Cicero Codex , Key to Roman Idea of Cognition

Graeco-Roman science was often contrary to experimental science, but its landmark observations on visual memory were mostly right. We know this thanks to an ancient codex which contained the barely legible but complete text of De Oratore by the Roman orator Cicero and was discovered in 1421 in Lodi, Italy, lent out to humanists and-- incredibly-- had vanished forever by 1425.

Only one direct copy of this lost Codex Laudensis (L) made during those four years exists. As our Easter present, the Vatican Library has just digitized Vat.lat.2901 (V) and placed it online.

Cicero mentions the science of visual perception while introducing the palace-of-memory method of memorizing what to say whenever you are speaking without notes. He starts by quoting the generally correct view of cognitive science of his own day that the keenest of all our senses is the sense of sight (acerrimum autem ex omnibus nostris sensibus esse sensum videndi -- Cicero, De Oratore II, 357.)

He develops from this the method to leverage your visual memory, a method of which he was not the inventor, but becomes a precious witness. It starts with the observation that:

... perceptions received by the ears or by reflection can be most easily retained in the mind if they are also conveyed to our minds by the mediation of the eyes ... (2.357: qua re facillime animo teneri posse ea, quae perciperentur auribus aut cogitatione, si etiam commendatione oculorum animis traderentur).

He then describes what we would now call gist memory:

... with the result that things not seen and not lying in the field of visual discernment are earmarked by a sort of outline and image and shape so that we keep hold of (as it were by an act of sight) things that we can scarcely embrace by an act of thought. (Ut res caecas et ab aspectus iudicio remotas conformatio quaedam et imago et figura ita notaret, ut ea, quae cogitando complecti vix possemus, intuendo quasi teneremus).

And then segues over to what we would call spatial perception and memory, pointing out its role in combination with the somewhat different visual memory.

But these forms and bodies, like all the things that come under our view require an abode, inasmuch as a material object without a locality is inconceivable. (2.358:  His autem formis atque corporibus, sicut omnibus, quae sub aspectum veniunt, [admonetur memoria nostra atque excitatur;] sede opus est, etenim corpus intellegi sine loco non potest.

The method of memorizing, which he attributes to the legendary Greek orator Simonides, is to imagine a familiar place and stock it in your imagination with visual marker tags for things you want to remember. The technique is still being taught nowadays. Here's the place, folio 53v, where it is set out:

The above text was also preserved in a lost Carolingian manuscript, known as M, but none of the copies of M existing today is a direct one, which is to say they are copies of copies (of copies).

V is one of 63 manuscripts just released online. Here is the full list:

1. Barb.lat.298,
2. Ott.lat.3368,
3. Reg.lat.846 (Upgraded to HQ), 9th century, from France, possibly theTours region; provenance Paris, St. Sulpice. One of the codices containing (fols. 106v-107r) a fascinating little text on the origin of the name Adam: it says that Adam was created from earth brought by the four archangels from the four corners of the world, sprinkled with water from the four rivers of Paradise, inspired by the four winds, and named after the four stars. Hence the four letters of his name. Charles Wright, creator of wonderful medieval manuscript surveys, has just published an article about this in The Embroidered Bible: Studies in Biblical Apocrypha and Pseudepigrapha in Honour of Michael E. Stone, eds Lorenzo DiTommaso, Matthias Henze, William Adler (ISBN: 9789004355880).
   
4. Reg.lat.2123,
5. Urb.lat.1251 (Upgraded to HQ),
6. Vat.lat.858.pt.1,
7. Vat.lat.858.pt.2,
8. Vat.lat.936,
9. Vat.lat.1473.pt.1,
10. Vat.lat.1473.pt.2,
11. Vat.lat.2169,

    Relative drought of Aristotelian material in @JBPiggin's latest list of MS @DigitaVaticana. Sententia on the Ethics by Henry of Friemar (Henricus de Alemania), an Augustinian hermit from the first part of the 14th c.https://t.co/yuDaHlbWSK pic.twitter.com/U7dN2SbMjY

    — Pieter Beullens (@LatinAristotle) March 25, 2018

12. Vat.lat.2212,
13. Vat.lat.2231,
14. Vat.lat.2244,
15. Vat.lat.2325,
16. Vat.lat.2330,
17. Vat.lat.2413,
18. Vat.lat.2517,
19. Vat.lat.2666 (Upgraded to HQ),
20. Vat.lat.2683,
21. Vat.lat.2688,
22. Vat.lat.2738,
23. Vat.lat.2739,
24. Vat.lat.2747,
25. Vat.lat.2749,
26. Vat.lat.2769,
27. Vat.lat.2775,
28. Vat.lat.2782 (Upgraded to HQ),
29. Vat.lat.2788,
30. Vat.lat.2798,
31. Vat.lat.2799,
32. Vat.lat.2801,
33. Vat.lat.2802,
34. Vat.lat.2807,
35. Vat.lat.2811,
36. Vat.lat.2812,
37. Vat.lat.2813,
38. Vat.lat.2814,
39. Vat.lat.2817,
40. Vat.lat.2819,
41. Vat.lat.2820,
42. Vat.lat.2824,
43. Vat.lat.2825,

    Not simply is this one of the earliest copies of the pseudo-#MacerFloridus, but it has a bonus: a list of medical texts. "Hi sunt libri medicinȩ. Panthechin. M[a]gategn. Liber febrium. Liber aureus. Passionarius. Antidotarius. Liber oculorum. Liber coitus. Liber urinarum. ... pic.twitter.com/tLRj2V2P8Z

    — Constantinus Africanus (@EgoConstantinus) March 25, 2018

44. Vat.lat.2826,
45. Vat.lat.2827,
46. Vat.lat.2829 (Upgraded to HQ),
47. Vat.lat.2831,
48. Vat.lat.2843 (Upgraded to HQ),
49. Vat.lat.2845, With incipit: Plato tria arbitratur esse rerum initia; author: Laurentius Miniatensis Bonincontri. See eTK
50. Vat.lat.2850 (Upgraded to HQ),
51. Vat.lat.2852,
52. Vat.lat.2862 (Upgraded to HQ),
53. Vat.lat.2865,
54. Vat.lat.2874 (Upgraded to HQ),
55. Vat.lat.2875,
56. Vat.lat.2881,
57. Vat.lat.2885,
58. Vat.lat.2892,
59. Vat.lat.2897,
60. Vat.lat.2901, key source of Cicero, De Oratore, manuscript V(above)
61. Vat.lat.2903 (Upgraded to HQ),
62. Vat.lat.2905 (Upgraded to HQ),
63. Vat.lat.2937,
64. Vat.lat.2943,
65. Vat.lat.2948,
66. Vat.lat.2949 (Upgraded to HQ),
67. Vat.lat.3024 (Upgraded to HQ),
68. Vat.lat.3077,

This is Piggin's Unofficial List number 155. Thanks to @gundormr for harvesting. If you have corrections or additions, please use the comments box below. Follow me on Twitter (@JBPiggin) for news of more additions to DigiVatLib.

Time Trials

Regular readers of this blog will know that a big topic hereabouts is the origin of timelines generally, and in particular how humans got the idea of construing synchronous series of events graphically by picturing them on parallel horizontal tracks.

Here is how it is done in the fifth century in the Great Stemma, with a track at top representing kings of Judah, at centre kings of Samaria and below it, the ancestors listed by the Gospel of Luke:

It is helpful here to use certain fundamental cognitive distinctions laid out by Rafael Núñez and Kensy Cooperrider not long ago in a review paper.

Humans can use (abstract) space to map the passage of time in three distinct fashions in their gesture and speech: projecting deictic time (from where "I" stand), setting an order of events in sequence time (distinguishing the placement of "landmarks" in time), and comparing one or more temporal spans. Scholarly discussions of time sometimes muddle these. As two authors remark:

Philosophers, physicists, and cognitive scientists have long theorized about time –along with domains such as cause and number – as a monumental and monolithic abstraction. In fact, however, the way humans make sense of time for everyday purposes is, as in the case of biological time tracking, more patchwork.

There is no reason to suppose that this typology in the mind transfers easily to a drawing. In fact, the two authors point out that investigating space-time mappings in non-English-speaking cultures by asking people to demonstrate with cards and paper may be handicapped by the fact that this "material realization " needs to itself be learned first:

... arrangement tasks are not well-suited for use in such populations, because they presuppose familiarity with materials and practices that, in fact, require considerable cultural scaffolding.

A similar point was made 20 years ago by Mary Bouquet, who rebuked anthropologists for asking Portuguese people unfamiliar with stemmata to draw their kinship bonds this way.

So what are the tracks in the Great Stemma doing? They don't tell us anything about the Latin concept of deictic time (though that has been very expertly figured out by Maurizo Bettini, who shows the Romans faced the past with their backs to the future), whereas the three tracks seem to demonstrate a Latin tendency to set out a sequence of time from left to right, in accord with the Latin writing system, and they do indeed suggest that Latin-speakers would have compared durations of temporal spans in a spatial way when speaking of them.

It could well be argued that the invention of this type of timeline was inspired by gesture, though I have considered other origins such as game-play. The spans are not exactly calibrated with one another, but match one another in lengths more precisely than a speaker would ever intend to do in gesture.

An intriguing aspect of the Núñez and Cooperrider paper is its mention of the spiral of time perceived in some cultures. The Great Stemma might have something going on in this respect where it loops up at the end and flips, with the script gradually rotating and terminating in a plaque with several upside-down sentences:

These are all aspects that require further study and analysis.

Bettini, Maurizio. Anthropology and Roman Culture: Kinship, Time, Images of the Soul. Translated by John Van Sickle. Baltimore: Johns Hopkins Univ. Press, 1991.

Bouquet, Mary. ‘Family Trees and Their Affinities: The Visual Imperative of the Genealogical Diagram’. Journal of the Royal Anthropological Institute 2, no. 1 (1996): 43–66. doi:10.2307/3034632.

Núñez, Rafael, and Kensy Cooperrider. ‘The Tangle of Space and Time in Human Cognition’. Trends in Cognitive Sciences 17, no. 5 (2013): 220–29. doi:10.1016/j.tics.2013.03.008.

Dreamers of dreams

Whatever downers this year has brought, it has been an upper in the science of the mind, thanks to blockbuster proof of the efficacy of deep neural networks. For about half a century, a debate has been under way about the human mind. Is it like a computer? Or just a messy-round-the-edges semblance of such a rational machine?

The New York Times had the story this week in a long-read article by Gideon Lewis-Kraus. The faction who reject the computational view are generally termed connectionists, since they propose that the nuances in the connections joining what we have learned with what we perceive are sufficient to explain thought.

The only way to scientifically prove this is feasible would be to build a synthetic device that works the same way to achieve human-like results. This year, both Google and Baidu succeeded in doing it.

Lewis-Kraus puts this in the context of a stockmarket investment opportunity in artificial intelligence, which is rather like saying the Enlightenment was a historic opportunity to invest in dictionary publishing. What's really happening here is that we are in the midst of developing a new paradigm for understanding ourselves or "what the brain might be up to" as Geoffrey Hinton puts it in this interview.

My research has been built around the hypothesis that humans partly reason with the help of spatial mechanisms in the brain. A diagram (and good layout generally) helps us to make sense of ideas, because it harnesses spatial thought. Like many revolutionary new views of the mind, this does not fit well with the rationalist view of the mind that has risen since the Enlightenment.

We are still immensely far from understanding the mind, but the practical benefits of this year's connectionist experiment make it far less likely that the mind is like a computer, and far more likely that it is an assembly of reasoning effects that simulate pure reason. A neural network cannot shut out irrational deductions, but it could integrate a very mixed bag of inputs.

This may even make us more open to older, pre-Enlightenment ideas such as the classical concept of memory, the western medieval theory of symbols and the idea that we are not natively rational, but learn to be rational. Cognition may not even be limited to one brain, but be distributed across individuals. We are not logical machines. We are dreamers of dreams.

Mental Space

To mentally "place" something is to know where it belongs. If you can place a hundred thousand words or faces or ideas, you command great knowledge. Often too, such a store enables you to quickly solve problems. Growing evidence suggests that "placing" is not merely a metaphor, but that we really do inwardly arrange concepts in spatial frames to think about them or recall them. It seems, indeed, that having extensive mental "spaces" is a key to intelligence.

One of the great goals of cognitive science is to understand how spatial-thinking skills assist -- and are perhaps fundamental to -- human thought. The mechanisms involved are not conscious ones, so simply reflecting on what it means to place, arrange and retrieve concepts in our mental space will not make us any the wiser.

How then are we to observe humans storing and retrieving ideas in the mental space they construct? The evidence we can use is of the indirect type, but useful nevertheless.

Metaphors and analogy provide one such monitor, most famously in our tendency to speak of time as "before" and "behind" us. Gestures are a second and rich source of evidence, since the upwards, downwards and sideways movements of the hands seem to unconsciously describe the mental space we are using. It has long been known as well that our eyes move in sympathy with our thoughts, so that a dart of the gaze to a place where there is in fact nothing to see is an indicator that we may be navigating an "inner" space. The devices we invent to visualize or spatialize our ideas, particularly diagrams, are a fourth tangent into this mysterious human capability. As I noted some time ago in another blog post, observing the thinking processes of the congenitally blind is a fifth method of observing pure visuo-spatial cognition.

At the annual conference of the Cognitive Science Society which has just finished in Philadelphia, interesting evidence was produced in two of these approaches.

In one paper, Gesture reveals spatial analogies during complex relational reasoning, Kensy Cooperrider with Dedre Gentner and Susan Goldin-Meadow observed 19 students explaining stockmarket bubbles and takeovers with spontaneous gestures to elucidate these complex mechanisms. "The participants constructed these spatial models fluidly and more or less unconsciously," the paper notes. To me, this does indeed suggest a "spatial mind" contributing to human reasoning.

In another paper, Spatial Interference and Individual Differences in Looking at Nothing for Verbal Memory, Alper Kumcu and Robin L. Thompson used gaze direction to show that people use an imaginary mental space to remember things, in this case words. Some years ago, Martin Wallraff amusingly alluded to oral examinations where students say, "I can't remember what the book said, but I can remember exactly where on the page it said it." In this paper, the authors tested 48 students and found their eyes darted to the place on a tiny page where a word used to be, leading to the proposal that there is an "automatic, instantaneous spatial indexing mechanism for words" in the mind.

As always, these experiments must be treated with a degree of caution. The subjects were students whose native language is English. We do not know if the results hold true in other cultures, or for the uneducated, or at other times in history. But they do suggest that we may one day succeed in mapping the human mental space and that the objective of this blog - understanding the "natural" mindlike ways to arrange information on pages and in diagrams - is indeed full of promise.

Cooperrider et al. note, "The ubiquity of abstract spatial models like Venn diagrams, family trees, and cladograms, for example, hints at the wider utility of spatial analogy in relational reasoning."

Philadelphia also had a co-located diagrams meeting (mainly on Venn diagams) and a conference on Spatial Cognition, but the interesting papers from those events are sadly not online.

Greatest Brain Hack of All Time

Human beings are mostly quite good at remembering lots of faces. We automatically classify faces by shape and complexion. We mentally associate similar looking faces into families and groups. After seeing a face, we rapidly assign that person to a known category.

But if we only have strangers' names and can't see their faces, how do we begin to encompass who they might be and where they belong? Human beings are terrible at remembering multitudinous connections between abstract things like names or ideas. Without a visible presence, these are hard to grasp.

Oddly enough, storing and retrieving data about connections is a ridiculously simple task to design into a computer program. But for most people, it can take hours of reciting and revision to learn by heart how a hundred facts or words or values are interconnected. We are not built to do that well.

About 2,000 years ago, some very clever people invented a method to get around this issue. They looked for a mechanism in the human brain which operates in some other context to solve similar problems. To understand what they discovered, let's imagine we go to some beach resort for the first time.

In the first hour, you figure out the path down to the beach, recognizing some landmark you need to pass on the way, like a restaurant. You immediately note a couple of other landmarks like an especially ugly hotel and an ice-cream booth. As you walk around the village, you discover a caravan park behind the ice-cream joint and a bus-stop past the hotel. In time, you realize that the bus-stop is in a street which leads to a boat-hire place and out to the main highway.

What's developing in your head is a mental map full of branching connections. Now strangely enough, most of us can remember hundreds of landmarks and waypoints when we are out and about. We retain them much more easily than we remember interconnections between abstract facts.

So the solution devised back in the Roman Empire was a hack. If you pretend to yourself that abstractions are landmarks along forking paths, your innate guidance system will do the heavy computing work for you, and aid you to grasp the interconnections among the concepts.

All you have to do is draw a branching path, plant the facts along it, and then walk this path with your eyes. This is a drawing of the descendants of Leah, a biblical woman, as it was devised around the year 400. The manuscript you are looking at (Florence, Plutei 20.54) was accurately copied from it about 600 years after that.

You might look at this and think: OK, that's just a family tree. For us in the 21st century, diagrams where you walk paths with your eyes are common and unremarkable. But back then the invention was very new. It had not previously been realized that abstractions like a genealogy of three generations could be visualized in this way.

Because this hack was very new, the design had to respect where its readers were at. Nobody was yet educated in how to read these abstract diagrams. Readers only had their instinctive human ability to walk branching paths and find their way by landmarks back to where they started.

In our mental maps of the world, almost anything can serve as a landmark. Every waypoint has a unique appearance, but is similar in its function. So in the Roman abstract diagram, every node had unique content, but was standardized in its circular shape.

In our mental maps, it's easy to learn waypoints, but hard to learn bearings. We imagine the waypoints of every path as one behind another and we ignore slight changes of direction. So in a Roman abstract diagram, the nodes are arranged in straight lines with as few turns as possible.

This Roman diagram was only recently re-discovered. It's the only chart of its type to have been copied in the Middle Ages. It's now the only one surviving from antiquity. Because the Roman diagram is stripped down to the bare essentials, it shows the essence of how we learned to harness the brain to do something new: grasp abstract facts by treating them as if they were landmarks on paths.

This may be the greatest brain hack of all time, a kludge that's so good that we no longer even realize we are harnessing our guidance systems to do something they were not designed to do.

And because it was devised for a world that did not yet use visualizations, it provides valuable clues to how all mental maps work in humans, and indeed in most animals, and even in many insects.

We humans are not as good at thinking about abstractions as we pretend to be. But if we had not adapted our mental navigation machinery to help in the task, we would be far worse at it.

Mistaken Improvements

The power of visual spatial displays often comes from their ability to simplify and abstract from reality, says Mary Hegarty in a 2011 paper.

Since figurative drawings are not so well adapted to the task of reasoning or explaining, the Late Antique inventors of node-link diagrams were careful to omit figurative elements from them.

Their successors since that time have repeatedly attempted to add figures, to regulate the distances between the nodes, to impose a standard orientation (for example, growing upwards like a tree) and to strictly align such diagrams. Those mistaken "improvements" indicate that later generations have not fully understood the genius of the original invention.

Hegarty quotes research suggesting why. We have a misplaced faith in fussily drawn diagrams,

with a strong preference for displays that emphasize high-fidelity spatio-temporal realism, even when these displays result in poor performance...  This may come from a folk fallacy that perception is simple, accurate and complete, whereas perception really is hard, flawed and sparse.

Markus Knauff's book (see my recent post) suggests an additional cause for the fallacy: if reasoning is largely spatial, and is taking place in a part of the mind that is not accessible by introspection, most of us are likely to be quite ignorant about what constitutes an effective explanatory method.

A similar point about why figurative art should be excluded from effective diagrams has been made by Manfredo Massironi in his theoretical account of Hypothetigraphy, the subject of a post on this blog in 2011. Massironi took the view that any diagram explaining abstract matters needs to be limited to what he called "precise marks" only: "Precise, clear lines contribute in conveying the impression that the depicted forms are mental constructs, not representations of natural objects."

Hegarty, Mary. ‘The Cognitive Science of Visuo-spatial Displays: Implications for Design’. Topics in Cognitive Science 3, no. 3 (2011): 446–474. doi:10.1111/j.1756-8765.2010.01113.x.

Massironi, Manfredo. The Psychology of Graphic Images: Seeing, Drawing, Communicating. Routledge, 2002.

Our Secret Reasoning Device

A book published a couple of months ago by the German cognitive scientist Markus Knauff contains some remarkable new evidence and discussion about the seat of human reasoning. Summing up a couple of decades of experiments, he argues that a brain structure which can demonstrably be shown to analyse and reason is the so-called dorsal pathway.

This is the "where" stream which handles our awareness of space, our actions and, as a recent review article by Borst and others argues, our expectations. (All references below.) There has been some criticism in another review article by Schenk and others of the claims that this pathway is entirely distinct from the ventral or "what" pathway, but the dichotomy does seem to be holding up well.

In Space to Reason: A Spatial Theory of Human Thought, Knauff emphasizes that this dorsal pathway is not a self-aware channel, so it is easy to overlook its operations. It shows up in brain imaging, but we cannot examine it by introspection.

... people certainly have no clue about the mechanisms that work on a symbolic spatial array, and they are certainly not aware of a complexity measure that results in certain preferences. (190) [and quoting Goodale & Westwood:] ... the processing of spatial information in the dorsal stream is impenetrable to our conscious awareness. (191)

Knauff does not mention diagrams in his book at all. Most of his experiments involve reasoning about very simple problems such as:

The blue Porsche is parked to the left of the red Ferrari.
The red Ferrari is parked to the left of the green Beetle.
Is the blue Porsche parked to the left or to the right of the green Beetle? (2)

However he proposes that these yield valid data about problems such as:

If the teacher is in love, then he likes pizza.
The teacher is in love.
Does it follow that the teacher likes pizza? (95)

The cars problem is not difficult but it requires effortful thinking, whereas the if problem is instantly understandable. You will probably have guessed at the conclusion before you were conscious of reading the last line, which is said by some authors to be a characteristic of dorsal cognition.

Now there are two competing established accounts of what is going on: one is that we might pretend to see a real teacher whom we know and because we are so smart at understanding from sight, and teasing meaning from sight. we can deduce from visual indications that he is biting a slice of pizza that he must therefore be in love, just as we deduce from a distended belly that a woman is pregnant.

The rival account - propositional reasoning - maintains that we have a kind of machine language inside our brains, a computational logic. It does not use a language like English, but perhaps a language like JavaScript, and it tells us from the if what the only logical conclusion is.

Knauff argues for a third option: if I interpret this correctly, we have a black-box process in which we use the dorsal channel to simulate the problem as if we were perceiving something real. A mental model is constructed where the teacher, his state of romantic excitement and the pizza are encoded as spatial entities. Putting them in the only possible logical order allows us to grasp the conclusion.

The heart of his argument is that evidence shows the ventral stream need not be involved. One of the salient points about the spatial-thinking model is that the mental representation excludes all unnecessary information. The shape or colour of the cars or the exact distance between them does not need to be encoded, nor does the shape of the teacher's face or the flavour of the pizza.

As I have said, Knauff does not mention diagrams, let alone the Great Stemma or the Compendium of Petrus Pictaviensis. But the sense of excitement his book generates in the diagram researcher comes from the fact that the sparse, austere mental models he envisages as the bearers of human reasoning resemble the simpler sort of diagrams that are drawn on paper or on displays.

Reviel Netz suggests in The Archimedes Codex and his various articles that the Greek mathematician did not use diagrams to merely illustrate ideas that he had been thinking through in some propositional fashion. Archimedes was doing mathematics by manipulating spatial representations in his head. Since he was thinking about space, not propositions, the diagrams were the closest external representation to his raw thoughts. As far as I can guess, Netz's ideas are partly rooted in the ideas about external representations generated by externalists in philosophy of mind debates over the past 20 years.

Stemmata and diagrammatic chronicles are not direct reasoning tools in quite the way that geometrical drawings are. Geometry can yield mathematical proofs without numbers or words, whereas chronicles are not there to reason with, but usually serve to re-express histories or genealogies that have already been set down in textual form.

Their purpose is communication. I have always maintained that they are a form of direct author-to-reader communication which eschews the need to convert their content into language. An author massages his ideas into the most lucid spatial arrangement he can come up with, puts them on paper, and the reader's spatial reasoning abilities are sufficient to decode what is meant with a minimum of textual input.

The nearest that Knauff comes to this is when he suggests that there is a kind of diagrammatic substrate to reasoning, and compares this to subway or underground-rail diagrams:

I used the metaphor of a subway map to show that a qualitative representation does not display the shares and sizes of the stations or metrical distances between the stations but only represents the data that preserve spatial relations between stations and lines, for example, that one line connects with another. ... a visual image is completely different from a subway map. It is more like a topographical map ... that captures distances, streets, buildings, landform information, and so on. In contrast, spatial layout models are like schematic subway maps... (192)

His findings and his interpretation have some interesting implications for diagram studies. If the  mental model in our heads is somewhat like a diagram, it ought to be possible to devise diagrams that can inspire such mental models with a minimum of translation.

Since the precise distances between the elements, and their sizes, do not encode any information, both of the following work equally well.

The left diagram is a 6th-century classification system drawn by Cassiodorus, while the right one comes from the 5th-century Great Stemma. I have translated the text from Latin to English. Whether the circles are large, small or non-existent, or whether the text is inside them or out, does not matter. Spatial reasoning merely needs apartness.

Overall orientation does not encode information, so all of the following directions of ramification are functionally equivalent.

Spatial reasoning is also likely to be highly tolerant of defective alignment, so that curved or crooked pathways in a diagram do not make them ineffective.

If this is correct, node-link diagrams which use a spatial encoding to express hierarchical relationships are likely to be a powerful means to manipulate a complex type of data while directly engaging with human intelligence. Working pragmatically and without any scientific evidence from cognitive research, the Late Antique inventors of node-link diagrams established an effective means of simplifying information without losing its essential structure.

Borst, Grégoire, William L. Thompson, and Stephen M. Kosslyn. ‘Understanding the Dorsal and Ventral Systems of the Human Cerebral Cortex: Beyond Dichotomies.’ American Psychologist 66, no. 7 (2011): 624–632. doi:10.1037/a0024038.

Goodale, Melvyn A., and David A. Westwood. ‘An Evolving View of Duplex Vision: Separate but Interacting Cortical Pathways for Perception and Action’. Current Opinion in Neurobiology 14, no. 2 (April 2004): 203–211. doi:10.1016/j.conb.2004.03.002.

Knauff, Markus. Space to Reason: A Spatial Theory of Human Thought. MIT Press, 2013.

Netz, Reviel, and William Noel. The Archimedes Codex. Revealing the Secrets of the World’s Greatest Palimpsest. London. Orion, 2007.

Schenk, Thomas, and Robert D. McIntosh. ‘Do We Have Independent Visual Streams for Perception and Action?’ Cognitive Neuroscience 1, no. 1 (26 February 2010): 52–62. doi:10.1080/17588920903388950.