- How do proofs in maths work? What had to happen before mathematicians were able to say that they ‘knew’ Fermat’s Last Theorem was actually correct?
- A reason that explains why numbers fit the equation without having to check every single number. Widely approved by mathematicians and is right in all situations. The initial “proofs” are called conjecture, which becomes a plausibility argument and lastly, rigorous proof.
2. In what ways is this proof in maths different from / similar to the method used to prove things in the natural sciences?
- The two methods are quite different because there is no limit to the values that can be used and it’s impossible to test numbers due to having infinite numbers. However it similar in a way where there is accidental discoveries that come from approaches of proof, as well as multiple trials required to try and prove the claim. Unlike natural science approaches, often ideas and approaches come at random times by subconsciously thinking about them. Mathematicians work with numbers, and very rarely will they need external/physical materials to run their trials.
3. Keep a separate list of quotations / moments from the film that support / undermine stereotypes about maths as a subject
- Proof ofr math requires many other mathematician’s perspective, calculations and aid. They approach a proof with another concept from another mathematician and different approaches can produce the same answer or proof. So one idea that is seemingly unrelated can aid with the understanding of another concept. It is said in the documentary that Fermat and Andrew’s proof are different because the way of approach is different due to the century they live in, perhaps signifying that proofs are influenced by existing theories, concepts and knowledge claims.
- Math as a subject is in its own subject area due to the fact that it can be done on it’s own without external information from other subject areas. It is possible for mathematicians to work solely with numbers. However, it can be applied to other subjects such as physics to support that AOK’s knowledge claims.
Does the problem of Induction mean that all of our scientific knowledge is fundamentally unreliable?
- I believe that all our scientific knowledge holds some truth to it, but it is under developed. Sometimes I wonder how much we’d learn in scientific knowledge if our planet had different laws of gravity, living organisms, elements on the periodic table. Since all our knowledge is based around things we’ve observed, there are some things that are speculation especially in areas such as dark matter. However until proven otherwise, it is generally accepted that it exists because it might lead us to a discovery that can either change or confirm our beliefs.
In other words sum up Khun’s theory of paradigm shifts and discuss some of the implication that this has for scientific knowledge.
Should scientist be held morally responsible for the application of their discoveries?
- Yes if they don’t oppose the idea even if it brings mass destruction or corruption and harm for other people. Many scientists such as Marie Curie researched radioactivity to build X-rays, as opposed to the discovery of chain reactions by E. Fermi and L. Szilard which lead to the nuclear bomb. Fermi and Szilard might have explored the destructive capabilities, but probably didn’t want to drop the bomb on anyone.
- I think it’s similar to blaming either the gun or the person in the Las Vegas shooting recently. Many article’s i’ve read talked about how the rapid fire gun was banned but is still available in six states. However I have yet to see any concern over the mental state of the criminal. Perhaps he had a mental disorder that could have been tended before it occurred. Yet most people blame the lack of gun control in the country.
Is there any area of scientific knowledge the pursuit of which is morally unacceptable?
- I think there is a moral code of conduct on areas such as human and animal experimentation, especially those that harm them. There are probably laws against killing a bird to look at the anatomy as opposed to letting it die naturally before examining it. Perhaps anything is acceptable as long as it doesn’t disrupt nature and harm other living beings.
Is there any area of scientific knowledge the pursuit of which is morally required?
- Both physical and mental health sciences, but physical more than mental are probably put to priority. Mainly due to never ending sickness and pursuit for a long lifespan, it would be “morally better” to study to cure. I think that is why nurses and doctors are put in such high regard, because their discoveries in medicine and human biology can end up saving lives.
How are models helpful or harmful in the acquisition of knowledge?
- Models are helpful because they allow people to look at a system or sequence holistically for those who don’t have the knowledge to connect certain concepts together. They are visual representations that can help students to visualise space relativity and relationships. They allow people to see the flow of feedback between each storage and how everything interacts. However they also may oversimplify and leave out many factors and implications. Additionally in order to be applied to real life, there must be case studies in which it was build from. The model can only be as good as the data and information gathered. It can also misrepresent reality, such as inconsistent scales of space and planet sizes in the solar system model. Or the Bohr Atom model where electrons are aligned on valence shells, but in reality they should be scattered randomly and the space in between neutrons to the electron wall is much larger than it is in all the models ever designed.
“The vagueness and ambiguity of language always limits the production of knowledge”. Explore this claim with respect to two AOKs.
If one was to describe a sculpture of a person with words, they would use adjectives that are open to a person’s interpretation. For example, the Mona Lisa is known as one of the greatest portraits of the Renaissance. It has been described as the pinnacle of art and the most famous piece by Leonardo Da Vinci. However art historians claim it only became popular because art critics proclaimed it to be, in a time where photography was not yet invented. Nowadays, as travel has become easier, I’ve had friends who’ve seen the actual painting and described it as underwhelming as the painting was small. If someone were to recreate a picture that’s only described in words, it’s practically impossible because the language isn’t specific enough to do so.
However, this aspect is incredibly useful in literature, where writers create a world and context that may not exist. Because the reader is only taking in limited knowledge at once, there is a lot of subtext that one can come up with. In film this is why semiotics are applicable, as the scenography is actually choosing what to exclude, and include in the scene. The connection of language and symbolic visual imagery is vague, yet it creates motifs that can maintain a theme throughout a work.
In ethics, language plays a huge role in influencing morals. Society has always taught us what is “right” or “wrong” yet there is so much debate about what fits within the categories. Even the words “ethics” and “morals” are technically undefined as everyone has different values and priorities. Someone would think eating meat was perfectly fine, yet it is often associated with “animal cruelty” and “higher risk of getting cancer.” Or, people can use language to create propaganda and make something sound better than the other. In the instance of natural disasters, Vox made a video opposing the use of war like language in the news. Their point was that describing disasters like a war puts the blame on “mother nature” rather than the government who failed to take responsibility for global warming, proper warnings and precautions. For example, Macau as opposed to Hong Kong, where people died as they were not warned of the typhoon last month.
Everyone is entitled to his own beliefs, but not to his own facts. Do you agree?
I agree with this statement because I classify beliefs as something that is personal but facts as something that is believed and supported as true to everyone. They can change depending on new knowledge or supporting evidence that is found. For example, the belief that the sun was in the centre was rejected by the church, yet scientists believes it is true because their evidence suggested so. People used to believe that the world was flat until someone proved them wrong, and now everyone knows that the world is round. Today we have many reasons to believe so, such as the satellites that orbit our planet and the connecting seas at the edge of our maps. Therefore the affected area for belief and fact are not separate, but they aren’t the same because fact is believed within a society.
It is much harder to sway someone through belief in modern society, mainly because there is such a wide variety. For example, not everyone is religious, there are some who are atheist. Yet religion continues to prosper not as the basis of living and creation for all humans, but as a culture and lifestyle for each and their own. What they believe in may be taken from the bible, the Quran or personal values in life, but no one has to enforce their beliefs on others to become fact.
One of the interesting valid but untrue claims from the Reasoning video was the argument that the world was black and white. The premises and statements were that comics were printed black and white because the artists only saw the world in black and white, therefore the world was black and white back in the days.
One of the statements were true but the argument was false. However when if the argument is true but the statements are false, I become baffled as to how we can argue against the statement’s validity. The example was that all teachers are human, said person is a teacher and therefore is a human. The conclusion is true but what if the person was not a teacher? What if we had teachers that were monkeys? What is the definition of teacher? Yet I find it mind boggling because I can agree with the final conclusion but disagree with the statements.
Another undefined area of knowing but still a good example would be the feelings many Taiwanese have against the Japanese after their colonisation, which are feelings of distrust and unforgivingness for acts of oppression and violence. Due to past experiences, they draw from memory that associating with a Japanese person may lead to violence and oppression which is a false premise, yet the colonisation was a true premise. In the end the argument is valid but it is not true as not all Japanese people believed in oppression of the Taiwanese.
Therefore I think this is why many essays about the same thesis exist, because deductive reasoning is used in essay writing, it is hard to determine whether the statements made are true or false but the argument may be valid. Debates about politics and discrimination are always relevant to reason as well because everyone has an experience that becomes one of the premises for inductive reasoning.
I really enjoyed the IB retreat we did on August 18-19, especially the free time we had. It gave us a chance to really mingle with the rest of the grade especially my friends who are doubling science as I rarely see them. I also found the hotel activities really interesting and nothing was boring. There was a good variety of things to do, such as Yoga, drama games, discussions, listening to poetry etc. I particularly enjoyed the movie because it was connected to TOK and gave me a better understanding as well of what the course was about. The random roommates was a nice addition because they weren’t dislikable or extremely random.
Particularly with friends in different classes, we were able to have fun as a large group outside and a small group in the rooms. We played cards in the lobby which was really enjoyable and a good way too kill time without utilising technology. It was a good break time from the upcoming stress of school, but also a good way to reinforce we understand what the IB is all about.
I found the Crossroad simulation to be very difficult. Mostly because I like chairs and we sat down for a long time, the other being squished in a small space with a lot of people. Overall the setting and surrounding environment was uncomfortable for me, but I really enjoyed the realism it provided to us. It was incredibly different to our life as privileged students. Only when I looked back did I realise that time was not a luxury to people in poverty, and that’s probably why it is up to developed communities like us who have the time to make a difference.
Another challenge I found was wrapping my head around the idea of Gustalt because I always thought of it as “thinking holistically and with an open mind”. Over the entire IB retreat, I had that idea but it was never given to me. The definition of Gustalt was never completely enforced by definition which made the main point of the retreat very confusing to me. Though, I guess that didn’t have to be the main takeaway from the retreat as I have mentioned above, I have learnt many.