Leonardo bridge. Da Vinci’s bridge design stands today

Leonardo
da 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 his
unmatched curiosity and creativity, Leonardo da Vinci designed mechanical
devices for war, manufacturing and transportation. It is uncertain that most of
his work went unrecognized in his time as well other more modern scientists
have taken credit for the things he did that had been assumed to be lost.

In 1502, the Sultan of the Ottoman Empire came to Rome
to hire a team of civil engineers to design a bridge to stretch across the
Golden Horn at Istanbul.

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Da Vinci offered
his services to the Sultan, modelling a structure in his notebook that
represented a beautiful synergy of creative artistry and civil engineering. The
bridge would have spanned 276 meters of water and the arch would have been high
enough for a ship with sails to pass under. Although the Sultan turned down Da
Vinci’s proposal, believing the architectural endeavour to be impossible, a
modern Swiss scientist, D.F. Stussi, concluded that the plans were
“technically feasible”.

In 2001, inspired
by Da Vinci’s design, an artist in Norway named Vebjorn Sand decided to
construct his bridge. Da Vinci’s bridge design stands today over a highway in
Norway as a monument to his genius. Da Vinci also influenced later bridge
builders with his method of bending wooden beams into arches. He devised a
technique of notching timber to prevent splitting and interlocking bent and
notched beams to create a bearing arch. More than 300 years later, Swiss bridge
builders used Da Vinci’s method in their arched wooden bridges.

In the world today, it is difficult to understand some
of the major problems in isolation. That is, the problems are systemic meaning
they 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 would
require a drastic shift in the thinking, perception of the world view in
science. To achieve this, there is need to adopt holistic and ecological
contemporary science, and disengage in the mechanistic scientific view.

 (Capra, 2002)
argues that evolution should not be seen as competitive struggle for existence
but instead the supportive dance in which constant emergence of novelty and
creativity are the driving force. Hence, this idea gives way to the science of
quality which is steadily emerging.

The scientific work of Leonardo da Vinci serves as a
great inspiration to this new science. To certain extend Leonardo’s scientific
work is among the least understood yet it is among the most fascinating. Most
authors that have wrote his works, have done so through Newtonian lenses. As a
result, the understanding of its essential nature that is a science of
qualities a science of organic forms. Which somewhat differs from the mechanistic
science of Newtown, Galileo or Descartes.

According to (Capra 2007,) Leonard’s worldview of his
contemporaries is partially influenced by his medieval thinking. That is, the
knowledge about the natural phenomena was handed down by philosophers and
Aristotle of antiquity that was influenced by Christian doctrine written by
scholars that presented it as an official account or creed and condemned any
scientific experiments as a dissident.

Leonardo’s interest in proportion of the body and
general human anatomy started when studying under Andrea Verrocchio. He began
studying human body by dissecting bodies. He approached scientific knowledge
visually; he states that it is through painting that some of natural forms are
studied. He argues that painting is both art and a science. That is, a science
of qualities, of natural forms that differs from the mechanistic science. These
forms are recurrently shaped, living forms, and essential processes. Thus, he
expressed his scientific work through paintings and artwork. For instance, he
painted the anatomy of animal, the growth of plants, and shaped their
metabolism.  Furthermore, Leonardo sort
at all times to understand the nature of life, something that had escaped many
analysts for a long time since until recently, nature of life was defined
strictly in terms of cells and molecules.

However, in the recent past, there has been new
understanding of the nature of life that is emerging. That is, an understanding
based on metabolic processes and their patterns of organization, which are what
Leonardo explored throughout his life. His studies in living form of nature
began through a painter’s eyes then later progressed to detailed investigation
of their inherent nature.

The connecting conceptual threads that links his
knowledge of micro- and macrocosm were life’s patterns of organization, its
fundamental processes of metabolism and growth, and its organic structure. In
microcosm, his main focus was the human body. That is, its proportions and
beauty, the mechanics of its movement as compared to other animal bodies in
motion. While macrocosm, dwelled with botanical diversity and growth patterns
of the plants, and movement of air and water, the geological transformations
and forms of the earth.

The intellectual aspect of the Renaissance was
resolutely shaped by the literary and philosophical movement of humanism that
made the capabilities of the human being its primary concern. For instance, in
Florence, human philosophers embrace of discovery and learning was the foundation
of new human ideal. That is, the ‘universal man’, they educated all this in
branches of knowledge. The historians later referred it as the ‘Renaissance
man’.

Leonardo became its model epitome. However, the
difference between Leonardo’s universality as compared to the rest was that his
inquiries were far more progressed as compared to the rest. He asked questions
that no one else had bothered to ask before, yet he transcended the
disciplinary limitations of his times. He did so by acknowledging the relationship
that exist between forms and processes in different domains and by
incorporating his discoveries into a fused vision of the world.  

According to Leonardo, being universal meant
recognizing similarities in living forms that interlock different features of
nature. For instance, the anatomical structure of diverse animals.
Acknowledging that nature’s living form reveal such vital patterns was an
important understanding of the school of Romantic biology back in the 18th
century (Capra, 1988 p.71). Today the idea is referred as the systemic
thinking. For Leonardo, understanding a phenomenon meant relating it with other
phenomena by applying a similarity of patterns.

For instance, when he studied the human proportions,
he compared them with the building proportions of architecture; patterns of
turbulence in water led him to observe similar patterns in the flow of air; his
investigation of bones and muscles led him to study and paint gears and levers
as a result, establishing a connection between animal physiology and
engineering. Lastly, he explored the nature of sound that enabled him to study
the theory of music and by extension the design of musical instruments.  

It is this exceptional ability to link observations
and ideas from various disciplines that has seen Leonardo on most occasion
getting carried away and extend his investigations beyond their initial goal in
the creation of a ‘science of painting’, which explores the entire range of
natural phenomena known during his time as well as previously unknown
knowledge. Although Leonardo’s scientific work had little direct influence on
the scientist that come after his passing, several centuries later, his idea of
science of forms would reemerge only this time the level of sophistication of
the matter was at a different level.

The scientists advanced their understanding of the
structure of matter, electromagnetism, cellular and molecular biology, and the
law of chemistry, genetics and the important role of evolution in sharping the
living world. Leonardo’s organic notion of life to date forms the fundamental
role in biology.

Yet most of the scientists of his time and several
generations after him did not see the importance of his renaissance work. As a
result, it was left to gather dust in the European libraries. As Galileo was a
perceived 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, he
imitated 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 designs
today (Capra, 2002).

 Moreover, while
designing palaces and villas, Leonardo put into consideration the movement of
people and goods through the buildings, through application the metabolic
processes to his architectural designs. Besides, he considered gardens to be
part of the buildings, as a way of integrating nature and architecture.

He also applied the same principle during the design
of cities. He viewed a city as an organism in which people, food water, goods
and waste need to flow with ease for the city to be healthy. This is an example
that clearly shows how natural processes can be used as models for human
designs, while working with nature instead of controlling it.      

Although little is known about Leonardo’s musical
activities, he has produced several musical instruments and made improvement to
the existing ones. He was a musical performer and teacher. Besides, he was the
best improviser if rhymes of his time. He was more curious on the origin of
sound and examined the sonorous impact of the bodies after bodies. He studied
the phenomenon of vibration and sympathetic vibration, of how the percussion of
a body makes it oscillate and communicate its oscillation to the surrounding
air or solid or liquid.

For instance, Leonardo studied the propagation of sound
waves as a differentiated from light waves refraction, and reflection of sound
waves and the phenomenon of echo, the speed of sound and the factors that
determine degrees of loudness, while he also investigated the laws that
governed the fading of sound through varying the distance between its source
and the ear.

Leonardo was more interested in the perspective of
sound, parallel to the laws of optical and pictorial perspective. Besides, he
was more concerned with the factors that determine a musical pitch and
experimented with vases of different shapes and varying apertures. He was
particularly interested in construction of drums. Apart from making them easier
to play he also expanded their musical possibilities, for example tonal range
that was beyond the limitations of the conventional instruments of his period.

He ensured that improve the traditional functions of
drums through making them capable of producing chords and scales. To achieve
this, he tried two different methods. One, he combined several drums or skins
of different pitch into single instrument. Secondly, consists of devices to
make one skin produce tones of different pitch in rapid succession.  

Leonardo
studied mathematics late in life. According to (Vasari, 1991) he put a lot of
effort in trying to solve the problem of duplication of cubes. During this time
people were faced with the problem of architectural conundrum that concerned
religious monument. The oracle had told them to build an altar to Apollo twice
as big as the previous one that was in cubic form.

The
problem was to determine the dimensions of the sides in order to achieve a cube
twice the volume of the original one. After several attempts by the
architecture to build the altar, they requested the mathematicians who at that time
had not come up with a formula to determine irrational quantities. Leonardo
used several approach. Which are:

•    A graphic approach: codex Arundel folio
283v

Leonardo
tried to determine whether it is possible for a simple extension from two to
three dimensional to exist. He further asked himself if Plato’s theorem on the
duplication 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 double
square twice the volume of a single unity cube.

•    An arithmetic approach; codex Arundel,
folio 283v

Leonardo
tried to extend Pythagoras’ theorem on right-angled triangles from squares to
cubes. If the sum of the squares of the sides of these triangles is equal to
the square of the hypotenuse, can the same apply to cubes? Taking the simplest
example, the 3-4-5 triangle, the calculation quickly appears disappointing

•    Another arithmetic approach: Codex
Atlanticus, folio 161r.

Which
is basically finding an approximate value for the cubic root of 8 would not
have solved the problem of the duplication of the cube nor the reverse
corollary, its division into two. Thus, only determining an approximate value
of the cubic root of 2 would have given an arithmetical solution to this
mathematical problem. 

•    A classical geometric approach: Codex
Forster I, folio 32.

Besides
looking for his own solutions to the duplication of the cube, Leonardo studies
the classical solutions of the ancient Greek mathematicians. For instance,
Hippocrates of Chios reduced the problem of duplication of a cube to the
problem of finding two mean proportional between two straight lines
representing two arithmetical magnitudes.  

Leonardo
also 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 is
through direct reading or only by second-hand knowledge. Either way, he remains
unsatisfied with the approximate ratio between the circumference and the
diameter as 22/7. As a result, he tries to take this approximation beyond the
96-sided polygon, as a way of varying the difference of areas between polygon
and circles to be as small as the mathematical point which has no quantity.

Another important
engineering idea that Da Vinci can be credited for is the gated canal. His
desire to provide Florence with a waterway to the sea led him to the invention
of the canal and locks to control water levels. His ingenious sluice gate
design 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 the
small trap door in the upper gate is opened and water flows through, raising
the water level and the boat in that section of the canal. This water flow equalizes
the pressure across the upper gate, thus allowing gate to be opened and the
boat moves to the next lock

Although James
Watt is credited with inventing the modern steam engine, Da Vinci had designed
a much simpler form of Watt’s engine that operated by flywheel and crank. As
Watt struggled with inventing a working steam engine in the mid-18th century,
he worked with complicated transmission systems because engineers feared that a
simple crank-and-rod motion would not work with the irregular stroke of the
steam piston.

Once again the
answer to a more modern dilemma was contained within Da Vinci’s drawings. He
had designed what is now called a flywheel, or a heavy wheel with high angular
momentum. In conjunction with a crank-and-rod system, the flywheel resists
changes in rotational motion caused by irregular strokes of the piston and thus
steadies the rotation of the shaft. However, Watt never saw Da Vinci’s design
and was reluctant to incorporate a flywheel system into his steam engine

Leonardo also worked
on a system for lifting heavy loads, which incorporated what is now known as
the worm gear. The “endless screw,” as Da Vinci called it, was turned
by a crank and meshed with the teeth of a gear that rotated and raised the
load.

Traditional worm
gear systems during his time only engaged a single tooth of the gear, so if
that tooth broke, the gear could reverse its rotation and the suspended load
would fall. He solved this problem by using the “endless screw.” In
other words, a longer threaded screw gripped multiple teeth on the gear and
therefore never lost traction. The design was particularly beneficial to
construction managers who were concerned with safety, because the load could
not 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 analog
clocks and many other engineering applications, it represents another instance
of Da Vinci’s ideas being credited to someone else.

In
conclusion, although this does not exhaust the scientific theories that
influenced Leonardo’s engineering work, it seeks to point out some of his
contribution from the fields of engineering to mathematics. His love for nature
was unmatched and perceived science in a different way that took fellow
scientists several centuries to really appreciate his work. He concentrated his
efforts in contemporary science, in that he argued that all states in life are
interconnected and interdepend.

Therefore,
one can par pot to solve one problem in singularity.  Our sciences and technologies have become
narrow in their focus because they are unable to understand multi-faceted
problems that touch on various disciplines of science. Instead, they are more
concerned with the corporations that are more interested in financial rewards
rather than the well-being of humanity.   

Moreover,
from the above, it is clear that solid geometry and stereometry were fields
that suited Leonardo in the area of theoretical mathematics. This is mainly
influenced by his interest in three-dimensional representations, which allowed
him to visualize the objects of his studies. Besides, he contributed to
mathematical and scientific research in the Renaissance period through
establishing that the power of the tool of three-dimensional representation as
a research device as well as a persuasive instrument.   Therefore, there is a need for a science
that honors the unity of all life, yet appreciating the interdependence of all
natural phenomena.

 

 

 

 

 

 

 

 

 

 

References

Brown, L. (2008). Plan B 3.0. NY:
Norton.

Capra, B. (2002). Hidden Connections.
NY: Doubleday.

Capra,
F. (2007). 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 of
Life. Chicago: University of Chicago Press.

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