How may the math nomenclature (system) that you use affect your understanding of Maths?
Today we learned about three systems: Roman, Mayan and Binary. The use of different math systems can definitely affect our understanding of math, since they require different ways of thinking and process and have their own strengths. For example with the Roman system, its very easy to add and subtract things, but for Binary it is very challenging to even just write a number out in binary. Some things, such as fractions, algebra etc are going to be a lot harder to do in systems like the Mayan system which is why we use our current 10 base system now.
So I think depending on the complexity of the mathematics we want to do, a different system may be more effective. One example can be that all computers and phones use binary, even though it can be very confusing for humans to think about math in terms of binary, computers work with a “yes” “no” function so only have 2 numbers is very effective for them.
Explain what is a MATHEMATICAL axioM?
An axiom is a rule in mathematics that can not be proven correct. I think most of the time instead of being able to prove it correct, axioms can only be “not proven incorrect”. A lot of the time, we also just “feel” these to be correct, but we can’t exactly show why.
Here are a couple examples:
I think that a clear example is that through any two points there is exactly one line, which I can’t prove to be true, but I can’t find any issues with the statement. It’s inductive reasoning in a way
A mathematical proof comes from deductive reasoning, and can be proven to be true. There are no exceptions to a mathematical proof. It is a mathematical statement that is viewed to be correct and true. An example of this is that on any map or set of shapes, only four colours are needed to colour it so that no same colours are touching.
I’m back again! So here is my diagram- it is very beautiful.
So the three WOK’s my groups selected are:
- sEnsE pErcEption
So we felt that when you first see the image you use sense perception as you have to try and decipher what is going on in the painting. Then you use your reasoning to better help you figure out what you’re seeing. This is especially important because the art work we were looking at is surreal therefore it IS DIFFICULT TO KNOW EXACTLY WHAT YOU ARE SEEING. Afterwards, we put imagination because often you need to fill in some gaps as some parts of the painting are open to interpretation and aren’t representing clear objects. Then from imagination you can either go back to reasoning or sense perception to further help clarify and gain a better understanding of what YOU ARE SEEING.
- Write about two separate networks that use the ways of knowing. The first network uses the ways of knowing to produce knowledge in the natural sciences while the second network uses the ways of knowing to acquire knowledge in the natural sciences. Each network should have a minimum of two ways of knowing in it.
Production of knowledge:
- Sense Perception
Sense perception comes into play in terms of qualitative observations, which can really help in understanding when doing experiments. Imagination is needed to come up with now ideas/ experiments to try out, since we’re trying to produce new knowledge. Finally, reason is used because we need to come up for an explanation for the data/results that we find, as well as come up with a hypothesis before we do our experiment.
Acquisition of Knowledge:
- Sense Perception
Language is important in the acquisition of knowledge because it is the main way we communicate ideas and concepts to one another. Sense perception can help in understanding these concepts, as visually seeing, hearing, touching, smelling etc things can really aid in a better grasp of the knowledge. Finally, faith is required because we have to trust the people that came up with this knowledge. Since we aren’t the ones producing it, we’re just accepting facts/ theories that others have created.
What were five key events in the Historical Development of the Natural Science?
Isaac Newton helped make the Scientific Method more well known, and now it is very commonly used in nearly all studies. So I think that the spread of this method has really developed the way we discover things now.
Invention of microscopes. Being able to see objects smaller than the human eye can see has allowed us to know more about an entirely new “world”.
Industrial revolution. This one isn’t a development in “natural science”, but I think it has significance because the industrial revolution allowed us to develop our civilisation further, and this led us to have time other than just feeding ourselves and keeping ourselves alive. Therefore, we wouldn’t be as advanced with where we are now if not for the industrial revolution.
Theoretical Sciences/ thinking. I think that being able to come up with theories that we may not be able to see/ easily prove has significantly helped develop our understanding of natural sciences.
The concept of Hypothesis. Being able to come up with hypothesis has allowed us to think more critically about our experiments that we are conducting.
Is it inevitable that the Historical Development of the N.S.’s has lead us to our current way of doing N.S.? Why or why not?
Yes. Absolutely?? As we learn more things within the Natural Sciences, we also learn more about how to learn things within the Natural Sciences. Having a general understanding of the basics in natural science (which can be considered historical development) can really allow us to understand that scope within natural science to conduct more accurate experiments. If we didn’t do any experiments/ have discoveries in the past, we wouldn’t know how to conduct experiments/ have any concept of them at all.
In what ways does this quote help us to understand the methodology in Natural Science?
I think that this quote helps us understand Natural Science’s methodology in the way that our methodology re-inforces this quote. In the scientific method, we are open to new ideas and theories, but our method also helps to make sure that the data we find is reliable enough to be considered knowledge. In one way, we want to try new things, but we are also skeptical of them. This contradiction really helps to find the truth or the knowledge within that fits into both categories: It’s a new idea/concept, but it also makes sense, and is “indestructible” where we can’t find something wrong with it.
What is Karl Popper’s theory of Falsification?
The theory suggests that we can’t ever prove things right, so instead scientists should try everything to refute their hypothesis. So we can’t prove it wrong, it must be right! right?
How is it different from the way most people view Natural Science?
Most people try to prove something right, and possibly find an explanation or reason for why something is correct, instead of finding reasons for it to be wrong. Even if we can’t find something wrong with our claim, that doesn’t instantly make it correct.
- What is intuition?
To me, Intuition is kind of like unconscious processing. It’s when we look at a problem or a situation and make an immediate judgement without thinking through our thoughts. I think a good question that supports my thinking was the “Linda” question that we watched in the video. I wouldn’t consider picking the wrong answer as a “gut” feeling, but more as unconscious processing because if we actually took time to think about the question, we would know our answer was wrong.
- What is System 1 and System 2 thinking?
System 1 thinking automatic, fast and effortless. It doesn’t require a lot of time to process. However, system 2 thinking is controlled, effortful and takes a lot longer. An example of system 1 thinking could be just looking at people’s faces and making an immediate judgement, while an example of system 2 thinking could be solving a math problem.
- How could you incorporate System 2 thinking into TOK?
Sometimes, when we look at real life situations or knowledge questions, we have an immediate response or answer on whether we agree with the question/ already have made a stance with the question. However, thinking about the question, and discussing different viewpoints can help us realise that a different opinion or answer may be something that we agree with more if we took the time to think about it.
- In your own words, explain the difference between deductive and inductive logic.
Inductive logic is based off general rules that are created from observing something a limited number of times.
Deductive logic is taking a general rule and applying it to a statement to coming to a conclusion. In more formal language this means moving from a two or more premises to a conclusion .
- What are the problems with each of these kinds of logic and what we can do to overcome some of these problems?
Some of the problems with Inductive logic is that there is no way to prove it true. Typically, Inductive logic comes from our own observations, but this may be limited. What we observe may always be the same, but it might be different somewhere else which can falsify our logic. Inductive logic also assumes that the world is a predictable place, but things can change at any moment and therefore our inductive logic may not be true.
And if you have time ….
Rabindranath Tagore said that ‘A mind all logic is like a knife all blade – it cuts the hand that uses it’ … what do you think he meant by this?
Maybe he’s trying to say thinking too logically isn’t always the best. Sometimes we need to use emotion or reason in making decisions, and and this may not always be easy to decide logically.
What are the characteristics that you feel best describe language? Why?
I think communication is the most important characteristic of language. The main purpose of languages are to help communicate with others, so being able to express ideas or communicate thoughts is very important. I also think another important characteristic that describes language well is the ability for others to learn it. As humans, we have created language on our own but we aren’t born completely fluent in any language. As we grow up we develop the ability to express ourselves more articulately, and with that our ability to speak a certain language will grow. Finally, I think another important characteristic of language is that some words within it have abstract concepts. Some of the words in any language are hard to define and don’t have a definite meaning. Some words have different meaning to different people.
What might be some of the weaknesses of language?
As I mentioned, one possible weakness is the fact that language includes abstract words that can have different meanings to different people. If the whole purpose of language is for communication, then the same word having a different meaning would be somewhat ineffective. Another weakness is that not everyone is born fluent in a language, and there are so many currently in our world that people have difficulty communicating with one another if they don’t speak the same language. We rely so heavily on language for communication that if someone can’t speak the same language as us, it’s nearly impossible to express meaning or have a conversation with them.
Do you think that language changes the way you think and therefore perceive the world? Why and what are the implications of this idea?
I think that language definitely changes the way you think and perceive the world. From looking at the examples mentioned in class, we learned that language helps us to think. If we don’t have a word for something, it’s because it’s not necessary or we don’t think about it – it’s not important to us. Having a word establishes that this concept/object is important and therefore we should know what it is.
Different communities lack certain words because they just don’t need it.
Do you agree more strongly with perceptual realism or perceptual relativism?
Honestly, I agree with both, and I think that both are valid and important perspectives to consider. Both prove that we do not see the world objectively. In fact, I think that perceptual realism can be considered part of perceptual relativism, as it can serve as an explanation for why we will never be able to see the world objectively. The explanation being that our senses can mislead us, and since we really only know the world through our senses, we will always see the world through a “filter” that is not always reliable.
That being said, I think I would have to agree with perceptual realism more. I think that in general, our senses are reliable and helpful to us, even when they “mislead” us. Through watching the video and discussing it in class, there were many examples brought up of our senses “misleading” us. One such example was two brown coloured squares on a cube, where one side was under a shadow.
In the left image, our senses tell us that the shadowed square is a lighter shade than the unshadowed square, but of course, they are actually the same shade. Personally, I don’t think of this as being “mislead” by my brain, as actually my brain has taken into consideration that the shadowed square is under a shadow, and this made it adjust the shade. I think this is actually quite helpful because in real life, shadowed colours appear darker than they would under a bright light, so my brain doing this for me is actually quite helpful.