Was maths discovered or invented?

I heard the usual buzz arising from the mathematicians in our TOK group. "How can math be discovered? Did we find math equations on rocks?" Mathematics is the study of patters; shapes, quantity and assumptions. It is a system of explaining/understanding the world. (Definition taken from the Math group presentation - do not know source). Sometimes Math is referred to the perfect system of knowledge. I think this is because Math, unlike the Natural Science cannot be 'falsified' I believe math rests on logic and reason, by definition they are backed by facts.

Moreover, math is used in most of the areas of knowledge. It has various uses in the real world, and is applicable universally. For example, there is math in natural sciences; when calculating moles in chemistry. Or even in art, the shapes used, especially tessellations by M.C. Escher. Although can we classify tessellations as art? Or are tessellations geometry that happens to look good? How can we decide if something is art?

The most interesting aspect of math for me is the everyday use of 'theoretical math.' The prime example that jumps to mind is algorithms. Algorithms are slowly creeping into everything in life, it is used in RSA algorithm which is used to encrypt messages. Our internet security and encryption is all based on algorithms that deals with theoretical math - "pure math" and is very complicated.

So was math discovered or invented?

In my opinion it is more a combination of the two options. I feel like mathematics was strongly influenced by nature. For example, perhaps early humans saw 6 peas in a pod, or 5 petals. Then humans came up with symbols to represent the quantity, and that was how mathematics was discovered. Although it is difficult to answer this question. We have to look at what we mean when we say "discovered" is it to find (something or someone) unexpectedly or in the course of a search. or "invented" create or design (something that has not existed before); be the originator of.  The key part is "something that has not existed before" can we really say math never existed before? Math has always been a part of nature, from our genes - chromosomes, mitosis which involves duplication (doubling number of chromosomes) and yet was it really there?

Overall, I think the best answer is to go with both were needed for mathematics to exist. Without mathematicians pursuing more and inventing theories based on previous knowledge perhaps discovered, we would not have math today. 

 
However math cannot answer all questions.
http://www.slideshare.net/plangdale/introdutory-presentation-on-reason-for-tok 

Sources:
https://www.quora.com/Why-does-pure-mathematics-have-any-real-world-applications
 http://www.livescience.com/38936-mathematics.html

TOK Essay research - History and Coherence [How do historians use coherence to draw conclusions about the past?]

Coherence is how something fits into the knowledge the already know. For example, did the Chinese discover America before Columbus. The information that Columbus discovered The Americas, fit in more logically therefore historians are able to draw conclusions about the past.

Historians have to look at multiple perspectives/accounts about an event in the past. They have to judge which perspective is most coherent or fits into the information they have already gathered or know. For instance, if the historians know that the world cup was won by Brazil in 2002. Yet the claim was that Brazil did not actually reach the finals. It does not fit coherently with the information known and there is evidence that Brazil did win in 2002 as approximately half a billion people did watch that match or read reports about the World Cup finals.

Historians generally arrange the even in a timeline. When they try to fit in the new information and it does not logically fit into the timeline they cannot draw conclusions or vice versa. They find that the event fits in logically so the historians gain new knowledge therefore using coherence to draw conclusions.

Overall, coherence is used often by historians by trying to see if claims actually fit in logically into the historical timeline and then they can use this to draw conclusions about the past.



https://www.cartoonstock.com/directory/h/history_teacher.asp

How does emotion assist us in making ethical decisions or impede us? [Ethics of Publishing Pictures]

We were posed a question in class: If you were the editor of a newspaper would you choose to print disturbing photographs? Immediately my intuitive reaction was yes, to post the image. It is interesting how everyone is programmed and have their own immediate decision made with 0 thinking and weighing both sides. For example, some members of the class thought it is not worth disturbing the public.

Looking at both sides of the coin, I tried to come up with pros and cons. There is historical evidence – in reference to disturbing pictures actually having an impact. Napalm Girl is the most obvious example of the girl whose clothes were burned off due to the bomb. This lead to many Americans changing their stance on the Vietnam war. When looking at the disturbing picture of the drowned Syrian boy on the beach, I feel like there would be a similar effect, that governments would actually react to this. Firstly, the fact that it is a young boy had drowned, this would interest/attract more people to read about the situation in Syria. Moreover, it is sad that it happens to be a boy, but this will work in favor of stirring the public into pressuring their country into doing something for the cause.  Of course, virtue ethics should be considered when looking at why the photographer/editor is willing to publish the picture – is it to attract more readers? Or to actually spread the seriousness and create a strong impact – that will allow more people to talk about the problems.

However, it may have a negative impact in the sense that it may offend people rather than be received for its true purpose. The media is known for its manipulative images, so the readers may dismiss this picture as another scheme to get more people to buy/watch a certain news outlet.

This brought me to thinking of two knowledge questions: what is the relationship between emotional instinct as a WOK and ethical decision making?

How does emotion assist us in making ethical decisions or impede us?

In my opinion, and using consequential ethics, I think it is better to publish the pictures, as I strongly believe the benefits outweigh the negatives.