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What this title is referring to is the relationship between the production of knowledge and the ability to replicate; the ability to repeat a trial, an experiment or a study a multitude of times until the obtainment of consistent results. As it is widely known, the production of knowledge is often tied to its ability to be duplicated in one way or another but there is definitely some knowledge that is independent of this attachment. This complex relationship, between the necessity of such replicability and knowledge, is what will be explored using two areas of knowledge of mathematics and the natural sciences.

The first area of knowledge chosen is mathematics whose knowledge is predominantly objective and which consists of many universal concepts adopted by all cultures across the globe and is therefore often considered to be objective to a great extent. Mathematics is divided into two major areas one of which is called pure mathematics with the second one being applied mathematics. Pure mathematics is the construction of new proofs, based on prior proofs, to a certain mathematical concept and is thus a domain majorly founded on replicability. On the other hand, applied mathematics incorporates this series of hierarchal successive proofs in real word applications, which reasserts the integral relationship between the production of mathematical knowledge and replicability.

There are many examples in mathematics that reflect the idea that replicability is a necessity in mathematics. One such example is the Sequences and Series theorem in that despite its apparent simplicity, is applied to complex real life tasks. The theorem basically consists of a sequential arrangement of numbers in a certain order or according to a set of criteria which is called a sequence. The terms of a sequence are added to create a series. One particular term may appear in several different places across a sequence. There are two different types of sequences: infinite sequences and finite sequences. Series are defined by combining the terms of the

sequence. In rare circumstances, a series may also contain a sum of infinite terms. It was introduced by Carl Friedrich Gauss and is a primordial illustration of replicability’s necessity in production of knowledge in mathematics. Each term in a sequence, whether it’s infinite or finite, is based on its previous term and thus replicability is indispensable as it’s the major tool in determining the constant “difference” by which the terms increase or decrease. Furthermore, in order to decide the nature of the sequences ( whether it’s a geometric sequence where the terms are multiplied or divided by the difference or an arithmetic one where the terms are terms are added or subtracted by the difference ), the terms must be replicated and thus this theory highlights the indispensable nature of replicability in the production of knowledge as the replication of the terms with the difference is the driving factor in determining its value.

There are also many examples in mathematics that reflect the idea that the production of some knowledge is not as heavily reliant on replicability as suggested. One such example is the Pythagoras theorem that is also characterized by simplicity, but is applied to complex real life tasks. This theorem is a simple mathematical concept that suggests that the hypotenuse of a right angle triangle can be calculated by squaring the other 2 sides then adding them together which will give you the value of the hypotenuse squared. It was introduced by Thales of Miletus and was then found years later on a 4000 year old Babylonian tablet, but it wasn’t as known till Pythagoras popularized it. This theorem is considered by all mathematicians to be a universal concept; a concept that will evidently forever stay the same as it’s execution is not tied to any other mathematical variables. Evidence of its independence from the notion of replicability is found in our everyday lives. The fact that this theory could be applied by everyone with a mathematical background, ranging from professional engineers to high school students, proves its unconstrained nature as it does not require any replicability to be exercised. An example further proving this is that architects all around the world use the technique of the Pythagoras theorem for engineering and construction fields while college and high school students use the same theorem, with the only difference being the reason for which they apply it. The universality of its application is immensely crucial as it explains its independent relationship of replicability by simply showcasing how it could be utilized by a multitude of individuals, all of different mathematical backgrounds. The need for replicability is thus negated by the universality of the theory, since it can be performed by anyone independent of replicating the context in which the knowledge was produced.

The second area of knowledge chosen for this analysis is the natural sciences. Similarly to that of mathematics, it is objective to a very great extent and simultaneously makes use of the scientific method ; thus rendering the obtained results reliable and accurate to a great extent, as the scientific method is predominantly reliant on replicability. The presence of the scientific method is due to this area of knowledge’s nature and consequently allows all results to be repeatable and generalizable; in order to decrease uncertainty and increase accuracy experiments must be repeated and following the provided scientific method will easily allow to do so. In addition to all of that, all knowledge published in this domain whether it is in physics, chemistry or biology is always peer reviewed. This lessens the level of subjectivity and accentuates the objective nature of the domain as a whole since peer review is essentially a means for quality control, a means for allowing only veritable information to be published.

There are many examples that prove natural sciences’ relation to replicability. A pertinent example of this is Michiaki Takahashi’s creation of the chickenpox vaccine. Takahashi's son developed a serious case of chickenpox and it is essentially what drove him to the creation of this vaccine. After moving back to Japan in 1965, Dr. Takahashi created the first iteration of the vaccine within five years. He began exploring with it in clinical trials in 1972. Vaccines are an exemplary model that demonstrates the dependance of knowledge on replicability. This is primarily due to scientists creating several test versions of a single vaccine, in order to finally obtain a functioning one. The replicable aspect in this case is apparent as each test version is merely an evolution of the prior one, meaning that the basis and foundation of each replica of the vaccine is transmitted from one embodiment of it to another. This notion highlights the significance of replicability in domains relating to natural sciences as it is necessary in the attainment of some medicinal antidotes such as the chickenpox vaccine. Another concept that further justifies this vaccine’s replicable tendencies is the nature of the virus itself. Chickenpox’s genome is double-stranded DNA. This essentially means that its genome is more stable and is thus able to be copied more accurately. Studies suggest that its evolution rate is one new mutation every 200-400 years. Despite the fact that in comparison to other viruses chickenpox has a very slow evolution rate, It still means that the vaccine developed will eventually have to evolve as well to comply with the virus’ new manifestation. This additionally emphasizes the prominence of replicability in the development of this vaccine as it was essentially replicated to develop the present version and will have to ultimately be replicated once again once a new mutation of the virus takes shape.

There are also various examples that equally deny natural sciences’ relation to replicability such as the ‘super blue blood moon’ that last occurred on January 31^{st} 2018. This phenomenon is part of astronomy which is the study of celestial events and space as a whole. The occurrence of this event is extremely rare as it requires three things to happen simultaneously: a super moon, a blood moon and a total lunar eclipse. Before this event happened on 2018, it had occurred on December 30^{th} 1982 and could only be observed from the eastern hemisphere. Only people in the western hemisphere saw it, before the last one, in 1866 and scientists predict that the next occurrence will be in 2037 although they are not sure of it. This incident is thus extremely uncommon which directly negates the involvement of any replicability as it is an unpredictable and spontaneous event; meaning that scientists don’t know when it will happen and when it does happen it can only be seen from specific parts of the world thus severely limiting scientists’ ability to truly research it and study it. This occurrence only lasts for 1-2 hours which in turn further justifies science’s incapacitation of properly studying it; due to its short time span, its unpredictable and rare nature and thus its inability to be replicated.

In response to the prescribed title, I believe that the production of knowledge is inherently dependent on replicability. Instances where replicability is not necessary are more so the exception, rather the rule, implicating that we can consider replicability, broadly speaking, necessary in the production of knowledge, as evidenced by the examples explored, which alienate the cases where replicability is absent.