessary recovery from an over-emphasized V-transform, the latter now evident in the decision making/problem solving imbalance (C-98: the other climate problem; C-148: D.M./P=>S >1+) and related imbalances (e.g., consumer/citizen>1; ADOPT/ADEPT>1; learn/know>1; ahistorical/historical>1).
Formally, the V-transform’s values emerge from the function of evaluation within Realization (App. XIX; C- 16,31). The earliest multi-step R-entity (C-119: pioneer; 147), in minding consequences while problem-solving, could assign value to any particular (body, step, outcome, relationship) – to anything (or any thingk [C-27]) that was the focus (aka “object”) of attention … and commit to memory (e.g., via “emotions” or “notions”) that value for subsequent behavioral and situational problem use….
… Where, in the course of that R-entity’s life, the memorized values could be called upon for a decision among available contributors to a solution rather than undertaking a new problem-solving adventure that might risk too much (e.g., ingesting a new substance when desperately hungry, or reaching for something beyond one’s grasp).
… And where the values could be subjected to technological developments by later pioneers in ahistorical representation (C-108) -- mathematics (C-153) most impressively. Some accommodation had to be made for the historical when Realization was transformed (and compacted) via logic’s “causation” to necessary and sufficient conditions for an observed consequence.
… And where R-entities were rendered into behavioral entities, bE (C-114: “persons who”), with the very historical steps transformed into ahistorical attributes of entities, such that bodies and steps could be freely interchanged (i.e., the flip-flops of 1/ body as both step possessor and instance of step as concept and/or 2/ step as both body possession or concept category [X]), with correlational analysis to follow as associational indicator, and perhaps indicator of possible history.
It seems clear that the Greek sense of lawfulness in nature would, in terms of value, emphasize frequency and regularity (Lewin). It also seems clear that the “natural” languages being developed would reflect this V-transformed view. And that these languages would differ by arbitrarily-sized and selected particulars abducted from local Realizations – and differing greatly in their development of Realization – i.e., process -- as well as in their Realization developments –i.e., products.
All this adds to our picture of behavioral history (C-113). It helps us to see why some of the sciences are harder … and some the hardest (C-152). The sciences are where they are now because the V-transform’s utility in solving situational problems has been monumental (C-155) and because its limited bE model has served knowing by finding … but the latter at the expense of serving knowing by trying and finding out (C-93) – i.e., Realization.
From a Realization perspective, given the Nature of Things and its consequentiality, general as well as particular (III), we could and should do better if we Grasp and Involve (C-105) the V- and R-transforms as interdependent technologies … and thus in need of a balanced emphasis (XI; C-71,122).
What holds this up? We have detailed many of the impediments (IV; passim), many of our own making (0:S-P), such as the BPO bias (C-39), for which the SGN correction (C-104) has been introduced and which the R-transform can serve (C-135). The step (S) and general (G) aspects are critical, because they have been stunted in the first instance and neglected in the second instance. Particulars have been abducted via the V-transform without consideration of the step’s molecularity and the R-entity’s needed functionality given the Nature of Things’ general persisting conditions (of partial order, consequentiality and discontinuity).
***
What also holds up a more effective interdependence for the two transform technologies is the lack of a needed independence for Valuation and Realization. Elements of the two are often confounded. Consider, for example, the ratings of R-particulars as functional or dysfunctional, as successes or failures, benefits or costs, and so on. Policy determination may then consist primarily of creaming the top and/or culling from the bottom among these R-elements – whether functions (behaviors) and/or functionaries (behavioral entities). Creaming bets on aggregate talent, without regard to an R-entity’s needed interdependency. Culling alienates the functionality and functionaries which and who may have only been under-developed. (Did they have a fair chance?)
Budgeting can have a deleterious effect if a D.M./P=>S imbalance exists and Valuation and Realization are confounded. “Taxes” have a much different meaning to individual decision makers (reducing opportunities) than they do to problem-solving community members (enabling opportunity). If a collective R-entity is to achieve the union (C-112) – i.e., the interdependence of individual and community it needs, that interdependence must come via Realization. (See App. XXII, which deals with the public as an R-entity … and “public” as an R-word [App. XIX; C-107].)
Collapsing Valuation and Realization into one array of valued particulars (C-155) misses some important points. The paired V- and R-transforms help us to see that their independence provides leverage in both directions: R => V (sources and tests of values) and V=>R (directives for needed materiality*: Needed functionality is our greatest value! Never enough (C-115: every function adds to needed functionality), especially of concerted <=>’s).
* This functionality is the other “invisible hand” – the guiding hand that is “invisible” because it is so often missing, when, as in the marketing technology, V-R particulars as exchanged are considered to be all that matters.
(c) 2016 R. F. Carter
Because Valuation departs from that Course, it should be helpful to see math as a transform technology: a V-transform, with V-protocols to parallel the R-protocols (C-151) that we introduce to help improve the productivity of Realization processes. Like the R-transform (C-111) it’s a way to introduce useful changes in the Course of human lives by introducing, following and attaching a tangent path forward. Like the R-transform, it must answer to the test of consequentiality. Thus, for example, getting the amounts, V, of ingredients right in a solution is criterial along with getting them righted sequentially, R. (See the two relevance questions of content and timing [C-103].)
V-protocols are many. The most basic are those of addition, subtraction, division and multiplication. How long should students – and the rest of us (!) – wait for this further V-transform introduction to math? To see that these “tools” were themselves inventions in consequence of Realized needed functionality, strengthened and exercised capabilities (Involving cognition, communication and composition) in order to become “tools that”? To begin to see more of the potential interdependence of the R- and V-transforms for problem solving?
We have developed Valuation technology much, much better than we have Realization technology. These technologies need to be brought together interdependently – once both are established independently, and for interdependence to come about most effectively they need to be balanced strengths (XI; C-71). Which now they are not.
Natural languages struggle to give expression to the Course of the human condition, somewhat better aided by the V-transform (e.g., the first factor derived in Osgood, Suci and Tannenbaum’s measurement of meaning – and the first three when the derived factors are rotated [Carter, Chaffee and Ruggles]). Even so, special languages in the Valuation domain have become necessary inventions (e.g., calculus as a V-protocol). With notable success … so much so that V-transform compositions have yielded models which (only then) can be used to express heretofore inexplicable observed conditions (Boltzmann; Heisenberg).
Realization has lacked a commensurate linguistic technology, mired as it is in a conceptual technology (0:S-P; C-81,85,114,124,155) predicated on, and biased by, an emphasis on bodies, particulars and an assumed order of things. (See C-153 footnote; also C-155.)
We can Grasp the Course of a planet in relationship to the sun via the V-transform’s technology. But we have a very weak Grasp of the human Course if that is the only transform technology available to us. This makes some sciences harder and some the hardest (C-152). “Know thyself” makes a point TO … where consequentiality, general as well as particular (III), most flourishes in quality and quantity (C-3).
Why is application of the R-transform so urgently needed? It may help if we see this as the necessary recovery from an over-emphasized V-transform, the latter now evident in the decision making/problem solving imbalance (C-98: the other climate problem; C-148: D.M./P=>S >1+) and related imbalances (e.g., consumer/citizen>1; ADOPT/ADEPT>1; learn/know>1; ahistorical/historical>1).
Formally, the V-transform’s values emerge from the function of evaluation within Realization (App. XIX; C- 16,31). The earliest multi-step R-entity (C-119: pioneer; 147), in minding consequences while problem-solving, could assign value to any particular (body, step, outcome, relationship) – to anything (or any thingk [C-27]) that was the focus (aka “object”) of attention … and commit to memory (e.g., via “emotions” or “notions”) that value for subsequent behavioral and situational problem use….
… Where, in the course of that R-entity’s life, the memorized values could be called upon for a decision among available contributors to a solution rather than undertaking a new problem-solving adventure that might risk too much (e.g., ingesting a new substance when desperately hungry, or reaching for something beyond one’s grasp).
… And where the values could be subjected to technological developments by later pioneers in ahistorical representation (C-108) -- mathematics (C-153) most impressively. Some accommodation had to be made for the historical when Realization was transformed (and compacted) via logic’s “causation” to necessary and sufficient conditions for an observed consequence.
… And where R-entities were rendered into behavioral entities, bE (C-114: “persons who”), with the very historical steps transformed into ahistorical attributes of entities, such that bodies and steps could be freely interchanged (i.e., the flip-flops of 1/ body as both step possessor and instance of step as concept and/or 2/ step as both body possession or concept category [X]), with correlational analysis to follow as associational indicator, and perhaps indicator of possible history.
It seems clear that the Greek sense of lawfulness in nature would, in terms of value, emphasize frequency and regularity (Lewin). It also seems clear that the “natural” languages being developed would reflect this V-transformed view. And that these languages would differ by arbitrarily-sized and selected particulars abducted from local Realizations – and differing greatly in their development of Realization – i.e., process -- as well as in their Realization developments –i.e., products.
All this adds to our picture of behavioral history (C-113). It helps us to see why some of the sciences are harder … and some the hardest (C-152). The sciences are where they are now because the V-transform’s utility in solving situational problems has been monumental (C-155) and because its limited bE model has served knowing by finding … but the latter at the expense of serving knowing by trying and finding out (C-93) – i.e., Realization.
From a Realization perspective, given the Nature of Things and its consequentiality, general as well as particular (III), we could and should do better if we Grasp and Involve (C-105) the V- and R-transforms as interdependent technologies … and thus in need of a balanced emphasis (XI; C-71,122).
What holds this up? We have detailed many of the impediments (IV; passim), many of our own making (0:S-P), such as the BPO bias (C-39), for which the SGN correction (C-104) has been introduced and which the R-transform can serve (C-135). The step (S) and general (G) aspects are critical, because they have been stunted in the first instance and neglected in the second instance. Particulars have been abducted via the V-transform without consideration of the step’s molecularity and the R-entity’s needed functionality given the Nature of Things’ general persisting conditions (of partial order, consequentiality and discontinuity).
What also holds up a more effective interdependence for the two transform technologies is the lack of a needed independence for Valuation and Realization. Elements of the two are often confounded. Consider, for example, the ratings of R-particulars as functional or dysfunctional, as successes or failures, benefits or costs, and so on. Policy determination may then consist primarily of creaming the top and/or culling from the bottom among these R-elements – whether functions (behaviors) and/or functionaries (behavioral entities). Creaming bets on aggregate talent, without regard to an R-entity’s needed interdependency. Culling alienates the functionality and functionaries which and who may have only been under-developed. (Did they have a fair chance?)
Budgeting can have a deleterious effect if a D.M./P=>S imbalance exists and Valuation and Realization are confounded. “Taxes” have a much different meaning to individual decision makers (reducing opportunities) than they do to problem-solving community members (enabling opportunity). If a collective R-entity is to achieve the union (C-112) – i.e., the interdependence of individual and community it needs, that interdependence must come via Realization. (See App. XXII, which deals with the public as an R-entity … and “public” as an R-word [App. XIX; C-107].)
Collapsing Valuation and Realization into one array of valued particulars (C-155) misses some important points. The paired V- and R-transforms help us to see that their independence provides leverage in both directions: R => V (sources and tests of values) and V=>R (directives for needed materiality*: Needed functionality is our greatest value! Never enough (C-115: every function adds to needed functionality), especially of concerted <=>’s).
* This functionality is the other “invisible hand” – the guiding hand that is “invisible” because it is so often missing, when, as in the marketing technology, V-R particulars as exchanged are considered to be all that matters.
(c) 2016 R. F. Carter
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