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Positionality Statement Revision

March 24, 2023 by adalal43 1 Comment

This section asserts my belief in the universe following mathematical rules and equations. This could be useful to add in my statement of positionality.

The author’s final argument to explain the unreasonable effectiveness of mathematics is that mathematical concepts are inventions that act as formalisms of the behaviour of nature and the cosmos or universe.

The patterns that build from these concepts are discoveries. Since this has not been proven mathematically, the paradox of unproven entities may apply to this. However, discussing this in a largely non- mathematical way I do agree to most of the author’s arguments.

I feel that there is a system according to which nature and the cosmos functions. Humans have discovered only miniscule fragments of this system and have represented their discoveries through the language of mathematics, the fundamental concepts of which are in fact formalisms to explain nature and the cosmos, but I consider to be discovered as they only state what exists in a different way.

I believe mathematics, as it is today, is the best way to describe nature, but is still not perfect. Mathematics works best on abstract concepts but leaves a small room for error in practical applications.

The study of probability and prediction, according to me, is purely an invention and is not a way to describe nature and the cosmos. I believe that assumptions are predictions that arise from the same inventions that are convenient for humans. The author says, for example, that the ring of smoke rising from a cigarette is unpredictable due to uncertain conditions. I believe that uncertainty is a human invention.

No one wishes to put much effort in showing the shape and the size of the smoke ring by measuring a number of variables, some of which probably have not been discovered yet.

(This can be attributed to the amount of time and effort it takes to do so, and also the small amount of materialistic rewards or prizes one would get in comparison to describing the nature of the fabric of spacetime. )

Some of these variables are air pressure, air velocity, air temperature and so on. The size or shape of a smoke ring might even change due to temperature flux or difference, sound in the environment, the smallest of convectional currents set up by differential heating caused by different light intensities, etc.

The theory of probability is a wonderful substitute, an abstraction that hides all these details that are extremely difficult to measure. However,

I believe that if each of these things is measured, along with the non- discovered things, a 100% accurate result can be obtained. I believe that the normal world behaves like the Platonic world, only that we have yet to gain knowledge of what differentiates a number like 0.999999999999999999999999999999……… and 1.

How this Book Shaped My Opinions

March 24, 2023 by adalal43 1 Comment

This could be important in terms of reviewing my positionality statement, with regards to the point about knowledge acquisition being independent of profession. The use of humour and the examples stated are also very applicable for my book.

◦This book has freed me of the bias that textbooks are always accurate and has also removed the very prominent bias for theories that are popularly accepted. It showed me that even these widely accepted theories may not be proven or their proof may contain multiple fallacies. Unless proven correctly, anything can be questioned and changed. Copernicus and Galileo showed the world the accuracy of the heliocentric model and the wrongness of the popularly accepted geocentric model despite the fact that there was severe opposition that they faced in doing the same. Descartes showed that being modern actually means the ability to question the past and present and to reshape the future.

◦I also was relieved of my bias against philosophy as a useful subject. Many around the world think philosophy is a redundant subject and that the scientists and mathematicians are superior to all of them. Much of Indian society particularly values engineering and medicine and looks down upon philosophy. However, the fact that philosophy, in some ways, gave rise to mathematics and to the scientific method of reasoning, showed me that philosophy may be the key to further evolving the sciences, mathematics and many other subjects. I am thankful of this book to remove this socially dogmatic perspective from my judgement of philosophy.

◦While maybe this book was not primarily written to show that knowledge is gained irrespective of one’s profession, the examples of John Graunt being a shopkeeper, but initiating the study of statistics through his observations and of George Boole being interested in linguistics and languages like Greek and Latin and even translating a poem by the Greek poet Meleager but still pioneering Boolean algebra and the study of logic, show how specialization in one field is not needed to study another. This showed me that a biologist is not inept to formulate a theory explaining planetary motion, and that unless proven, a theory about quantum physics formulated by a bus driver is as correct as that of a renowned physicist, if both are proven right or wrong. It removed my bias for theories formulated only by those specialized in the subject of that field. It specifically removed my bias against philosophers who wished to explain mathematics. In other words, I learnt that credibility and knowledge are independent of status.

Humour/ Relatable examples:

◦I found Archimedes’ stories to be the most interesting part of the book. As Plutarch mentioned, Archimedes looked down upon anything dedicated to profit and practical uses and devoted himself to things that were beyond practical uses. He found these things to be splendid and beautiful. This shows his exemplary love for mathematics and knowledge and his contempt for greed.

◦The story of him leaving his bath and running out on the street shouting, “Eureka,” the legends of his ability to move large weights with little force, his inventions like the hydraulic screw and a planetarium for demonstrating the motion of heavenly bodies, along with the legendary wartime machines that invented by Archimedes to defend Syracuse during a Roman siege by the Roman general Marcus Claudius Marcellus, are not only intriguing, but also show his command over knowledge.

◦How he invented things but said that the practicality of such things was incomparable to the abstract beauty of mathematics showed his unfaltering conviction, lack of complacency and his pure desire for knowledge.

◦Another part of the book I particularly enjoyed was the story of Kurt Godel applying for his American citizenship. This story exemplified the power of observations and of thinking.

◦Godel, a mathematician and physicist, clearly took interest in the task of studying for his citizenship interview, a task considered boring by most people. However, he studied more than that was required of him and even noticed a flaw in the democratic system of America that could lead to autocracy or dictatorship.

◦It is amazing to see how a person took interest in doing a thing well even though it was not a thing nearly as important to him as his major professions. It showed how observation could reveal facts about things even the most learned of people in the concerned field could not notice. This also showed how curiosity alone can give such insights that learned people could not imagine. It shows that true knowledge is not acquaintance and remembrance of facts, but is the insights that come only out of inquisitiveness and a dedication to whatever one does. Aside from learning this, it was also slightly amusing to see Albert Einstein explaining a joke of Godel stepping into his grave as Godel thought of it technically.

◦Another thing I found intriguing was Rene Descartes’ that education increased perplexity and made him increasingly aware of the ignorance of mankind. This shows that he was a truly modern person not afraid to question anything that he found to be ignorant or thought to be wrong.

Bias Mitigation by Balancing Perspectives

March 24, 2023 by adalal43 1 Comment

This could be useful to reduce biases in my research.

◦The author presents balanced arguments and perspectives throughout the book. He acknowledges the merit of various schools of thought, including formalism, intuitionism, Platonism and neo- Platonism. In the last chapter, for instance, the author shows the views of true or pure Platonists like G.H. Hardy, who regarded mathematical objects as part of another reality, and also shows the views of Edward Kasner, James Newman, Stanislas Dehaene, etc. He also examined the view of Max Tegmark that the universe is mathematics.

◦Even while stating his views on Wigner’s Enigma that mathematical concepts are invented formalisms which can be used to discover new things, the author, like most great authors, acknowledges the fact that everyone will not be convinced with his arguments.

◦Therefore, it can be stated that though the author has reasoned out his arguments well, the author acknowledges, states and considers opposing views and counterclaims wherever necessary.

◦More or less, this book covered both sides of the argument of whether mathematics is a discovery or an invention. The author’s argument itself is somewhat a representation of both these views.

Argument Effectiveness

March 24, 2023 by adalal43 3 Comments

This continues the Argument Presentation section and is important for my book because I am taking inspiration from the strategies of the author.

◦I think that most of the arguments are very effective and valid as enough evidence has been provided. Certainly, scientists’ quotes and references from their books are effective enough so as to explain theories formulated by them and explain their stances about particular or specific.

◦The logical structure of how the author places his arguments or proves his claims is also extremely effective, according to me. He asks questions in the first chapter of the book, provides relevant examples throughout, and states his arguments at the end. He also uses credible sources to prove some claims and clarify concepts within chapters.

◦However, as I have learnt from this book, there has been no mathematical way to prove the logical arguments proposed by the author even though the author backs them up with citations from credible sources, quotations from authoritative personalities and from various stories.

◦The author himself, as can be inferred from his support of Descartes’ method, believes strongly in the scientific method of proving things. However, his argument is unproven.

For fun, I even created a small proof of a paradox in the author’s work:

Let X be the superset of sets of unproven statements and arguments.

Hypothesis 1: X ϵ X, X is unproven, meaning it is unproven that any statement U ϵ X is unproven. If U is proven, X≠ {Statements that are unproven}. It can also be thought that it is unproven that X={Statements that are unproven}.

Conclusion 1: X ∉ X.

Hypothesis 2: X ∉ X, X is proven, so X={Statements that are unproven}.

Conclusion 2: X ϵ X.

I call this the paradox of unproven entities.

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