SUMS

Dr. Kim H. Veltman

Epilogue


The problem is rather the unity of his thought. Every subject he approaches seems to absorb him completely and yet so expands under his gaze that we gain the impression that nothing else could have mattered to him throughout his life and that even his art should best be approached from this angle.

E. H. Gombrich


1. Introduction
2. Verbal Thinking
3. Kinds of Notebooks
4. Thematic Presentation
5. Stages
6. Explanations and Truth
7. Encyclopaedia of Practice
8. Continuity and Innovation
8.2 Individual Genius
8.3 Culture
9. A New Vision

 

1. Introduction

    This journey into Leonardo's writings has been to reconstruct the inherent system underlying his work and give some indication where his claims stand in the modern framework of science, asking positivistically: what did he do and what did he get right? To understand Leonardo, however, also requires insight into why he arranges his notes in the way he does. Why does a potentially organized mind produce such seemingly disorganized notes: This problem permits no simple answer.

    His ideas keep changing and developing. As a young man in Florence he does not yet have the systematic view of knowledge that he begins to put to paper in Milan in 1492 as he turns forty. In the years that follows, under Luca Pacioli's influence, he studies Euclid's Elements and incorporates a more formal geometrical framework into his world-view, especially in the period 1505-1508. The focus of his thought also changes. In the 1480's and 1490's he believes that mathematics and science can explain the whole of Nature. The four powers promise to solve not only everyday problems of mechanics but even the intricacies of the human body which he sees as a wondrous mechanical instrument created by God, "the Inventory" (K/P166r, W19073-4r). At this stage his emphasis is on the regularity of Nature, its objectivity and predictability.

    In the period after 1508 the unpredictable aspects fo Nature come to the fore. There is, for instance, geological evidence of multiple layers of shells in rocks high in the mountains. Had there been only one Deluge there would be only a single layer.2 There are also reports of earthquakes and other natural disasters.3 In the end, Leonardo continues to approach Nature mechanistically, but is also aware of her irregularity and mystery. The Landscapes of his late paintings are one expression of this new sense of wonder, the Deluge series, a second; his long notes on earthquakes a third.

    There is a span of forty years between his first recorded notes (c. 1478) in the Codex Atlanticus, to his last notes (c. 1518) in that same work. At the outset his notes are often sporadic and, if systematic, tend to reflect models of verbal thinking associated with scholasticism (S2). As his work progresses he composes no less than 18 other notebooks.4 Their different sizes provide clues to their divergent functions (S3). In these notebooks thematic presentation is a key to his organization. The problem is that his themes and combinations thereof are often unexpected (S4). Further study of the notebooks reveals distinct stages in the development of his ideas, ranging from near chaotic scribble sheets to folios intended for publication (S5). These developmental stages in turn throw light on four types of presentation ranging from purely verbal to fully visual.

    As long as verbal thinking had dominated there had traditionally been a series of different kinds of explanation each of which dealt with aspects of a problem. The advent of visual thinking brought with it a single standard of truth with different levels of abstraction (S6). While Leonardo is probably the first to discuss the advantages of visual thinking and presentation explicitly, his approach has its origins among the very Greek philosophers who favoured verbal thinking. And he, in turn, is only partly aware of the consequences of this new way of thought which points to a separation of physics from metaphysics and implies a new system of experiments (S7). The tension between his emergent visual thinking and his inherited verbal thinking helps explain his problems in presenting knowledge. Part of the disorder of the notes reflects the conflict of two modes of thought.

    This tension is again better understood when it is seen as part of a tradition of architect-artist engineers that includes Villard de Honnecourt, Buonaccorso Ghiberti, Francesco di Giorgio Martini and leads to later authors such as Besson, Ramelli, Bettini, Kircher, Weigleb and the Encylopaedists. Leonardo's notebooks thus reveal developmental and cumulative dimensions of knowledge both in the case of an individual, and of a culture as a whole. They can be seen as part of an encyclopaedia of practice (S8) as well as of theory, that offers new insights into problems of continuity and innovation (S9) and provokes us to think afresh about the organisation of historical knowledge (S10).

 

2. Verbal Thinking

    In his notebooks Leonardo often presents his idea, then introduces the opinion of an adversary, which he, in turn, refutes. This approach to knowledge as if it were an argument, here termed "verbal thinking," stands in a long tradition that goes directly back to the Greeks. Many of us remember it simply as the Socratic method, which Plato made famous in his Dialogues.

    Aristotle, in the Analytica priora gives this approach a cloak of respectibility and in the process reduces demonstration to premises, terms and syllogisms. Premises he subdivides into: universal, particular and indefinite. Particular he defines as that which "belongs to some or not to some or not to all."5 This definition reduces the particular to being aprt of the universal and thus subtly removes the autonomy of the individual. This is important because it means that while Aristotle may pay lip-service to the value of particular objects, the thrust of his verbal argument is in terms of logical universal categories which exclude the visual evidence of individual objects that a modern mind associates with demonstrations.

    The result of Aristotle's assumptions is a form of treatise which is a discussion or argument in disguise, in which verbal thinking dominates. In De Caelo, for instance, he introduces the opinions of Empedocles and Democritus and soon afterwards insists: "this they are obliged to assert and do assert."6 In this verbal struggle there is no room for points of view. What seems at first an open discussion is, in fact, a clsoed net leading the unwary into a reductio ad absurdum.7 The adversary is ultimately a straw man whose freedom is purely rhetorical.

    Roman thinkers such as Seneca unconsciously adopt this type of verbal thinking and present it in less subtle terms. His Natural Questions is actually structured as an argument. Hence he writes: "These objects which you have put forward as well as others that no less call for refutation, I will endeavour to refute."8 On other occasions he reports on what his opponent says9 or retorts10 or how "some one interposes, I can draw from this same material an argument to confute you."11

    In the Mediaeval period this argumentative type of verbal thinking flowers as is shown, for instance, by Biagio Pelacani's Quaestiones de perspectivae. His fourth questio asks:

Whether the rays of light passing through triangular apertures naturally tend towards rotundity and are always larger the further they are from the aperture.12

    From a modern viewpoint this is a question of physics requiring a simple yes/no answer with a possible definition of the parameters within which it is true. Biagio's reply is less direct. He begins with an argument on the negative side. This is followed by a second, third, fourth and fifth argument on the negative. The master then replies in three parts. In the first part he limits the question with six pieces of evidence. Five interim conclusions follows, then a corollary, a second part of the fifth conclusion and a sixth conclusion. In the second part of the master's reply, two difficulties are raised. In the third part he gives his final reply to each of the six arguments raised earlier.

    An awareness of the tradition which produces such convoluted forms of verbal thinking casts light on some aspects of Leoanrdo's presentation of ideas. On CA270vc (c. 1490), for instance, he introduces an argument in favour of extromission (see above p. ). To support this he gives an example, following which he explains that this is "to confute" the intromission theory. A second example in defence of extromission follows and under the heading of "examples," he cites six further cases in defence of extrmission. Two more follow on CA270vb.

    It is only now that he itnroduces a contrary position in favour of intromission, beginning with four examples, followed by three more on CA270rb. These /seven/ opinions, he explains, are to establish that vision takes place through intromission. He then introduces a "contrary opinion" in favour of extromission, which he eliminates by means of both a "confutation" and a "proof to the contrary."

    Leonardo's presentation of these pro's and con's of argumentative verbal thinking may lack the elegant numbering of Biagio Pelacani's university approach, but is clearly in the same tradition.

    It is very likely that Leonardo's many references to an adversary also grow out of this tradition of argumentative verbal thinking. Indeed, if the adversary is a rhetorical straw-man, this would explain why scholars have such difficulty in trying to identify who might have been intended.

    There remain, hwoever, many aspects of Leonardo's thought which cannot be explained through this tradition of verbal thinking as, for instance, his answer to the question Biagio had posed concerning light passing through triangular apertures. Where his mediaeval predecessor had launched arguments, Leonardo simply draws six stages in the situation (figs. 783-788) demonstgrating visually how the projection changes as the relative distances of light source, aperture and projection plane are altered. Involved here is a method of visual thinking and demonstration that deserves closer examination. But before so doing it will be useful to examine his different kinds of notebooks, his thematic presentation and stages of organisation.

 

3. Kinds of Notebooks

    It is customary to refer to the notebooks as if they were all very similar. In fact they differ considerably in format from tiny pocketbooks to large folios, and in function from field, studio, study and research notes, through drafts at various stages, to presentation sheets. The smallest notebooks are 320o in format13: Forst II, which is devoted almost exclusively to weights and balances and Forst III, which treats a diverse number of themes. Forst II is characterized by a number of folios headed "experimented," which suggests that it served to record a series of experiments in statics.

    Only fractionally larger are a series of five other notebooks in 24o format: H, I, K, L, M. In these manuscripts he is studying grammar and mathematics and collecting material for later treatises. In H (1493-1494) he concentrates on water, devotes sections to allegory, grammar and mechanics, and some notes to optics and music. In I (1497-1499), he again concentrates on water, and includes sections on geometry, grammar and allegory. In M (before 1500) he devotes a first section to geometry (1-36), a second to weights in connection with the four powers (36v-62v) and a third to the four powers with special reference to bows and cross-bows (63-94). In between he adds notes on water and allegories.

    L (1497, 1502-1503), by contrast, is much less coherent. Its only sustained theme is military architecture. There are brief sections on the flight of birds, mathematics and water, as well as a miscellany of notes on topography, architectural details, clocks, and mechanical devices. He almost certainly used this pocketbook for making quick sketches and field notes during his travels.14 K (after 1504-1509) has four clearly defined themes. The most important of these is mathematics (both geometry and arithmetical proportion). The flight of birds constitutes a second important theme. Optics and painting are a third theme and water is a fourth.

    Four notebooks are in 16o format: Forst I, E, F and G. In the early period he uses this size for advanced drafts. Hence Forst I2 (c. 1489) is a treatise on water screws and other water raising devices. Forst I1 (1505) is a near finished treatise in three books with numbered propositions on transformational geometry. The three later notebooks in this format have multiple themes and are less near completion. In F (1508) he makes drafts for his treatises on water, optics (see above p. ) and astronomy (see above pp. ), interspersed with notes on geometry, the four powers, the elements, and painting.

    In E (1513-1514) he makes an advanced draft of a treatise on the flight of birds. He also devotes sections to weights, painting, geometry, the four powers, water and optics. In G (1510-1515) he is primarily concerned with a draft devoted to light and shade in plants and trees for his projected treatise on painting. He also drafts notes concerning a mechanical device (the sagoma); quadrature of the circle; water, the four powers and the flight of birds.

    He employs both a small and large 8o format. He uses the small version for two study books: Triv and Fol B. In triv (1487-1490), he is chiefly concerned with learning the vocabulary befitting a courtier. Between these lists of words he adds sayings, a few architectural drawings and related mechanical devices. In Windsor Fol B (K/P39-81) he makes studies of the human body beginning at the head and ending with the feet.

    He uses the larger 8o format for seven notebooks (B, A, Mad I, Mad II, Turin, D and BM) which range from rpeparatory to advanced drafts. B (1490), the earliest of these is primarily a collection of notes and ideas on military and civil architecture and related mechanical devices, with a section at the back devoted to manpowered flight.

    A (1492) contains an advanced draft of a treatise on perspective (see Vol 1, part I.2), drafts for his projected treatise of painting and esections on optics, geometry and the four powers. In Mad I (1493-1494) he devotes sections to fortification, transformational geometry, topography, surveying and construction of his equestrian monument. Mad II (1503-1504) contains drafts of a treatise on mechanical devices and parts such as screws, wheels and gears, as well as a treatise on weights and balances, for which he has numbered some two hundred figures. The Turin notebook is an advanced draft of a treatise on the flight of birds with an introductory section on weights and balances to deal with the principles of equilibrium in flight. D. (1508), as has been shown (see above pp. ) is an advanced draft of a treatise on the eye intended to serve as a chapter in his astronomical work (see above pp. ). A number of the folios in BM Arundel are also a large 8o format and deal chiefly with weights and balances, mirrors, optics, geometry and water. In the case of this notebook he explicitly states that he is concerned with arranging things roughly, and hopes to improve upon the order later.

    He reserves the 4o format for specialized studies: C, Leic (Hammer), Fols A, CI and CII. In C (1490) he concentrates on light and shade, and as a result of analogy devotes some folios to percussion and water (see above pp. and figs. 1760-1761). Leic (Hammer) is an advanced draft of a treatise on water, with some notes on astronomy. Fol A (K/P134=151) is an anatomical treatise on arms, hands and legs and feet. C (K/P153=161) concentrates on the diaphragm and internal organs. C (K/P162-183) is also anatomical and devoted to the heart.

    In addition there are two works of folio format. Of these the Codex Atlanticus is the largest (650 x 440 mm) and the longest. Its folios range from very large size (eg. CA103rb, 450 x 285 mm) to extremely small (eg. CA11vd, 35 x 32 mm). It is very likely that these small pieces were originally parts of larger folios, as Pedretti15 has shown to be the case with a number of fragments at Windsor.

    When Pompeo Leoni compiled the Codex Atlanticus in the sixteenth century he referred to it as "Drawings of machines, the secret arts and other things." By secret arts he no doubt meant (1) military studies including burning mirrors; (2) transformational geometry using lunules, by means of which he believed he could master all changes in shape in objects and (3) perspective, which provided a method for reproducing Nature and a means of analysing Nature's powers such as heat and force (see Vol 1, parts I-II).

    In modern terms Leoni attempted to collect sheets dealing with the physical sciences in the Codex Atlanticus. Those dealing with the life sciences he put together in a second group which is now the Collection of Her Majesty the Queen at Windsor. Here the chief themes are human anatomy, drawings and caricatures of the human figure, studies of horses and of Nature, with a few folios on animals and gometry.

    Before Pompeo Leoni compiled them the CA and Windsor folios almost certainly lay about loose in piles in Leonardo's studios. These loose sheets primarily served as an interim stage in the development of his ideas, between the rough notes in the field and more advanced drafts in notebook form, which explains why they range from scribble sheets (fig. 1817) to carefully presented folios (figs. 1812). Among these loose sheets he also kept his advanced technical (fig. 1811) and artistic drawings. This is a further reason for the remarkable variety of the folios in CA and Windsor.

    Hence the notebooks contain seven quite distinct kinds of notes: (1) random field notes; (2) thematic and/or systematic field notes; (3) study notes especially concerning grammar, geometry and arithmetic; (4) research notes on a specific subject such as anatomy, weights and balances; (5) studio notes; (6) drafts for technical and artistic drawings and (7) drafts for treatises.

    The contents of these notebooks are often cited as evidence that Leonardo was a universal genius. Closer inspection reveals, however, that the themes which fascinated him were considerably more specialized than is usually assumed. Mediaeval learning had directed its energies on three major fields; theology, law and medicine. Leonardo ignored theology and law and focussed on one branch of medicine: anatomy.

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Chart 31. Survey of the format and function of the notebooks

    At a more general level mediaeval learning had been based on the seven liberal arts; the trivium of grammar, rhetoric and dialectic and the quadrivium of arithmetic, geometry, astronomy and music. Leonardo has a passing interest in grammar, ignores rhetoric, (except insomuch as it serves him practically in his paragone) and dialectic; learns a minimum of arithmetic; becomes fascinated by geometry in his later forties and then concentrates on lunules and transformational geometry; appears to have learned little traditional astronomy but develops his own views on the subject and with the resepct ot music, concentrates on its practical aspects.

    Although there are at least 50 topics which receive mention in the notebooks, the themes which interest him profoundly and concerning which he writes or plans to write treatises are, roughly in the order of their importance to him, about a dozen: geometry, mechanics, water, optics and perspective, painting, anatomy, the four powers light and shade, the flight of birds, nature, mirrors and regular solids.16 His mediaeval predecessors would have clased most of these among the illiberal arts. In other words, Leonardo the so-called universal man is, in fact, a specialized researcher whose energies are focussed on technology, the physical and the life sciences. How is it possible, one might ask, that he has been so utterly misunderstood? An important clue lies in the themes he uses to present his ideas.

  

 4. Thematic Presentation

     With the exception of a few scribble sheets, (see below pp. ), Leonardo devotes most folios to a specific theme or combination of themes. One might expect that this should be obvious but there are at least three reasons why it is not: (1) he employs very general themes; (2) the themes are often unusual, and (3) he presents unexpected combinations of themes based on analogies which assume an understanding of the material.

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Fig. 1760: Percussion of hammers and light on C22r.

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Figs. 1761: Percussion of hammer, knife, light and water on C7r.

    The first of these requires little explanation. Because he employs generic themes such as mechanics, a folio often contains a variety of apparently unrelated machines and devices. His choice of unusual themes is best illustrated with examples. As Dr. Keele17 has shown, the four powers (percussion, force, movement and gravity) play a central role in his concept of science. Leonardo frequently uses one or more of these powers as the theme of a folio. On C22r (fig. 1760, 1490-1491), for instance, the theme is percussion. At the bottom of the folio he draws three diagrams showing percussion of light in the open air (see above pp. and figs. 476-478). In the central portion of the folio he draws four diagrams in which different sizes of candle and distance produce shadows of varying intensities (see above p. and figs. 398-340). In the right-hand margin he draws three diagrams of an axe striking wood and finally three diagrams of a nail which is driven in a straight or a bent form. In Leonardo's mind these diverse topics are intimately connected: direct or oblique light striking an object and a direct or oblique hammer striking an object are all cases of percussion which deserve comparison.

    Percussion is also the implicit theme on C7r (fig. 1761, 1490-1491). Here he arranges in a row the blows of hammers, of a knife, of light passing through an eight sided aperture (see above p. and fig. 819 ), and of water passing through multiple apertures Once one recognizes his logic, it is surprisingly sensible.

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Fig. 1762: Light and shade studies on CA195va.

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Figs. 1763-1764: Light striking a St. Andrew's cross and apertures on CA177rb and ve. Comparison of four shadows and four lights.

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Figs. 1765-1766: Shadows produced by St. Andrew's cross and variants on CA37vd and BM243r.

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Figs. 1767-1768: Preparatory demonstrations involving a St. Andrew's cross on CA229rb and BM248v.

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Figs. 1769-1770: Advanced demonstrations involving a St. Andrew's cross and pinhole apertures on CA241rbc, vbc.

    A third reason why the underlying structure of many folios is difficult to discern is because he combines themes on the basis of analogy. On CA195va (fig. 1762) for instance, the chief theme is clearly light and shade. Indeed a reader unfamiliar with Leonardo's through, may assume that it is due to a quirk or simply a mistake that he interjects a paragraph on hammers in the midst of this folio. In Leonardo's mind, however, light and hammers are both examples of percussion.

    Analogy sometimes leads him to combine obvious themes in unexpected ways. For instance, he thinks of shade as a negative light and hence compares the effects of multiple shadows produced by one, two or more columns with the effects of a light source passing through multiple apertures in a camera obscura on CA177ve, 177rb, 229vb, and 241rcd. The same basic associations lead him to compare irregular projections of shade and light on CA241vbc (fig. 1770).

    This does not, of course, prevent him from dealing with the problem of columns in isolation on CA37va, 229rb, BM243v and 248v. Indeed such folios with isolated themes play a basic role in the development of his ideas. Hence the CA drafts (figs. 1763-1765, 1767) lead to BM248v (fig. 1768) which, in turn, serves as a draft for CA241rbc (fig. 1769).

    On D10v (fig. 1771) his starting point is a straightforward analogy between eye and camera obscura. His studies of the camera obscura have revealed that boundaries of light and shade inside such a chamber are unclear. By way of analogy he considers the unclear boundaries of an object in front of the eye in his third diagram on D10v. On CA190vb (fig. 1772), an earlier draft, these same themes are in evidence. In addition, he is aware that a camera obscura inverts imnages and that a mirror reverses images. He therefore compares the two in relation to what happens in the eye.

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Figs. 1771-1772: Eye-camera obscura analogies on D10v and CA190vb.

Figs. 1773-1774: Parallels between light/shade and sight on CA204rab and CA298va.

Fig. 1775: A preparatory sheet on BM104r.

Fig. 1776: A development of the foregoing on BM25r.

Figs. 1777-1778: Optics and astronomy on CA112ra and CA208vb.

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Figs. 1779-1780: Optics, water and astronomy on CA237ra and CA251rb.

    The underlying analogy between light and sight of the above folios, recurs in another form on CA204rb (fig. 1773,** ) where he implicitly compares the angles of light passing through a camera obscura with the maximal angle of vision. This leads on CA204ra to a study of how angles of light produce shade. On CA298va (fig. 1774) this sight-light/shade analogy leads him to compare effects of occluding objects in front of both eyes and light sources.

    His reasons for relating themes frequently assume an understanding of his work. We have examined why he relates the size of pupils to the size of the sun in water (see above p. ) and why he associates the sun's reflection from waves of water with the moon (see above p. ). This explains why studies of the sun's image in water occur on folios which also deal with optics as on BM25r (fig. 1776) and astronomy as on BM104r (fig. 1775).

    In this context it also makes sense that the theme of sunlight from waves and the moon should appear on the same folio on CA112ra (fig. 1777) and CA208vb (fig. 1778 cf. 2779) or that water and the moon are discussed together on CA251rb (fig. 1780). Because he is also concerned with possible illusions in astronomy produced at the eye, he includes both visual angles and reflections from eyebrows on CA208vb (fig. 1778). Viewing distant planets and stars reminds him of the question of minimal size of objects seen. Hence occlusions at the eye and astronomy occur together on CA112ra (fig. 1770) and CA237ra (fig. 1779). Moreover, because he thinks of the eye as a camera obscura, he compares these problems of visual angles and occlusion at the eye with those in a camera obscura on CA112ra (fig. 1777).

Fig. 1781: Optics and water on F95r.

Fig. 1782: Intersecting circles in water and geometry on cA281ra.

Figs. 1783-1784: Geometrical lunules and convex mirrors on CA241ra and 279ra.

Figs. 1785-1786: Transformational geometry and transformations of images in camera obscuras on CA187ra, va.

    The reasons for his analogies between water and optics run deeper. Water produces visible equivalents to the invisible waves of light, sight and sound in the air. It is thus fitting that his optical treatise withint the manuscript F should begin on F95r amidst studies on water (fig. 1781). Circular waves of water produce complex transformations of shapes. By analogy, water and transformational geometry appear together on cA281ra (fig. 1782). Circular waves of light passing through comera obscuras also produce complex transformations of shapes. By analogy, camera obscuras and transformational geometry appear together on CA187ra, va (figs. 1785-1786). Circular waves of light striking convex mirrors produce similar transformations. By analogy, convex mirrors and transformational geometry appear together on CA242 (fig. 1783, cf. figs. ) and CA279ra (fig. 1784, cf. figs. ).

    Such examples illustrate how themes dominate his draft folios and how anlogy often leads to unexpected combinations thereof. The drafts, in turn, mark a stage in the development of his ideas and with each stage his presetnation changes.

 

5. Stages

    Leonardo is very conscious of the provisional nature of his notebooks and plans to arrange them more systematically. This is on his mind when he starts the Codex Arundel, (fol 1r):

Begun...in Florence in the house of Piero di Baccho Martelli on the 22nd day of March 1508. And this will be a collection without order taken from many pieces of paper which I have here copied hoping later to put them in order in their places according to the material of which they treat and I believe that before I am at the end of this, I shall have to repeat a same thing many times. Hence, reader, do not reproach me because the subjects are many and the memory cannot retain them all and say: this I do not want to write because I wrote it earlier. And if I did not wish to fall into such an error it would be necessary that every time I wished to copy something out, in order not to repeat it, I would have to read all that came before and especially if there is so much with long intervals of time in writing from one time to the other.

    In the Codex Leicester he makes a further comment concerning the organisation of his notes (2v):

I shall not consider the demonstrations here because I shall reserve them for the ordered work; my concern how is to find cases and inventions, gathering these as they occur to me; then I shall have them in order, placing those of the same kind together; therfore you will not wonder nor will you laugh at me, reader, if I here make such great jumps from one subject to the other.

    His conscious efforts to organize the notes first become evident in the late 1480's in the Codex Trivulziano. Among his earliest attempts are folios dealing with unrelated subjects, such as grammar, historical anecdotes, physics and optics as on Triv 11v (fig. 1787, 1487-1490). In the simplest cases an optical diagram on such a folio can lead directly to a folio such as C21r (fig. 1788, c.1490-1491) where the diagram recurs in the right-hand margin of a sheet devoted to light and shade.

Fig. 1787: Preparatory sketch on light and shade on Triv. 11v.

Fig. 1788: Advanced version of the same sketch on C21r (upper left).

Figs. 1789: Preparatory sheet on Triv. 29r.

Fig. 1790: Development of same on A90v.

Figs. 1791-1792: Three themes in no apparent order on CA37va and one theme in no apparent order on CA144va (Stages 1-2).

Figs. 1793-1795: Rough columns with figures interspersed on K/P 22v; columns with figures to the side in some order on K/P 118r and CA237rcd (Stages 3-4).

    In other early cases his starting point may be a folio dominated by a single theme, such as Triv 29r (fig. 1780), which may lead directly to a systematic treatment of an individual item as on A90v (BN2038 10v, fig. 1790). Here a heading introduces a centrally positioned diagram which is followed by an explanatory passage.

    He first mentions this manner of presentation on CA109vc (c. 1490): "Make the simple propositions and then the demonstrations with figures and letters." On A31r he considers a modified version:

I remind you that you make your propositions and that you adduce the above said things with examples and not with propositions which would be too simple.

    In more complex cases an idea may undergo a number of drafts in the Codex Atlanticus and/or elsewhere. Sometimes a draft will contain several themes as on CA37va (fig. 1791). At other times a draft may have but one dominant theme as on CA144va (fig. 1792). Crossed out passages indicate that he has developed his ideas elsewhere.

    As his ideas progress, he organizes them in columns. In the early period these columns are frequently rough with figures interspersed throughout, as on W19147-19148v (K/P22v, fig. 1793). By the late period the columns are regular and figures tend to be in the right-hand margin, as on W19149-19152r (K/P118r, fig, 1794) and CA237rcd (fig. 1795).

Fig. 1796: Single theme, columns, with figures to the side in some order on A56r (1492).

Figs. 1797: The same topics C. 20 years later on Leic.3v.

Fig. 1798: Text with systematic figures on Leic. 14r.

Fig. 1799: Text without figures on Leic.16.

Fig. 1800: Figures with captions in the Sketchbook of Villard de Honnecourt.

Figs. 1801-1803: Text and captions on CA92vc, 92ra and 167rab.

    Sometimes as on CU524 (TPL507, 1510-1515) the figure has been drawn in the centre of the folio, but with a note indicating that it is to be moved later: "Placed in the margin this figure will be put into the 42nd of perspective." A format using a single column of text with figures in the right-hand margin emerges as a method of presentation in manuscript C (fig. 1788, c. 1490). Comparison of two folios, Manuscript A 56r (fig. 1796, 1492) and Leic 3v (fig. 1797, 1504-1509), both dealing with water and analogies between underground rivers and arteries in the body, gives some indication how constant this mode remains.

    Some folios in the Codex Leicester are more sophisticated. On Leic 14r (fig. 1798), for instance, he begins with the heading "26 cases," each of which is introduced by a capital letter in the column that follows. In the right-hand margin he illustrates fifteen of these with diagrams. On Leic 16r (fig. 1799), he lists 23 propositions in a similar fashion, except this time without illustrations.

    Villard de Honnecourt, in his Sketchbook, (fig. 1800) had used another method of presentation, arranging a series of diagrams horizontally, each with a brief caption underneath. Some of Leonardo's drafts lead to this mode of presentations (figs. 1801-1803). Such examples show that Leonardo uses between two to five stages in arriving at a finished folio with text and figures (Chart ** ). There are, however, three further alternatives for finished folios: some have only text; others have a series of diagrams in sequence and some have presentation drawings, either technical or artistic. Each of these have their own stages of development (Chart 32).

Chart 32: Stages in the development of different kinds of folios.

Figs. 1804-1505: An early case of text only with headings above the paragraphs on A 104r, 1492 and a late example of text only with headings in the margin on D 5v, 1508.

Figs. 1806-1808: Three stages in the organisation of Leonardo's visual demonstrations on A87v, CA274va and CA149rb.

Figs. 1809-1811: Three stages in the case of a technical drawing on CA353va, CA15ra and CA391va.

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Figs. 1812-1815: A case where an early drawing is more elaborate than later ones. Fig. 1812, CA1vb; fig. 1813, Forst.III 56v; fig. 1814, CA298rb; fig. 1815, Mad. I43r.

Figs. 1816-1817: Detailed drawings of the three ventricles on K/P 104r (1506-1508) and later rough sketch of same on K/P 127v (c. 1510).

    In the early period finished folios which have text only, have headings followed by paragraphs as on A104r BN2038 24r (fig. 1804 1492). By the late period the headings have become miniature passages in the columns as on D5v (fig. 1805, 1508). Series of figures have their own development. They begin with rough folios, as in cases with text and figures. At a second stage a series of diagrams is arranged in columns, without any particular order (fig. 1806). At a third stage a clear sequence in the diagram evolves (fig. 1807). At a fourth stage diagrams are both carefully arranged and numbered (fig. 1808).

    In the case of technical and artistic drawings, a diagram often makes its first appearance as a quick sketch among others devoted to a given them. On CA353va (fig. 1809), for instance, a first draft of a rampart appears amidst other military sketches. At a second stage, such a rampart may recur as one of the dominant drawings on a folio (fig. 1810). At a final stage a single drawing dominates the folio (fig. 1811).

    While Leonardo's approach is basically developmental and cumulative, it is important to recognize that this is not always the case. On CA1vb (fig. 1812, 1490) he draws an elaborate crane for digging canals. Some ten to thirteen years later he draws a much more primitive version of such a crane on Forst III 56v (fig. 1813). He subsequently makes a series of drafts on CA298rb (fig. 1814, c. 1495) which then lead to a further presentation drawing on Mad I 43r (fig. 1815).

    One further example of this "retrogressive" tendency may be cited. On W19127r (K/P 104r, fig. 1816), he makes his famous wav injections of the three ventricles. Some two to four years later, a rough sketch of these three ventricles recurs amidst sketches on geometry, optics, statics and caricature on W12669v (K/P127v, fig. 1817). To an untrained eye this folio has all the appearances of an early draft. It is, in fact, an exception: one of the very few late examples which is effectively a scribble sheet, not devoted to a clearly defined theme. That it is a late folio is confirmed by the numerous sketches relating to transformational geometry, a theme which concerns him in the period after 1505.

    An understanding of these stages in the development of the note-books confirms that he aimed at a much more systematic form of presentation than some rough folios might suggest. He is not just writing for his own sake. His many references to "O reader" are no accident. Nor can his comments about intended publication be dismissed so lightly.18 As Vasari reminds us, the possibility of publishing the work was still being explored after Leonardo's death.19

    A prerequisite for visual thinking is a firm belief in the veracity of vision, in the importance of observation and the visual evidence that it brings. In a sense, Ancient writings on optics were attempts to establish criteria for the reliability of visual evidence (see above pp. ), but their success was limited. Plato and Aristotle both developed an ambiguous position on the reliability of vision. Plato, for instance, praises the importance of vision in the Timaeus:

we must go on to describe the chief benefit of the function of sight, which was God's reason for giving it to us. For I reckon that the supreme benefit for which sight is responsible is that not a word of all we have said about the universe could have been said if we had not seen stars and sun and heaven.

As it is, the sight of day and night...has...given us the notion of time and made us inquire into the nature of the universe; thence we have derived philosophy, the greatest gift of the Gods ever given or will give to mortals. This is what I call the greatest good our eyes give us.21

    However, the same Plato becomes famous for his attacks on the deceptiveness of vision in the Sophist, the Republic22 and elsewhere. Aristotle's position is no less complex. In his biological writings he emphasizes the paramount importance of vision and observation. In De generatione animalium, for instance, he emphasizes the priority of observation; over theory:

The facts however have not yet been sufficiently grasped; if ever they are, then credit must be given rather to observationthan to theories and to theories only if what they affirm agrees with the observed facts.23

    In the same treatise, he emphasizes the need to examine all particular cases of a problem:

This mistake, then, was due to his speaking generally without examining all the cases, but this is what we ought to do, for any one who makes any general statement must speak of all the particular cases.24

    He again mentions the need to include sense evidence in De motu animalium:

And we must grasp this not only generally in theory, but also by reference to individuals in the world of sense, for with these in view we seek general theories, and with these we believe that general theories ought to harmonise.25

    In De generatione et corruptione, he critizes those who disregard sense perception in favour of the arguments of verbal thinking: "Reasoning in this way, therefore, they were led to transcend sense perception and to disregard it on the ground that one ought to follow the argument."26 Notwithstanding this criticism of others, he himself argumes both in terms of sense evidence and theory as in De generatione animalium: "This is clear not only tot he senses (for it is so) but also on theoretical grounds,"27 which idea he restates in the Physica: "not only on the strength of observation, but also on theoretical grounds."28 In Meteorologica he mentions his criteria for phenomena inaccessible to observation:

We consider a satisfactory explanation of phenomena inaccessible to observation to have been given when our account of them is free from impossibilities. The observations before us suggest the following account of the phenomena.29

    But in his theoretical writings the role of observation emerges in a different light. In the Posterior Analytics, he makes a clear separation between scientific knowledge and perception:

Scientific knowledge is not possible through an act of perception. Even if perception as a faculty is of 'the such' and not merely of 'this somewhat,' yet one must at any rate perceive 'this somewhat' and at a definite place and time: but that which is commensurately universal and true in all cases, one cannot perceive, since it is not 'this' and it is not 'now'.... Seeing, therefore, that demonstrations are commensurately universal and universals imperceptible, we clearly cannot obtain scientific knowledge by the act of perception.30

    It is possible to interpret this passage as claiming that perception is a preliminary stage to the higher abstractionsof science. It is equally possible, however, to read this passage as a claim that temporal-spatial knowledge of the particulars of sense perception is ultimately incompatible with the universals of scientific knowledge. This interpretation could seem forced. But the passage in the Posterior Analytics goes on to point out that:

there are cases when an act of vision would terminate our inquiry, not because we should be knowing, but because in seeing we should have elicited the universal from seeing; if, for example, we saw the pores in the glass and the light passing through, the reason of the kindling would be clear to us because we should at the same time see it in each instance and intuit that it must be so in all instances.31

    Hence visual sense perception is only of interest in exceptional cases. By implication, the acquiring of scientific knowledge can basically do without observation. Aristotle's statements in favour of observation clearly outnumber this rejection of sense evidence. In the centuries that followed, however, the fate of individual works varied considerably. The Analytica Posteriora became a standard textbook while biological works such as De generatione animalium remained virtually unknown.32 Aristotle could thus play a significant role in undermining attention to visual evidence.

    Meanwhile, within the optical tradition study of the criteria for accurate vision continued (see above pp. ), and the study of individual cases grew in significance. Alhazen's work provided a compendium of specific phenomena relating to vision and mirrors. Witelo added a repertoire of mathematical works to his optical thesaurus, and his contemporaries Roger Bacon and Dietrich von Freiberg emphasized the importance of collecting examples of visual evidence when trying to solve a given problem.33 Others emphasized a metaphysics of light34 and stressed the religious and scientific implications of vision (Pecham).

    Leonardo inherits this late mediaeval belief in the veracity of vision and the importance of observation (see above p. ). At the same time he emphasizes the significance of recording observations in the form of diagrams and drawings, and insists on their supremacy over words (see Vol 1, pp. ). Or to put it differently, he insists on the primacy of visual thinking and visualisation over verbal thinking and verbalisation.

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Chart 33. Eleven types of visualisation.

    Visualisation today connotes a rendering of the natural world as if seen through a perspectival window: the equivalent of a photographic approach. Leonardo inherits this simile from Alberti, produces such a window and explicitly describes its importance for the artist, a suggestion which his younger contemporary Dürer popularizes (see above Vol 1, part I.4). Nonetheless, a small minority of Leonardo's paintings and drawings have anything approaching this photographic effect. This is partly because his concept of visualisation involves a spectrum of possibilities including many dimensions of the inner world of the mind (see Chart 33).

    Moreover, when he represents the natural world he often draws in a type of shorthand whereby he isolates a function or essential aspects of a given phenomenon as, for instance, in the case of the camera obscura, where he shows how rays are inverted without showing the details of the chamber within which this occurs (figs. 690-699). This tendency to reduce objects to skeletal two-dimensional geometrical diagrams reflects his inheritance from the Euclidean tradition (see below p. ).

    What sets Leonardo apart from his predecessors, however, is his committment to visualize verbal claims and theories. This applies to Ancient theories, such as Seneca's similes concerning percussion (see above pp.**) or his analogies between arteries in the human body and underground waters in the earth35 (figs. 179601797). It applies equally to mediaeval theories. Hence he illustrates visually the techniques for exploring the heart which Mondinus36 described verbally (see Vol 1, figs. 894-897). He visualizes his own theories about the spinal cord functioning like the mast of a ship with equal vigour (see Vol 1, fig. 928).

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Figs. 1818-1819: Leonardo da Vinci, Lady with an Ermine (Cracow, Czartoryski) and detail from Carpaccio, Portrait of a Knight (Lugano, Thyssen).

Fig. 1820: Ermine in J Camerarius, Symbolarum et emblematum ex animalibus...centuria, Nurnberg 1595.

    Hence his interest in visualisation is not in opposition to verbal images. Indeed, the great development in visualisation is part of a more complex phenomenon which involves a new literalism in the interpretation of the word - the theological and philosophical aspects of which Ong has explored - which process may be termed visual literalism or literal visualism (see Vol 1, Epilogue). A revolution of words and pictures thus goes hand in hand, and its effects on literature, art, religion, science and philosophy constitute much of that which we associate with the renaissance and reformation.

    Imprese and emblems, the depiction of verbal ideas in visual form are one manifestation of this new approach to words and pictures. Leonardo is exploring these in the late 1480;s (see Vol 1, Epilogue) and his interest reflects a popular social game of the time as Castiglione reports in his Courtier:

...and sometimes ingenious games were played (now on the suggestion of one person and now of another) in which, using various ways of concealment, those present revealed their thoughts in allegories to this person or that. And occasionally there would be discussions on various subjects, or there would be a sharp exchange of spontaneous witticisms and often imprese as we call them nowadays were devised for the occasion.37

    Courtiers wear such imprese, "appropriate mottoes and ingenious devices"38 on their clothing and armour. The depiction of such emblems varies. In Leonardo's Lady with an Ermine (fig. 1818) the ermine appears simply as a visual representation of chastity. In carpaccio's Portrait of a Soldier (fig. 1819) the ermine is accompanied by the caption: "malo mori quam foedari" (I prefer to die rather than be soiled). In the North this is reporduced by Camerarius39 in an emblem book (fig. 1820).

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Figs. 1821: Big fish eating little fish in Mariano di Jacopo detto il Taccola, Liber tertius de ingeniis, (1427-1433).

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Fig. 1822: Pieter Breughel the Elder, Big fish eat little fish, 1556 (Vienna, Albertina).

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Fig. 1823: Pieter Breughel the Elder. The Land of Cockaigne, 1567.

    Closely related to this is Leonardo's literal visualisation of proverbs in the form of pictograms and sketches. Breughel's Netherlandish Proverbs (see Vol 1, Epilogue, plate 69) is again an extreme expression of the same approach. The same Breughel makes elaborate engravings of a proverb such as "big fish eats the small"40 (fig. 1822, cf. fig. 1821) or of a Flemish verse concerning the land of Cockaigne:

All you loafers and gluttons who love to be lying:
Farmer, Soldier, or Clerk - you can live minus trying.
Here the fences are sausage, the houses are cake,
And the fowl fly 'round roasted, all ready to take.41

    Striking in Breughel's engraving (fig. 1823) is how he literally draws fences of sausage and houses of cake. This literal depiction is part of another phenomenon: the upsurge of illustrations in literary text, such as Sebastian Brandt's Narrenschiff attributed to Durer. In chapter eight, for instance, the verse reads:

Viel sind von Worten weisen und klug
Die ziehen doch den Narren Pflug

Many are wise and clever in words
Yet they draw the Fool's plough.42

    The woodcut attributed to Durer shows a fool literally drawing a plough (fig. 1824). Chapter 31 in the same work reads:

Der ist ein Narr
Der singt Cras, Cras der Rabensang
Und weiss nicht ob er lebt so lang.

Who sing cras, cras* the whole day crow's song
And does know whether he lives so long.

 (* the Latin word for tomorrow.)

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Figs. 1824-1825: Sebastian Brandt, Narrenschiff, 1494.

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Figs. 1826-1827: Till Eulenspiegel.

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Fig. 1828: Virgil, Opera, Lyons, 1529.

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Figs. 1830-1831: Albrecht Durer, Apocalypse, (1511) and Neues Testament, (1522).

     The woodcut attributed to Durer (fig. 1825) again shows a fool and crows literally singing "crass cras" (tomorrow, tomorrow). This literal illustration is also apparent in Till Eulensprigel. The protagonist is meant to throw hops (Hopfen) into a tank and instead throws in a dog named "Hops" (Hopf),44 (fig. 1827). Or he is requested to cut a measure of cloth termed a "wolf" and instead cuts a measure in the shape of a wolf45 (fig. 1827). Such examples are the more interesting because they reveal that more than literal illustration of the text is at play. Taking words literally, too literally, is now an aspect of literary style, and a new source of humour.46 Rabelais uses a related literalism when he derives the etymology of Beauce from Beauce47 or Paris from Par rys.48

    Nor is this tendency to illustrate verbal textx visually restricted to vernacular literature. The same artist responsible for the woodcuts to Sebasian Brandt's Narrenschiff, also produces woodcuts for the Comedies of Terence49 and the Apocalypse in the New Testament50 (fig. 1829). The writings of Virgil undergo a similar visual transformation51 (fig. 1828). Hence a new interpretation of language in terms of literalism generates emblems, illustrations to verse, vernacular writings, classic texts and introduces new dimensions in literary expression and humour. It also generates the upheavals of protestantism.

    Luther's literalism emphasizes the importance of "sola scriptura" and leads to an attack on the loose allegorical and metaphorical tradition of interpretation associated with the Church fathers,52 and mediaeval writings such as Jacobus de Voragine's Golden Legend.53 This new literal interpretation of words goes hand in hand with a more literal representation of words as illustrations. Thus Cranach and his school produce a more literal version of Dürer's conceptions54 (figs. 1830-1831).

    The iconoclast tendencies, especially among the Calvinists, are not in contradiction to this approach. Ultimately the Calvinists are quite content with visual images, witness their many portraits. Their proviso is that visualisation should be limited to the natural world and should not intrude upon supernatural realms. This is a religious expression of a distinction which Leonardo as a scientist states the other way round, namely, that speculations concerning metaphysics and the invisible supernatural realms should not intrude on physics and the visible natural world (see above p. ). The subject-object distinction55 is a philosophical expression of the same phenomenon: a distinction between invisible claims which remain subject and visible evidence which is objective and quantitatively measurable.

    Approached in this way many seemingly disparate phenomena of the Renaissance and Reformation are recognized as expressions of a basic shift in the meaning of words. Leonardo's tendency to take words literally and render them as pictograms or emblems is also that which leads him to take ancient verbal analogies and visualise them as quantitative experiments. Further changes in literature, science, art and philosophy emerge as aspects of a European phenomenon.

    Hence the long standing debate whether early modern science is Protestant (Merton)56 or Catholic (Russo)57, misses the point. The religious controversies were not the cause: they themselves were an effect of something more basic. The new approach to words and pictures that inspired the rise of science also prompted the debates between protestants and catholics. It is equally misleading to pretend that the shift is fundamentally a Northern phenomenon, that visual thinking or "eye language"58 belong primarily to Dutch art, while Italian art remains part of a "textual culture." Brunelleschi's perspectival experiments with mirrors differ from Van Eyck's. But both are exploring how to record the visual world. So too are Leonardo and Dürer, although the details of their procedure varies considerably.

    Ultimately it is a question of North and South; an interplay between English, Netherlandish, French, Burgundian, German, Swiss, Austrian, Hungarian, Polish, Spanish and Italian cultures that serves as a prime catalyst for these developments in literal interpretation and visual thinking. And because this phenomenon affects the whole of Europe, it becomes easier to understand its impact on the concept of truth itself.

 

6. Explanations and Truth

    Verbal thinking led to an argumentative tradition of disputations with alternative explanations for the same phenomena. In the case of optics there emerged, in Antiquity, no less than four of these explanations on the part of natural philosophers, philosophical, mathematical and medical opticians (see above p. ). This helps explain why the Greek concept of truth (episteme) retains connotations such as "acquaintance with a matter," or "understanding" as well as "skill" or "professional skill,"59 thus dovetailing with the meanings of "craft" (techne), an ambiguity that continues in Latin with the terms scientia and ars.60 Aristotle may argue for a single scientific truth,61 but he also assumes that different professions should concern themselves with other aspects of a given problem or object.62

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Figs. 1832-1835: Diagrams concerning diplopia from Ptolemy's Optics.

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Figs. 1837-1837: Diplopia experiments in Alhazen (III.12) and Witelo (IV.108).

    Visual thinking and visualisation introduces an objective standard of truth, because a visual claim has built into it a challenge of matching a drawing or picture with the original, and the extent to which it matches or fits can be measured quantitatively. Or, to use Popper's term, it is open to "falsification." Verbal claims, which cannot be translated into visual demonstrations or experiments, lose their authority. Contending explanations give way to a single concept of truth and a new science based on measureable visual evidence emerges.

    What is so difficult to understand in retrospect is that these simple logical steps took centuries. As has been shown (Vol 1, part I.4) the perspectival window invented in the 1420's, is first drawn by Leonardo in c. 1490, published by Dürer in 1525 and is not extensively used for practical military purposes until the turn of the seventeenth century. Similarly, Leonardo makes mechanical models of the human eye, but a model that matches physical reality is first made by Scheiner63 (fig. 1870) more than a century later. Hence the matching process implicit in visual thinking only develops very gradually.64

    The roots of this matching process can, of course, be traced back to Antiquity. Euclid, for instance, renders physical situations abstractly as a series of geometrical lines (figs. 1839, 1842). In the mediaeval period problems gradually become rendered less abstractly, as is apparent from a comparison of diplopia diagrams in Ptolemy, Alhazen and Witelo (figs. 1832-1837). By the fifteenth century, the anonymous author of Della prospettiva includes both abstract and concrete diagrams (fig. 1838). A surveying problem which Euclid had drawn abstractly (fig. 1839), is translated into three-dimensional figures (figs. 1840-1841) by the sixteenth century authors. Similarly, they present in quantitative terms (fig. 1843) a related problem which Euclid discussed qualitatively (fig. 1842).

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Fig. 1838: Abstract and concrete diagrams in Della prospettiva, (Florence, Riccardiana n. 2110) attributed to Alberti and Paolo dal Pozzo Toscanelli.

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Figs. 1839-1841: Euclid, Optics, Theorem 19; Apianus, Quadrans, fol. E2r, 1532.

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Figs. 1842-1843: Euclid, Optics, Theorem 10 and Cornelius de Iudaeis, De quadrante geometrico, Nurnberg, 1594.

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Figs. 1844-1847: The same problem illustrated at various levels of abstraction. Figs. 1844-1845, BM248v; fig. 1847, CA177rb; fig. 1847, CA37va.

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Fig. 1848: Johannes Zahn, Oculus artificialis, 1685.

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Fig. 1849: J. Doppelmayr, Dissertatio visionis, 1699.

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Fig. 1850: A crane and hoisting device in Villard de Honnecourt, Sketchbook, Paris, Bibliotheque Nationale, Ms. 19093 fol. XLIV.

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Figs. 1851-1852: A crane on CA** and a hoisting device on Mad 1852.

    Leonardo often devotes a series of figures ranging from abstract figures to concrete sketches of the same situation (e.g. figs. 1844-1847, see above pp. ). By the seventeenth century this leads to textbooks containing both two and three-dimensional diagram (figs. 1848-1849). A single concept of bruth is now expressed at different levels of abstraction.

 

7. Encyclopaedia of Practice

    This enormous rise in visualisation serves, in turn, to form a new encyclopaedia of practice.

    Such encyclopaedic collections of practical knowldge again have precedents in Antiquity, such as Vitruvius. But the focus of presentation is different. Vitruvius describes, for instance, how he will:

give brief explanations so that they may be committed to memory; for thus expressed, the mind will be enabled to understand them the more easily.65

    Verbal thinking is his main concern. In his text he also refers to diagrams66 but these are no longer extant. By the thirteenth century practical knowledge in the form of sketches and diagrams emerges within the encyclopaedic tradition, as, for instance, in Villard de Honnecourt's Sketchbook (figs. 1850). Some of his rough sketches recur in more elaborate form in Leonardo's notebooks (figs. 1851-1852).

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Figs. 1853-1854: Hoists in Buonaccorso Ghiberti and Francesca de Giorgio Martini, Cod. Torinese Saluzziano, 148, fol 52r.

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Figs. 1855-1857: Hoists on CA 309rb, 37vb and 349ra.

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Fig. 1858: Water hoisting devices in Francesco di Giorgio Martini, (Turin, Cod. Saluzziano 148, fol 48r).

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Figs. 1859-1860: Water raising devices on CA386vb and in a sixteenth century manuscript (Florence).

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Fig. 1861: Francesco di Giorgio Martini, (Turin, Cod. Saluzziano 148, fol 38r).

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Fig. 1862: Weigleb, Die naturliche Magie.

    Leonardo also borrows from other sources. As Reti67 and Scaglia68 have shown a crane drawn by Buonaccorso Ghiberti (fig. 1853) recurs in the Codex Atlanticus (fig. 1857). A similar drawing is found in the work of Leonardo's elder contemporary, Francesco di Giorgio Martini (fig. 1954). The same Francesco makes numerous drawings of water hoisting devices (fig. 1858) which, in turn, are copied by Leonardo (fig. 1859) and his sixteenth century followers (fig. 1860. In the case of a horse driven mill grinder drawn by Francesco (fig. 1861), effectively the same device recurs nearly three centuries later in a work by Weigleb (fig. 1862). These random samples give a hint of the complex cumulative tradition of encyclopaedic practical knowledge, which is the context for Leonardo's notebooks.

    At the time of Villard de Honnecourt in the 1230's this tradition is limited to a record of isolated practical experiences. By the fifteenth century a greater number of examples are collected. Leonardo's esystematic play with variables (se Vol 1, part I.3; part II2-3) takes this process a significant step further. This is another reason why his notebooks are so much richer visually than the treatises of his predecessors and why his work prefigures the encyclopaedias of the seventeenth century.

 

8. Continuity and Innovation

    A detailed study of this encyclopaedic tradition of practice would reveal how interest in isolated examples led gradually to systematic records and to that sense of mastery over Nature in all her particulars that inspired seventeenth century natural philosophers to search for universal laws to account for these.

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Figs. 1863-1865: Life jackets. Taccola, De ingeniis (Munich, BSB Cod. Lat. 197, fol. 91r); fig. 1864, Guidoccio Cozzarelli, (Florence, Bibl. naz. Palat. 767, fol. 10r); fig. 1865, Francesco di Giorgio Martini, (London, British Museum Ms. 197, b2).

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Figs. 1866-1867: Life jackets in Francesco di Giorgio, (Florence, Bibl. Naz., Cod. Magl. II.1.141, fol. 196v) and Guidoccio Cozzarelli, (Turin, Cod. 148, fol. 66v.

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Figs. 1868-1869: Life jackets on B81v and CA276va.

    Francis Bacon, in his New Organon,69 describes an inductive approach involving a collection of all possible examples. This is partly an idealized version of empirical science. In part, however, it describes the activities of the encyclopaedic tradition, characterized by a cumulative development of visual images. As long as practice is recorded verbally a distinction between one source and another remains difficult to determine. Once recorded visually, it is possible to trace how an idea is copied and/or developed in time. Hence visualisation makes continuity a measurable factor and as such provides a new key to understanding continuity and innovation both in terms of individual and cultural development.

 

8.2 Individual Genius

    In the case of individuals such as Leonardo, scholars tend to look at the end products of his work without examining how he got there. Attention strictly to his finished works gives him an aura of being universal, unapproachable and superhuman.70 On the other hand, attention to his preparatory studies reveals how his work evolves step by step, how an idea may haunt him for 20 or 30 years and slowly mature from a rough sketch into an impressive drawing.

    Moreover, when seen in the context of an encyclopaedic tradition, many of the problems which concern him are recognized as part of his heritage. That which we have shown in the case of perspective and optics needs to be applied to the other domains of his study. He is, for example, credited with having invented the life jacket which, in fact, was familiar to his predecessors Taccola, Cozzarelli and Francesco di Giorgio Martini (figs. 1863-1868).71

    A full awareness of the encyclopaedic tradition in which Leonardo is working will diminish his reputation as an isolated innovator. It will also bring into focus the distinguishing characteristics of his genius. Whereas his predecessors were content with collecting examples, Leonardo searched for underlying principles, a new king of universal theory based on particulars of experience. And one who had appeared as a mythical figure emerges as an individual who interprets a great tradition in developing a remarkable work view. In the context of this visual encyclopaedia of practice genius becomes humane and accessible.

 

8.3 Culture

    That which applies to individuals applies equally to cultural development. Historians of technology search for the first instance of an invention and for its latest development. This often leads to emphasis on end products of technology with little or no understanding of their evolution. Historians of science and of culture have a similar approach. As a result there is an emphasis on isolated formulae and masterpieces out of cotnext and the humane dimension fades, while ergonomics becomes an issue.

    Study of the eycyclopaedic tradition of practice would reveal the cumulative nature of technological knowledge. It would show how machines and inventions of increasing complexity gradually develop. At the same time it would confirm how an even more systematic recording of practice leads to a sense of mastery over Nature. In the twelfth and thirteenth centuries observations and experiment are frequently rhetorical and theoretical, or if practical, they involve a demonstration of an isolated case. By the sixteenth century Leonardo is exploring cases systematically by playing with variables. By the seventeenth century such studies are recorded mathematically and become summarized in terms of formulae.

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Fig. 1870. Systematic experiments with camera obscuras, eyes and lenses in C. Scheiner.

    Devices of the fifteenth and sixteenth centuries frequently recur in the seventeenth and eighteenth centuries (eg. figs. 1861-1862) but the cotnext has changed. What had previously been a random instance now exemplifies a specific branch of the mathematical sciences and illustrates universal mathematical and/or mechanical principles. In other words, the encyclopaedic tradition of practice helps explain how the universal formulae of schientific theory become possible.

    A new solution to the paradox of continuity and innovation thus emerges. One can accept that many problems of the thirteenth century continue into the seventeenth century (Duhem).72 One can accept also that basic terms such as "observation" and "experiment," present in the thirteenth century, remain seminal in the seventeenth (Crombie).73 The words remain the same, but their meaning is transformed. A new visual standard has introduced a quantitative criterion for truth that makes it possible to search for universal laws in terms of particular cases of experience. Truth is no longer a theoretical quest, but a practical goal.

    Seen in this context Leonardo is no longer an eccentric genius at the fringe of culture. He emerges as a figure in a long tradition whose contributions to visualisation are of central importance to the Renaissance and of seminal importance for the modern world. He may not be ahead of his times, but he lays the foundations for times ahead.

 

9. A New Vision

    The great eras of civilisation have been periods of taking stock, with a reassessment of past and present learning, when a new encyclopaedia of knowledge has brought fresh awareness of the continuity of ideas and a deeper sense of the degree to which culture is a cumulative process. Among the Greeks the efforts of Socrates and Plato lead to Aristotle's corpus in which he surveys existing knowledge. Under the Abbasid Caliphs a great translation project by Hunain ibn Ishaq and Ishaq ibn Hunain preparest he way for Arabic contributions to learning in the ninth and tenth centuries.

    From the eleventh through the thirteenth centuries there is an even greater wave of translations from Arabic back into Latin. This prepares the way for Grosseteste's efforts at Oxford which lead to Roger Bacon's survey of learning. Meanwhile, in Paris, Albert the Great's compendium leads to Saint Thomas Aquinas' Summa of all knowledge. Leonardo da Vinci's writings mark an attempt in specialized fields. The Encyclopedie of the Enlightenment is perhaps the last serious attempt to survey the whole of learning.

    Today, when increasing numbers of persons find it difficult to relate to modern developments and a majority live with little or no historical consciousness, the time may be ripe for a reassessment of the past in terms of a new encyclopaedia. In the past century historical research has thrown much light on the contributions of other civilisations, especially that of China and Islam. In the past decade it has even been shown that Guterberg's printing press with movable type had its precedents in eleventh century Korea. But the question remains why these countries did not take this and other inventions a critical stagefurther, why it was ultimately in Europe and not in Asia, India or the Middle East that the Industrial Revolution took place. I McNeill's answer to Spengler a rash hypothesis or an outline of a viable answer?

    The problem also has political dimensions. In the nineteenth century Europe was a natural centre of a world of colonies. In the past decades virtually all these countries have gained independence and Europe has shrunk to a small community of less than 440 million in a world of more than three billion. In this context the equality of man has rightfully become a central issue. There is a profound danger, however, that in attempting to assert man's essential equality, the necessary inequality of man's culture is forgotten.

    Europe's value once lay in the knowledge and technology she gave the world. In her monuments, museums, libraries and archives she retains an untold wealth of experience. Her future contribution could be that she uses these sources to throw new light on the cumulative dimensions of knowledge and technology. By means of a comprehensive encyclopaedia of practice and theory she could bring awareness of how and why the world has reached the point if has, and prompt a reassessment of concepts of genius, elitism, culture and values in which many would like to believe, but dare not. It would be fitting if a study of the tradition in which Leonardo stands, sparked a re-examination of the tradition he helped to shape.


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Last Update: July 11, 1999