TOK: Mathematical Method

Using examples from your own education, describe the ‘Mathematical Method’

Currently we are learning logarithms and I think that this illustrates the mathematical model in the sense that there are a set of rules that we must follow. These have proofs that allow us to conduct our work without disputing whether the foundation of the work is valid, which saves a lot of time.

How is it both similar and different from the scientific method?

 

I think that the mathematical model is based on inductive reasoning with the use of deductive reasoning to further expand the inductive knowledge while the scientific method is a loop between the two reasonings. By loop, I mean that we make theories and generalisations based off inductive reasoning however make predictions off these theories and experiments off these theories using deductive reasoning which is then tested and further inductive/deductive reasoning is done. Although math may be deductive, inductive reasoning is still used. This inductive reasoning is typically used in axioms.

What are the strengths and weaknesses?

The strength of the mathematical model is that there is certainty that there is a framework or foundation to the rest and this framework/foundation is certain to be true. This however cannot be applied to Science due to the nature of Science. Mathematics is created by humans to understand stuff. We set arbitrary values in the process and these are in a way used to communicate. When I say there are two stones over there. There are two stones over there because I have established that there first are two objects over there that resemble stones; they are separate entities; 1+1 is assumed; and therefore there are two stones. Science does not have this level of certainty. Science is understanding the universe we are in and inductive reasoning may lead to being blind to future knowledge.

Mathematics even though with that foundation can seem like Science. I have heard of research in prime numbers which seemed interesting and in a sense resembles Science. It’s not that we created prime numbers. We created the rules for what a prime number. The exploration of prime numbers, twin primes, and other primes resembles Science cause we may never be certain of the patterns these numbers follow.

 

(Not sure about the last two paragraphs.)

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2 thoughts on “TOK: Mathematical Method

  1. I agree a lot with what your saying. I found it interesting about how you mentioned the strengths and weaknesses of the mathematical method and also how you compared it to the scientific method.

  2. I like how you established a link between what you are currently learning in maths. Very well done.

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