Yixia Gu response to AOK: Mathematics "Is Mathematics the Grand Design of the Universe?"

Herd of Elephants:
Maths is an abstraction. Yet from these abstractions, we are able to draw conclusions from the facts presented. When we count things, we are already subconsciously doing calculations such as 1+2=3. Compared to science which is a social construct which needs to be tested against external reality, Math can be applied and is compulsory in obscure subjects such as Physics. However, in Biology, mathematics plays a less fundamental role because of the complex arrangement of matter which is described. Because science is a social construct, many scientists can only determine whether they agree with each other and whether what they have observed is consistent with their theories. Nevertheless, there is maths all around us is it just that the calculations are too complicated for us to comprehend. Thus, I am able to conclude that Maths can be practical and quite important, because with Quantum Theory of a structure of a crystal for example was founded based on their mathematical patterns, later called atomic lattices.

Lottery illusion:
If you look closely at the Nature around us, every tree and shrub, we can find plenty of things which fit Mathematical patterns. One example is of the number of petals on a flower which can be calculated with the Fibonacci sequence. And indeed, evolution has encouraged this type of pattern. Yet, what we see and how we interpret these patterns and detecting them may have just been Mathematics put to work as an instrument of understanding nature. So is the supposed sequence in lottery numbers merely an illusion? Perhaps, we may have just imagined these patterns because they are already imprinted within us. The human mind could not have plainly invented these ideas, or come up with pattern seeking in Lotteries, so as Stewart explains, it must have evolved due to the mathematical element in the Universe.

AoK - Mathematics - Homework Response - Hey Tou Chiu

Is mathematics the grand design for the Universe, or merely a figment of the human imagination?

Nature’s Patterns
Stewart in this section puts forward numerous patterns that we see in everyday life to illustrate how mathematics can be seen as the basis of the Universe. He then quotes from different scientists and philosophers some saying that God is a pure mathematician and that “the Universe is made from information, the raw material of mathematics”. However, he puts forward the other side of the argument – where “fundamental mathematics is in the eye of the beholder…in the beholder’s mind”. This is because we use sense perceptions to experience the universe and then interpret these senses in our minds. Stewart then tells us how he believes that mathematics is a combination of invention and discovery. Using examples of Columbus landing in America and Livingstone’s discovery of Victoria Falls, he displays how invention and discovery can both happen at the same time as many things cannot just fall into one category. I think the examples he uses here are good illustrations of the differences between invention and discovery and I believe they are quite convincing.

I am able to learn from this subsection that mathematics is really not what it seems to be. From here, I realize that mathematics is everywhere around us and that we see it everyday in our lives. The idea of mathematics being the grand design of the universe was only first considered when I read the article.

Lottery Illusion
This last section of the article again focuses on mathematical patterns. Stewart tells us how Fibonacci numbers can be traced to the behaviour of cells at the tip of a growing shoot and how lumps of cells (primordial) develop into arranged patterns that leads back to the Fibonacci numbers. He then presents the fact that lottery numbers on the contrary, do not follow patterns of mathematics suggesting that mathematics may not be inherent in nature after all. One important point he makes is that – ‘mathematical minds cannot evolve in an unmathematical universe’ meaning that it is impossible to be mathematical if the universe itself is not mathematical at all! Here, we see that Stewart himself believes that the mathematics is the grand design of the universe even though he does not explicitly conclude so.
I find myself agreeing with Stewart on the fact that our minds have evolved to learn detecting patterns as I think this is very true. However I do not think this is enough evidence to suggest that mathematics is the grand design of the universe. For example, the number of petals on flowers may just coincidentally be the same as the Fibonacci numbers; we can never know whether they are truly following mathematical patterns.

AoK1: Mathematics -- Lesson 1

Guiding questions to Lesson 1:

1. What is mathematics?
2. How and why is mathematics an important area of knowledge?

Stimuli used to consider guiding question 1 include:

• What do you know about maths?
• 'To speak freely, I am convinced that it [mathematics] is a more powerful instrument of knowledge than any other…'. (Rene Descartes, 1596-1650)
• 'Everything that can be counted does not count. Everything that counts cannot be counted.' (Albert Einstein, 1879-1955)
• 'The mark of a civilised man is the ability to look at a column of numbers and weep.'(Bertrand Russell, 1872-1970)
• 'Survival' maths' vs. Maths 'believed necessary' in society.

We began addressing guiding question 2 by considering:

• its Greek etymology (máthema) = learning, study, science.
• its main concepts -- namely, 1) quantity, measurement (e.g. numbers – mass, time, distance, heat); 2) structure (e.g. set theory, proof theory); 3) space (e.g. geometry); 4) change (e.g. calculus)
• the differences between 'pure' and 'applied' mathematics.

Homework -- to be completed by January 14th and 16th

Read carefully the Ian Stewart (1996) article given out in class, 'Is mathematics the grand design for the universe, or merely a figment of the human imagination?' Stewart starts with the question that is in its title and lies at its heart: "Where does mathematics dome from?" Though he opens by saying that mathematics is both "already out there [in the physical world], waiting for us to discover it" (p. 1) and "in the mind of the beholder" (p. 1), waiting to be invented, he goes on to suggest that neither "discover" nor "invention" "adequately describes the process" (p. 2) that, for him, is mathematics. Stewart argues his case in four main sub-sections: Nature's patterns, Baking bread, Herd of elephants, Lottery illusion.

For this week's blog posting assignment, you are to pick two of these four sub-sections to focus on. In particular, you are:

• to summarise the main point(s) made in each sub-section you've selected (hint: what does the heading itself suggest?)
• to consider carefully the evidence Stewart uses in each sub-section to convince readers of his point of view (hint: identify the evidence -- e.g. appeal to sense perception, language, reason, emotion, another area of knowledge? does it convince you -- why? why not?)
• to discuss what you have learnt about mathematics in each sub-section.

Each of your two sub-section treatments should be about 125 to 175 words long (i.e. 8-12 sentences); you may want to group the 'summarise'/'consider carefully' foci into one paragraph, and make the 'discuss' focus its own and separate paragraph... which means that each sub-section treatment should be two paragraphs long.

Please contribute your post to the blog by Monday, January 14th.

Please comment on someone else's post by Wednesday, January 16th. Choose posts that DO NOT treat the same two sub-sections you have focused on (if one of two is the same, that's fine... but both is not). Your comment should:

• retell (i.e. summarise their post's point);
• reflect on what you've learnt by reading it -- feel free to agree and/or disagree with them; and
• relate it to your developing understanding of mathematics as an area of knowledge).

Reminder: Please bring coloured pencils to the next lesson!

Emotions: Jacqui

I think that emotions are something that we learn. Emotions cannot be a biological part of us because if it is, we would all be the same, there would be no difference between everyone and we wouldn't be who we are.

A little girl at the age of 3 needed to go to the toilet at night, still awake as she only went into bed not long ago. She couldn't reach the switch and went in the dark. Having not been taught or experiences anything bad yet or seen horror movies or thrillers, she didn't have these haunting visions in her memory to scare her so she didn't feel scared or feared the dark.
A major percentage of the world are scared of the dark, and a main contribution to this are the fantasies we've been taught. The media nowadays are a major influence and this includes horror movies and thrillers. A human's brain processes this and under a simliar circumstance, we tend to remember this and fear it. This emotion cannot be "biological". It is learned. Although the reaction of it is linked to biological factors, the emotion itself isn't. Without being taught the scary things, it would be very hard, but not necessarily impossible to feel fear.
Fear could also be of losing a person, losing a game or even phobias. Fear of losing a person and a game is 'cause of what experiences you've been through and learnt from them. A phobia is due to extreme experiences we've had before which we don't necessarily remember therefore with this shadow in our memories, it could develop into a phobia. Yes, this is biologically related but without learning from the experience, the phobia itself wouldn't have developed.

Although I've only given examples of one emotion, I still strongly believe that emotions are gained from learning and experiences rather than biologically. I mean, how would you explain that the little girl wasn't scared due to biological reasons? I know for a fact that the brother of the girl is scared of the dark being 10 already. It's definately not biological. Emotions are learned.

Emotion - Robert Win

I believe that we are born with the basic emotions which allow us to communicate our feelings to other people from the start, but we gradually learn new emotions as we mature and develop the basic ones. An example would be that a baby would cry when he/she is hungry and uncomfortable, or after being told off by their parents, which is the expression of the emotion of sadness. These emotions are then developed as we grow older, from our experiences and education as well as our general environment. Evidence to support this is that everyone is psychologically unique, as no two people are able to think, feel, do, say the exact same things, all at the same time.

We are born like a memory stick, a blank piece of hardware with only the basics installed. As we mature and increase in experience, the memory stick gains more and more data, the data being anything we absorb during our lives experiences, including emotions, giving us a wider range and variety of emotions to feel or to choose from. Each memory stick would also gain different data in different orders to other memory sticks, making each one unique.

Emotion- Ming

Emotions are innate. From the very day we were born, we would weep and feel sad when we were hungry, sick, uncomfortable. We would feel happy, when our parents play with us, watch TV, amused by objects or beings. We smile and laugh, since when we were babies.
However, when we grow up, mature, we learn other feelings of this society, like guilt, ashamed, disgusted of what we have done. This can only be known when we have something to compare to, what is good or bad to do. Also, many of these emotions, we learn how to express them more effectively. Example, when we're sad, we do not only cry, but invent ways expressing our feelings, this maybe singing, become silent, speechless and even stoned. Of course, we can learn not to show our emotions, for example not to shout, scream, tremble when we are scared. . Therefore, emotions are innate, but some are learnt from other people and how to filter and express their emotions.

Emotions: ZOHA

Some may argue that emotions are in us from birth. Hence, they believe that expressing emotion is a completely biological process. If emotions are something we feel inside shouldn’t this be related to something un-physical? If one is saying that emotions are innate then we’re simply interpreting how we feel as psycho-chemical reactions in our brain.
Therefore “love” should be our reaction to hormones, and “fear” is just the result of high blood pressure and the release of adrenaline into the blood. It has been argued that if emotions weren’t innate how could a baby cry at birth.

The crying of a baby at birth isn’t an expression of “sadness” whatsoever but a reflex action. A baby doesn’t learn to cry due to “sadness’ or ‘anger’ until a certain age where he/she acquires that emotion. Before this, the act of crying is an exercise of vocal cords and the means of communication, a baby may cry because it’s hungry or thirty are these emotions? If one placed a nervous system into a robot who could then express laughter, crying, fear, sadness one would then have to support the idea that the robot is human.

Emotions are what makes us human and distinguishes us from animals. We don’t see a crying dog, or a laughing cat even though they have a nervous system too. Sure, one may argue that they express their emotions in another manner but it is scientifically proven for now that animals don’t have emotions. Therefore I would have to say that emotions are something we learn through experience and the environment.. As we get older we forget the last time we did something for the first time. For example if you’ve never touched snow would you know what it feels like?

Emotion: Yixia Gu

Emotion, I believe is something that a human is equipped with, and can be expressed from birth. Take a neonate for example: it greets the unfamiliar and quite intimidating world with a cry- an obvious emotion which also functions as a biological check to see if the vocal chords are is working properly. The baby had already knows how to cry without the influence of the environment. Many emotions also involve the brain triggering a response, as in the response to anger or sadness. In addition, certain parts of the limbic structure such as the Amygdala is responsible for production of negative, fear emotions, whilst the Insula is important in producing feelings of disgust, which contribute the notion that emotions are innate and biological.

Nevertheless, as we grow and learn from others around us, we begin to imitate different emotions and thus are shaped by the surrounding environment. According to the Social learning theory, we are incipient of the emotions modeled by people we come in contact with so we reproduce them, and this is also the time when we ‘acquire’ new emotions such as anxiety in precarious situations, and embarrassment when we do something out of the social norm.

Thus, the emotions we have are through a mixture of what our body is programmed with and also through the way were nurtured and other environmental factors.

Emotion: Chloe Chan

I think we learn the physical side of emotions from observing models but we have innate emotions. I think that the common idea that people who have never experienced sadness and therefore will never be sad is untrue. I believe all individuals will feel sad in some point in their life, but they either don’t know how to express it or they don’t recognize the feeling as sadness.

In more detail, emotions such as sadness are learned in the way that we can see emotions expressed physically and therefore we can imitate and express sadness ourselves. But in order to be able to express our emotions we must be able to relate it to the right physical expression. This is where the structure and wiring of the brain also comes in. Perhaps one brain maybe more able to relate to a certain emotion than another. Therefore, if someone has a growing tumor in an area of the brain that is supposedly responsible for a certain emotion, the emotion will become disordered.

WoK#4 - Emotion - Hey Tou Chiu

Responding to the ‘nature-nurture’ question, I believe that our emotions are both learned and in us from birth (innate). I think that emotions are within us when we are born, however when we express these emotions i.e in what situation, are learnt socially. I read Jason’s post, and I find myself agreeing with him. The fact that new born babies cry when they leave their mother’s womb is strong evidence to support how emotions are within us. The child has no environmental influence and yet, they show emotions right from the beginning of their life.

However, why do we show certain emotions in certain situations? Why do we smile when we are happy? Why do we cry when we are sad? We learn to do this through the environment we are in, and the people around us. In psychology, this is referred to as ‘Social Learning’. Albert Bandura claimed that our behaviour is learnt and that we first observe a model, and then we imitate them. So for example, a child may see her mother breaking her favourite plate and sees her mother starting to cry. The child would then understand that her mother is sad because she has lost something she treasures a lot. The child will therefore also cry in the same situation i.e when the child is unhappy or sad. This example shows how the child learns when to cry - when the child experiences something unpleasant or feels unhappy.

I think that the way we acquire emotions is something that cannot be explained by only one side of the ‘nature-nurture’ questions. Our emotions are related to the environment and are also in-born.

WoK 4: Emotion - Jason

In response to the 'nature-nurture' question. I believe that our emotions are both innate and learnt through experience. We'll take an example, a new born baby. When babies are first delivered from their mother's womb, they will usually be crying because they are uncomfortable (sadness). From the fact that they were just delivered from their mother's womb, there were no nurturing in the process. This suggests that some emotion such as sadness is innate(rationalism).

New born babies cry when they are hungry or uncomfortable. My brother showed happiness, sadness and joy in his first few years. He cried when he was hungry or uncomfortable. As he grew up, I notice that he began to show other emotions such as anger and fear and learned how to use those emotions that he showed from his early age. Now, he does not cry when he is hungry or when he feels uncomfort. With nurturing from the day he was born, he was able to learn how to use emotions. This suggests that emotions are also learnt through experience(empiricism).

Immanuel Kant once said, "Intuitions without concepts are blind, concepts without intuitions are empty".This basically means that you cannot grasp the truth without using both experience and intuition. How this quote can help support my view is that without nurture, you would not be able to learn how to use your innate abilities; and without innate abilities, experience itself alone would be nothing.

Emotion

I think that we are born with emotion and its not something you can actually control for example outbursts, they just happen you cant "learn to have an outburst", that just sounds ridiculous. I do agree that our emotions are deep within us and our life experiences bring them out of us all differently maybe even depending on the people around us. I also think emotion is very vital for us to have because without it life would be pretty blunt and boring and I also believe certain people only fit in with certain other people because of simularities in their emotional personalities and types.

Alyssa

Norbert - WoK Emotion

To expression our emotions, i.e. whether we are happy or sad, we look at others, and ‘copy’ how they express their emotions. It is scientifically proven that people often copy what others do, then act the way others do appropriately. However, how we feel (our emotions) are felt deep within us, and that is affected by our upbringing and experience. This is why parents are very important to a child’s upbringing. Parents guide them on how the child should think, and how to FILTER the physical raw data we are given everyday. It could also be innate. When you see a situation, everyone reacts differently, regardless of your upbringing and experience, and has different feelings and emotions. This could be different depending on your genetic layout.

WoK3: Emotion

In our first lesson, we operationalised a working definition of emotion -- i.e "reactions or responses related to sense perceptions, internal states, thoughts, or beliefs about things or people, real or imagined" (Dombrowski et al., 2007: 50) -- by

• responding to the viewing of Aerosmith ('Sweet Emotion') and MadTV (Tickle me Elmo/Emo); and
• exploring the physical sensations we experienced in response to 'core' or 'basic' emotions identified by behavioural psychologists Paul Ekman and Robert Plutchik: anger, fear, sadness, disgust, surprise, curiosity, acceptance and joy.

Alchin (2006: 102) notes that emotions can be:

• either instinctive (e.g. anger, love)
• or social (e.g. guilt, shame); and

• either inward-looking (e.g. fear) -- i.e. 'drawn into ourselves'
• or outward-looking (e.g. wonder) -- i.e. drawn 'out of ourselves'.

Problematising our initial responses and explorations, we then used a BBC article (Generosity 'may be in the genes') to consider the 'nurture-nature' guiding question: Are emotions learned (i.e. acquired through interactions with the environment and others) or innate (i.e. genetic and pre-programmed into us at/from birth)?

Building on this first lesson's classwork, you are now to blog a one-paragraph:

• post that responds to the 'nurture-nature' guiding question -- Do you believe that emotions are learned or in us from birth? What evidence can you offer to support your claims? Be sure to craft your paragraph so that it includes a connected series of statements intended to establish your position... convince us through evidence and inductive/deductive reasoning; and
• comment to someone else's post that either supports or challenges their claims/conclusions (and, of course, explains why or why not).

Please post your response by Monday, 17 December; your comment to someone else's post by Wednesday, 19 December; and use your first name in your post's title.

If you so feel inspired and want to learn more about your own 'emotional intelligence', then consider completing the on-line EQ test and reflecting on the results. It's free to do and receive the abridged results.

References

Alchin, N. (2006). Theory of knowledge (2nd ed.). London: Hodder Murray.

Dombrowski, E., Rotenberg, L. & M. Bick (2007). Theory of knowledge: Course companion. Oxford: OUP.

WoK3 Puzzles #1 & #4 - Robert Win

Puzzle #1: The man who lives on the tenth floor of the building is short, too short to reach the 10th floor button in the elevator, that is why he when he returns to his apartment, he presses the button of the highest floor button he can reach (seventh floor) and then walks from that floor. He is able to take the elevator all the way down from his tenth floor apartment because the ground floor button is at the very bottom, which he is able to reach.

Puzzle#4: The man in the snorkeling kit was swimming in the nearest lake, when a fire fighting helicopter came and swooped some water from the lake along with the man who was snorkeling, to place it on the forest fire. The water (and the snorkeler) were dropped onto the forest fire. The man was killed sometime during the event, either by drowning, or by falling from a height.

WoK : Reason - Jason

Puzzle #1:
The text never told us that he took the elevator from the 10th floor. So i assume that the elevator only goes up to 7 floors.

Puzzle #5:
As there Cleopatra and Mark Anthony was not poisoned, and there were no mark on either of the bodies. I assume they died from starvation, the broken bowl signifies that there was nothing to eat.

Puzzles

Puzzle #3: Looking at the situation, it seems to have died without anything else interfering. An explanation would be the package fell out of a cargo aeroplane and hitting the man on the head unluckily. Another one might be, he went to the field to suicide, and the unopened package was for his and family and friends to look at when they found out what happened.

Puzzle #4: It seems impossible for a deep sea diver to have died in a forest. It must be a very odd occasion to have a deep sea diver, or rescuer to have accidentally fallen out of a helicopter when travelling to its destination. Another explanation might be he got scooped up from the sea when water is needed for saving bush fire. Ultimately leading to him falling and dying in the forest.

Puzzles.

I found it very difficult to anaylze and try to understand these puzzles although i am happy to say i had a go.

Puzzle 1 and 2.

Puzzle 1 - I think the man was a short man, so as he went down he could press ground floor button but when he went up the 10th floor button is very high in the lift so he cannot reach.

Puzzle 2- This could be because the man through a rope over and had someone pulling him up therefore he could hang himself.

Cole Pamuk

Norbert-Reason (1 and 5)

Frankly, I am absolutely hopeless, but I will try my best to attempt to solve these puzzles. To me they are sort of tricks. There are many different answers, and you may argue that there’s more to it.

 

I think I know the answer to the 5^th puzzle. I think A and C have both drank the contents that was originally in the bowl; they could have thought it is some sort of medicine, but in fact it is poison. They drank it, they faint, they drop the bowl, they drop, and they die.

 

The answer to number 1 I think is that he isn’t tall enough to reach to 10^th floor button in the lift. So when he leaves, he needs to press the ground floor button, which is usually at the bottom. When he returns, he tries to reach for 10, but could only manage 7.

 

As you might be able to see, I wasn’t sure whether I solved them correctly. But I gave out reasons, to why I think my answer is correct, and hoping you will be persuaded that my answer is correct.

WoK3: Puzzle #5

Anthony and Cleopatra are lying dead on the floor of a villa in Egypt. Nearby is a broken bowl. There is no mark on either of their bodies and they were not poisoned. How did they die?