# Is mathematics independant of culture?

Mathematics is one of the eight areas of knowledge and therefore, it is present in all countries of the world. Even people who have never attended school and are illiterate use maths in their daily lifes; for example when they have to count cows. However, even though everyone uses it, is it really independant of culture or is maths interpreted in different ways depending on the country and culture you belong to?

For example religious knowledge systems which is another area of knowledge is clearly linked to culture but mathematics is completely different; it has nothing to do culture.

An english person, a spanish person, a chinese person and an arab; every type of person would come to the same result of an equation if done correct, without having anything to do with where they are from. It is true that spanish and english people don´t use the same method of doing divisions, but the result is the same in both cultures.

One plus one equals two in all parts of the world. In Arabia Saudi the number one is written like this: وَاحِد and in Spain like this: 1; but in both countries it represents a unit of something.

In conclusion, mathematics is an area of knowledge which is independant of culture bearing in mind some aspects as methods or symbols might differ; however, the meaning and result doesn´t change.

Bibliography:

1O, G. (2017). GRAMATICA 25 – NUMEROS DEL 1 AL 1O. [online] Lenguarabe.blogspot.com.es. Available at: http://lenguarabe.blogspot.com.es/2008/12/gramatica-25-numeros-del-1-al-1o.html [Accessed 13 May 2017].

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# How does reason work differently in the arts and maths?

As we saw in class, maths is a reasonable AOK. It’s completely created in reliance of this WOK. Were we to think about it, there’s no possible way to solve mathematical problems without the use of deductive logic, not even when using the known method of “induction”. On the other hand, the intention of the artist make the arts be reasonable. There is a reason why artists create art no matter if we regard paintings, books or even films.

Reason is used in both AOK. However, it works completely differently in each. Maths uses deductive knowledge to reach any conclusion. As we saw in class, even the process known as “induction” uses deductive knowledge to reach the mathematical correct solution. Nonetheless, the arts also uses reason. There are always logical or illogical reasons why the artist creates what he/she creates. E.g. I feel sad. Sad is expressed with the blue color. My painting (which expresses my feelings) will be blue.

Therefore, deductive reasoning is used in the same way in this almost opposite AOK. However, it’s used more often in maths than in the arts, where imagination rules over the other WOKs.

# To what extent is a film useful as an historical source?

In our previous history class we saw a film called Taegukgi to understand better and in more detail the Korean war. Our teacher asked us a TOK question which I found quite interesting: To what extent is a film useful as an historical source?

A film is an audiovisual representation of a story or fact. This visual contextualization is the reason why films are extremely useful when investigating a historical event. It’s mostly because of its easy comprehension.

In the film we were watching, appreciating how the war and the soldiers’ situation was in every moment helped us see the constant violence and horrible and difficult surviving  in every moment. Our imagination cannot reach that point of precision a lot of times , mostly when we’re talking about unaware contexts like, for example, Korean culture.

On the other hand, scriptwriters aren’t normally expert historians. This is why details shown in films always contain imaginary facts. This is why we say films are “based in real life” and they are not “real facts”.

In conclusion, films are helpful historical sources when trying to contextualize an event. However, they are not completely reliable and that’s why they cannot be considered as good sources.

# How does inductive reasoning work in maths?

Mathematical knowledge is quite peculiar. This AOK is the only one that explores its own information, that is to say it doesn’t use any other AOK to carry out contributions which expand its information.

Both deductive and inductive knowledge are used to expand knowledge. Although deductive knowledge is the mostly used, inductive knowledge is also useful.

It is a method that goes from particular to general, so it is always used when talking about series, for example. In this mathematical area we start with few numbers and suppose a general formula is followed by all the terms in the series. We’re not completely sure about it, since numbers don’t need to follow this rule and maybe in infinity numbers follow a different pattern or don’t follow it at all. However, it is the way from which mathematicians solve this problems since there are no other previous facts from which we can deduce the series.

This way, we prove by deduction an inductive fact.

In conclusion, in an AOK based in reasoning, inductive knowledge is used when there’s no possibility to use deductive knowledge because of the lack of specific information. However, there’s a deductive methodology.

# How is faith used in Mathematics?

Faith is one of the least accepted WoK, since it is considered by many to not bring any new knowledge to several AoK, and only really be useful in Areas such as Religious Knowledge systems. Although this is not true, since Faith can actually be used in many other AoK (such as Natural Science when doing experiments), the statement that it does not apply to all AoK may not be completely false.

Faith finds its complete opposite in Mathematics. Mathematics is based entirely on proof: the way in which we understand and explore it is through theorems, and in order to be approved theorems need proof. For example, the Pythagoras Theorem states that in a right triangle (a triangle in which to of the sides make a right angle), the square of the side opposite the right angle (hypotenuse) equals the square of the other two sides: c2 = a2 + b2. It can be proven with this simple image:

(Here, c represents the hypotenuse, and a and b represent the other two sides of each triangle.)

Since Faith implies believing without proof, it seems that there is no way in which Mathematics and Faith could ever be reconciled. Though it could be argued that theorems are based on axioms, which do not require proof, this is not a very solid argument, since axioms are, by definition, “self-evidently true, and therefore do not require proof”. However, it may be fair to say that, in order to create a theorem, one must put together different axioms and have faith that they will work out the way they are supposed to.

To sum up, though Faith may have some minor uses in Mathematics, it is not used much, if at all, when gaining knowledge in this particular AoK.

Bibliography:

https://www.mathsisfun.com/pythagoras.html

# Can intuition be used as a way of knowing in maths?

Intuition is one of the eight ways of knowing and maths is one of the areas of knowledge. Therefore, bearing this in mind, we can use intuition to gain knowledge in maths. But, is intuition always a liable way of knowing? Let’s have a look at the Monty Hall paradox to answer this question:

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

The contestant should switch to the other door in order to have more possibilities of winning. Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance.

The given probabilities depend on specific assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 that was not available at the beginning of the game, when the door 1 was chosen by the player: the host’s deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally. Another insight is that switching doors is a different action than choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities.

The problem is a paradox of the veridical type, because the correct result (you should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true¹.

In conclusion, intuition is not a liable way of knowing regarding the area of maths as reason can prove it wrong in some cases as the one we have studied. Therefore, we should not use intuition as a way of knowing in maths.

Bibliography:

¹En.wikipedia.org. (2017). Monty Hall problem. [online] Available at: https://en.wikipedia.org/wiki/Monty_Hall_problem [Accessed 25 Apr. 2017].

# To what extent is the Golden ratio used in the Arts?

The golden ratio is a number represented by the Greek letter “phi” that is formed when a line is divided into two parts, so that the smaller part divided by the longer part is equal to the entire length of the line divided by the longer part. Its represented as such:

a/b = (a+b)/a = 1.6180339887498948420 …

the Fibonacci sequence, discovered by Leonardo of Pisa, is directly linked to the Golden ratio. This is because when you calculate the ratio of two successive Fibonacci numbers the result gets closer to the Golden ratio. As the numbers grow, the result gets closer to 1.618.

This number can be applied into the composition of a rectangle, creating a shape called the Golden rectangle. It has been proven that humans have a psychological reaction towards this geometric form as it transmits visual satisfaction, for this reason it has been used in several works of art throughout the centuries.

Artists like Leonardo da Vinci have used the golden ratio to correctly place the compositions of the human figure within a portrait, in order to study the relationship between the anatomy and the mathematical geometry of the human body.

“Many books claim that if a rectangle is drawn around the face of the Louvre ‘Mona Lisa’, the ratio of the height to width of that rectangle is equal to the ‘Golden Ratio’.” http://monalisa.org/2012/09/12/leonardo-and-mathematics-in-his-paintings/

This shows us a direct link between the arts and mathematics. That geometry is not only applied to virtual shapes but also esthetic and symbolic arts, aside from paintings we can witness it also in architecture and sculpture.

http://www.livescience.com/37704-phi-golden-ratio.html

https://en.wikipedia.org/wiki/Golden_ratio

# Are humans born with Knowledge?

As the definition says, Knowledge can be defined as facts, information, and skills acquired through experience or education.

Within reading the definition we can understand that knowledge is information that we gain over time. Through the years, many Philosophers have tough about this and many of them agree in the same thing, according to them when humans are born, they are born as a ” Black slate” and after it they gain knowledge and ideas through new experiences .

Back in the past they didn’t have the technology to prove this fact, but with the new technologies many neurologist are currently gaining neuroscientific evidence that could validate the belief that we are born with innate knowledge of our world.

In my opinion, even though neurologist are currently gaining neuroscientific evidence, i still think that we are born without knowledge and we learn it through out information and experiences.

Source:

https://en.oxforddictionaries.com/definition/knowledge

http://sites.bu.edu/ombs/2012/02/22/are-we-born-with-knowledge/

https://www.google.es/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=0ahUKEwjsyuf3wtPTAhWCahoKHY8CAJgQjRwIBw&url=http%3A%2F%2Fwww.cadabamshospitals.com%2Fspecialties%2Fneurology.html&psig=AFQjCNFxTueUATQmc-OlLcjYBeTQw8g6uQ&ust=1493893991937578

# To what extent can a cultural and social context have an influence on the comprehension of a text?

As students we tend to work and study with a whole range of different texts. This might vary depending on the subject, topic and even language in which it is written. During the Spanish A classes, we normally have to read certain books, analyse them and with the information that we take out, we either have to write a creative essay or a piece of writing like an article.

In order to analyse this text, the reader must take into account the cultural and social content. Meaning where the text we written, when for example the year and the history periods, and the social issues that up come the author for example if he was Spanish and wrote about the civil war 10 years ago or 70 year ago because the meaning of the text will be different and the analysis will give different information.

A clear example can be seen in text and books from Shakespeare. Othello, Hamlet or Romeo and Juliet were written in the XV century by and English author who had certain social an political ideas, for example being against the royalty.

If we change the context of this to another country saying Japan, that is was written 20 years ago and instead of a men by a woman, the text as much as it will be a good one, would not express the same.

Language helps to understand this but we can see that when talking about knowledge, language is just a method to share information through patterns in a simple way but it does include the only way to share knowledge.

Indeed, social and cultural references take an important part in the understanding books because in more occasions that we think, the author bases his ideas into was is happening in the current days or basing his statements into pasts history situations like a war, a victory or a royalty succession.