TOK Prompt 14

Read two of the four articles in the Maths folders and do the following:

  • Summarize the main points of each
  • Write at least two KQs that you arise from the readings

Article #1:

Why Math Works

  • Mathematics is unreasonably effective at expressing physical concepts in the natural world
  • Two branches of thought, Formalism and Platonism.
    • Formalism: Math is an invented set of tools
    • Platonism: Math is discovered by humans
  • Math is able to quantify real-world phenomena to remarkable accuracy
  • Sometimes math is developed without any application in mind, yet later are discovered to be applicable to real-world phenomena
  • Scientists pick solutions from vast math`ematical knowledge to apply to their observations


  1.  How does knowledge in Mathematics shape the development of knowledge in the natural sciences?
  2. To what extent does scientific discovery precede mathematical discovery?

Is mathematics an effective way to describe the world?

  • Platonism is an inaccurate view of reality. Formalism, mathematics is a product of human imagination
  • Math is an approximation of reality that has limitations that break down.
  • Reasonably ineffective at representing reality


To what extent is mathematics an effective representation of reality?


The Arts Ifolio Task #12

Arts vs Science

In this paragraph, the author expresses the view that the Arts possesses the capacity to “tell
the truth”, depicting reality in a new and insightful way. Art as a language is unique in that there are no clear cut definitions, words or phrases, yet are still able to convey truths that can be understood by anyone. This is something that other AOK’s are unable to do. Though other AOK’s can convey “truths”, the “truth” that this refers to are veritable pieces of information, events experienced or information discovered in the history of our world. The “truth” that art is different as it is  “a conveyance of the honest tendencies and experience
of the human condition.” The paragraph ends by saying through the AOK’s are different, they are inexplicably linked to art, the “truths” expressed by other AOK’s can inform or explain the beauty of art, while arts is used to communicate these “truths” to the common man.


Arts and Truth

This paragraph evaluates the consensus that the arts can and should be used to convey truths to the people. Artists hold the responsibility to communicate factually correct information, they hold the responsibility to listen to the people, understand and interpret reality, then use artistic expression to convey that understanding to people. The paragraph then evaluates arts ability to tell the truth. The arts are to convey truths to the people, but the “truths” are inexplicably vulnerable to falsehood; an art piece will communicate truth, but the artist’s decision of what to portray can assert their own beliefs and opinions to distort the information. Alternatively, the audiences ability to interpret the truths expressed are also hindered by our own beliefs.  The paragraph concludes that there is, in fact, there is no need to always seek truth in art, our “addiction to facts” and finding the truth to things that we diminish the true value of art. Art should be experienced as it is so that audiences can truly appreciate the artwork.

How do both of these essays reflect what is presented in chapter reading about truth in art?

They explore the view that art holds the ability to express the fundamental truths of our reality as perceived through human perception. Art is created to evoke specific emotional responses in audiences which, in conjunction with the information in the artwork, communicate the artists understanding of reality.


Arts: Entertainment or Knowledge?


The arts are concerned with entertainment, not knowledge.

Unlike knowledge in other areas of knowledge, art is concerned with the individuals conceptual understanding of their own experience, rather than an understanding of the nature of the universe. Though the arts to be taken with its aesthetic value in mind, the arts main focus is not concerning others interpretation or appreciation of the piece, but to express and convince oneself of observations and understandings of the universe. Shared knowledge in the arts is also very unique because the knowledge that is recieved from a painting is different for each individual and different over time, the understanding that conveyed by the artist could be entirely different to the one received. Though this is the case, the knowledge from an artwork is still valuable as the accumulated understandings of each artist help us gain a deeper understanding of our universe and ourselves.


Occam’s Razor

How can scientists decide between competing hypotheses?

Scientists decide between competing hypotheses by choosing the one which is the most probable given the evidence and information on the subject. The hypothesis is also chosen based on the number of assumptions being made, given 2 hypotheses, provided both successfully explain the phenomenon, scientists will lean towards the one with the least number of assumptions. This idea is known as the Occam’s razor and is used in determining the validity of scientific hypotheses. I believe that this is true to an extent, in some instances, assumptions being made can be the most probable given the information that is known on the subject. For example, when the periodic table of elements was being created, only a few elements were discovered but empty spaces were left for undiscovered elements and the known ones were treated as if the undiscovered ones were there. Characteristics of the undiscovered elements were also assumed and applied to the known ones. Though this process made many assumptions, the provided information had sufficient evidence for the assumption, so this hypothesis was taken as correct regardless. Assumptions also have to be made in order to create hypotheses so there is still value in exploring hypotheses that are improbable.


Mathematical knowledge promt 1

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

Theorems in mathematics must begin as a conjecture before it can become a theory, the two are differentiated by a matter of substantial evidence. A conjecture is a statement that is unproven but is believed to be true while a theorem is a statement that has been proven through reasoning. In the video, Cabezon shows that until a statement is proven with mathematical evidence, a principle can only remain as a conjecture and cannot become a theorem. He gave the example of the Pythagorean theorem, because the theorem is true regardless of the situation, it is timeless and becomes a universal truth.

2. In THE VIDEO  Eduardo 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?

Based on intuition alone, when being told that folding a piece of paper 50 times could cover the distance from the moon to the earth, it seems incorrect. But contrary to our intuition, the geometric growth of this hypothetical experiment is quite sufficient to reach the length to the moon. This indicates that mathematics can work contrary to intuition, thus dominating our predisposed ideas on the topic. as humans we exhibit boundless creativity, the mathematics provides a guide for the direction of such creativity as it allows for them to have a direction in which to apply such creativity.

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

I believe that Cabezons claim is absolutely valid after a theorem is proven, it is true regardless of the time or context of the situation. Thus a mathematical principle is eternal. I do not believe that this is a privelaged position as it is simply discovering truths of the universe, it is eternal simply for the fact that is is, not that us humans made it eternal.


Science vs Pseudoscience

Similar to the problem of defining art, the distinction between science and pseudoscience is equally unclear.


A pseudoscience is defined as beliefs, theories or practices that are considered scientific but have no basis in scientific fact. They cannot be disproven scientifically, tested or lack much evidence to support the claims. Unlike art,  pseudoscience and science can be distinguished through the use of rational thinking and careful evaluation, the ‘sciences’ that are proposed should be able to be tested through the scientific method, with results directly caused by the experiment. If this can not be done, then it is a pseudoscience. Art, on the other hand, is entirely situational and unique to the individual, such as the common phrase “beauty is in the eyes of the beholder”.  The individuality of the experience makes defining things as ‘art’ or ‘not art’ quite problematic, the distinction is not clear because it’s definition changes with the individual.

Intro to Natural Science

Natural science is distinguishable from other AOK’s because it is an accumulation of collective experience and observation through generations of expertise on specific subjects, understanding the world through the use of theory.

Natural science vs arts

  • theoretical disciplines
  • both are based on theory, not proof
  • Science relates to the physical world and observations of natural behaviours while art is not limited to the natural world

Natural science vs Maths

  • Science and math are both not based on authority, instead, they are based on collective thought
  • Natural science is based on inductive reasoning while math is based on deductive reasoning
  • they are both open to change if a more prevalent theory or proof is presented

Natural science vs human sciences

  • human science explores the human mind while natural sciences explore the physical world
  • the scientific method is used for both

Natural science vs history

  • History looks into the past while natural science looks into the future and makes predictions
  • history is not testable or verifiable as it is not in the present
  • both are based on inductive knowledge

Natural science vs ethics

  • they can both be biased
  • Natural science is based on theories and experimentation while ethics is not
  • both change with new information, there are paradigm shifts in both

Natural science vs Religious knowledge

  • Natural sciences are open to change while religion isn’t
  • religion does not need evidence while science does
  • religion is based on belief and decided by faith while natural sciences are based on theory and experimentation
  • Neither can answer all questions or be certain



Real life situations

Articulate the ‘real life level’ claim(s) being made

  • some cheap cars have the same functionality as expensive ones but people prefer the more premium brands, people buy expensive cars as commodities instead of utilities
  • people buy expensive items to demonstrate your wealth or that you have a lot of resources.
  • purchasing expensive cars are not everything, the car must be unnecessarily expensive for its use in order to be considered attractive

Explain what makes your TOK radar go off (2nd order)

  • people take appearance or apparent value over functionality
  • Preconceived ideas or beliefs about an object affect people’s perception.

Articulate a relevant KQ

How do presumptions affect our perception of the world and how does this deviate our morals in the realm of ethics?

Explain why answering the KQ is relevant to the 

The real life situation presented in this article is relevant as the article describes the decisions individuals have made when purchasing cars given two cars of nearly  the same functionality. People were willing to spend more money on the same car because of the preconceived notion that one is better than another. My question addresses this phenomena and asks how do our presumptions on objects or ideas affect the decisions we make?

Provide an example of another RLS that the KQ can apply to

This KQ could also relate to university students and their choices of study. When choosing majors, many students have been told that it is impossible to make a living while doing art, this presumption has led many students to choose a different major instead of art.

implicit and explicit claims

Article one: Invasive plant in Iceland

Explicit claims:

Blue Nootka lupine is an invasive plant native to North America introduced to Iceland in 1970 to halt soil erosion.

Lupine has spread across Iceland at an exponential rate, eradicating some of the native plants and animals.

After lupines introduction to Iceland, the soil has become much more fertile, while also attracting many tourists.

Implicit claims:

Invasive species are harmful to the environment and will potentially destroy the native ecosystem.

Species should never be introduced to an environment as a ‘quick fix’ to a problem, in this case, soil erosion. The cause should be addressed before looking for quick solutions.

Volunteers are needed to eradicate the growing lupine problem.


Article 2: Foreigners in America

Explicit claims:

The rate of immigration from Asia in America has increased in recent years, but they still only make up  31% of the foreign-born population.

The foreign population in America tend to be more educated than the American born population,

The foreign population tended to be more liberal, voting for the democratic party rather than the conservative party in the 2016 elections.

Implicit claims:

The more foreigners there are the less likely the conservative party will win in 2020. (go Asians!)

Globalization around the world is becoming more rampant, as immigration and emigration become more common.

Foreign imports and services will increase as more foreigners come to America.


Map-like vs Story-like Knowledge

Knowledge in the arts is clearly story-like, whereas knowledge in natural science is clearly map-like.

The most prominent characteristics of art are very storylike, there is never a single interpretation of art and there is never a single way to produce art. Every artist is unique, developing their own styles and trademarks. Art represents the human condition as it describes emotions indescribable by words; each art piece incites a feeling individual to each person. But, art does have some map like aspects, there are conventions and techniques each artist must know in order to make good art, that is why the average person cannot create an art piece with the same effect as an artist. Conventions such as one, two and three point perspective, golden ratio, light and dark, hue, etc, must be known and used to different degrees in order to create art to a high level of proficiency.

Natural sciences mostly embody map like characteristics, there are defined theories and variables that describe our world, are facts that remain true until proven otherwise. Even so, sometimes theories are given as narratives that try to explain how the world became how it is now, giving it a storylike aspect.