1. What is the difference between a conjecture and a theorem?

A conjecture is a statement that is believed to be true, but has not been proven true yet. A theorem is a statement that has been proven true as there is strong imperial evidence backing up the statement.

  1. In this videoEduardo Saenz de Cabezon uses the example of people being surprised that folding a normal piece of paper 50 times, will reach a thickness as high as the sun. He challenges us to ‘do the math’ and see that he is correct. What do you think meant when he said that Maths dominates intuition and tames creativity? Do you agree with this?

Eduardo Saenz de Cabezon claims that Math dominates intuition and tames creativity, and he uses the example of folding a piece of 0.01mm paper 50 times, it will reach the thickness from the sun to the earth. After first hearing it, our intuition says that it is impossible, however as he challenges us to ‘do the math’, to see that he is in fact correct. I agree with this statement because I think what he means by this is that in Math, when we get a situation as the one he gave, our intuition clouds are judgement, as we immediately think that it is impossible from a logical point of view. When you first hear him say that, you think that it is impossible and ridiculous. Because we used our intuition, we came up with the conclusion that it was impossible, whereas if we were to think about this creatively, we may have come up with another conclusion. Maths can tame creativity as there are limitations to Math (such as having to use certain formulas at certain times in order to achieve the correct answer). It’s not impossible to get creative in the field of mathematics, but it seems that we do primary use our intuition as we (sometimes incorrectly) feel/assume that using our intuition will lead us to getting an correct or more logical answer.

  1. Saenz de Cabezon claims that the truths in maths are eternal. Do you think this gives maths a privileged position in TOK?

I agree with this statement and I think that it does give maths a prividliged position in TOK. Math is eternal as it cannot be erased from our society, regardless if it is a conjecture, theorem, right or wrong. Math is in a priviliged position in TOK due to its application in the different AOKs, such as in the Natural and Human Sciences. For example, almost all Physics fundamental laws have a mathematical formula associated with it, or involve calculating something. Math is used in chemistry as well to find things such as wavelength and is used in Biology to find the growth and decay of organisms. It is also used in the human sciences, such as in Economics and Business to calculate profits and many other things. All these equations that are used will be used forever, unless someone comes up with another more efficient, more ‘correct’ way to correct these things.

  1. List any of the knowledge questions related to maths that came out of your discussion in class.

Who should study math?

Should everyone be required to study Math in school?

What is Math actually about?

What are the best methods to solve Math problems?

 

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In art, we can have types of knowledge such as moral, conceptual and aesthetic knowledge. Moral knowledge shows us why something is to believed as true or ‘correct’ and helps us inform whether something is right or wrong, or whether it is justified or unjustified. Art can help us develop our conceptual knowledge as well as it can allow us to build a better picture of the world beyond what we interact with everyday, as it allows us to connect different concepts in our daily lives. Aesthetic knowledge can help us deepen our experience of the world, or give us a feeling/appreciation of beauty.

The role of the ‘group’ (generally deemed to be society) does allow for the verification of knowledge (making it shared knowledge). One could say that the group does play an important role in the pursuit of knowledge. It does depend on what type of group it is, but let’s take a group of art experts who are widely respected throughout the art community as an example. If they were to make a claim and attempt to say that this type of an artwork is not an art, many would believe them immediately. There would be some who might still hold their own opinion that it is art, but many would agree with these artists. Why? Because they  are high-up in the art society’s hierarchy, and having this status commands them respect and adds weight to what they are saying. Because they believe that this piece of an artwork is not truly art, and they are such experts on the subject, they must be right. This would provide shared knowledge in arts as everyone many would come to the same opinion that these experts have, making it the  ‘truth’.

The group in this hypothetical scenario are people with a great deal of knowledge in a specific field and the main role of someone who is an ‘industry-leader’ is to make important decisions and talk about knowledge that has been produced in that particular field. As an expert, the profound experience they have gained within that area  allows them to be proficient in the act of identifying patterns, trends, and predictions. Hence, in the field of art, it gives them the ‘ability’ to judge a work of art based on ‘standards’ that they themselves have set. However, a question that comes out of this claim is that: “must an art piece meet certain ‘standards’ set by people with a great deal of knowledge and experience in the field of art before the public considers to be knowledge relating to art? And if yes, what are the standards in this context and won’t they differ from person to person based on experiences and emotions?

A counter claim is that the group plays no role in the verification of knowledge and that the group is not required to verify knowledge in order for it to be considered to be true. Art allows us to gain personal knowledge through the way we interpret different pieces of art. Society cannot dictate the way we interpret art because we all have the potential to interpret artwork differently based on our experiences. One could say that shared knowledge cannot be gained from the arts and as a result there is nothing for the group to verify, but the individual has still gained something for themselves (some form of knowledge whether it is conceptual, moral etc). The group has no right to identify what is art and what is not art and the group also has no right to verify personal knowledge as it is different for each individual.

One could also say that despite art being fairly subjective, people can agree a similar interpretation/develop a similar understanding  based on their collective experiences. As a result, there is no group in the production of knowledge and no one to verify what is considered to be right or wrong because in art, there is no such thing. The shared knowledge gained in art is knowledge that is shared by those who have similar understandings and interpretations which therefore form a group of people, but they are in no place to say if other knowledge is true or not.

 

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TOK: Arts, Science and Truth

by 042690 on November 17, 2017

Art v Science

This mini-essay brought up some interesting points but I though that one quote that summed it up well was that: “Art and sciences are inextricably linked: science can sometimes explain the beauty of art, and art is often used to convey scientific “truths” to the common man.” Both science and art has to be applicable to understand the real truth. Truth is not solely based on facts and information, but also involves other things as well that can be related to emotions. Science focuses more on the facts and information which explains reactions from humans whereas art can provide the emotional attachment to the same reactions and experiences.

 

Art v Truth

This essay talks analyses the claim that art provides truth and talks about how artists can convey the truth, even if it is biased. The way they communicate the truth is on a unique platform like no other. Art can transmit and show us the truth in many different ways, but truths can be asserted even if they have bias in them. It also examines how it is almost impossible to rid the arts of bias by brining up the point “The artists have their own responsibility to convey their truth, even if it is upon bias. Their method of communicating this ‘truth’ gives them a type of power because of it’s unique platform. Arts can transmit the truth in different ways possible, unique to the arts, truths can be asserted however often with bias hindering within.”

Both of these mini essays show that regardless of whether the art is truthful or not, there is knowledge that is produced from art. Every story has two sides, even if the truth is not necessarily a classification of one story. They both also represent art as a raw emotional experience for a human. Without art or without science, knowledge can still be produced as facts, but the facts that are produced will be missing something (whether it be statistical, numerical data or emotional qualitative data).

 

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TOK: What is Art?

November 15, 2017

In our most recent TOK class we were looking at the area of knowledge of Art for the first time formally, and discussing what we believe is art, the definition of art and if and how art can provide us knowledge.  In this blog post, I will be outlining evidence for and against the claim “Unlike The Arts, […]

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TOK: Intro to Natural Sciences

October 20, 2017

Recently, I watched a TED Talk titled “Why we should trust scientists” by Naomi Oreskes. She brought up a few interesting points in her talk. One of them is that faith and science are separate, but belief is what binds them together. Belief allows us to trust the science behind all objects in our world […]

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TOK: Faith and Intuition

October 18, 2017

Distinguish faith and intuition as WOKs. Intuition is knowledge that we develop from our experiences and natural mechanisms and they are stored in the subconscious part of our mind. They help you make instinctual or split-second decisions without processing anything in your conscious mind. They could also be described as a ‘gut-feeling’. Faith can be […]

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TOK: Imagination and Memory

September 22, 2017

Despite the imperfections of imagination and memory as ways of knowing, the Areas of Knowledge have developed in such as way as to overcome them. Discuss this claim with reference to at least two AOKs. I think that the main AOK that has developed in a way to overcome the imperfections of imagination and memory is the […]

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TOK: Reason

September 14, 2017

Pure logic is only concerned with the structure of arguments. The validity of an argument is independent of the truth or falsity of its premises. Sometimes, this can be true but this is not always the case (this depends on the Area of Knowledge). For example, take the general statement related to medicine that “Drugs are harmful […]

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TOK: Language

September 9, 2017

“The vagueness and ambiguity of language always limits the production of knowledge”   Personally, I disagree with the statement above. I do believe that vagueness and ambiguity of language can limit the production of knowledge but this is not always the case. For example, we can look at the AOK (Area of Knowledge) of The Arts. […]

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TOK: Emotion

September 4, 2017

  Emotion plays a key role in our daily lives and it is a part of us that impacts the decisions we make and shapes our judgement of certain situations. Claim:  A good historian strives to be as unemotional as possible, this is the only way to write accurate history Some may agree with this claim […]

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