Maths: Axioms and Conjecture

If mathematics is created by people, why do we sometimes feel that mathematical truths are objective facts about the world rather than something constructed by human beings?

Maths is an interesting topic full of rules. But why do we feel that sometimes mathematical truths and simply objective facts about the world. Why do they get this status of being completely true and objective when rather they are something constructed by human beings. Did humans invent mathematical truths or did they simply find them? What is the nature of maths when it comes to being completely objective and true. I believe that the idea that math truths are objective come from that within the system of maths that human beings have created, it is impossible to prove them wrong. Within the human constructed form of maths, these truths become ultimate truths as they are objectively true within the system. Axioms come around, rules or statements that are accepted as true without proof. We can see mathematical truths as being objective facts only within human systems. Human created mathematics is the way humans interpret part of what the world we have been offered and though these human created mathematical truths cannot be seen as objective within the greater world, when we step back to see maths as something made by man, these truths hold up.

 

History and the Role of Bias

“We should always aim to acquire knowledge that is free from Bias. Evaluate this statement in History and one other AOK.”

In class, we have been looking at the role bias has within history. We examined events such as the shooting of students at Tiananmen Square in China. In Western media, the event is referred to as the Tiananmen Square Massacre whereas in China it is known as the Tiananmen Square Incident and public information is limited. The way the event is viewed in China versus the rest of the world is radically different, showing the role that bias has in historical narratives. Is it possible to have history without an element of bias? In the books we read and the documentaries we watch, the creators all have their own opinions and this kind of world view with this lens can severely impact the messages present in historical narratives. If we have an unbiased version of history, it would presumably just be facts about what happened. But this raises questions as to where we are actually getting these facts – for instance with Tiananmen, the Chinese government  reported significantly less deaths than other media and bodies. Another implication raised is that history then is just facts, which may devalue the AOK itself, and disregard the work of analysis and other perspectives within the AOK. Perhaps then history can be seen as a collection of facts and narratives as viewed through many different perspectives. If we are always striving to get knowledge which is free of bias in history, we have to ask ourselves – is anything truly unbiased? Are the sources of our information and facts truly bias free and can we trust them as such. On the other hand as well if we truly wanted to learn from history and about the multiple perspectives out there on earth, wouldn’t we want to see the bias? The presence of bias in history can teach us even more about history, such as the values and ideals of government bodies or groups such as in China. Bias may be a key part of history as it is definitely something that works closely within historical narratives.

If we were to look at this statement within another AOK such as natural sciences, the way we view bias may be very different. If we were conducting experiments in the natural sciences wherein results would be there to inform the way we view the natural world, we would want to strive to a further degree to find unbiased knowledge and would want to spend less time analysing the possible bias of sources. A natural science study into something such as climate change may have bias depending on the group producing it. Climate change deniers would report it differently and what would come of this is a set of very biased results. But whereas in history where we could look at the different views to gain further knowledge, in natural sciences it would be much better to have clear unbiased results about the climate, showing the different roles bias can play in different AOKs.

My CAS Project

What I have chosen as my CAS project is my involvement in the rehearsal process and the performance of the musical theatre charity concert ‘Applause For a Cause.’ The concert was organised by students and teachers within the school in partnership with the charity Worldwide Action. The purpose of the project was to put on a concert featuring some of the most well-known songs from musicals around the world. The goal of this was to raise enough money through tickets for the event to fund the building of a new classroom in a school in Nepal. As students we got the chance to choose our songs as well as run rehearsals and organise choreography and vocals. The rehearsals ran from the first week of January, eventually culminating in a final concert in the final week of February. We were able to raise enough money to reach our goal, and the concert was a huge success overall, with many coming to enjoy some of their favourite songs from musicals. The process of this project fits well with the CAS stages.

Investigation and Planning

In the stage before the start of rehearsals, myself and a few other students were involved in the initial investigation and planning of the concert. Before the actual concrete planning, Ms Alborn introduced the concept of a musical theatre showcase and tried to gauge interest within our theatre class. All five of us in class were very interested in the idea and in being involved in the planning. We looked at different groups of people that would be interested in getting involved and managed to begin to collate everyones different skills and interests together. For instance some of us were well versed with more recent and modern musicals whilst others knew classic musicals and in coming together we were able to start planning. When the entire cast came together, we began to decide upon songs (and thus roles and responsibilities) within the show and rehearsal process. We looked at the timeline of the show, and additionally organised rehearsals and times that certain logistical tasks would need to be complete by. We grouped up into different ensembles and different duets or groups as well as working together to figure out responsibilities within them. I was assigned to be involved with 4 different ensembles, and within this I would be helping with choreographing 2 of them.

Action

The stage of action was incredibly collaborative. It was essentially the rehearsal stage of the show and this is when we implemented the plans that we had put in place. In my ensembles and my pair pieces we rehearsed at least once a week, putting together choreography and working on the songs themselves. Coming together with these teams, I believe we managed to use many different learning styles due to the diversity in all the ways we thought. Decision making and problem solving was needed constantly, especially in the older female ensemble I was a part of wherein it was necessary for us to take action by ourselves. I learnt a lot about collaborative work on a high level, especially in an environment where we had a limited amount of time and high goals. Most of the problems I encountered that were overcame had to do with working within these large groups as sometimes with things such as choreographing there would be many ideas thrown out in the room, and you would have to avoid working in a cyclical way and actually try to finish work. Finally at the end of this action stage we performed, and it was a test of confidence and risk-taking abilities as well as a challenge to the skills of all of us as individuals and as a team. Additionally we were able to achieve our goal through the action of raising enough money to fund the building of the classroom in Nepal!

Reflection

Many questions and thoughts were generated throughout the entire process. In the action stages I felt some initial stress and nerves over the time limits we had and being under pressure to choreograph and rehearse. Ultimately I think that I’ve realised in some of these situations however, pressure can aid in the production of work, especially when it is important and there is limited time. I also kept thinking about the relationship between arts and service and how it seems to work very well with myself as a learner and my interests. Though the service may be indirect, throughout the entire process we were keeping the end goals in mind and always striving to put on a show that people would want to come and see (and ultimately to donate money to). I think arts and service aspects can go very well together because of the way arts manage to engage individuals and communities and how you can apply many different issues and charities to different celebrations and types of art, such as what we’re doing with our charity concert.

Demonstration and Celebration 

Going onto stage the first time that night, under the lights and in costume, I was initially very nervous. I hadn’t been involved in a show or a project before where it was solely about singing and the performance through song. I had been in musicals before where singing was accompanied by acting and plot but it felt like a much more concentrated performance environment. In my duet I definitely felt stress and anxiety but I also felt an immense sense of pride. Because of the goals of this project, in raising money to fund the building of a classroom, it suddenly felt like this was much bigger than ourselves and how well we could sing. Once I took this into account, the pride really aided me in reaching a level of comfort wherein I really enjoyed the performance itself and being on stage, despite still having some jitters. All in all on this helped greatly with my skills and abilities on a personal level, not just performance-wise. Despite growing more comfortable as a performer I also learnt how to work better with people to a higher extent under pressure and finding ways to incorporate many people’s ideas together. We were able to share all that we accomplished and learnt through the final performance which was hugely successful.

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Human Sciences Experiment

“I can calculate the motions of heavenly bodies, but not the madness of crowds.”

– Sir Isaac Newton

In TOK, we have been looking at the area of human sciences and looking over many aspects. Is it a science? What makes a science? We conducted studies of our own choice in class and found ways to present our data. The key part of our presentations however, were to make actual errors in our methods and to show unreliability, as a way of finding even more ways to be reliable and as a practice of really examining data. Lolo and I conducted a survey asking people what school house they were in and if they were allergic to anything. Our presentation can be found here. The errors in our presentation were that we were assuming a certain type of causation which was already unlikely and our sample size was fairly small and not selected randomly.

There are many factors that contribute to (or take away from!) reliability and the certainty we can have in all experiments, not just human sciences. For instance the sample method and size. If the sampling method isn’t controlled or isn’t random there may be room for possible bias or discrepancy in the data. Additionally if the sampling size is too small, it becomes difficult to generate an analysis that could work for a larger population. There are also factors concerning the relationship of causation. Two variables you are looking at may not be actually related to each other. For instance we found that raven house was more likely to have an allergy but realistically there is not likely a causation between house and whether people have allergies. Types of questions can be a factor in reliability or certainty. Some questions may be leading or the way they are asked may provoke the interviewee to answer in a certain way. Going along with this there is also the possibility of the observer effect wherein people act differently based on whether they are being watched or not. Finally the actual presentation of data can impact reliability or the certainty we may have, if the wrong types of charts are used or data is misrepresented.

There are ways however that scientists can increase the reliability of their claims. The main way to do this is to increase the amount of data you collect. By getting more samples / trials then you can conceivably find more repeating data and be able to draw a more solid conclusion. In all cases science wise, the best thing to do is collect a lot of data and ensure questions and sampling are unbiased and that the presentation of data is appropriate.

Reflecting on Reflection

A profound experience I had before was going on a backpacking trip through the Sierra Nevada mountain range. It was a four day and three night trip through a section of the mountain range that ended in the Yosemite national park. This was an extremely important experience as well as being one of the most physical and mental challenges of my life so far. We had to carry all of our food and equipment with us in our backpacks and the terrain itself was tough, with long stretches of ups and downs in relatively warm and sunny weather. This was an experience that allowed me to reflect in a variety of ways. Since the trip there have been many chances for reflection over the various aspects of the experience. The experience and the chance for reflection have changed me as a person.

Throughout the entirety of the trip, I kept a diary of events of the day, and although these were mostly recollections of which parts we walked and some issues of difficulties, keeping track of it also helped me reflect and remember the experience. After the trip, when I really did begin reflecting, I thought the best way that I felt I could convey the experience of the trip and to remember and be able to later reflect on it myself would be to perhaps make a video. Throughout the trip I had taken many photos and short video clips of moments that stood out to me as being significant – whether due to an incredible view or a skill or something I learnt in that moment. For instance some horse riders passed us at one point, which allowed me to later research and learn about the history of the use of horses on the Sierra Nevada mountain range and transportation in general. I took a video of this moment which allowed me to later recall and reflect on it to a better extent. Another example is that when we reached the highest point of the entire four day hike, I felt this immense sense of accomplishment as it really had possibly been the most physically demanding thing I had ever done. Having a photo of the view really helped me with my reflection as it aided in recalling this sense of wonder and pride in the moment looking out on that view.

I reflected on these aspects of the trip as well as many more through this video and multiple times, recounting it to friends and loved ones over the holidays and in school. The strength of these reflections were that they helped me to shed a light on really what I had learnt from this experience. In the moment you aren’t always taking into consideration what the big lesson being learnt is but reflection and self-examination helps you to see what really changed you and what you’ll take away. From this experience I learnt that will can really be an amazing thing. Before the hike I had doubts about my own strengths and worried as to whether I would actually be able to finish the walk. Also it helped me to fully appreciate the beauty of nature as being completely immersed in traversing it over four days really gave me a clear view of how easy it is to overlook the earth and what is given to us. Reflection is a great thing as it allows us to see these lessons and also the ways in which we reflect best. I believe my video reflection approach worked very well for myself as a reflector due to my strengths and interests and this style of reflection additionally made me more interested in film and photography as well, showing that both an experience and a reflection can change you as a person.

The Global Issue I Will Engage With

There are countless global issues in the world to be engaged with. From the problems faced in less economically developed countries such as poverty, to worldwide issues being faced regarding the environment and sustainability, to issues such as gender or social equality on many fronts, it is clear that there are still many ways we can continue to help the earth and its inhabitants. Looking at these areas of inquiry, each provide their own unique challenges and lenses, and beyond that there are countless ways of looking into each global issue and framing it. Through the five CAS stages – investigation, planning, action, reflection, and demonstration and celebration, there is a clearer framework of how we can approach these global issues and work with them.

The global issue I will engage with is related to the media, and the impacts of a heightened media and pop culture on people’s perception of the world. This is a more psychological issue, but one that I believe is entirely valid, as in the media landscape of the past decade, there have been vicious reactions and growth in the power of public opinion, which gives everyone the chance to speak their mind but also boxes people into communities with like-minded people. When pop culture gets brought in and we see this very moulded lense of the world which we are expected to look through, bias and ignorance may come through, with people not being able to see the other side of the world or of people. Media nowadays allows for people to see the world but it also allows them to find more like-minded people, which can be an issue when these values are negatively geared i.e racist or homophobic. The media gives all values a safe space in a sense, which can be good but also quite dangerous. This is the issue I want to engage with as being a teenager in 2017, it is apparent that this type of media has enormous impacts on both me and people around me.

Looking at it from the perspective of the five CAS stages and my strengths and passions, I believe a way to present this global issue and take action may be through the arts. A play that is particularly powerful to me is The Laramie Project. It follows the case and the murder of Matthew Shepard, a gay college student at the University of Wyoming in 1998. It has the potential to showcase and relate to the present day issues to a high extent in the way it portrays the growth of the media in the 90s and the consequences and byproducts of this new heightened media landscape. Simply increasing the coverage of news lead to a big change in the way people viewed the world as continued coverage led to more people knowing more about issues and perhaps being driven to action or a more solid opinion on matters. If I could present this play as a means of showcasing the global issue, then I can begin to work in the 5 CAS stages. Firstly with investigation, much contextual and perhaps psychological research would need to be done to lay a strong foundation. I would need to educate myself on the issue and how it has changed and evolved over the years, relating it both to the play and to the world today. In the planning stage, the logistics would come in of how I would stage this production, why it matters, who needs to see it, how it can actually be presented etc. The action stage would be highly practical and hands-on, involving a lot of leading, growing, discovering, participating, and connecting with others and with other issues. I would need to lead explorations of the play as well as direct a version but additionally I would be bringing in others and connecting and discovering the ways this issue impacts them. We would all be participating in this action-based approach in an almost investigative manner to make a difference. After the play, the reflection would involve examining how this issue was presented and examining if it was appropriate or made an impact somehow. This could also involve getting feedback as well as self-evaluating the feelings on the global issue and its connections. The demonstration and celebration, beyond presenting the play to others in the community, would allow for us to all truly come together over the arts and see the ways in which we can communicate these global issues and why its important to engage with them beyond a CAS perspective. This is an idea for a CAS project that I believe would be great to take on as it allows me to explore and engage deeply with a global issue that is important to me through a form (theatre) that I am passionate about.

 

How Will I Challenge Myself

Another thing to consider going into 2 years of creativity, action, and service is how I can challenge myself. It’s important to ask what you really want to achieve through your CAS experiences as well as what my goals are within the realms of creativity, action, and service. It’s also important to keep in mind what an appropriate level of challenge actually is. In my own opinion, something that is challenging is something that will test my limits in different aspects. It is something that you are able to do but that you don’t find necessarily easy to do. The whole point of a challenge is really – to challenge. To push yourself to achieve a goal that will better you overall and prove your own strength and goals. I enjoy challenging myself as a way to provoke myself into more action and to accomplish more of what I believe I am capable of or what I could become capable of.

Firstly for the creativity side of things, I have many goals in mind and skills I hope to learn or develop further that will challenge myself. In terms of completely new skills, I think it would be great to take up guitar as another instrument to learn. I have always considered learning guitar but never actually taken the steps towards actually learning it properly. I believe it would be challenging as all instruments take a lot of time and dedication but ultimately because I want to really learn and take on the challenge, I hope I will be able to learn this new skill. I have many skills I would like to develop further in the area of creativity especially in terms of theatre and music. With theatre, I want to become more involved within the community within the school. After talking to teachers, it seems the next steps may be towards taking action to create my own work or direct shows, which would definitely be a huge challenge. It would possibly be one of the largest ways in which I could challenge myself both artistically as well as logistically but it is absolutely something I would want to take on as a way of pushing further into my passions and interests. With music as well I would like to get better at playing the piano and singing and maybe even start to write some of my own music.

In terms of action, a skill I would both like to learn and refine is dance related. Dance is my main sport currently, and I train multiple times a week in a studio as well as doing exercises outside but ultimately it is a sport that is vast and contains a lot. I would really love to learn some new styles of dance, possibly from different cultures as I feel a lot of the dance I do is rooted in more Western cultures. This would definitely be a challenge to undertake as it would likely involve learning a completely new way of moving and training. I have studied some Japanese traditional dance types before in some classes but I’ve only really scratched the surface and it would be an interesting and in-depth way to look into training. I would want to also continue strengthening my current dance skills, which is already – I believe – an appropriate level of challenge because as I increase my skills, the difficulty goes up and more is expected. Additionally with action, I would like to take up running. I already know from experience that this is a challenge but I think it would be worth it to put my stamina and determination to the test.

Finally, service is the area overall that I believe is most open to challenge. I have definitely had CAS related service activity experience before with things such as environmental club, beach cleanups, charity walks, volunteering at events, and so on. This year I am already on the upper school student council, a service activity that has already required a lot of challenge in terms of risk taking and putting in work, but ultimately as with all service it is worth it to make a difference in the community. An activity I would very much like to uptake is perhaps volunteer lifeguarding or first aid. I have qualifications in these areas and it would be a good way to use skills I already have towards new skills and service activities. The previous summer, I volunteered at an iron man in Canada as beach support which involved some lifeguarding but I would definitely like to continue this service activity. It is absolutely sufficiently challenging due to the focus demanded by the position but service and all CAS challenges are really rewarding in what you get out of them and the difference you can make to others.

Arts VS Natural Sciences

Why might the question of whether or not The Arts should be considered an AOK seem much less problematic when we consider Maths or Natural Science? 

Essentially when looking at the arts as an area of knowledge, there is discourse and disagreement over what proper constitutes what ‘art’ is and often in the nature of art itself it sometimes defies clear and coherent definitions. Fundamentally I believe the question of whether or not The Arts should be considered an AOK comes from the fact that it is much less clearly defined than other AOKs such as Maths or Natural Science which typically have clearer set rules, methodologies, and ideology. This leads the question seeming less problematic when posed towards the AOK of The Arts. The areas of knowledge are what we use to categorise the knowledge we have and regarding arts knowledge, it can be seen sometimes that knowledge gained from the arts is inherently individual or even visceral rather than put into words and clear information. When looking at the knowledge we can say we possess in areas of knowledge such as Maths or Natural Sciences, we can point out statistics or laws or rules or things that have been proven or disproven in both of these areas knowledge-wise. This is something that would be difficult to do in an area of knowledge such as The Arts as at its core the arts is about creation and expression and the typical mindset for this area is that there are no rules or limitations or things to be proven or disproven. There can be intentions, purposes, and a lot of overrun into other AOKs but essentially the knowledge we possess from the arts is really just less straightforward. This is likely where the discourse comes from and the reason that asking these kinds of questions towards The Arts are less problematic.

In my own opinion, I would dispute this claim of the posing of this question being less problematic and defend the AOK of The Arts. Of course I may be inherently biased in my opinion as someone who participates heavily in arts related activities and wants to work towards a career in the field of the arts. The Arts aids us in categorising certain knowledge which is fundamentally creative and visceral. The lack of rules and guidance sometimes may lead to it being less conventional compared to other AOKs but it is hard to question the legitimacy of the knowledge we possess based around The Arts and would be even harder to categorise this expressive knowledge in another AOK should there be no area for The Arts. Art is about producing work that can be representative and becomes even more personal and individual when shared. Moreover, I would argue that questioning whether The Arts are a proper AOK or not is still just as problematic as questioning the other AOKs despite my understanding of how it could be regarded as less problematic. To question this area would be to put down all the work of artists throughout history and through the world and would be ignorant of the power and influence that The Arts have had on our world through educating us on not only other events and themes but ourselves and our place in the world.

 

Essays On Art and The Truth

When looking at arts versus the other areas of knowledge, we have to look at the role and perhaps the responsibilities of art as well – what might distinguish art as something individual yet significant and intrinsically linked in with everything. We read through two different essays: “The Truth, the Whole Truth, and Nothing but the Truth: The Merits of Art versus Science” by Martine Powers and “Art and Truth.”

“The Truth, the Whole Truth, and Nothing but the Truth: The Merits of Art versus Science” – A Summary

The first essay deals with art and its power to convey or reveal the truth in comparison to other areas of knowledge and ways of sharing information. It references pieces of art about war such as Elie Wiesel’s autobiographical piece of literature Night and Pablo Picasso’s art piece Guernica. It talks of how sciences or history and other areas may be used to find the truth but it really depends on what the definition of the ‘truth’ is. These area of knowledge may be able to find facts, statistics, or data but ultimately Martine Powers, the author of the essay defines truth in a different way. Powers talks of truth as being the ultimate revealing feelings and experience of humans at the time – more truths on the human condition and experiences rather than a recount of the ‘truths’ that happened at the time. Powers argues that the power of the truth is measured by the extent to which it is able to allow individuals to fully understand the extent of experiences, trends, occurrences, etc. They conclude that “only arts” can fully comprehend these universal truths and convey them to an audience so that they can viscerally understand.

“Art and the Truth” – A Summary

The second essay fundamentally deals with the relationship between the area of knowledge of art and the ‘truth.’ It begins by discussing the belief that some hold that art has a responsibility to convey social truths and situations. The author believes this derives from the “unusual power” that art has in transcending language and conveying truths in that sense. This essay also references Pablo Picasso’s Guernica as an example as it conveys the truths of the situation of the war at the time and informed others what was happening through art. The author goes on to discuss the validity of these claims that art has a responsibility to convey truths or if it even does convey the truth. Though it does not dispute the value of arts of whether art can educate us but the author does lead us to question this and delve further into what arts really means in terms of sharing truths or what its role even in our society is. The author finishes the essay by posing the question as to whether we need find any truth in art and whether our focus on art and truth comes from our societal need to find truth and facts in everything.

What essay do I agree with more?

I agree with the claims made in both essays to an extent but I believe the essay I agree with more slightly is the second essay as it really starts to get into questioning how art stands in our society and conveys truth. More importantly it also questions whether it need convey truths or anything absolute that we can interpret and take away. Whilst the first essay says that art can wholly help the audience understand situations and experience in a visceral way that other areas of knowledge cannot, the second essay ultimately goes into a deeper psychological discussion of the nature of art and what it need do to us and for us.

CAS Personal Profile

Going into the new school year as well as the next two years of CAS in IBDP, it’s important to examine yourself and your strengths, skills, talents, passions, and affinities to see the ways in which you could apply yourself in the fields of creativity, action, and service. Though I feel it will be harder to manage time and activities overall in the next two years, I will still strive to do my best in continuing activities that I enjoy and make a difference in the school community and beyond. This will compile of continuing activities that I already do and maybe even taking up new hobbies and activities.

Firstly with my strengths, skills, and talents, I believe I have quite a variety personally that I could apply to many different activities and action. I am a strong writer and communicator, and I have been writing both creatively for myself and for different forms of media and publication for many years. Last year for my personal project, I wrote a full-length original screenplay, a project that took a lot of time and dedication to enhancing my writing abilities. As well as writing I also act and perform in theatre a lot, having been in productions both in and out of school in the past few years. I have also taken steps to directing and creating my own pieces of theatre and I hope in the coming years to continue to do so and continue to creatively explore the realm of theatre, writing, and directing. Musically, I can play the flute, piano, and I sing, which are all activities that I enjoy doing immensely. As it may be apparent, many of my strengths and skills lie in the fields of the arts. Beyond just these arts I am also a strong speaker persuasively and I work well in a team dynamic, often taking on a leadership or counselling role.

My passions and affinities also lie heavily in the arts. I have a lot of passion for theatre, dance, music, and writing, which drives me a lot of the time within school. In the MYP I participated as much as I could in different forms of art and now as a double arts student in DP (taking HL theatre and film) I will get great opportunities over the next two years to go deeper into my passions and get a wider view of the world of the arts and how I fit into it. My other passions include nature and the environment. I love the outdoors and activities such as hiking and trail biking and I have advocated a lot before for environmental issues, such as when I was in E-Club last year. This year I am taking environmental sciences and already I am fascinated by this subject as it offers a highly interesting approach to the various ecosystems of the world and the environment as well.

Going into this year I hope to be able to continue exploring my passions in the arts and environment as well as participating in other activities that will make a difference in the wider community. I hope to continue being in school productions and bringing a joy to people through this as well as now being on the upper school student council to make a difference in the daily lives of students. Overall, after building my personal profile, I will now be able to understand to a better extent where my interests lie and how I can apply these to the CAS requirements for IBDP.