Introduction to Mathematics

On the last lesson we had an introduction to the though subject which is mathematics. We discovered patterns, learned why people started using mathematics in first place and how mathematics is just like music. 

I think you can call mathematic "art" as you have to discover hidden meanings behind few weird symbols and uncommon formulas that are nearly impossible to understand for an average mortal human being just like me. 

Except for reading the text about the history of mathematics we spent the most of our time discussing whether mathematics can be called beautiful. There was this question "Can we say that mathematics is beautiful if we do not understand it?". Well, to me the answer is yes. I will start from simple examples while explaining my point of view.

For me most of the things occurring in this word are hard to understand. I can tell you that the movie is beautiful but I do not understand how TV works. How can I fit small people inside the plastic box? I know it sound ridiculous and I probably show my lack of intelligence right now, but have you ever thought about it? The answer is most likely: no. But hey, TV is different than mathematics because we can experience it with our senses and the content we are provided with is in some point understandable. Well, mathematics is also understandable. It is like a painting. You see something, you know some parts but individual parts of the equation does not make any sense.

When I showed this to my sister she made big eyes and told me she does not understand anything. When I asked her to tell me if she knows any of the symbols she easily recognized the sign of equality, subtraction and that we have to divide 1 by something. The same goes for paintings. If you look at Vincent van Gogh’s portrait of madame Roulin rocking on the chair you can tell “This is a beautiful painting, I can see a friendly looking lady sitting on the chair and the colors are nice”. But did you know that the painting is also called “Lullaby” an it was started before painter’s mental breakdown and finished after leaving the asylum?

So why the equation above can be ugly to some people? For the same reason the picture above can be ugly. Ugliness and beauty are hard to define because they depend on your personal beliefs. I don’t understand very constructed mathematical theorems and equations but they greatness amazes me and I find them beautiful.

Which does not mean I enjoy math. I don’t really understand it even when I how to do it. I still think that some parts are unnecessary and we should learn more useful skills than calculating delta but what can you do.

The end of history

09/05/2016

Today was the end of history. Well, not literally "the end" because the history will not end as long as...I don't really know what was I supposed to write. The point was that today was the last lesson of TOK in history. 

"Life is like a game of cards. The hand you are dealt is determinism; the way you play it is free will"

That is one of the quotes we were to discuss on today's lesson. I liked this one the most because it was (in my opinion) the most truthful of them all. I mean, people are born it different societies and families with different traditions and issues but it is up to us how we "play" our lives. No one has the same cards (opportunities) but when you are brought up it a similar environment chances are cards you have to play are the same. With that being said, when you are complaining that your classmate has better grades or is having better time or is "cooler" than you have to stop dwelling in self pity because we were all born naked and ugly and probably crying and screaming. We all went to school and it was only up to us what approach we will take from the beginning and the same goes for the other two; we are constantly working on our character and unless you are too lazy to do anything, you can be everything you want to be. Obviously you won't be as fit/social/hard working as somebody else but that is what is amazing in our life. We have the power to be whoever we want to be and even though we are starting with the almost identical set of cards as somebody else  you can grow up to be a totally different person. I think it is pretty amazing. 

Enough of my thoughts, let's get into some important definitions. After reading sad, alternative version of "Billy Elliot" where instead of following his dreams boy and up as a beer loving 35 year old corpses "squelched into the shape of a pancake". Not very optimistic or even not optimistic at all but we tried to determine what were the causes of Billy's tragic end and as we spoke we discussed two terms.

Accidentalism-the idea that everything is a result of random events we are not able to control. 

For example Billy wasn't accepted to ballet school because one of the judges was earlier that day swimming in the river where a mosquito bit her and while Billy was presenting himself instead of watching she decided to scratch her arm and she missed the important part.

Determinism-everything is a result of something that occurred before.

Billy died because the driver was lacking sleep because his baby was crying all night, because it was hungry, because it's parents could buy him food because shopkeeper decided to finnish his work earlier yesterday. Therefore the shop owner killed Billy.

pact

14/03/2016

PATC is not some serious, legally bonding document (as it is easy to think) but a very helpful method when it comes to finding sources for our favorite activity, obtaining knowledge. 

Purpose-Why the source is produced?

Author-Do we know anything about the author of the source we are using?

Context-Are there any other sources that would back up this one?

Tone-Are we reading dry facts or emotional opinions?

To be honest, PACT is not some new, magical invention that was discovered like washing machine, but something that was exiting for a long amount of time before it was named. According to my observations most teenagers are skeptical so they unconsciously use PACT when reading newspapers or articles online. I think that PACT should be mentioned in every school curriculum not only IB and it should be done in middle school, when kids are crating their personalities individually and not with their home habits. I would help with so much aspects of growing up because as I already said PACT is universal and can be used not only for historical sources but also for medical online sites. 

history oh history

29/02/2016

What subject starts with "H" and has been dreaded by me since I was 10? History!

 At the beginning of this school year I marched confidently into the glorious hall of our schools looking at all this poor people who were about to spent entire year learning about long and for most parts boring events and failures of dead men and here was I. The happiest person it this school. Well, at least that is what I thought until I discovered thrilling and exiting parts of IB that I was warned about but somehow I missed all of the warnings. Anyway, I managed to deal with the difficulties of an average IB student and then... History happened. To me more precise tok lessons involving History. I will run through the subject of history briefly since I can't pay attention to it. Here we go.

On that lesson I realized how bias is our history. During WWII the amount of propaganda existing all over the world made it hard to tell what really happened during some events. For example, photographs were manipulated in a way that if some figure occurring on one photograph was not beneficial to the whole event it was erased and people who were not present there and just known the event from the photograph can still live to this day in lie. Al off the tok lessons made me think about how easy it is to manipulate other people and I think I started develop trust issues when it comes to the things I learn at school. Also I know now that the problem with changing someone’s mind when the idea is heavily rooted in that person's mind is not only my problem, but the widely occurring issue. And this is why war happens and why society gets divided and racism and basically a lot bad things in history happened because people couldn't cooperate.

reasoning

Reasoning is the way we put together fact and events in our brain and make them work together as a logical whole. Logical is a very important part of this definition. Why? We will get to this.

First of all, there are this important terms that we must know and remember. Induction and 

Deduction. They sound almost the same to me but as I now know, they aren't. Induction is assuming some fact basing on the greater group to which these fact apply. For example: 98% of children likes sweets therefore the kid I just met will probably enjoy chocolate he is about to buy. Deduction is in my opinion a little bit like a mathematic equation. If A equals B and B equals C then A equals C as well.  Obviously, the results of our inductive and deductive reasoning will not be right because exceptions are almost always existing. The statement - every dog I know has a tail so your dog also have a tail- can be incorrect. This particular dog could be a victim of an accident and in result he has no tail. Deduction and induction may lead to prejudice as we approach new problems with experience from the past. "Every blue eyed person I met was a murderer so she must be as well!"

It all starts to be confusing as we dive into it. But here is why I said LOGIC is important. We can't just blindly connect the dots and believe that the picture is correct. We must follow the numbers next to these dots and that way we will end up with a nicely drawn picture. Also it is important not to connect dots with squares because it will create nonsense and false ideas. "Potato has skin, I have skin, therefore I am a potato.". It makes no sense because we connected squares with dots. Speaking more clearly; we connected facts that have nothing to do with each other and we got an answer which is complete absurd. 

emotions emotions emotions

08/02/2016

How to use emotions? 

Fear and disgust are both are responsible for keeping us away from my potential danger. For example; while you walking through the woods after sunset and you hear some suspicious noise, your heart starts to beat faster, you might feel cold, your muscles get tense and you became more alert. That is called fear. Your adrenal glands produce adrenaline which is responsible for fight-or-flight response. In moment of fear you can either run away or fight and both of these solutions are more likely to keep you safe than just walking through these woods without any concern about possible danger. The same goes for disgust. When you pick up your favorite dish and you see some white or green fur you won't eat it. Your brain knows that this "fur" is mould and there is possibility that after consuming that used-to-be delicious slice of pizza you can end up dead. Or at least at the hospital bed. 

Disgust prevents human from taking harmful actions but the problem is that disgust and fear are the easiest emotions to manipulate. You learn them through the association and that feature has been used repeatedly in history. During WWII German Nazi decided that the best way for spreading hatred towards Jews is to start from the youngest age. It resulted in crating anti-Semitic children book when they described how and why Jews are disgusting. Of course, the word "disgusting" was never used. It was the smart move because people were not aware of the fact that the emotions they felt were created by other people and not because of biological factors.

What is interesting, disgust is not only manipulated through vivid descriptions or  nasty images where you are shown and presented clearly what is your threat. Some researches were carried out and the proven that liberal people are harder to disgust than conservative. That explains why sometimes the political views are extreme. If used in correct way during voting, our senses would manipulate the voters o choose certain political party. Thankfully it is illegal, because I can't imagine the world where my own immune system and natural instincts that are meant to keep me safe, would be used to manipulate my thoughts. Or maybe they already are and I just can't see it? 

Lesson no9

11/01/2016

We can name 6 basic emotion:

·         Joy (or happiness)

·         Sadness

·         Anger

·         Disgust

·         Fear

·         Surprise

It’s kind of weird to me that only one emotion is on a positive side. But I could understand people disagreeing with me. I mean, some of us like to fear something so they watch horror movies or maybe another person would like to be angry. I don’t judge but basically it is commonly stated that only feeling joy make us feel positive. Anyway, that wasn’t the point of the lesson. We watched short Disney move about emotions and how Hitler used fear, sadness and anger to manipulate others. And about how we should use reason and emotion at the same time. I think that even though some people say it is impossible to say “emotions over reason” or “reason over emotions” If I had to stick with only one to the rest of my life I would probably chose reason. I never came across any mention in a pop culture of a case where protagonist lived without reason so I think I’m not the only one who is on “team reason”.

Lesson no8

Another post without a date.

We talked about how the language we are using affects our thoughts. For example Japanese women answered differently on similar questions if they were asked in English than when asked in their mother tongue. Also when reading article I got to know that apparently women speak differently than men. Were told to express our thoughts in more childish and unprofessional way but I don't really agree with it. I also had a hard time thinking about the example when while making a presentation or speaking in class my female friends were more childish than male ones. Anyway. maybe it depend on the continent but I also can't really believe in that. 

Lennson no7

So since it has been a long time without even visiting this blog ( I have no idea why I did not post anything) I can't really remember what day was it but on Lesson no.7 we talked about well...talking? Speaking? Expressing your thoughts verbally? What exactly is talking? And what are the words. After reading the text about Traxoline I had a lot of questions. I was able to read the whole text and answer basic questions as for example "What is Traxoline?" but the whole text was made by mainly non existing words. I could answer those questions because my brain followed pattern and somehow knew which words were nouns, verbs etc. Interesting. Then we discussed the idea of freedom in "1984" by George Orwell where in the world presented certain expressions were banned or had different meaning than in our world (free meant not freedom but being free from insects).

Lesson no6

9/11/2015

Last time was the continuation of previous movie assignments. I had my presentation about the movie "Truman Show". The comedy was amazing I loved how it had a deeper meaning rather than just being another pointless comedy. I also was glad that I wasn't the only one who choose that movie. Even though we seen the same movie we understood some parts differently. It was fascinating how the same thing as simple as a movie could be experienced in different way. We seen the same exact thing yet our brain processed it in its own unique way. 

"Truman Show" made me over think and question a lot of things. Sometimes I feel like everything is going exactly as I wanted and after seeing the movie I had a moment when if someone came up to me and said "your life is a TV show" I would easily believed in it. Thankfully as time flew by my emotions caused by the movie cooled down.

Lesson no5

26/10/15

On these two hours of ToK classes we had presentations from our movie assignments. Only three movies were presented due to the lack of time but they were interesting. I enjoyed the most presentation about the movie "Memento" directed by Christopher Nolan. It is about man who lost short term memory, do not remember things that happened recently and he is trying to find the killer of his wife. The trailer looks good so I probably will watch that movie if I find some free time. 

lesson no4

19/10/2015

I wasn't present on the half of that lesson so I can only write about first 45 minutes. The first thing we did that lesson was simple exercise: our teacher asked us what in our opinion is:

1.the most important sense

2.the one we could live without

3.the one that we like for some reason but is not the most important

Most of the people agreed that the most important is either touch or sight, but there was one person to whom the most important sense was/is hear.  At the first glance the idea of not feeling pain is pretty cool; you wouldn’t have to suffer while wearing braces, smashing your smallest toe on the corner of your desk, getting waxing done etc. When you think about it and all the possible dangers you wouldn't feel it's getting scarier. Simple example; first you wouldn't feel the pain of burning your throat and tongue while drinking hot liquids and it might seem okay for 2 or 3 times but when you constantly burn your throat it may lead to the cancer and cancer usually lead to death.

For the one we could live without everyone said either smell or taste and it's simple. When the fall/ winter season come every year majority of people catch a cold and end up with stuffed nose so they are not able to enjoy much smells or tastes for about one month in the year.

I don't know how to write it in the way which will not make it sound awkward or strange but i enjoy smelling. I really love the smell of the air in the morning, the smell of the night, air smells differently in every season which I find fascinating. I love the smell of freshly baked cake, smell of the lavender. Every time I smell old perfume or the shampoo I used on vacations 4 years ago it brings back the memories. 

It's really interesting that all of us have these 5 senses but we perceive the world in different way. I might love the deep red color and the person next to me can say that this is the ugliest color they've seen. Why? Both of us look at the same color, so why do we perceive it differently?

We also seen some optical illusions and the video which showed us that most of us are not able to identify the same color if it is on a different background. So we start to think: Can we rely on our senses? 

Lesson no3

12/10/15

Last lesson was dedicated to knowledge questions. What I learned is that they ask about knowledge ("how can mathematic formula help us in..." rather "that can we calculate that using this") and they must be open, meaning that answer is not "yes" or "no". We tried to understand it watching short documentary about alien abduction  and trying to construct knowledge question relevant to the film. Later on we did this excercise where we got a handout with descriptiopn of 4 situations and then we had to think out a knowledge question to each situation.

Lesson no2

21/09/2015
On last ToK lesson we discussed very intriguing text about these situation where there were couple of people and one of them staded that cheese was eaten by a mouse and tried to prove his opinion to the rest. What was important was the fact that the other poeople haven't seen the situation on their own eyes an one of them belived the boy and the other did not. Their statements were also justified. I liked the text but tater on that day when I went to bed and had plenty of time to think before I fell asleep I found myself overthinking a lot of informations recieverd from other people during my life and it gave me a little anxiety. How can I belive some people? Very often I have no proof which would
support the stories I am told. Most of informations I know might be untrue. I could as well live in one big lie my whole life. I don't know if upcoming ToK lessons will be confusing and make me think so much my head hurts and I start question everything I know but if so I hope I will get used to that because as for now I kind of enjoy the lesson at first but then when I think about it I'm getting tierd.

Lesson no 1

07/09/2015

 These Monday was  my first real ToK lesson. What can I say? We had these text about how some proffesor tried to convince his student that God does not exist and the other student proved mentioned before proffesor that the way in which he was trying to justify his rights is wrong because following his method the proffesor brain did not existed.

 To my way of thinking, proffesor was kind of ignorant assuming that God is bad because he created evil things. It's like you said that apple tree is bad because one of the apples had worms in it. Stupid. Anyway, I agree with the student that you shouldn't try to understand the world around you only with your senses. Also you should know that sometimes you don't need physical proof that something works. I'm not talking about religious faith because that can be personal to many people, I'm talking about things that you can't touch like mathematics. Why do we belive that pi is equal to 3.14....? I never had pi number of apples. I know that it exist but I don't really undersant it. How does it look? How you calculate pi? How ancient Babylonian people found it? I have no idea. I just blindly follow whatever my math textbook said because I have faith that it is true. From last lesson I learned that faith is important in ToK but I hope that I'll understand the topics that will be discussed. For now ToK does not look like it will be hard subject but I saw some posts that ToK is hell so I will have my fingers crossed that it only depends on the teacher. 

  I have no idea how many words should my post have. I will leave it the way it is and (maybe) change it next time.