Paradigm Definition – A mental model which helps us organise our reasoning and create knowledge.
Examples Discussed/RLEs:
Buzz’s ‘paradigm shift’ in toy story. In the clip shown we could see how as the events unfolded, buzz’s mentality changed throughout as he found himself in new circumstances. A quick summary would be that Buzz initially thought that he could not overcome a challenge and the TV advert showed him that he could. Yet he soon realised that this was not reality. This change in beliefs is a representation of paradigm shifts and how new ideas and perspectives can change our own beliefs.
This brings in the idea of how paradigms shifts can occur, which is perspective. In the example shown on slide 14, the zoomed in image offered a view of a man that looked angry and scary. However, when the same image was zoomed out the same man appeared to be frightened and scared for his own life. This shows how in the real world one would always have different perspectives which then affect our paradigms. Being exposed to new perspectives can occur when we experience new things and meet new people and thus look at things with an alternative perspective.
In the following slides we discussed how other people from different backgrounds would feel about different things.
What I found most striking was the robbery paradigm which shows how as humans we automatically assume things and make generalisations based upon what we have seen before. This shows how we can perhaps never not be bias and that our previous experiences will always, whether subconscious or not, influence the way we form opinions and ideas.
Conceptual Understanding(s):
The perspectives we contain, which are determined from our cultural backgrounds, affect the personal knowledge we obtain.
Knowledge claim: Human behaviour can be influenced by an observer.
Real-life example: Hawthorne Studies – Hawthorne was considered a progressive place to work due to benefits workers received such as paid pension plans and sickness disability pay. An experiment was conducted there on the effects of illumination on worker efficiency. Output increased in general but was not affected by light as both workers working in light and in dim light had an increase in output. The study was ceased due to lack of results. However a similar idea was experimented on women making relays. These women were given rest breaks and different hours were tried. As a result, output increased by 30%. The observers studied workers producing more in less time.
TOK analysis: We must acknowledge that output increased wherever these tests were tried, and thus wherever workers were observed and studied. There is a knowledge issue presented here as the observers did not notice this with the Hawthorne studies. There was a connection found that simply did not exist. The conclusion that was ignored was that human behaviour (in this context, the output produced) changed drastically when these workers were observed. The observers influenced the workers behaviour and resulted in an increase in output. They were now in a more pressured environment where they could not slack in their work and thus were in general more efficient. To avoid this issue, we must consider the effects of the experimental process itself on the results and not just the factor(s) (independent variable) that is tested/changed in the experiment.
In both cases, four people die so the number of people in the car and on the street was not a factor that played a role in my decision, neither was the type of person, for example an athlete over just a normal woman. I chose the option on the right because, first of all, the pedestrians were walking when there a green light so they are abiding by the law and therefore were not in the wrong place. Secondly, for the passengers, it makes sense to me that the car would do what it could to avoid killing other humans by crashing into them.
Scenario 2
For this case, I chose the option on the right because firstly, the passengers were not abiding by the law, so they were in the wrong place. Secondly, the car was already going in that direction, it would not make sense to swerve towards a larger group of humans, who are in fact abiding by the law.
Scenario 3
These cases both had the same number of people, so I made my decision to choose the option on the left based upon which pedestrians were in the wrong place. I did not think about the types of people, such as their occupation or social class.
Scenario 4
For this scenario, I chose the option on the left because firstly, there was three people crossing rather than five, which was the other situation, and therefore less people would die.
Scenario 5
Although the woman was not abiding by the law, I would find it difficult to directly crash into her when I believe it would be an instinct to swerve away from any human contact. In both situations, one person dies, and although the passenger is not at fault, I think it would be better to crash into the barrier. Additionally, even though there is a regular woman and a large woman, this did not factor into my decision, and I believe that I would have made the same decision if the women were swapped positions. As a result, I chose the option on the left.
Scenario 6
I found this decision very difficult because I would find it challenging to crash into five animals. However, I believe that as a human, I would value human life over the lives of the animals. As a result, I chose the option on the left.
Scenario 7
For this situation, I chose the option on the right because as I mentioned before, I personally think it is instinct to swerve away from crashing into humans directly. The fact that the pedestrians had an older woman did not play a role in my decision, however after looking at my final results, it said that I had a preference towards the elderly, which is not something I agree on.
Scenario 8
My decision to choose the option on the right has the same explanation as the others. I did not realise until after that the passengers were solely men and the pedestrians were only women. My final results said that I had a preference towards women, which I guess makes sense since I am a girl myself. However, I am not sure that I agree with this because if the passengers were all women and the pedestrians were all men, I think I would have made the same decision.
Scenario 9
I chose the option on the left, solely based on the fact that the woman was not abiding by the law, and it would not make sense to me, if the car were to swerve and kill and man crossing the street at a green.
Scenario 10
Although I did mention before that I would value human life over animal life if I had to make the choice, I chose the option the right because again it would be instinct, if I saw something ahead of me on the street, to swerve into the barrier.
Scenario 11
For this scenario, my reasoning is the same as the previous one, but also because this option would save three people rather than one, and so I chose the option on the left. In this case, there is also a pregnant woman which I do think influenced my decision, as for me it would count as two lives. The fact that I also saved the criminal is not that much of a factor as although this person does not abide by certain laws, I do not believe that they would then deserve to die by being crashed into on the street.
Scenario 12
For this situation, I chose to swerve into the humans (option on the left), because firstly they are not abiding by the law. Secondly, the barrier is in the direct path of the car, and so I would swerve the car away from this threat.
Scenario 13
For this last scenario, I chose the option the left, because again I find that it would be more of an instinct to swerve away from the humans, despite the fact that they are not abiding by the law, by crossing the street on a red.
Faults of logic arise from the way we think, and therefore changing our thinking can help us to become more logical, whilst biases come from “cognitive machinery” which enable us to think a certain way, and allow us to process information.
Biases can become a sort of prejudice, but are referred to as a habit in our thinking. They lead us towards a certain perspective which help us to make useful conclusions. It is a product of mental processes which allow us to make sense of new information.
Dan Gilbert Ted Talk
Looking at the past as a way of reasoning our future decisions can impact us negatively. (Memory)
For example, a previous deal that was great can make a present good deal appear awful and therefore we miss out on good deals because we refuse to settle for anything less that the original deal that was in the past.
The Arts enables interpretation and emotion in order to establish understanding
A Sunday Afternoon on the Island of La Grande Jatte – Georges Seurat
Illustrates people relaxing in a park in the Seine River, a place where the middle and upper class of Paris go for a retreat.
The concept of Pointillism was created a result of this painting as the artist used dots to show light, shadow, and shapes, rather than using more traditional methods at that time.
Seurat observed that small dots would appear in “solid and luminous” forms when seen from a long distance.
Seurat had a theory to support this chosen method, in order to justify his work to critiques. He believed that “employing tiny juxtaposed dots of multi-colored paint really can allow the viewer’s eye to blend colours optically.”
The most astonishing aspect of this work is the implicit detail of the individuals in the painting and how these details help to express truths of society back in late 19th century Paris.
Seurat paid more attention to the shapes of the figures rather than show their personalities, and cared more about their sophistication and how they would all contribute to the piece as a whole.
Seurat was able to convey a surprising message that this “high-class getaway for the Parisian community,” appears to be more intimidating and terrifying, as the piece shows silence and order as everyone seems to be alone no matter if they are placed to another individual.
Something that is hard to notice at first is the fact that there is a shadow cast on every individual in the painting, whether it is from a tree, another object, or from a different person. This could have been a way to show that these people are lacking a sense of individuality and autonomy and that they all play different roles which contribute to the conventional nature of society. There is in fact strange things happening in this image, for example the lady on the right with a monkey on a leash. The painting shows individuals with no illustrated expression and who all seem to be facing in one clear direction, further implying the idea of a very orderly and rigid society. The figures are also described as “robotic,” perhaps to show the traditional french society at that time.
However, there is one girl standing in the centre of the canvas, who is the only person in the painting that is clearly lit up with no shadow cast over her, almost as if she were looking directly at the observer.
Seurat also drastically changes the proportions of different figures, not only to show their physical position in relation to the observer, but perhaps to identify a sense of hierarchy and the idea that in the middle/upper class society, there is the presence of a higher level of respectability and ‘worship’ towards those more wealthy and fortunate.
In conclusion, Seurat uses different artistic techniques in order to pay more attention to the composition and structure of the piece to enable an understanding of the typical french society in the late 1800’s.
V., Andrey. “A Sunday Afternoon on the Island of La Grande Jatte – A Study.” Widewalls, 28 Jan. 2018, www.widewalls.ch/a-sunday-afternoon-on-the-island-of-la-grande-jatte-georges-seurat/.
What is the role of intuition in mathematics? How about imagination?
I believe that although mathematical knowledge must be proven with rigorous proof, initial ideas are sparked by intuition and imagination. A mathematician might choose to use certain proofs in order to prove their conjecture based on their own intuition, and then use logical steps to see if it would work.
How important is logic(al reasoning) within Mathematical knowledge?
I think that logical reasoning is required within mathematical knowledge because in order for a conjecture to be believed and be ‘true’ it must be proved with rigour and clear steps to show how one came to that conclusion.
How connected is Maths to the real world?
Although maths might be more involved in topics such as the natural sciences, I believe that it can be used as a measure for other values. Despite that, maths might not always be effective. For example, numerical values have started becoming more popular to measure one’s attractiveness. Many might say that beauty is subjective, however we must admit that there are some people or animals that we would consider “beautiful,” or “cute,” and therefore certain values could be set to determine who is more attractive compared to someone else.
Of the methods trying to prove the conjecture “the internal angles of a triangle sum to 180º ”, explain why only one provides ‘rigorous proof’.
Out of the three method uses to prove this conjecture, I think that two of them provided proof, whilst the other showed ‘rigorous proof’. The two that showed proof were the ones that took the edges of a triangle and either cut or folded them to create a semi circle, which represents 180º. These methods did not show rigorous proof because it did not demonstrate an unbroken chain of steps that led to this conjecture. Furthermore, there was a lot of human error involved within these methods which questioned the reliability of the proof. The third method that provided rigorous proof was the one that used three axioms to prove this conjecture. However, these axioms were not proved themselves but are just universally agreed truths that we came to believe by imagining different situations. Additionally, by adding these axioms together, there was a continuous chain of reasoning that proved this conjecture to be true, and something that we could not question.
Explain the difference between ‘proof’ and ‘rigorous proof’, using the SHIP -> DOCK example.
In the SHIP -> DOCK example, all the intermediate words contained at least one vowel, which could not be proven using experimental evidence. This is because no matter how many words we found that demonstrated this, there would always be the possibility of more words that could also. This example demonstrates rigorous proof as there are steps to show that all intermediate words do contain at least one vowel. Firstly, we have to accept and acknowledge that all “valid” English words contain a vowel. Secondly, the intermediate words between SHIP to DOCK must at some point have two vowels as only one letter at a time can change. In order for the previous statement to be false, the vowel in position three has to become a consonant and the consonant in position two has to become a vowel in one step. However, this involves two letter changes which is impossible as only one letter can change at a time, thus all intermediate words must contain a vowel.
How does the term proof apply differently in maths and the natural sciences?
I think that proof in mathematics is much more rigour than in natural sciences, and this is because scientific knowledge is at first discovered and then tested, and referred to as “evidence.” Whilst, mathematical knowledge is something that can be seen and proven at any time and will always be correct, especially with the use of rigorous proofs where steps are clearly laid out. I believe that in natural sciences, we cannot always see things that we claim to be true, but we have different examples and evidence to back up scientific knowledge.
Where can maths be ‘found’ in nature?
Honeycombs – Bees can easily create the hexagonal shapes found in honeycomb, whilst it would require a lot of effort for humans to recreate the shapes. Honeycomb demonstrates a repeated pattern that covers a plane, similar to mosaics or tiled floors. Mathematicians have suggested that this shape is created in order to have to an efficient and large storage for honey with the use of minimal wax. For example, circles would have spaces between each shape and therefore have less efficient storage of honey. However, some believe that the symmetrical shape of honeycombs is accidental and that bees would never been able to perform such an intricate task.
Faces – Human faces have bilateral symmetry, that some believe is an aspect that determines physical attraction. Research has shown that mouths and noses are placed at “golden sections” of the space between the eyes and the chin. A spiral shape is formed by the comparable proportions from the side of the face. Statistics have shown that averages are close to the value of phi, and that it is believed that the closer the proportions are to phi, the more attractive one is perceived to be. Some say that it is possible that we as humans are designed to comply with the “golden ratio” as it promotes reproductive health.
Starfish – Starfish have bilateral symmetry, however they can show radial symmetry through the process of metamorphosis, where the organism that be divided into halves. Starfish have at least five limbs, which can form ‘pentraradial symmetry’. However, this symmetry has been inherited and slightly modified through evolution from their previous ancestors.
Briefly explain why Galileo may have said: “Nature’s grand book, which stands continually open to our gaze, is written in mathematics.”
When I first saw read this statement I was initially unsure about what it meant and in fact I still am, but from what I understand about it I do agree. First of all, Galileo states that what we know about Nature, will always be “continually open to our gaze,” meaning that perhaps there is always more that can be discovered about nature and we can never truly know everything. The most significant and potentially controversial part is Galileo’s belief that “Nature’s grand book, is written in mathematics.” I personally believe that mathematics is more discovered than invented as although humans have invented units and numbers, they are just values that represent life. We use these values to explicitly show why or how something might work, but in order to explain different concepts mathematics is vital and had to be initially discovered in order for humans to explain what we know. I believe that this statement is true as mathematics is constantly demonstrated through the natural sciences. However, this concept is perhaps difficult to show as with Science there is always the question of whether there are examples that will falsify this pattern. Although there is still so much that we don’t know, I think that in nature, maths in the reason why we explain why different processes happen and why organisms grow to show different characteristics.
After a few weeks of TOK, I have come to believe that we can never be truly certain of the things we claim to know. Across the different areas of knowledge there are perhaps different ways of knowing that might seem more reliable than others. For example, in Natural Sciences we tend to base our knowledge of off scientific studies and evidence that has been gathered for many years. Although, it is important to think about the extent to which we should let our knowledge be influenced by scientists. For example, after my brief research on the Piltdown Hoax, I have learnt that although something is believed by many to be true, it does not mean that it is. However, at the same time I think that we cannot be completely certain of the things that we know, because in order to do so we would perhaps have to see it ourselves, which can be impossible to do in most cases. An example would be Religion, where just because we cannot see something does not mean it isn’t true. Although in some areas, such as the Arts and Ethics, I believe that what we know about them is based more on interpretation and imagination, and that there are not “correct” answers but there are more socially accepted beliefs. Furthermore, just because knowledge from Natural Sciences tends to be based more evidence, and has been proven using the scientific method and processes of falsification and repetition, it does not mean that the quality of knowledge from it should be seen as of a higher quality than Ethics for example.
To what extent can you rely on these results to accurately predict your final IBDP grades?
I think that only using these results to determine our predicted grades would be slightly inaccurate as it is just one test on one day, which might not have gone as well as you hoped for. I also think that the design of the test might not be the best way to measure the knowledge of someone as it tests only certain skills under pressure.
What process do you think we should use to come up with your final predictions?
I believe a good amount of factors should be considered when coming up with our final predictions. These would include our end of year exams, our class assessments, and what level the teacher honestly thinks we are at.
What are the strengths and weaknesses of knowledge acquired in this way?
I particularly did not enjoy this test as much, especially because of the time limit. This is because I felt that I had the ability to complete the questions successfully, but due to the time limit I was more panicked and so ended up answering some questions without thinking through it properly.
To what extent is intelligence fixed?
I don’t think that intelligence is fixed because I believe that we can always expand our knowledge and learn more. However, there are several different types of intelligences and I believe that some might be harder to control than others.
Adaptation -> There is an interesting history of the concept of adaptation before Darwin’s research was brought about. In natural theology, adaption was “interpreted as the work of a deity and as evidence for the existence of God.” Several people had certain views of adaptation that “shadowed” others. Leibniz, a German mathematician, had believed that God had introduced “the best of all possible worlds.” However, Charles Darwin had falsified this and emphasised the “flaws and limitations” which existed in the world of different organisms.
Animal Echolocation -> The term of echolocation was first invented by a zoologist named Donald Griffin, who worked to demonstrate this concept with bats in 1938. Griffin had pointed out that an Italian scientist, Spallanzani, had performed a series of experiments that showed that “when bats fly at night, they rely on some sense besides vision.” Later on, a Swiss physician, Jurine, repeated the experiments done by Spallanzani, and concluded that the other sense that bats used at night was hearing. The production of scientific knowledge in this case was done by the process of repetition as other scientists build upon past research done by others in order to prove this concept.
“Adaptation.” Wikipedia, Wikimedia Foundation, 28 Aug. 2019, en.wikipedia.org/wiki/Adaptation#History.
“Animal Echolocation.” Wikipedia, Wikimedia Foundation, 7 July 2019, en.wikipedia.org/wiki/Animal_echolocation#Early_research.
