The prescribed title lends a positive correlation between the construction of knowledge (either the process of generating new knowledge or changing pre-existing knowledge) and the number of individuals involved. In this context, “never” and “always” as absolute terms assert rigidity. The title additionally underlines the intervention of individuals – a single entity controlled by one, single person or a “collaborative” group i.e. when two or more people come together to achieve a certain goal or task. Examining the title further, “production of knowledge” restricts itself to the development and methodology of creating knowledge through practical and/or theoretical means and not the output, or end result. Although the title assumes group work equates to better quality production compared to an individual’s production and consequently its success, in this essay, I will consider areas of knowledge as the collaboration of respective individuals in the fields. Moreover, I will explore the extent to which areas of knowledge like Mathematics and Natural Sciences are dependent on each other, i.e. their intersections and disjunctions. Integrating the influences of the ways of knowing on this quest to produce knowledge and discussing contemporary, real world examples pertaining to the subject areas along with my own personal experiences hopes to balance this essay.
In the Natural Sciences, some of the knowledge is a product of collaboration with the methodology and application of concepts borrowed from Mathematics, thereby both subject areas’ individuals work together to yield positive results.
For example, Genetics is a branch of Biology concerned with the study of genes, genetic variation, and heredity of organisms. This study incorporates statistical tests (Chi Square), ratios (Genetic crosses) supported by laws proposed by Gregor Mendel and other experts, have generated accessible and reliable information across the world. ‘Mendelian inheritance’ laws formulated by experimentation and repeated procedures on 19000 pea plants and their seven traits gave him the incentive to come up with three proposed laws: The Law of Segregation, The Law of Independent Assortment, and The Law of Dominance.
Although based on principles in Biology like Meiosis and Reproduction of plants, the predictions and assumptions of future generations are only due to the mathematical acquisition we possess – fractions, ratios, percentages, etc. Even though the “production of knowledge” in terms of Inheritance is incomplete without the biological reasoning and logic behind gene transfer and exchange. Language in terms of mathematical notation is essential in this “production of knowledge” to express the final outcome i.e. the likely characteristics of the generations.
A dihybrid cross proposed by Mendel was developed after crossing the outcome of the previous generation pea plants – all heterozygous (RrYy – Round and yellow seeds). After genetically crossing the two pea plants denoted by (RrYy X RrYy) repeatedly, Mendel observed that his F2 progeny had a 9:3:3:1 ratio which produced nine plants with round, yellow seeds, three plants with round, green seeds, three plants with wrinkled, yellow seeds and one plant with wrinkled, green seeds. Surprised to find interesting recombinants due to crossing over of genetic matter across the pea plants and expressing the reliable, verified data as a percentage, Mendel coined his Law of Independent Assortment.
The product of Biologists Gregor Mendel, Thomas Hunt Morgan, Charles Darwin along with Mathematicians such as the Pythagoreans have collaboratively produced knowledge which rises above the independent, individual’s creation of knowledge. Although Mendel’s spark of personal knowledge (his laws and theories), it was the built on other experts’ personal knowledge. These influences and intersections together have formed shared knowledge. Its findings have paved the way for research activities and have had a tremendous impact on the advancements we have made in Genetics today. This relationship between shared and personal knowledge in the light of the contributions individuals have had on the creation of Genetics as the subject focus can be explored further through the knowledge question – To what extent can personal knowledge deviate from shared knowledge in the process of producing knowledge? Throughout the procedure of Mendel’s experiment, i.e. the “production” of this “knowledge,” one can see how the way Mendel communicated his knowledge of Natural Sciences (Biology) with Mathematics (Arithmetic) and combined the two ways of knowing (Reason and Language). This pursuit of creating knowledge has been a “collaborative task” and confirms the title’s assumption.
On the contrary Biology as a Natural Science discipline can “produce knowledge” independent of Mathematics. A Food test is a qualitative method, independent of Mathematics that allows to detect individual’s certain components, i.e. nutrients of a food mixture. The individual biochemical food tests – Biuret solution for proteins and benedict's reagent for reducing sugars have been explored by scientists individually. The Biuret solution reaction was first observed by Ferdinand Rose, the solution changed colour from blue to lilac. The Benedict's Reagent discovered by Stanley Rossiter Benedict, changes from its blue colour to green, yellow, and brick-red, depending on the amount of sugar present in the food sample. At the same time, although each one of these tests began as personal generation of new knowledge, we as receivers of this acquisition of knowledge view the ‘food test’ as a collective methodology in the process of producing it. This ‘test’ in Biology is an example of how Biology works as a separate entity, devoid of any Mathematical influences and hence can be a disjunction between the two areas of knowledge and its specific disciplines – Natural Sciences (Biology) and Mathematics (Arithmetic).
In the case of the test for reducing sugars, Stanley Rossiter Benedict proposition was opposed by the E.V. McCollum. McCollum was a part of the scientific community and waited for Otto Folin’s results of parallel researches. Thus, in an individual’s quest to produce knowledge, competition can hinder the process. It was Benedict versus the whole scientific community which is of course, the outcome of individuality. Acceptance of knowledge once created is significant element to its production. As a case in point, it is worth considering how an individual’s “production of knowledge” does not require intervention of other members. Individualistic freedom with regard to ability to express one’s own opinion, put their own respective ideas into perspective and channelize his/her “production of knowledge” in their own style is only possible in an individual’s process of developing knowledge. There is no tussle as to who gets credit or acknowledgement as the producer of knowledge is the sole proprietor of his or her “production.” Using Emotion and Reason as ways of knowing, they both work together in the process of generating knowledge in groups – process of omission and selection because of emotions preceding reason or vice versa. This is influenced by individual perspectives and backgrounds – gender, age, expertise, race, religion, etc. In contrast, an individual’s process of creating knowledge has no scope of group members’ bias, but instead subconscious bias through one’s own emotions and previous experiences generates inherent individual bias in the sphere of personal knowledge.
Through this essay, I have been able to see how the collaboration within Areas of Knowledge, in the above case Biology and Arithmetic’s can play such an important role in the “production of knowledge.” Furthermore, through the collaboration between these subject areas one can see the dependence of Mathematics in our knowledge systems. Mathematics as an area of knowledge is interlinked to every other discipline. Personally, I believe that Mathematics forms the foundation of other disciplines and other areas of knowledge having strict evidences, proof and collation of data apply for areas like Human Sciences and Natural Sciences. But, areas like History and Arts evidences – primary and secondary sources in terms of History and influences or real-life experiences in Arts – are less rigid and can follow varied methods in their respective knowledge production. It can be said that every individual has gained knowledge and produced any form of knowledge through subconscious or conscious influences – either people or existing prior knowledge. Exploring collaborative works’ successes examples like Genetics and Ratios, and its intersections have made me realise the interdisciplinary nature of subject areas. However, this doesn’t mean Natural Sciences cannot be benefitted without the use of Mathematics, for example, in the food tests the results can be obtained without the application of ratios and its collaboration with Mathematics – this does not go with the claim stated in the title. In fact, it is a qualitative result i.e. solely based on knowledge obtained from Biology. Both ways with or without collaboration of Areas of Knowledge play a very important role in producing healthy knowledge.