Archimedes: Mathematics and Enlightening moments
“There is nothing new under the sun.” A quotation derived from the Book of Ecclesiastes explains the infinite and cyclical connection that proceeded on Earth. Knowledge, any information or facts acquired through personal or shared experience, develops throughout life and shapes the identity and intellect of an individual. Past knowledge, the knowledge an individual has already acquired in the past, influences one another and creates a huge branch of knowledge developing and expanding over time. Especially at school, where a vast amount of knowledge is involved, teachers use their past knowledge for education, which then forms the present knowledge of students. The teachers, as well, have gained past knowledge through both personal and shared experience. However, the statement that present knowledge is wholly dependent on past knowledge does not apply to every Area of Knowledge, due to the different perceptions of individuals. I partially agree to the claim that present knowledge is wholly dependent on past knowledge, since past knowledge shapes an individual’s ability to understand and acquire present knowledge, however, not entirely.
Enlightening moments such as “Eureka!” are not a sudden acquisition of completely novel knowledge. It is a consequence of the persistent gathering of different experiences and investigations for a long period of time. Archimedes, the one who shouted out that interjection, was given a difficult problem from the king, which was to find out whether the goldsmiths had used pure gold when making his crown. Archimedes was able to find a way to solve the problem while taking a bath, where he noticed that the displaced water when he stepped out of the bathtub is equal to the volume of his body. This led him to find out that a crown mixed with silver and a crown with pure gold would have the same weight, but a different volume. This cannot be a sudden acquisition of knowledge, since Archimedes already knew that gold is heavier than silver, and he was a physicist with a vast amount of scientific knowledge that could ease him to solve the problem. If the person given the problem did not have any prior knowledge, the story would have been different. This represents the mandatory involvement of past knowledge in the Natural Sciences when trying to acquire present knowledge.
After a theory is created through observation as Archimedes did, it functions as past knowledge for the people and contributes to the evolution of theories over time. In the Natural Sciences, developing or falsifying a pre-existing theory causes a paradigm shift, which is a fundamental change in a concept, theory or assumption. Paradigm shift clearly shows how past knowledge plays a role in creating a solid and credible theory, the present knowledge, especially in the fields of Science. Therefore, present knowledge, or the present theory, is the best possible conclusion that can be reached through the combination or elimination of past knowledge. If past knowledge and past discoveries did not exist, the present knowledge and the developed theories would not have existed as well.
The shifting of perception plays a big role when considering the dependence of present knowledge on past knowledge, especially in the Natural Sciences. Although the progress until reaching a theory involves past knowledge, this is perceived as a completely new discovery when it comes to the fields of Natural Sciences. The fact that the amount of water is displaced when a person leaves the bathtub already existed as a natural phenomenon, however, not as a theory or scientific knowledge before Archimedes discovered it. This means that, if we consider the theory itself in the scientific field, in this case, Archimedes’ principle, it is the very first case to convert those particular natural phenomena into a theory, a learnable subject, and into scientific knowledge. If the natural phenomenon was a stone, there is no way to find out whether it is an ordinary pebble or a rough diamond until someone discovers it. Through recognizing the presence of the rough diamond, the diamond, which is the knowledge, can be revealed and considered a new knowledge or a theory in the fields of Natural Sciences.
The Arts, although it seems as a subject that involves completely new knowledge, is also affected by past knowledge and experiences of an individual. This can be explained through the process of imagining, whenever we are trying to create a new image on our head. Although we have never seen a goldfish walking around with two legs, we are able to draw the image by combining the different components that we already have knowledge on, which are the legs and the goldfish. This is called mental synthesis, a process driven to create a new image through the combination of other images that were previously stored in one’s memory. Therefore, creativity and imagination, which are mainly involved in the Arts, are not a process that involves a sudden creation of a completely new image, but the joining of different distinctive ideas and memories for a new pathway and a new combination. Other than mental synthesis, the process of creating a piece of work in general essentially involves past knowledge regarding that particular area of art, such as knowledge on musical chords, playing instruments, or drawing skills. One famous example is Pablo Picasso, a Spanish painter well known for his analytical cubism art style. This technique of drawing often shocks viewers and leads to confusion. However, he studied art for approximately 70 years and spent nearly 10 years before the creation of cubism. This indicates that his style of drawing, although it might seem quite unprofessional, requires a basic understanding of shape and the ability to observe objects in different perspectives. Therefore, it cannot be said that present knowledge in the Arts, such as a music piece, a painting, or architecture, is not dependent on past knowledge because these involve pre-existing knowledge, such as mental synthesis, in order to create original work.
The overall process of creating new work in the Arts does involve past knowledge, however, this might not apply to the observer or the listener of that particular work. One of the factors that significantly affect the observer’s understanding of an art piece is the change in trend and perception of the Arts. As generation changes, the trend changes rapidly as well, which in turn changes people’s perception. This connects to my experience a few years ago when I visited a museum of contemporary art for the first time. Although I had some basic knowledge on art, the museum was full of abstruse and incomprehensible work in my perspective. Therefore, in the case of contemporary arts, past knowledge was no longer functional when I was trying to understand the meaning behind it or the intention of the artist. Contemporary art, the present knowledge in the field of Arts, was perceived as a novel way of drawing for me, which did not depend on my past knowledge. Nowadays, it is a subject causing controversy in the fields of Arts, with people insisting that some of modern art pieces are unacceptably bizarre. One example is the work by Tracey Emin, “My Bed”, which is a bed consisting of the artist’s own bedroom objects. It caused art critics to claim the lack of professionalism shown in the work and that nearly anyone could display that kind of work in an exhibition. For the art critics, Tracey Emin’s work was unacceptable and could not be connected to their past knowledge, which led them to criticize the work. This indicates that a change in trend in the Arts might leave the past knowledge of an individual to become independent from present knowledge.
Overall, it is hard to state that present knowledge is wholly dependent on past knowledge since some exceptions still exist, such as in the fields of Arts and Natural Sciences, with present knowledge partially being independent from past knowledge. However, it can be said that it is more skewed toward the dependent side than the independent side. The world is the proof - it is like an enormous spider web where each individual’s knowledge or experience is connected and eventually creates an infinite construction of another set of knowledge. Living in an era full of digital technology that eases communication worldwide, this process has become even more rapid and convenient.
