Leonardoda Vinci was widely known as an artist, inventor, architect, and an anatomist.He was therefore seen as the best example of a universal genius. Driven by hisunmatched curiosity and creativity, Leonardo da Vinci designed mechanicaldevices for war, manufacturing and transportation. It is uncertain that most ofhis work went unrecognized in his time as well other more modern scientistshave taken credit for the things he did that had been assumed to be lost.
In 1502, the Sultan of the Ottoman Empire came to Rometo hire a team of civil engineers to design a bridge to stretch across theGolden Horn at Istanbul. Da Vinci offeredhis services to the Sultan, modelling a structure in his notebook thatrepresented a beautiful synergy of creative artistry and civil engineering. Thebridge would have spanned 276 meters of water and the arch would have been highenough for a ship with sails to pass under. Although the Sultan turned down DaVinci’s proposal, believing the architectural endeavour to be impossible, amodern Swiss scientist, D.F. Stussi, concluded that the plans were”technically feasible”.
In 2001, inspiredby Da Vinci’s design, an artist in Norway named Vebjorn Sand decided toconstruct his bridge. Da Vinci’s bridge design stands today over a highway inNorway as a monument to his genius. Da Vinci also influenced later bridgebuilders with his method of bending wooden beams into arches. He devised atechnique of notching timber to prevent splitting and interlocking bent andnotched beams to create a bearing arch. More than 300 years later, Swiss bridgebuilders used Da Vinci’s method in their arched wooden bridges.
In the world today, it is difficult to understand someof the major problems in isolation. That is, the problems are systemic meaningthey are interconnected. For instance, in his book ‘Plan B’, (Brown, 2008)describes how poverty and demographic pressure leads to depletion of resources.
The books highlight the need for mankind to come up with solutions that wouldrequire a drastic shift in the thinking, perception of the world view inscience. To achieve this, there is need to adopt holistic and ecologicalcontemporary science, and disengage in the mechanistic scientific view. (Capra, 2002)argues that evolution should not be seen as competitive struggle for existencebut instead the supportive dance in which constant emergence of novelty andcreativity are the driving force.
Hence, this idea gives way to the science ofquality which is steadily emerging.The scientific work of Leonardo da Vinci serves as agreat inspiration to this new science. To certain extend Leonardo’s scientificwork is among the least understood yet it is among the most fascinating. Mostauthors that have wrote his works, have done so through Newtonian lenses. As aresult, the understanding of its essential nature that is a science ofqualities a science of organic forms. Which somewhat differs from the mechanisticscience of Newtown, Galileo or Descartes. According to (Capra 2007,) Leonard’s worldview of hiscontemporaries is partially influenced by his medieval thinking.
That is, theknowledge about the natural phenomena was handed down by philosophers andAristotle of antiquity that was influenced by Christian doctrine written byscholars that presented it as an official account or creed and condemned anyscientific experiments as a dissident.Leonardo’s interest in proportion of the body andgeneral human anatomy started when studying under Andrea Verrocchio. He beganstudying human body by dissecting bodies. He approached scientific knowledgevisually; he states that it is through painting that some of natural forms arestudied. He argues that painting is both art and a science. That is, a scienceof qualities, of natural forms that differs from the mechanistic science.
Theseforms are recurrently shaped, living forms, and essential processes. Thus, heexpressed his scientific work through paintings and artwork. For instance, hepainted the anatomy of animal, the growth of plants, and shaped theirmetabolism. Furthermore, Leonardo sortat all times to understand the nature of life, something that had escaped manyanalysts for a long time since until recently, nature of life was definedstrictly in terms of cells and molecules. However, in the recent past, there has been newunderstanding of the nature of life that is emerging. That is, an understandingbased on metabolic processes and their patterns of organization, which are whatLeonardo explored throughout his life. His studies in living form of naturebegan through a painter’s eyes then later progressed to detailed investigationof their inherent nature.
The connecting conceptual threads that links hisknowledge of micro- and macrocosm were life’s patterns of organization, itsfundamental processes of metabolism and growth, and its organic structure. Inmicrocosm, his main focus was the human body. That is, its proportions andbeauty, the mechanics of its movement as compared to other animal bodies inmotion. While macrocosm, dwelled with botanical diversity and growth patternsof the plants, and movement of air and water, the geological transformationsand forms of the earth.The intellectual aspect of the Renaissance wasresolutely shaped by the literary and philosophical movement of humanism thatmade the capabilities of the human being its primary concern.
For instance, inFlorence, human philosophers embrace of discovery and learning was the foundationof new human ideal. That is, the ‘universal man’, they educated all this inbranches of knowledge. The historians later referred it as the ‘Renaissanceman’.
Leonardo became its model epitome. However, thedifference between Leonardo’s universality as compared to the rest was that hisinquiries were far more progressed as compared to the rest. He asked questionsthat no one else had bothered to ask before, yet he transcended thedisciplinary limitations of his times. He did so by acknowledging the relationshipthat exist between forms and processes in different domains and byincorporating his discoveries into a fused vision of the world. According to Leonardo, being universal meantrecognizing similarities in living forms that interlock different features ofnature. For instance, the anatomical structure of diverse animals.Acknowledging that nature’s living form reveal such vital patterns was animportant understanding of the school of Romantic biology back in the 18thcentury (Capra, 1988 p.
71). Today the idea is referred as the systemicthinking. For Leonardo, understanding a phenomenon meant relating it with otherphenomena by applying a similarity of patterns.
For instance, when he studied the human proportions,he compared them with the building proportions of architecture; patterns ofturbulence in water led him to observe similar patterns in the flow of air; hisinvestigation of bones and muscles led him to study and paint gears and leversas a result, establishing a connection between animal physiology andengineering. Lastly, he explored the nature of sound that enabled him to studythe theory of music and by extension the design of musical instruments. It is this exceptional ability to link observationsand ideas from various disciplines that has seen Leonardo on most occasiongetting carried away and extend his investigations beyond their initial goal inthe creation of a ‘science of painting’, which explores the entire range ofnatural phenomena known during his time as well as previously unknownknowledge. Although Leonardo’s scientific work had little direct influence onthe scientist that come after his passing, several centuries later, his idea ofscience of forms would reemerge only this time the level of sophistication ofthe matter was at a different level.
The scientists advanced their understanding of thestructure of matter, electromagnetism, cellular and molecular biology, and thelaw of chemistry, genetics and the important role of evolution in sharping theliving world. Leonardo’s organic notion of life to date forms the fundamentalrole in biology. Yet most of the scientists of his time and severalgenerations after him did not see the importance of his renaissance work. As aresult, it was left to gather dust in the European libraries.
As Galileo was aperceived to the father of modern science. Leonardo’s pursue of engineering and science was not to dominate nature,but rather learn it. For instance, while designing his flying machines, heimitated the flight of birds to an extent that one would mistake his desires.His attitude of seeing nature as a model has enabled the ecological designstoday (Capra, 2002). Moreover, whiledesigning palaces and villas, Leonardo put into consideration the movement ofpeople and goods through the buildings, through application the metabolicprocesses to his architectural designs. Besides, he considered gardens to bepart of the buildings, as a way of integrating nature and architecture. He also applied the same principle during the designof cities. He viewed a city as an organism in which people, food water, goodsand waste need to flow with ease for the city to be healthy.
This is an examplethat clearly shows how natural processes can be used as models for humandesigns, while working with nature instead of controlling it. Although little is known about Leonardo’s musicalactivities, he has produced several musical instruments and made improvement tothe existing ones. He was a musical performer and teacher. Besides, he was thebest improviser if rhymes of his time. He was more curious on the origin ofsound and examined the sonorous impact of the bodies after bodies.
He studiedthe phenomenon of vibration and sympathetic vibration, of how the percussion ofa body makes it oscillate and communicate its oscillation to the surroundingair or solid or liquid. For instance, Leonardo studied the propagation of soundwaves as a differentiated from light waves refraction, and reflection of soundwaves and the phenomenon of echo, the speed of sound and the factors thatdetermine degrees of loudness, while he also investigated the laws thatgoverned the fading of sound through varying the distance between its sourceand the ear. Leonardo was more interested in the perspective ofsound, parallel to the laws of optical and pictorial perspective.
Besides, hewas more concerned with the factors that determine a musical pitch andexperimented with vases of different shapes and varying apertures. He wasparticularly interested in construction of drums. Apart from making them easierto play he also expanded their musical possibilities, for example tonal rangethat was beyond the limitations of the conventional instruments of his period. He ensured that improve the traditional functions ofdrums through making them capable of producing chords and scales. To achievethis, he tried two different methods. One, he combined several drums or skinsof different pitch into single instrument. Secondly, consists of devices tomake one skin produce tones of different pitch in rapid succession.
Leonardostudied mathematics late in life. According to (Vasari, 1991) he put a lot ofeffort in trying to solve the problem of duplication of cubes. During this timepeople were faced with the problem of architectural conundrum that concernedreligious monument. The oracle had told them to build an altar to Apollo twiceas big as the previous one that was in cubic form. Theproblem was to determine the dimensions of the sides in order to achieve a cubetwice the volume of the original one. After several attempts by thearchitecture to build the altar, they requested the mathematicians who at that timehad not come up with a formula to determine irrational quantities. Leonardoused several approach.
Which are: • A graphic approach: codex Arundel folio283v Leonardotried to determine whether it is possible for a simple extension from two tothree dimensional to exist. He further asked himself if Plato’s theorem on theduplication of the square can be extended to the duplication of the cube.Furthermore, he asked himself if the volume of a cube built from a doublesquare twice the volume of a single unity cube.• An arithmetic approach; codex Arundel,folio 283vLeonardotried to extend Pythagoras’ theorem on right-angled triangles from squares tocubes. If the sum of the squares of the sides of these triangles is equal tothe square of the hypotenuse, can the same apply to cubes? Taking the simplestexample, the 3-4-5 triangle, the calculation quickly appears disappointing • Another arithmetic approach: CodexAtlanticus, folio 161r.Whichis basically finding an approximate value for the cubic root of 8 would nothave solved the problem of the duplication of the cube nor the reversecorollary, its division into two.
Thus, only determining an approximate valueof the cubic root of 2 would have given an arithmetical solution to thismathematical problem. • A classical geometric approach: CodexForster I, folio 32. Besideslooking for his own solutions to the duplication of the cube, Leonardo studiesthe classical solutions of the ancient Greek mathematicians. For instance,Hippocrates of Chios reduced the problem of duplication of a cube to theproblem of finding two mean proportional between two straight linesrepresenting two arithmetical magnitudes. Leonardoalso solves a second classical problem, which entails squaring of the circle.He uses an approach inspired by Archimedes, although it is not clear if it isthrough direct reading or only by second-hand knowledge.
Either way, he remainsunsatisfied with the approximate ratio between the circumference and thediameter as 22/7. As a result, he tries to take this approximation beyond the96-sided polygon, as a way of varying the difference of areas between polygonand circles to be as small as the mathematical point which has no quantity. Another importantengineering idea that Da Vinci can be credited for is the gated canal. Hisdesire to provide Florence with a waterway to the sea led him to the inventionof the canal and locks to control water levels. His ingenious sluice gatedesign works under the same principle as the modern locks of the Panama Canal.
The boat enters a lock of the canal, and the lower gate is closed. Then thesmall trap door in the upper gate is opened and water flows through, raisingthe water level and the boat in that section of the canal. This water flow equalizesthe pressure across the upper gate, thus allowing gate to be opened and theboat moves to the next lockAlthough JamesWatt is credited with inventing the modern steam engine, Da Vinci had designeda much simpler form of Watt’s engine that operated by flywheel and crank. AsWatt struggled with inventing a working steam engine in the mid-18th century,he worked with complicated transmission systems because engineers feared that asimple crank-and-rod motion would not work with the irregular stroke of thesteam piston.
Once again theanswer to a more modern dilemma was contained within Da Vinci’s drawings. Hehad designed what is now called a flywheel, or a heavy wheel with high angularmomentum. In conjunction with a crank-and-rod system, the flywheel resistschanges in rotational motion caused by irregular strokes of the piston and thussteadies the rotation of the shaft. However, Watt never saw Da Vinci’s designand was reluctant to incorporate a flywheel system into his steam engineLeonardo also workedon a system for lifting heavy loads, which incorporated what is now known asthe worm gear. The “endless screw,” as Da Vinci called it, was turnedby a crank and meshed with the teeth of a gear that rotated and raised theload.Traditional wormgear systems during his time only engaged a single tooth of the gear, so ifthat tooth broke, the gear could reverse its rotation and the suspended loadwould fall. He solved this problem by using the “endless screw.” Inother words, a longer threaded screw gripped multiple teeth on the gear andtherefore never lost traction.
The design was particularly beneficial toconstruction managers who were concerned with safety, because the load couldnot fall down once it was raised. About two centuries later, an English clockmaker,Henry Hindley, took credit for inventing the worm gear. Used in all analogclocks and many other engineering applications, it represents another instanceof Da Vinci’s ideas being credited to someone else.
Inconclusion, although this does not exhaust the scientific theories thatinfluenced Leonardo’s engineering work, it seeks to point out some of hiscontribution from the fields of engineering to mathematics. His love for naturewas unmatched and perceived science in a different way that took fellowscientists several centuries to really appreciate his work. He concentrated hisefforts in contemporary science, in that he argued that all states in life areinterconnected and interdepend. Therefore,one can par pot to solve one problem in singularity.
Our sciences and technologies have becomenarrow in their focus because they are unable to understand multi-facetedproblems that touch on various disciplines of science. Instead, they are moreconcerned with the corporations that are more interested in financial rewardsrather than the well-being of humanity. Moreover,from the above, it is clear that solid geometry and stereometry were fieldsthat suited Leonardo in the area of theoretical mathematics. This is mainlyinfluenced by his interest in three-dimensional representations, which allowedhim to visualize the objects of his studies. Besides, he contributed tomathematical and scientific research in the Renaissance period throughestablishing that the power of the tool of three-dimensional representation asa research device as well as a persuasive instrument.
Therefore, there is a need for a sciencethat honors the unity of all life, yet appreciating the interdependence of allnatural phenomena. ReferencesBrown, L. (2008). Plan B 3.0.
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The science of Leonardo:Inside the mind of the great genius of the Renaissance. NY: Doubleday.Capra,F. (1988).
Uncommon Wisdom. NY: Simon& Schuster.Richards,R. (2002).
The Romantic Conception ofLife. Chicago: University of Chicago Press.