diagrams of knowledge

[Update: this is turning into an article, the most recent draft of which can be found here]

Introduction

This is the page that will (by the end of October) hold all of the diagrams of knowledge from my upcoming talk about the history of knowledge structures [preprint]. Suggestions of new material are welcome in the comments, and I plan on continuing to update this page whenever I find a new one. I am particularly interested in non-Western diagrams (and translations if possible!), of which I currently have no examples. This page will also include short contextual descriptions and commentary, but for now it’s just a placeholder for pretty pictures.

It’s worth pointing out that this page is very drafty. Its purpose is to provide examples of illustrations for a forthcoming talk, but it is also quite preliminary, and I haven’t yet done the scholarly work of going back to double check all the original sources. Caveat lector; don’t use the references provided here without double-checking them.

Tree of Knowledge

Section of Paradise by Lucas Cranach the Elder, 1530, depicting the biblical trees of life (left) and knowledge (right).

[via]

Paradise by Lucas Cranach the Elder, 1530 [via]

Jesse Tree

A genealogical depiction of descendancy from Jesse (father of king David) to Christ, and the origin of the “family tree”.

[via]

11th century Codex Vyssegradensis. [via]

Capuchin's Bible, 12th century. [via]

Capuchin’s Bible, 12th century. [via]

Porphyrian Tree

Porphyry classified Aristotle’s Categories into a series of branching dichotomies, a metaphorical tree, in the third century C.E. By the sixth century at the latest, the metaphorical tree was being illustrated as an actual tree in Latin editions.

Porphyrian Tree translated into English, originally dating from the sixth century. [via]

Porphyrian Tree translated into English, originally dating from the sixth century. [via]

The destruction of a Porphyrian Tree as depicted in the early 16th century. [via]

The destruction of a Porphyrian Tree as depicted in the early 16th century. [via]

Early Scholarly Divisions

The first, an eleventh century manuscript from Italy, separating practical knowledge into ethics, economics, and politics. The second, a twelfth century manuscript separating philosophy into natural, ethical, and rational knowledge, which are each subdivided further.

Eleventh century Italian manuscript. [via Murdoch's Album of Science, p. 39]

Eleventh century Italian manuscript. [via Murdoch’s Album of Science, p. 39]

A twelfth century manuscript splitting philosophy into dichotomies. [via Murdoch's Album of Science, p. 40]

A twelfth century manuscript splitting philosophy into dichotomies. [via Murdoch’s Album of Science, p. 40]

The Seven Arts

Grammar, rhetoric, logic/dialectic, arithmetic, geometry, music, and astronomy/astrology. From the twelfth century Hortus Deliciarum.

Seven Liberal Arts, Hortus Deliciarum, twelfth century. [via]

Seven Liberal Arts, Hortus Deliciarum, twelfth century. [via]

Ramon Llull

A thirteenth century philosopher and logician who created many diagrams of interest related to knowledge structures and trees.

Llull's thirteenth century version of a Porphyrian Tree, illustrated in the sixteenth century. [via]

Llull’s thirteenth century conception of a Porphyrian Tree, illustrated in the sixteenth century. [via]

Tree of Knowledge by Ramon Llull ca. 1295 [via]

Tree of Knowledge by Ramon Llull ca. 1295 [via]

Llull’s late thirteenth century work actually contained 16 trees of knowledge, with each subject having its own root, trunk, and branches.

Arbor Scientiae, late thirteenth century. [via]

Arbor Scientiae, late thirteenth century, from a sixteenth century woodcut. [via]

Arbor Vegetalis, originally thirteenth century, from sixteenth century. [via]

Arbor Vegetalis, originally thirteenth century, from sixteenth century. [via]

Arbor Sensualis (ibid) [via]

Arbor Sensualis (ibid) [via]

Arbor Moralis (ibid) [via]

Arbor Moralis (ibid) [via]

Analysis of being/existence and its subdivisions (cause, effect, substance, accident, etc.), as transcribed by Llull's disciple (fourteenth century). [via]

Analysis of being/existence and its subdivisions (cause, effect, substance, accident, etc.), as transcribed by Llull’s disciple (fourteenth century). [via]

Aristotle’s Square of Opposition

From Nicole Oresme’s late fourteenth century translation and commentary of Aristotle, opposing generable and ungenerable with corruptible and incorruptible.

Oresme's fourteenth century square of opposition. [via Murdoch's Album of Science, p. 67]

Oresme’s fourteenth century square of opposition. [via Murdoch’s Album of Science, p. 67]

Virtues and Sciences

This fourteenth century dichotomy divides God into virtus (virtue) and scientia, from which the usual suspects branch out and divide further.

A fourteenth century dichotomy of science and virtue. [via Murdoch's Atlas of Science, p. 44]

A fourteenth century dichotomy of science and virtue. [via Murdoch’s Album of Science, p. 44]

Divisio Scientiae

A division of the sciences from a fourteenth century manuscript. Sciencia divides into philosophy, eloquence, poetry, and mechanics, and further divides from there.

Fourteenth century division of the sciences. [via]

Fourteenth century division of the sciences. [via]

Student’s Aid

A fifteenth century student’s study aid, splitting mathematical knowledge into its constituent parts, under which the scribe scribbled relevant books of reference for each branch.

Fifteenth century student's study aid. [via Murdoch's Album of Science, p. 42]

Fifteenth century student’s study aid. [via Murdoch’s Album of Science, p. 42]

Summa de Arithmetica

Pacioli’s fifteenth century tree of proportions, illustrating the various potential types of proportions (for example, geometric proportions could be continuous or discontinuous, continuous could be rational or irrational, etc.)

Pacioli's tree of porportions, fifteenth century. [via]

Pacioli’s tree of porportions, fifteenth century. [via]

Petrus Ramus

A sixteenth century humanist and logician, arguably representing the culmination of the medieval tradition of thinking in dichotomies.

Ramuys, sixteenth century, the structure of logic. [via]

Ramus, sixteenth century, the structure of logic. [via]

Another sixteenth century Ramus dichotomy. [via]

Another sixteenth century Ramus dichotomy. [via]

Margarita Philosophica

A textbook/encyclopedia from the sixteenth century by Gregor Reisch. The book had many illustrations depicting the organization of knowledge within.

Subjects within Gregor Reisch's Margarita Philosophica, early sixteenth century. [via]

Subjects within Gregor Reisch’s Margarita Philosophica, early sixteenth century. [via]

Depiction from Margarita Phiosophica, early sixteenth century, where the disciplines branch out. [via]

Depiction from Margarita Phiosophica, early sixteenth century, where the disciplines branch out. [via]

Theodor Zwinger

Zwinger’s sixteenth century encyclopedia Theatrum Humanae Vitae was organized into chapters, not in alphabetical order, but according to a diagram of a tree, as below.

The taxonomy for Zwinger's sixteenth century encyclopedia. [via]

The taxonomy for Zwinger’s sixteenth century encyclopedia. [via]

Groundplat

John Dee’s ‘Groundplat’ in his 1570 preface to Euclid’s Elements

Full text transcription: http://www.gutenberg.org/files/22062/22062-h/files/groundplat.html

[via]

John Dee’s ‘Groundplat’ in his 1570 preface to Euclid’s Elements. [via]

Athanasius Kircher

Kircher’s Philosophical tree representing all branches of knowledge, from Ars Magna Sciendi (1669), p. 251.

Kircher's Philosophical tree representing all branches of knowledge, from Ars Magna Sciendi (1669), p. 251. [via]

Kircher’s Philosophical tree representing all branches of knowledge, from Ars Magna Sciendi (1669), p. 251. [via]

Various Reconstructed Classifications (sixteenth & seventeenth century)

The various classifications of knowledge in this time period are too numerous to list, however here are a few. The via links provide context.

Paxmannus and Clainerus, organizations of philosophy. [via]

Paxmannus and Clainerus, organizations of philosophy. [via]

Organizations of book catalogs. [via]

Organizations of book catalogs. [via]

Hobbes classification of Leviathan (1676). [via]

Hobbes classification in Leviathan (1676). [via]

Encyclopédie

Though it should need no introduction, this late-eighteenth century encyclopedia by Diderot and d’Alembert included a map of the structure of knowledge held within. Below are a few versions of that map.

English translation of the system of human knowledge. [via]

English translation of the system of human knowledge. [via]

The original late eighteenth century tree. [via]

The original late eighteenth century tree. [via]

Chrétien Roth’s 1769 depiction of the tree. [via]

Chrétien Roth’s 1769 depiction of the tree. [via]

Coleridge

Samuel Taylor Coleridge tried his hand at an encyclopedia in the early nineteenth century, and this tree represented the organization of each volume.

Coleridge's 1818 encyclopedia breakdown. [via]

Coleridge’s 1818 encyclopedia breakdown. [via]

World Brain

H.G. Wells describing how students ought to learn in 1938.

H.G. Wells' idea of how students should be taught. [via H.G. Wells, 1938. World Brain. Doubleday, Doran & Co., Inc]

H.G. Wells’ idea of how students should be taught. [via H.G. Wells, 1938. World Brain. Doubleday, Doran & Co., Inc]

The Map of Physics

Bernard H. Porter’s Map of Physics, placed in a number of contemporary physics textbooks, 1939.

Bernard H. Porter's map of physics, 1939. [via]

Bernard H. Porter’s map of physics, 1939. [via]

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Comment

18 Comments

  1. Very very nice. I’ve got two things for you:

    1. A tangent that might tickle you
    Possibly you will fancy Sociology of Philosophies by Randall Collins.

    2 A question that might nudge you
    Have you ever thought of translating these in some visual language (keeping the proposed structures of knowledge) and then playing the entire sequence as a movie on a timeline?

    Cheers
    Oh, it stopped raning outside, great.

    Reply to Vuk

    • Thanks for the tip, Vuk. I particularly like your 2nd idea: it would be interesting to see how the interplay between different parts changes over time, and whether some periods have some strong relationships that others don’t. The one thing to watch out for is the changing meaning of the various disciplines (ie, what science means and used to mean, what philosophy means and used to mean, etc). Thanks!

      Reply to Scott

    • John, that’s a great point. A lot of these trees of knowledge are rightly interpreted as genealogies rather than ontologies, and have a very temporal component hidden in the structure. Thanks for the link.

      Reply to Scott

  8. In the 80′ the Enciclopedia Einaudi published a quite innovative encyclopedia organised neither in alphabetical order nor as a tree but as a sort of venn diagram with an index of recurrencies of terms inside other terms. The structure of the encyclopedia was a precursor of the hypertext. Unfortunately the project was not very successful, so on-line there are very few traces, I have found this image that can give you an idea http://htmlimg1.scribdassets.com/9bm1goi0ao1vib2v/images/2-4bab5953f1.jpg

    Reply to Ermete

  9. The International Baccalaureate Diploma Programme (IB) has its own diagram of its curricular framework: http://www.ibo.org/diploma/curriculum/ – this is for high school students. An interesting current application. Theory of Knowledge, by the way, is sort of an epistemology course, about ways of knowing, that both my kids, who took this curriculum, benefited from quite a bit.

    Reply to David

    • This is absolutely brilliant, many thanks for bringing your project to my attention. I probably will take you up on that offer soon.

      Reply to Scott

  11. You might be interested in the links on my Boethius page to manuscripts containing the arbor porphyriana: http://www.piggin.net/stemmahist/boethiuscatalog.htm Briefly, the oldest evidence for the figure comes from Boethius, so we don’t know if Porphyry used it. As for the idea that it resembles a tree, that’s a medieval spin to it. The early node-and-link diagrams are not arboreal at all.

    Reply to jbpiggin