tabula congratulatoria

Palmer, Carleton


            A true phenomenologist, Dave would never summarily reject an idea without examination. Since ideas qualify as artifacts for examination we had occasion over many years to enjoy examining some that were silly and some that were profound. The following draft paper was meant to serve us to continue an ongoing speculative conversation when we were next able to get together. That was not to happen, and it is shared here in its every imperfection in loving memory of a good friend with a great mind.
-Carleton Palmer


Cover Letter

August 15, 2013

Dear Dave,

            Our telephone conversation provoked me to draft the enclosed paper as a take on your N of One mention. I am mailing it in case something prevents me from visiting you as soon as I would like.

            The elements of the previous draft fragments I've sent you dovetail with this one as I see phenomenological method as a means of achieving the integration discussed. The reason that I happen to think that is you guided me to that understanding.

            I have stacked up about a hundred pieces of work that I would be pleased to have you curate for my one man show in the new ISALTA Gallery, and which I will bring when I next visit Ecker House.

            Although it would be good to see and work with Sandro, my experience with your worthy student graduates is that they are into their own affairs and do not see the monumental implications for world peace and general welfare implicit in the work of ISALTA, so I might be inclined to budget my investment of time and energy.

See you soon,


N of One

© Draft Notes 8/15/2013

Carleton Palmer

"N of One" Abstract

            "N of One" proposes that the biological principle of differentiation and integration derived from general systems theory finds expression in the cognitive styles related to qualitative and quantitative problem-solving characterized as artistic and scientific processes. The differential proposition is supported by observations concerning the development of inferential statistics, and it is speculated that a natural and beneficial course of events will result from integration of these problem-solving strategies. Implications are left for further study.

Anecdotes of N's of One

Voltaire was the first to suggest that the universe was created in a gigantic explosion.

Goethe was the first to suggest that spiral nebulae were swirling masses of stars.


            Differentiation and integration is a well-known biological principle. In the early formative stages in the development of a biological organism cells differentiate into separate kinds of tissues. Mere masses of differentiated tissue might not be interesting, except that such differentiated tissues become organs that can eventually integrate into a functioning whole, an organism. The order is differentiation, then integration.
This rich metaphor applies usefully elsewhere than biology, and will illuminate this discussion.

Meme of Two Cultures

A persistent meme regarding the relationship of art and science originates in a misunderstanding phrased as "the two cultures," derived from C.P. Snow's 1959 Rede Lecture. This is despite the fact that Snow's text itself observed the flaws in binary thinking, and that he was speaking against an intellectual/literary turn of mind he believed misrepresented science. The art/science dyad has more profound meaning, and scientific revolutions have more studied discussions, such as in Thomas Kuhn's influential work. A genuine future revolution may be found in the integration of the differentiated processes characteristic of the elements of this dyad.

Cognitive Style

            It is an unusually rarefied problem-solving atmosphere in which only one kind of thinking prevails, but it explains why dissertations in mathematics can be very few pages of symbols, while M.F.A. exhibitions and performances can be large participatory events.
The quantitative/qualitative distinction implies preferential ways of reasoning conforming to the literature of cognitive styles. The general systems cognitive style concept moves from Bertalanffy, through Werner, to Witkin. Among the problems of cognitive style research are thinking in terms of paired opposites, and defining one characteristic as the failure to perform successfully on a test of the other. It is a common error to suppose that poor performance on quantitative tasks implies a qualitative cognitive style, explaining the instances when a child failing out of math gets a double dose of art. If one accepts this form of diadic reasoning for the sake of argument, it would be more productive to observe lability between cognitive styles, the ability to move between assumedly polarized cognitive styles as tasks demand as a form of mental efficiency.


A significant change occurred in the educated human psyche at the time of the Western Enlightenment that had not happened at any other time or in any other culture. Correctly or not, it is called the Scientific Revolution, and it is characterized by methodological processes collectively known as scientific. Among those methodologies were changes in problem-solving. Qualitative and quantitative problem-solving became more distinct, and the application of probability applied to descriptive statistical data permitted the differentiation and development of inferential statistics.

Leonardo, and other such extraordinary figures found in many times and places, are characterized as polymaths, each having been combinations of scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, botanist, musician, writer, etc.. It is not co-incidental that such roles differentiated and became compartmentalized during and after the Enlightenment's intellectual revolution encouraged fundamental forms of problem-solving to develop.

Before Probability Mathematical Inferences Descriptive

The earliest cuneiform writings still in existence are account ledgers. Ancient writings refer to censuses and surveys (including those of Moses in 1491 B.C., and King David in 1017 B.C.). In 1085 William the Conqueror commanded his civil servants to survey the 34 Counties that then constituted England, ordering the making of the Domesday Book. Double entry bookkeeping developed in the fifteenth-century to revolutionize accounting, and mathematics developed magnificently since the invention of zero. The commonality is that whatever predictive inferences were made from such descriptive statistics were made on the basis of processes more qualitative than quantitative, as are those that distinguish alchemy from chemistry.

Francis Bacon's astonishing powers of observation are not what inhibited him from making gold from base metals. His purpose was limited partly by the available qualitative problem-solving process of inductive method. "Gold hath these Natures: Greatnesse of Weight; Closeness of Parts; Fixation; Pliantnesse, or softnesse; Immunitie from Rust; Colour or Tincture of Yellow." Weight, density, malleability, durability and color are qualities whose reproduction by qualitative means can result in the production of art, but not an element. This is qualitative problem-solving. Science is today grounded on deductive principle, using a process which derives conclusions from a hypothesis and proceeds to support or deny that hypothesis with regard to its probability. This is quantitative problem-solving.

If the problem is duck-determination, then qualitative problem-solving holds that if it looks like a duck, smells like a duck, etc., then it must be a duck; quantitative problem-solving holds that if measurable characteristics (such a dna) between a sample in question and known characteristics reaches statistical significance, then there is a specific degree of probability that it is a duck.

Intelligent human organisms seem to have always recognized likelihood, luck and probability as factors important to solving problems. Aristotle several times mentions luck and fortune as notions expressing deviations from reasonable qualitative expectations. What mathematical pursuit could be more qualitative than the Pythagorean search for the perfect number? Historical discussions generally agree that a turning-point in the development of problem-solving through the evolution of mathematical probability to data occurred between 1650 and 1750 in Europe, and that Pascal and Bernoulli were central to this evolution in quantitative understanding.
Differentiation of Problem-Solving Strategies

The conventional wisdom, which coincidentally happens to be true, is that we can find in gambling the origin of inferential statistics: Liber De Ludo Aleae (Book on Games of Chance) by Gerolamo Cardano, which, although written in the mid-1500's, was published in 1663. A more distinguished paternity is found with Galileo’s treatise on probability "Sopra la scoperte dei dadi" (On a Discovery Concerning Dice) published first in the 1718 three volume second edition of his collected works. Blaise Pascal's 1654 correspondence with Fermat, which was fundamental to the development of modern concepts of probability, also concerned a historic gambling problem expressed by the Franciscan Friar credited with developing double-entry bookkeeping, Luca Pacioli (1494), and others. Bookkeeping and gambling, therefore, are the ancestors of the inferential statistical quantitative problem-solving method kick-started in the Enlightenment.

Having differential problem-solving strategies, the contemporary psyche is divided, compartmentalized.

Qualitative and Quantitative

Neither qualitative nor quantitative reasoning is the exclusive province of either art or science. A qualitative problem in physics might be, “In a collision between a small car and a large truck, which exerts the greater force on the other?” The expected solution to the problem would be an application of Newton’s Third law with a quantitative demonstration.

“Qualitative Reasoning/Analysis,” sometimes called qualitative physics, is an important part of artificial intelligence study. Studies in qualitative reasoning investigate the non-quantitative processes involved in what is sometimes called common-sense reasoning about complex systems, as is prevalent in everyday thought about physical systems. In this way artificial intelligence research is working toward modeling that characteristic of human intelligence that allows the kind of decision-making on the basis of limited information which C.S. Peirce, with considerable wit, added to the list of “deduction” and “induction” as “abduction.”

Artists’ processes take the form of self-reflective and iterative low-detail overview of a problem described by Ecker: “Artists at their work think in terms of relations of qualities, think with qualities; their thought, in a word, is qualitative.”

Conversely, it is not unknown for artists to employ quantitative means to achieve their qualitative purposes, from the computational automata of the ancient Greek theater to 3D modeling, animation, and manipulation of computational rules.

It is proposed that qualitative and quantitative problem-solving processes, having become compartmentalized post-Enlightenment, may be usefully integrated in the organization of the human psyche to the benefit of the management of human affairs. Concerning the benefits of expanding management skills with art experience, the core argument is that problem-solving skills before the "Scientific Revolution" were undifferentiated.

The differentiation of qualitative and quantitative processes attending the Scientific Revolution may have been as necessary to the development of each as the differentiation of skeletal and nervous systems in the growth and development of a biological organism. The next step after differentiation in biological growth and development is integration of previously differentiated systems toward the ontogenetic evolution of a functioning organism.

Demonstration of the Compartmentalization of Knowledge

Duke University's J. A. Jones distinguished Professor of Mechanical Engineering, Adrian Bejan, in his recent and widely discussed Design in Nature, proposes a unifying proposition he names 'constructal law' which he asserts is as fundamental as, and perhaps is one of, the ruling laws of thermodynamics. This principle determines form in nature and artifacts by parsimoniously distributing energy in flow systems. The author mentions D'Arcy Thompson's On Growth and Form only once, and that is in the context of observing of Darwin''s and Thompson's domains that "I became acquainted with this vast literature only after discovering the constructal law in 1995." The millennia of art that made the world in such a way that he could make his discovery in 1995 bears no further mention in the book than this disclaimer.


"N" stands for "number," or sample size in inferential statistics. In general, the larger the "N" the more reliable is the result. The larger the data set the higher the probability that statistical treatment will produce a finding with a high degree of validity. (Of course, the finding having a high degree of validity might be that what one is seeking is not there at all, but that case would be known with greater certainty with a larger than with a smaller sample.) For this reason any entity with an interest in knowing something about a population gathers as much relevant data as it can in order to make statistical predictions about that population's characteristics and predictable behavior. Governments and powerful businesses come first to mind.

This mind-set, this "cognitive style" fundamental to the scientific method of quantitative problem-solving is demonstrably very powerful. The individual, the anecdote, the N of One is of no importance, in fact useless in this context. There is, however, another context, mind-set and method of problem-solving of great power that advantages the N of One, and that is the previously discussed qualitative problem-solving process associated with art. Quantitative science might have conceived no problems to solve except for the qualitative observations of art.
Although highly differentiated, these distinct problem-solving strategies might become more powerful if successfully integrated into a more labile organism than is presently found in the present historical state of compartmentalization. The possible ways in which this could be accomplished are matter for later discussion, but it would be useful to reflect that scientist, artist or otherwise, the reader of this essay is an N of One.    

Piaget, Jean. Biology and Knowledge: An Essay on the Relations between Organic Regulations and Cognitive Processes. Chicago: The University of Chicago Press, 1971.

Snow, C.P., The Two Cultures and the Scientific Revolution: The Rede Lecture, 1959
New York, Cambridge 1961

Kuhn, Thomas S., The Structure of Scientific Revolutions, Chicago, University of Chicago Press 1962, 1970

Bertalanffy, Ludwig Von. General System Theory: Foundations, Development, Applications. New York: Braziller, 1968.

Werner, Hinz, Comparative Psychology of Mental Development. New York: International Universities Press, 1940, 1948, 1973.

Witkin, H.A., Dyk, R.B., et al. Psychological Differentiation. New York: Wiley, 1974.

This section on the making of gold is included in Century IV of Francis Bacon's Sylva Sylvarum, or a Naturall Historie in ten Centuries, London, 1627, which was part of Bacon's unfinished Instauratio Magna ("Great Instauration").

(Metaphys. 1065a; Rhetorica 1361b)

(Magna Moralia 1206b, 1270a)

Oscar Sheynin credibly outlines as an "antenatal stage" the early history of the mathematical treatment of observations in the freely available Theory of Probability. A Historical Essay, Second revised and enlarged edition, Berlin, 2009

Hald, Anders, A History of Probability and Statistics and Their Applications before 1750, Wiley, 1990, 2003.

Pacioli’s Summa (Summa de Arithmetica, Geometria, Proportioni et Proportionalita (1494).

Tartaglia (1556), and Cardan (1545)

Ecker, D.W .. "The Artistic Process as Qualitative Problem Solving," The Journal of Aesthetics and Art Criticism, Vol. 21, No.3 (Fall 1963), pp. 283-290. Reprinted in Readings In Art Education (ed. Eisner and Ecker). (Waltham, Mass.: Blaisdell, 1966) pp. 468. Also reprinted in Contemporary Aesthetics, Matthew Lippman, ed., Boston: Allyn and Bacon, Inc., 1973, pp. 407-15.

Bejan, Adrian and Zane, J. Peder. Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization. New York: Doubleday, 2012 p. 18

Thompson, D'Arcy Wentworth. On Growth and Form. New York : Macmillan, 1945.
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