## InVentiOns iN maThematiCal nomenclature

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.

## bLoG queSTION

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.

## mY dIaGrAM FoR aQuisITioN oF kNowlEdgE iN aRt

Hello everyone,

I’m back again! So here is my diagram- it is very beautiful.

So the three WOK’s my groups selected are:

• sEnsE pErcEption
• rEason
• Imagination

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.

thanks<3

## aRt mEtHodolOgY

What is the methodology behind the lightsaber as a piece of art?

George Lucas had many intentions for the lightsaber. He wanted it to represent a weapon of nobility and more as a defence weapon instead of an attack weapon. So in order to implement this he decided to make the light savers heavy as the light power was very strong. George Lucas used his imagination and creativity to create the Jedi’s and he wanted the light sabers to support this concept of the Jedi’s.

## Definition of Art

My initial definition of the arts are a set of creative activities that humans use, often to express emotion. The arts can also be reflective. The arts can include photography, visual arts, performances, music, literature etc…

My new definition of art is still a set of creative activities that humans can use to express themselves and possible communicate to others. However, skill, soul and intention can be three major factors in helping to decide whether art is good or bad. Some art may not require a lot of skill to create, but can still be considered very good art if someone put a lot of soul or intention into the artwork. I think intention is very important in defining good art.

## WOK Language and Concepts

• 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
• Imagination
• Reason

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
• Faith

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.

## TOK Post: History of Natural Sciences

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.

## Natural Science Methodology – TOK

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.

## TOK Natural Science Post

• Create your own definition of the term Natural Science based on the TOK questions and dictionary definitions.

Natural Science is the study of science within the real (physical) world that can sometimes be observed in the real world. Culture plays a minimal role in this, and knowledge possessed can be derived from observations or abstract/ theoretical sciences. Imagination is often necessary, for example, many things studied may be too small to see by the human eye, therefore we must use our imagination, along with reason, to find knowledge. Natural science often produces generalised statements which can help with understanding.