This latest installment looks at the mathematical and scientific complications posed by or implied in Nkrumah’s “Consciencism” and “categorical conversion,” analytic capsules of his scientific philosophizing.

Perhaps, the most important question to ask at this juncture is, how empirically does Dr. Dompere evaluate the philosophical concept of “categorical conversion,” as abstractly employed by Nkrumah, from the analytic angle of mathematics and science? In other words, how does Dr. Dompere derive a distillate of socio-political equilibria or stabilizing forces from a chaotic system, of which the internecine covariates of polarity, opposites, tension, identity, continuum, duality, information, and energy are typical? There is an important caveat we need to bring upfront. He writes thus: “The universality of categorical conversion is yet to be understood, appreciated and made applicable across scientific spectrum in theory applications.” Elsewhere Dr. Dompere dialectically relates the concept of categorical conversion to the qualitative laws of motion which he sees implicit in “Consciencism.”

Nonetheless, for reasons of analytic simplicity and philosophical convenience, we may usefully have to substitute this “chaotic system” for an assumed preset of internecine conditionalities derivable from the socio-cultural tensions in African societies, supposedly accruing from the cultural and spiritual collision between the world of “traditional” Africa and the worlds of Islam and of Euro-Christianity. This phenomenological or cosmological collision is qualitatively evocative of Newtonian motion, particularly of Newton’s Third Law of Motion, though, arguably, the relational assessment is certainly if additively and qualitatively one of unequal dichotomy in many parts of the cultural landscape of Africa, historical and contemporary. Admittedly, Dr. Dompere’s rigorous mathematical and scientific re-interpretation of “Consciencism” is highly technical, dense, complicated, although, among other things, it integrally takes the complexity of the preset of internecine covariates into equational consideration.

Yet, an equational appraisal of Africa’s tripartite situationism, contemporary and historical, may have to assume a formulaic state of fuzziness. Precisely how is this possible? Let us assume the collision between Islam and Euro-Christianity, on the one hand, and Africa on the other, theoretically took place and still does in an “open system.” By “open system,” we simply mean a system or scheme in a continuous interface with its surroundings. Africa is that “open system” and its “surroundings” is the influences she incurred from Islam and Euro-Christianity. This is not to assert presumptively that Africa did not reciprocally impact these cultures. She surely did. It is merely to “dampen” that variable for the larger picture, a simplistic equationization of the “categorical conversion.” What is more, let us assume that “open system” is a football pitch, say. Yet, instead of the eleven African players theoretically playing among themselves, we have eleven Euro-Christians and eleven Islamic adherents, twenty-two in all, mutually playing against the eleven African players.

The above scenario is emblematic of the operational rules governing “game theory” and “linear programming,” to name but two. But, this dynamic-system setting is more intricate than descriptively presented in the preceding paragraph, which we merely offer as a philosophical microcosm of a larger picture. There are the additional variables of player psychology; referee incompetence; match fixing (bribery); unforeseeable player injuries, sickness, or deaths; vandalism; refereeing biases; patriotism; self-scoring (own goal); racism; pre-match financial inducements or post-match financial compensations; weather; physical fitness; how well or bad soccer rules are applied; expert coachability; tactics and strategies; and what have you. The “game theory” part primarily deals with questions related to a network of tacit psychological processes one team integrally makes subject to both the implicit decisions and explicit tactical moves of the opposing team. In any event, there is another factor, a confounding or interacting variable, that of spectator support.

Then again, player psychology and spectator support, particularly, interact in a strange and meaningful way, two essential variables that may constitute the deciding factor in a team’s success or failure in a tournament. These impactful individual variables together take the place of “constraint” in the formulation of a “linear programming” equation, an algebraic recipe whose canonical form is represented by an “objective function,” which is a linear equality, otherwise Nkrumah’s overriding concern to move Africa from an “underdeveloped world,” or Africa losing the match against Islam and Euro-Christianity,” to a “developed world,” or Africa winning the match against Islam and Euro-Christianity.” Generally, “constraints,” on the contrary, are linear inequality constraints, theoretically our preset of internecine conditionalities, which are interacting variables in the “objective function,” much like Nkrumah’s internal enemies in the CPP or those from without, the National Liberation Movement (NLM), say.

Moreover, in relative terms, a linear programming problem with two or three unknown variables is always intellectually economical to solve without the aid of computer software (simplex algorithm developed by George B. Dantzig). However, a linear programming problem with tens, possibly hundreds, of unknown variables with its corresponding linear inequality constraints to solve requires heavy intellectual investment in setting up an extended family of correct equations with appropriate underlying assumptions. Fortunately, computer software is readily available to ease the emotional burden of psychological traffic in solving cumbersome equations but, as is always the case, the mathematician, engineer, and scientist diligently has to collaborate with it, the computer software, by generally framing up correct equations. This is one of the major qualitative (theoretical) problems which Nkrumah’s philosophically dense text “Consciencism” in general and “categorical conversion” in particular poses to intellectuals like Dr. Dompere. He successfully overcomes the qualitative problems nonetheless.

Perhaps, the trickiest part of this entire mathematical formulation activity is converting those qualitative ideas, like patriotism, player psychology, wicked intentions of political enemies, into useful underlying assumptions to make the nuclear family of equations algebraically functional and computationally operational. However, once that aim is fully realized a theoretical solution optimally worked out should definitely bring a semblance of algebraic equality or equilibrium to the “objective function.” Technically implied elsewhere, the “objective function” represents a team’s loss or win in our particular case, which, in turn, depends on combined tactical manipulation and creative interaction of the variables for qualitative optimal benefit. These together probabilistically determine or predict the behavioral trajectory of the “objective function.”

Again, the algebraically-derived optimal solution(s) unique to the nuclear family of equations under study has to be correctly if objectively interpreted, qualitative-wise, else the wrong meanings will be woefully misapplied to social settings or will derail the qualitative purposefulness of the “objective function.” Importantly, the algebraic exercise of optimization may assume two instrumentalist forms, “minimization” and “maximization.” The former relates to “decreasing” the chances of a team’s loss and the latter “increasing” the chances of a team’s win. Other instances of “maximization” may be enhancing the psycho-physical preparedness of a given team, while “minimization” may regard curtailing training expenditure, the chances of team members’ receiving bribes from managers or owners of the opposing team, or ensuring players do not incur excessive injuries while training for a given tournament.

This set of mathematical considerations is conceptually intricate, hence the term “fuzziness,” one of Dr. Dompere’s levels of mathematical expertise. Clearly, the concept of objective chance is not causally deterministic, an idea constituting the bedrock of our qualitative assumptions. This is what mathematical modeling is fundamentally about. It is what Dr. Kofi Kissi Dompere is good at. He is one of America’s best in that regard. Besides, game theory is integral to his intellectual bailiwick, just as it was with David Blackwell, the great African-American statistician, and John von Newmann, John Nash, Yaw Nyarko, Glenn Loury, among others. Game theory, an important field of rigorous mathematical analysis, is alternatively described as “interactive decision theory.”

Moreover, as already pointed out elsewhere, game theory deals with matters of cooperation and conflict where intelligent rational decision-making through testable mathematical models is the point of objective study. Adam Smith’s “rational self-interest” is not far off at all. It is applied in philosophy, political science, mathematical science, marketing, computer logic and science, biology, economics and business, psychology, finance, stochastics, engineering, etc. Likewise, linear programming which essentially addresses issues of optimal resource allocation has numerous applications in diverse fields, among which are telecommunications (internet traffic, network design, queuing, call routing, etc), manufacturing and transportation, traveling salesman problem (Very-Large-Scale Integration (VLSI chip, vehicle routing, etc), crew/fleet scheduling, portfolio management (optimization), econometrics, profit maximization/cost minimization, finance, agriculture, marketing, etc.

These mathematical and scientific ideas and their underlying assumptions are implicit in Nkrumah’s “Consciencism” and “categorical conversion,” which Dr. Dompere expertly teases out via his appropriately-devised mathematical models, that is, to test as well as to confirm their scientific viability. As a matter of principle, game theory and linear programming share a system of analytic conjunction with such major fields of scientific inquiry as simulation, engineering, econometrics, mathematical optimization, decision analysis, psychology, operations research/management science, neural networks, and the like. For instance, simulation will provide useful insights into the feasibility of our equational analyses vis-à-vis Nkrumah’s “categorical conversion” in a real-world setting. Dr. Dompere is well-grounded in these theories and many others outside his immediate professional specialties, which, incidentally, he brings to bear on the exegesis of Nkrumahism. This explains why the analytic power of Nkrumah’s mind can neither be undervalued nor his rational predictions about the fate of Africa, his progressive ideas about human and race relations, his wise counsel to the world, and his prophetic and rational statements on the political economy of neo-colonialism be ignored.

We should add that Dr. Dompere does not approach “Consciencism” and “categorical conversion” the same way we have done here in this essay. It is to hypothetically give readers a simplistic mathematicization or equationization of the “categorical conversion” question as put forward by Nkrumah in his philosophically convoluted text, “Consciencism: Philosophy and Ideology for Decolonization.” We merely want to give readers a taste of the huge mathematical and scientific challenges Dr. Dompere has to overcome in order to make qualitative sense out of Nkrumah’s convoluted thinking. Going back to our initial analysis, however, we may also have to theoretically equate “equilibrium,” “stabilizing force,” or “optimal solution” with our “objective function” in the context of Nkrumah’s restorative project or his intellectual desire to see the seeming internal contradictions in African societies, occasioned by Euro-Christian and Islamic influences, averaged out to the barest minimum as a precondition for Africa’s development.

Thus, in hindsight, Nkrumah had wanted Ghana’s and Africa’s development to take off as the exemplary life, our “objective function,” of the African-American Dr. Ben Carson, one of the world’s leading pediatric neurosurgeons and former Director of Johns Hopkins Hospital Pediatric Neurosurgery. His widely known and read books “Gifted Hands: The Ben Carson Story” and “Think Big: Unleashing Your Potential for Excellence” figuratively speak volumes about Nkrumah’s own imaginative prowess, industry, foresight, and about Nkrumah’s ability to turn crushing challenges and defeats into successes. Yet the two men have one notable feature in common: To make the human mind more qualitatively efficient and constructively operational. “Consciencism” and “categorical conversion” are fundamentally about the qualitative re-engineering of the post-colonial psychology of Africans and about re-orienting it towards their collective self-actualization, toward their positive contributions to Africa’s growth and development, and toward improved race and human relations.

And as we remarked before, a miscalculus certainly points to misapplication(s) of the qualitative optimal solutions. We have seen most if not all of Nkrumah’s pessimistic prophecies about Africa materialize now and then, all because African leaders have conveniently and ignorantly refused to hearken to the “objective function” of Africa’s wisest son (See Rodney Worrell’s “History Has Vindicated Kwame Nkrumah”; Robert Woode’s “Third World to First World-By One Touch: Economic Repercussions of the Overthrow of Dr. Kwame Nkrumah”). Yet Nkrumah’s drive to appreciate human psychology led him to other unresolved paths of serious philosophical analysis. Nkrumah even ventured into the mind-body conundrum as others, such as Baruch Spinoza, Rene Descartes, and Antonio Damasio, have done (See Damasio’s “Looking for Spinoza: Joy, Sorrow, and the Feeling Brain” and “Descartes’ Error: Emotion, Reason, and the Human Brain”). Dr. Dompere also looks painstakingly if briefly at Nkrumah’s general understanding of the mind-body problem in his overall appraisal of “Consciencism” and “categorical conversion.”

The fact is that a thorough evaluation of human psychology is technically incomplete without a philosophical or scientific recourse to the mind-body problem, which deals with the correlation between the brain and consciousness (mind versus matter). Those observations aside, Nkrumah made African humanism, social justice, and African Personality the philosophical fulcrum of his development model. These ideas are theoretically intertwined in the mathematical and scientific memory of “categorical conversion.” Indeed, the colonial and post-colonial psychology of Africa cannot be sufficiently appraised without a comprehensive understanding of the relationship between consciousness and man’s environment. Thus Nkrumah took up the challenge. That said, according to Dr. Kwame Botwe-Asamoah, credit for the seminal theoretical founding of African Personality should go to Mary Kingsley. Nevertheless, we do also believe Edward W. Blyden should share in that credit as well.

Yet, after all is said and done, Dr. Dompere’s “The Theory of Categorical Conversion: Analytical Foundations of Nkrumahism” is a highly technical and intricate text. Among other things, this book does not make Nkrumah’s “Consciencism” any less interpretively comprehensible for the average reader, because that potential average reader will definitely require a high level of analytic sophistication and theoretical grounding in mathematics (topology, logic, set theory, fuzzy laws, etc), Afrocentric theory, philosophy (ontology, epistemology, phenomenology, etc), science (physics, chemistry), conflict theory, postcolonial theory, engineering, Pan-Africanism, political economy, psychology (cognitive science (consciousness); science of mind control or manipulation, etc.), African culture, etc., in order to plow through it just to achieve a semblance of full comprehension.

Nevertheless, in another interestingly related context, Prof. Richard H. Bell, another American scholar, has noted the signal contributions of Nkrumah’s “Consciencism” and of world-famous Brazilian critical pedagogist Paulo Freire’s influential text, “Pedagogy of the Oppressed,” to the founding of postcolonial studies. He writes: “I think it would be fair to say that Freire’s literature along with Nkrumah’s were major precursors of what is now called ‘postcolonial studies’” (See “Understanding African Philosophy: A Cross-Cultural Approach to Classical and Contemporary Issues,” p. 148). Finally, “categorical conversion” is presumptively our “open system” or “objective function,” a powerful concept of which Dr. Dompere writes: “The establishment and the understanding of the mechanism of transformations and changes in Nkrumah’s conceptual system require the development of the theory of categorical conversion to examine conditions of qualitative and quantitative states of change and convertibility of categories.”

Further, Dr. Dompere makes note of another critical observations: “The theory of categorical conversion is not explicitly developed by Nkrumah. He, however, provides reasonable conceptual and analytic materials for one to develop the needed theory for the establishment of the internal mechanism for qualitative transformation and change if one has good knowledge of category theory, theory of formal and informal languages and foundations of fuzzy logic and mathematics as they relate to the principle of opposites and basic Africentric conceptual system.” What is the solution then? He answers: “This monograph [The Theory of Categorical Conversion: Analytic Foundations of Nkrumahism] is about the development of the required theory which constitutes a point of entry into Nkrumah’s conceptual system whose analytical foundations and directions of application are provided in his book ‘Consciencism.’”

“The problem of categorical conversion is general across all scientific boundaries and socio-natural elements,” he adds. In fine, Dr. Dompere hopes to explicitly develop “the theory of categorical conversion” and then to extend it to “a general or unified theory of categorical conversion,” a dialectic exercise in the likeness of Albert Einstein’s and others’ extension of Special Relativity to the General Theory of Relativity. The success of this project, which Dr. Dompere has already mathematically and scientifically realized, signals the world’s first major original contribution to scholarship on Nkrumah and Nkrumahism!

We shall return…