How to solve Essay Title 2 for the Nov 2024 TOK series
Title: In the production of knowledge, is ingenuity always needed but never enough? Discuss with reference to mathematics and one other area of knowledge.
Mathamatics as AOK 1
Ingenuity is essential
Ingenious thinking by mathematicians can lead to effective problem solving, which is so beneficial it can result in breakthroughs. For example, both Newton and Leibniz independently invented calculus in the 17th century in order to address problems related to motion and change. Their creative problem solving laid the foundations for modern calculus.
Secondly, ingenuity can lead to the creation of entirely new branches of mathematics. For example, topology is a branch of mathematics that was born out of the creative insights of mathematicians like Euler and Poincaré, in the 18th and 19th centuries respectively. Thus, we can mathematical ingenuity can expand the scope of mathematical knowledge
However, ingenuity alone may be insufficient
An ingenious idea may not be sufficient to contribute to mathematical knowledge if it lacks logical foundation. For example, Francis Guthrie conjectured the Four Colour Theorum in 1852 but the theorum contained logical inconsistencies and was only solved more than a century later. Mathematical proofs must maintain logical consistency to be accepted by the knowledge community.
The collaborative nature of the mathematical community also requires ideas to be verified and validated before it can be deemed new knowledge. For example, Fermat’s Last Theorum was proposed in 1637 but it remained unproven for over 350 years until someone was able to announce a proof for it in the late 20th century, which allowed the theorum to finally be proven true.
The Arts
If you think going with the Arts would be a good idea, you can claim:
Ingenuity is essential
Ingenious ideas allow artists to contribute their unique styles and imaginative approaches to create innovation in the arts. For example, Pablo Picasso and Georges Braque decided to break away from traditional artistic perspectives and represent objects from multiple angles simultaneously, leading to the creation of the Cubism movement.
Secondly, artists are expected to use their ingenuity to find creative ways for the expression of their ideas. For example. Jackson Pollock invented a very unique ‘drip painting’ technique, seen in works such as No. 5, 1948, which allowed him to convey complex emotions and ideas through his abstract forms and dynamic compositions.
However, ingenuity alone may be insufficient
An artist can have ingenius ideas but lack the technical skills that are crucial for executing their creative expression. For example, Leonardo Da Vinci is renowned for his technical mastery, such as his utilisation of sfumato technique while painting the Mona Lisa, which gave his paintings an exquisite life-like quality.
An artist can have ingenuity but not be aligned with the cultural perceptions of their time, which is also important for successful production. For example, Vincent Van Gogh’s innovative use of colour and expressive brushwork was way ahead of his time but he was not widely appreciated during his lifetime since his unconventional approach did not align with mainstream artistic norms at the time.
The Natural Sciences
If you think going with the Natural Sciences would be a good idea, you can claim:
Ingenuity is essential
Ingenuity in the natural sciences can lead to the development of new theories. For example, Einstein’s creative thinking expanded on Newton’s existing framework, which led to two groundbreaking theories: special relativity (1905) and general relativity (1915). We can say ingenuity can increase our understanding of the scope of certain knowledge.
Secondly, ingenuity can create new and innovative scientific progress. Kary Mullis invented a technique that made it possible to generate millions of copies of a specific DNA sequence from a tiny sample, which transformed genetic research, medical diagnostics and other fields. Ingenuity can thus be critical to create advancements within scientific knowledge.
Ingenuity alone may be insufficient
Certain scientific ideas can be ingenious but lack sufficient empirical evidence to support it. For example, Alfred Wegener proposed the theory of continental drift in 1912 and got dismissed by the scientific community, until the emergence of new paleontological evidence in the 1960s which led to the eventual acceptance of his theory as plate tectonics.
Secondly, ingenious ideas have to go through peer review and validation before being deemed credible. For example, in 1989, Fleischmann and Pons announced their achievement of cold fusion, which generated excitement within the scientific community for their ingenious idea and its possibilities. However, subsequent experiments failed to replicate their results, and their claim was rejected.
Related: The Complete Guide to the Nov 2014 TOK Essay Titles
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