Mathematics: Essay Questions

For homework, we have to come up with 3 TOK-style essay questions that may derive from the quote: “God used beautiful mathematics in creating the world.”.

Here are some answers to questions, which will help me come up with the questions:

a. What areas of knowledge & ways of knowing should be investigated?

AOK: Mathematics, Religious Knowledge Systems,  Indigenous Knowledge Systems

WOK: Reason, Language, Intuition, Faith

b. What’s the question getting at?

First of all, the question is putting us to think if whether or not mathematics was used to create the world, on the premise that the student agrees to the existence of ‘God’. This question is discussing three different topics:

  1. ‘Did God exist?’
  2. ‘Did God create the world?’
  3. ‘Did God use Mathematics to create the world?’

The first and second question asks the student to explore Religious and Indigenous Knowledge systems, referring to Reason, Intuition, Emotion, and Faith. These WOKs require the student to give an opinion of their own religious beliefs. The third question can only be answered if the answers are both ‘Yes’ to the first and second question. The AOKs the student would explore here is, Mathematics. The question asks the student to define the relationship between God and mathematics. This can be answered using Reason, Language (Mathematics as a form of language: Axioms, Theories, Proofs, etc), Intuition, and Faith. It is difficult to tackle real life situations, which support claims on the existence of God. However, the student can use real-life situations, which help support the Axioms advocated in math (for example: to give evidence to the golden ratio, use the patterns seen in sunflower seeds as a real life situation).

c. What are the potential knowledge issues? (The 3 Essay-Style Questions)

  1. In the field of Mathematics, to what extent do axioms conflict with theories that support the existence of God?
  2. If God used Mathematics, then to what extent can Mathematics be used to prove the existence of God?
  3. If Mathematics is a form of language consisted of Mathematical symbols invented by mankind, then to what extent can Gödel’s ontological proof be proved to be true?

The 3 Knowledge Issues -Provocative artworks collection

To what extent is it possible for ‘My Bed’ to provoke the emotions of the audience, if Tracey Emin had just brought her bed to the museum and called it an ‘art piece’?

To what extent is the emotion and sense perception of the audience towards Hitler’s water color painting affected, by the contextual knowledge of the artwork?

To what extent could have Rembrandt’s emotions played a role when he drew his own self-portrait?

Thoughts on Ethics

The definition for ethics is, 1. the moral principles that govern a person’s behavior or the conducting of an activity. 2. the branch of knowledge that deals with moral principles. From this, I think the following quotes best answer the nature and purpose of ethics.

“Ethics is nothing else than reverence for life.”
-Albert Schweitzer

“Morality is the herd-instinct in the individual.”
-Friedrich Nietzsche

From the given definitions, I think that ethics are set codes within an individual that influence/act as standards of their behaviors. To that point, I agree passively to Friedrich’s quote that moral is about the herd-instinct in an individual. The behaviors of a person will mostly depend on their environment/background stance they are raised in, as well as their genetics. For an example, the hunting tribes may be instinct to act more individually as where agricultural tribes may be more instinct to act as a group, as the process of aggregating crops require the people to stay within the same location as where hunters are required to hunt for preys at the location each is in charge of.

  1. Which other AOKs do you think resemble ethics in terms of the nature of knowledge they represent?

As mentioned previously, I think that ethics is about standards of morality that acts as a reverence of life for an individual. I have also mentioned that it can be affected by the genetics as well as the raised environment of an individual. For this reason, the nature of knowledge ethics present is about the cultural, physical, religious aspect of one’s environment, as well as the natural science aspect of one’s genes. This leads me to a conclusion that ethics may resemble to every single unit that consist the area of knowledge. As an example, the ‘natural sciences’ as well as ‘mathematics’ may influence the physical intuition aspect. Adapting to the previously given example, a child born in a hunting tribe may be scientifically adapted to being able to walk as soon as they are born. The analysis of their genes may also allow to mathematically calculate the trend in their behaviors such as, more quicker response to stimulants. The ‘arts’, ‘indigenous knowledge systems’ and the ‘religious knowledge systems’ may interfere within the cultural aspect of a group one locates in. If the group does religious practices, the individual may be likely to act in a certain way. For example, Japan is a multi-traditional country however, Buddhism and Shintoism was popular amongst the earlier ages. Such religions still affect the way the Japanese kids are raised in their homes although the parent may be part of another religion. A great example, the majority of the Japanese go to shrines on the new year’s. Minor example may include what I have been taught from my parents: to not cross my legs whilst sitting (only men are allowed to do so), and to not stand my chopsticks amongst the rice in my rice bowl (this represents the rice is for the dead). The ‘history’ and the ‘human sciences’ may involve in the personal way each individual acts. If one has experienced a stimulus, the drove feelings from it such as ‘happy’ or ‘hurt’ may set a standard for one’s ethical implications. An example includes, ‘neglecting’, where if one embraces an unhappy feeling from being neglected from a particular group, it may influence the person to not to do so to others.

  1. Which ways of knowing function as the key means of acquiring knowledge in ethics?

Every WOK except for language may have a function amongst our learning in the knowledge of ethics. I think that the WOKs could be split into two different sectors, with one being about ‘evidence’ and the other being ‘unprovable senses’. In the ‘evidence’ section there will be ‘memory’ and ‘reason’. These WOKs could be qualified proofs amongst identifying the influences of one’s standards of ethics. As from the previous example on neglecting, this is related to one’s memory from the past, which will act as a reason one will act in a particular way. ‘Not crossing my legs’ would be a valid ‘reason’ from my cultural practices. ‘Language’ will not be a part of ethics because in my perspective, it is not possible to write ethics in the form of text, so that every descendant will follow. Ethics has a different meaning for everyone and therefore, it is impossible for everyone to have a common list of ethics. Of course, cultural/religious practices can be written in the form of text (eg. deny the consumption of pork in Hinduism) however, that is only common to a certain group of people. The ‘unprovable senses’ include the rest of the WOKs, which include, ‘perception’, ‘intuition’, ‘imagination’, and ‘faith’. These are all dependent on one’s senses that do not rely on valid physical evidence. For example, ‘faith’ is when a person believes for something to be true when there is no actual evidence. ‘Imagination’ consists of one’s thinking, ’emotion’, ‘perception’, and ‘intuition’ relies on one’s feelings from their past experiences/observations. Although they do not give any physical proof, they affect one’s ethics to a great extent and therefore, I think all of the mentioned WOKs have a function when we acquire our knowledge on ethics.

  1. Which WOKs and AOKs does ethics seem to clash with?

Ethics can clash with any AOKs and the previously mentioned WOKs however, I think it majorly clashes with ‘human sciences’ (AOK), and ‘intuition’ (WOK). Analysis and acquiring our knowledge on ethics is about the identification of the set codes that act as a reference guide to any behaviors of an individual. As the TOK syllabus states, ‘human sciences study the social, cultural, and biological aspects of human existence’. I think this interferes with the definition on the study of ethics, ‘moral values that seem to embody the obligations for action’ as, obligations for action is greatly influenced by the aspects researched in the human sciences. ‘Intuition’ is also described in the syllabus to being, ‘immediate cognition, or knowledge which is immediately evident without prior inference, evidence, or justification.’ As discussed, the human sciences justify the ‘evident’ sector as where ‘intuition’ justifies the ‘unprovable’ sector.

  1. Which quotes do you find surprising, or do you disagree strongly with?

‘Action indeed is the sole medium of expression for ethics.’
Jane Addams

I disagree with Jane Addams’ quote, to the point that it is not always necessary to express ethics. Ethics is in fact a ‘reverence of life’ as quoted by Albert Schweitzer, and therefore it is not always necessary that action needs to take place in order to express ethics. Ethics can exist within the soul/mind of an individual, and therefore it is not always the action part that defines it.

Friends or ‘Friends’??

In the previous lesson, as a class we read an article written by Randi Zuckerburg, the sister of the FaceBook founder, and I found it very interesting to the point that she was criticizing this new era of all social networking including her brother’s FaceBook had entirely changed the way people interact and how it has affected our daily ‘balance’ of attention. Smartphones have made our lives very convenient to the fact that we can use a variable of applications that empower our lives such as maps, which help us navigate to our destination, alarm clock/setting, which help us act in accordance to punctuality however, as the author denotes, it has made our lives more stressful to a certain extent. A smartphone or any technological device has great connectivity to the internet, which means, that we can access a social networking site at anytime we want to, as where in the past, it had only been when we stood in front of a computer. Not only is it that us users, connect to the networking site however, the networking sites automatically connect to us as well. Whenever a social activity that involves you goes on, the device automatically gives you a notification with a buzzing sound. Such as, when you receive a message or a poke on FaceBook, when you receive a favorite or a retweet on Twitter, or when you receive a daily push from your favorite news report site. Now this, has caused us, users, to spend a lot of our attention onto this ‘Online’ virtual world. In fact, as the author also mentions, all of this insta-connectivity and this new age of convenient mobile devices has indeed brought us to a level where we actually pay less attention to the natural world. She mentions an example of paying great attention to cat videos online, and less towards our actual cats. This had greatly reminded me of how when I take my dog out for a walk, I am always on my phone whilst walking, going on my FaceBook application and texting my ‘friends’ and multitasking. Also, her example of being at a concert but actually watching the live show through a smartphone screen just reminded of a recent live show I attended, where I mostly spent more time taking photos and uploading them to Instagram and Snapchat rather than enjoying the actual music and live performance. I went to the performance with a friend from school however, because of the acts of taking photos and uploading them to the online network had caused both of us to talk less to each other. I agree with the author to the point that we need to keep our eyes on our daily balance of attention, and particularly to the point that we need to restore our ability to be present at any single moment. I personally think using phones during dinner is immoral, as ‘dinner’ is one of those chances your family gets to unite and have a great communication. Therefore, I agree to the author’s idea/attempt, and her brother’s attempt in prioritising your attention to your real world friends or family. Most of all, I was moved when the author reminded about how all the connectivity the digital world has brought, had changed or disturbed, the way we embark our relationships with people.

“When deciding who to pay attention to, we need to understand the difference between our friends and our “friends”. It’s hard to remember now, but there was a time when “friend” was still only a noun and not yet a verb. Back then, our friends were the people closest to us, who we hung out with regularly, drank with, and confided in.”

Especially to the point where she mentions, “…was a time when ‘friend’ was still only a noun and not yet a verb.” I remember that the first time I had started using the internet so rapidly was when I became a middle school student. It had become more necessary for me to use the computers to finish my school homework and researches and I started to spend more time in front of a display. Then, because we all use the internet, we (the students in my grade) are introduced to the online networking sites. Since then, FaceBook has been involved in a major part of my communication with others. To be frank, I now even have people who I have never met in real life adding me on FaceBook, and I have confirmed their requests. In this case, I can conclude that it is very true that I cannot tell the difference if these ‘friends’ are really my friends or ‘friends’. After all, I would like to conclude that social networking has affected my life to a great extent and that I agree to the author randi Zuckerburg, that we must make an effort in spending our limited time and attention, to those we really care about.

After reading the article along with other articles on Teenage social networking and social media, we came across with the following discussion questions.

1. Does social media strengthen or weaken relationships between people?

One of the articles from the document, ‘Teenagers and social networking – it might actually be good for them’ suggest that, in contrary to what the social media is often perceived as; a tool that will make kids and teenagers unable to make face to face communications, there has been an evidence that show that online socialising does not prevent real life socialising however, it enhances it. The Oxford Internet Institute reports, that amongst their interview with British teenagers, they have found that as those teenagers gain more experience being online, they gain new communication skills. From this evidence, I think that social media can be one form of tool to build the communication skills of teenagers, which may eventually impact the social behaviours and interactions of these teenagers in the real world, finally strengthening their relationships with other people. Another statement is suggested that a study has shown, teenage participants of hobby sites were more likely to engage in real world volunteering. This may hint that the usage of internet will act as a catalyst towards encouraging teenagers to involve in volunteering, finally strengthening their relationships with others in their community. However, another article, ‘Is social media making you anti-social?’ reports about a college dropout, who had spent years on videogames and the internet, and upon his return to school, his ability to focus had to be restored, as well as his ability to read and write. Such example can show a circumstance where one can lose their communication ability, and relationships can weaken between other people. Overall, in my opinion, whether a social media will strengthen or weaken a relationship between people will depend on your purpose amongst using it.

2. To what extent is interaction via Facebook and other sites ‘real’ interaction?

On FaceBook, communication can be taken upon the form of text within a chat. This will involve interaction between two or more participants to some extent however, it will not reach the same comparable level as to real world interaction where one will talk face to face with another. This will be because in the text format, one will not be able to recognize some features of real world communication such as, tone and mood. As you are not able to see other’s face expression or hear their voice, you are given a limit to how much you can understand the other person. For such reasons, I think interaction via social sites can not be fully interpreted as for being a real interaction.

3. Does documenting our life in minute detail enrich it?

As mentioned previously with my example of uploading photos on Instagram whilst participating in an event with a real friend, such act prevents my interaction with the other friend. Although taking photos and uploading them will enable us to view this later and recall our memories, if we are obsessively adhered to our smartphones and are concentrated on uploading them on social network, we are not able to fully enjoy our moments. Therefore, I think that although I document my life very often, it does not enrich or benefit my life however, on the contrary it disturbs my attention towards the real world.

Can Science answer moral questions?

-A Response to Sam Harris’ argumentative talk on applying science to resolve issues concerning moralities for a better life constitution. –

In the TED Talk, Harris argues that morality can all be answered through scientifically proven facts however, this may only be done if the global population of different religions and cultures converge to agree to the only answers that these morality questions embark and merge a universal conception. Furthermore, he states that in order to resolve answers to such disputable questions on human flourishing, it is necessary that we exclude personal opinions, and only discuss based on facts by admitting what is correct and what is wrong.  In my perspective, I believe science can answer questions concerning morality to a certain extent however, facts only account for a partial sector when deducing answers concerning values.

First of all, as Harris had stated, it is true that science is generally understood as a factor that can aid us in getting what we value however, it will not remind us of what we should value. I think that science is a constitution of proven facts or theories, and that it does not consider morality values. Therefore, it is not possible to answer these questions as science does not embrace any opinions.

However, I do agree with Harris’ statement that the separation of science and human values is an illusion, to a certain extent, and that science can answer question concerning values, to a certain extent. Although science discuss about facts and values discuss about the well being of the conscious, these two factors can be merged to a certain extent, but not at all situations. For example, a question concerning the food pyramid Harris discussed about, ‘Should we all become vegetarians?’. This question can be argued through the support of measured nutritional values (Insufficient amount of—)  however, it will also require ethical implications (We can stop killing livestocks).

Overall, I believe that Sam Harris is correct to some extent that science and human values can be converged to answer questions that require acknowledgment of moral implications however, it is not a factor that we can completely rely on and consider to answer argumentative questions. Therefore, my answer is that science can not completely answer moral questions.