Lottery Illusion is about how numbers relate to the way we behave/biology. The example given is that a flower has the number of petals which adds up to the Fibonacci numbers. It basically prooves that maths relates to your daily lives and that different numbers can send out different vibrations.
Humans have a tendency to link our daily lives to number patterns by having this tendency it has led to a number of laws on mathematics and the universe. But any patterns we think we see are illusions.
Human minds develope this tendency as we adapt to the real world for survival skills. "Mathematical minds cannot evolve in an unmathematical universe." If maths had nothing to then it would eventually die out.
Everyone has their own way of picking out these patterns and solving equations, "but i doubt that they would have anything like the pythagoras theorem", people adapt to the world in different ways and use maths for different reasons.
Thursday, January 17, 2008
Jacqui.W: Herd of Elephants & Baking Bread
Herd of Elephants
Stewart believes that mathematics are simply problems that interlink us humans between the world of maths and the real world. The solutions to maths may answer something that isn't related to maths but something just as real and important but physically unrelated. By using "flow" and "backflow" Stewart gives us the impression that the maths problems are ongoing in a never ending nature's cycle, like tidal waves.
Stewart addresses maths as an abstraction and he strongly believes that human mathematics is so complicated that it's hard to grasp the idea or even write it down on paper. He says that the structure is totally impenetrable therefore being too much info for us to take in and that our behaviour is even related to mathematics being applied to our constituent atoms.
I agree with Ian Stewart and that mathematic problems can be related to something else other than maths, as maths does relate to lots of daily activities we do. However, I disagree with Ian Stewart when he says mathematics can relate to our behaviour as I don't think it can be. I think our behaviour is dependant on our mind and heart to decide, not human mathematics.
Baking Bread
Ian Stewart compares Mathematics to Baking Bread as he mentions that Mathematics starts in the real world, therefore firstly he compares it to an activity in real world and secondly to express his thoughts more easily. Stewart brings attention to whether things in life are a discovery or invention and the different cases in Mathematics between discovery and invention. Stewart says people often oversee the most important things of Mathematics, 'significance, simplicity and elegance'. This could be related to baking as often known, to bake bread, the amounts of ingrediants used must be significant and exact for the perfect texture and taste. The more simple the ingredient is, usually the more delicious and easier the bread turns out to be. Lastly elegance could relate to the feeling and pride gotten from the entire process and of completing and successfully baking bread.
When Ian Stewart says, "Mathematics has an internal structure of logical deduction that allows it to grow in unexpected ways" I think not only does he apply this concept to Mathematics but he's relating this directly to baking bread as well. The difference between Mathematics and baking bread is that for Mathematics, we can generalize theories to make our calculations easier but for baking bread, this is impossible and it must be done the long, hard way and there's no easy way to it because if there was, the bread wouldn't turn out as good anyway.
Stewart believes that mathematics are simply problems that interlink us humans between the world of maths and the real world. The solutions to maths may answer something that isn't related to maths but something just as real and important but physically unrelated. By using "flow" and "backflow" Stewart gives us the impression that the maths problems are ongoing in a never ending nature's cycle, like tidal waves.
Stewart addresses maths as an abstraction and he strongly believes that human mathematics is so complicated that it's hard to grasp the idea or even write it down on paper. He says that the structure is totally impenetrable therefore being too much info for us to take in and that our behaviour is even related to mathematics being applied to our constituent atoms.
I agree with Ian Stewart and that mathematic problems can be related to something else other than maths, as maths does relate to lots of daily activities we do. However, I disagree with Ian Stewart when he says mathematics can relate to our behaviour as I don't think it can be. I think our behaviour is dependant on our mind and heart to decide, not human mathematics.
Baking Bread
Ian Stewart compares Mathematics to Baking Bread as he mentions that Mathematics starts in the real world, therefore firstly he compares it to an activity in real world and secondly to express his thoughts more easily. Stewart brings attention to whether things in life are a discovery or invention and the different cases in Mathematics between discovery and invention. Stewart says people often oversee the most important things of Mathematics, 'significance, simplicity and elegance'. This could be related to baking as often known, to bake bread, the amounts of ingrediants used must be significant and exact for the perfect texture and taste. The more simple the ingredient is, usually the more delicious and easier the bread turns out to be. Lastly elegance could relate to the feeling and pride gotten from the entire process and of completing and successfully baking bread.
When Ian Stewart says, "Mathematics has an internal structure of logical deduction that allows it to grow in unexpected ways" I think not only does he apply this concept to Mathematics but he's relating this directly to baking bread as well. The difference between Mathematics and baking bread is that for Mathematics, we can generalize theories to make our calculations easier but for baking bread, this is impossible and it must be done the long, hard way and there's no easy way to it because if there was, the bread wouldn't turn out as good anyway.
Baking bread and lottery illusion
The baking bread section suggests that in any area of human activity there is neither "invention nor discovery" but a "complex context-dependent mix of both." Ian Stewart compares the technique of baking bread to mathematics, the ingredients- or in another sense the basic number skills, once you have ditermined and made assumptions , then everything "flows" and is "predetermined'.
He later goes on to argue that math in a universe makes abstact sense. Hence since the abstraction came out of reality , it's no surprise if it applies to reality.
- generalising theories help it to apply to differential equations and suddenly you find applications again, but to dynamics, not to bakery.
The authors use of rhetorical questions "what is medicine?" "where does it live?" "is it invented or discovered?' has a persuasive element, as the reader wonders the posibilities of the answer.
Lottery Illusion
- mathematical patterns are evident in nature and biology, for example the number of petals on a flower are part of the "fibonancii numbers"
- seeking out mathematical patterns is biologically innate in us, as Stewart calims our minds havr a dendency to seet out these.
- this "natural" ability has led to the discovery of Newton's law of gravity and the equations of quantum mechanics in additon theres astrology and the great Pyramid's, which examplify the accuracy and measurements, human kind could achieve.
- Although, what mathematics tells us about choosing lottery nubmers is that any patterns we think we see are illusions.
- He then asks the reader how does our mind develop this tendency for pattern seeking.
- Mathematics is our way of understanding ceartain features of nature.
- It is in our brain to think mathematically
- Only Geometer God can create beins able to come up with geometery.
He later goes on to argue that math in a universe makes abstact sense. Hence since the abstraction came out of reality , it's no surprise if it applies to reality.
- generalising theories help it to apply to differential equations and suddenly you find applications again, but to dynamics, not to bakery.
The authors use of rhetorical questions "what is medicine?" "where does it live?" "is it invented or discovered?' has a persuasive element, as the reader wonders the posibilities of the answer.
Lottery Illusion
- mathematical patterns are evident in nature and biology, for example the number of petals on a flower are part of the "fibonancii numbers"
- seeking out mathematical patterns is biologically innate in us, as Stewart calims our minds havr a dendency to seet out these.
- this "natural" ability has led to the discovery of Newton's law of gravity and the equations of quantum mechanics in additon theres astrology and the great Pyramid's, which examplify the accuracy and measurements, human kind could achieve.
- Although, what mathematics tells us about choosing lottery nubmers is that any patterns we think we see are illusions.
- He then asks the reader how does our mind develop this tendency for pattern seeking.
- Mathematics is our way of understanding ceartain features of nature.
- It is in our brain to think mathematically
- Only Geometer God can create beins able to come up with geometery.
Wednesday, January 16, 2008
Alyssa Wootten - Mathematics Lesson 1
Is mathematics the grand design for the universe, or merely a figment of the human imagination?
"Mathematics exists only in the mind of the beholder"Baking Bread
Ian Stewart speaks persuavingly about maths and other things such as medicine, plumbing, ballet, football, language and cycling and he generally compares them all against one another and he says that they are 'nor invention of discovery, but a complex context-dependent mix of both'.
It works in with the title as well because its something that is found then turned into different kinds of bread.
I would say that I agree with Stewart here, then again I myself think that mathematics is a figment of the human imagination AND ALSO a grand design for a universe as there are different kinds of maths in the world that we need for different sorts of things. Maths can of course lead to new ideas though and Stewart mainly asks us why maths is so important if it was invented by people ourselves, and that you cant go about maths simple minded because there is allot more to it than meets the eye.
William Wong : Is mathematics the grand design for the Universe, or merely a figment of the human imagination?
Nature’s Patterns
Ian Steward in his article believes Mathematics is a “complex context-dependent mix of both” invention and discovery. His example of the ripples on the sand dunes being similar to the wave patterns in liquid crystals illustrates that Mathematics already exists as a design of the universe. However he also believes “mathematics is in the eye of the beholder” meaning that it is also discovered. “We human beings do not experience the Universe raw, but through our senses, and we interpret the results using our minds.” Next steward tells us that invention and discovery can happen at the same time within a particular context by using Edison as an example, “Edison would have felt as if he had invented the idea of electric lighting, but then spent many years trying to discover how to make it a reality.” The title “Nature’s Patterns” suggests that the surrounding environment displays evidence of both invention and discovery.
I agree with steward as his argument claims valid and he has reinforced my beliefs towards this particular subject.
Baking Bread
In this sub-section Stewards explains that Mathematics is derived from the “real world”. From observation of two sheep and two more sheep make four sheep, 2+2=4, we have produced Mathematics that can be applied to “reality”. In addition Steward also claims that “Mathematics has an internal structure of logical deduction that allows it to grow in unexpected ways” which is reinforced by the title as it suggests that an idea in Mathematics can be used to create other ideas.
I have learned much.
William Wong : Emotions
I believe that emotions are both innate, already exists at birth, and natured, developed by the surrounding environment. One way to prove that emotions are innate, is the observation of a new born baby. At birth, a baby can show several different emotions, one could be sadness suggested by crying which shows hunger. During this time, the baby has not been able to develop his/her emotion unless you regard the development of the body in the womb as development of the emotions. Paul Ekman who created a theory on emotions found that even members of an isolated, Stone Age culture could reliably identify the expressions of emotion in photographs of people from cultures with which they were not yet familiar with.
However emotions are also developed, as one grows older and encounters different situations, their body will adapt to it so next time when a similar situation is being experienced, the body will be able to achieve a better outcome by doing whatever is necessary. If we take an identical twin, having minimal variation in genetics, and place them into different environments then we will find that there will be a large difference in their emotions or reactions to events.
Emotions are a function of the sensory and motor areas of the neo-cortex. Emotional reactions also require the use of the limbic system including the hypothalamus, anterior thalamus, cingulate gyrus, and hippocampus. These areas of the body have been proven different in all humans because of variation in the genetic makeup. If what controls our emotions are different, then we can assume the outcome which is the emotion will also be different if they are not developed by the environment into the same.
AOK: Mathematics, Ming Fung
Nature's Pattern:
Ian Stewart is stating that mathematics is imprinted on earth itself, "God was a mathematician". He says that we can see this from the natural trends we see in everyday life, e.g. circular ripples honeycombs are perfectly shaped mathematically. However, he states that these raw material or data we do not experience. But we use our senses to capture these data and interpret rationally with our minds. After that, he discusses that maths, maybe a combination of discovery and invention. I guess Stewart is right, I think many of the things that we invent, would be a mixture of both. And if we do not invent things we cannot possibly discover new things, and vice versa. This maybe why mathematics is incorporated in nature, as we extracted it from nature, and invented new theories and codes like numbers to rationalise what we actually sense.
Herd of Elephants:
Stewart compares mathematics to science. He states that we can put science into practice, but how about maths? Scientists use maths to calculate quantitative chemistry, and also physics. Then he writes that we, human beings may well be behaving according to mathematics, but it would be just be too hard to understand. Mathematics is everywhere, and is linked to everything. This suggests the world is programmed by these numbers, figure, mathematics, everything having direct links and correlation to each other. This reminds me of the matrix, how Neo should be quite a good mathematician because he can comprehend the mathematical matrix and manipulate it.
Ian Stewart is stating that mathematics is imprinted on earth itself, "God was a mathematician". He says that we can see this from the natural trends we see in everyday life, e.g. circular ripples honeycombs are perfectly shaped mathematically. However, he states that these raw material or data we do not experience. But we use our senses to capture these data and interpret rationally with our minds. After that, he discusses that maths, maybe a combination of discovery and invention. I guess Stewart is right, I think many of the things that we invent, would be a mixture of both. And if we do not invent things we cannot possibly discover new things, and vice versa. This maybe why mathematics is incorporated in nature, as we extracted it from nature, and invented new theories and codes like numbers to rationalise what we actually sense.
Herd of Elephants:
Stewart compares mathematics to science. He states that we can put science into practice, but how about maths? Scientists use maths to calculate quantitative chemistry, and also physics. Then he writes that we, human beings may well be behaving according to mathematics, but it would be just be too hard to understand. Mathematics is everywhere, and is linked to everything. This suggests the world is programmed by these numbers, figure, mathematics, everything having direct links and correlation to each other. This reminds me of the matrix, how Neo should be quite a good mathematician because he can comprehend the mathematical matrix and manipulate it.
Robert Win - AoK Mathematics1
Natures Patterns
Here, Stewart explains that in nature, we see similar or the same mathematical shapes and patterns on different things, such as the circular shape of waves on sand dunes similar to the shape of rainbows. Using this, he tries to demonstrate that mathematics is an aspect or even the basis of nature and the universe. Stewart also tries to promote his view, that us, people, both invented and discovered mathematics (as, in his view, mathematics already existed in nature, but we took advantage and developed it further), using the example of how Columbus discovered America while trying to invent a new shipping route to India. This suggests Stewart believes we stumbled upon mathematics while trying to figure a way to interpret and sort things simply.
This particular example does not convince me, however I do believe that mathematics was both discovered and invented as mathematics, in my view, is just a psychological tool we use and a way to technically interpret things, which is what i also learnt from reading the article.
Lottery Illusion
Here, Stewart mentions that mathematics is embedded in biology, conveyed using the example of the number of petals on a flower usually being one of the Fibonacci numbers, which is a number pattern group, therefore implying that mathematics is also embedded in nature. This example is quite convincing to me, and has allowed me to consider the link between nature and mathematics more, however, i cannot say whether i agree or disagree with this statement, as I am not currently sure.
Stewart also discusses whether the mathematical patterns seen in nature are actually by chance, and that they do not represent any significance between maths and nature. Stewarts evidence supporting that humans discovered patterns which are of mathematical significance, and that maths exists within nature, is by implying that early humans noticed patterns, whether or not it was by chance or not, they knew that patterns discovered could be used in future and relied on these patterns. This reliance on patterns and has developed into what we know now as mathematics, as we use patterns and figures to prove or disprove a point.
Stewart also tries to share his view that mathematics is universal by suggesting that aliens would also be able to do mathematics, although not identical to our maths, they would probably also notice similar patterns which they could use to benefit themselves in understanding things
Overall, I have learnt form the article that mathematics is (in my view) a technical way of interpreting things, and a way of knowing and understanding things (as i mentioned above) and is also one tool we use to explain and to simplify things to allow us to understand complex theories.
Here, Stewart explains that in nature, we see similar or the same mathematical shapes and patterns on different things, such as the circular shape of waves on sand dunes similar to the shape of rainbows. Using this, he tries to demonstrate that mathematics is an aspect or even the basis of nature and the universe. Stewart also tries to promote his view, that us, people, both invented and discovered mathematics (as, in his view, mathematics already existed in nature, but we took advantage and developed it further), using the example of how Columbus discovered America while trying to invent a new shipping route to India. This suggests Stewart believes we stumbled upon mathematics while trying to figure a way to interpret and sort things simply.
This particular example does not convince me, however I do believe that mathematics was both discovered and invented as mathematics, in my view, is just a psychological tool we use and a way to technically interpret things, which is what i also learnt from reading the article.
Lottery Illusion
Here, Stewart mentions that mathematics is embedded in biology, conveyed using the example of the number of petals on a flower usually being one of the Fibonacci numbers, which is a number pattern group, therefore implying that mathematics is also embedded in nature. This example is quite convincing to me, and has allowed me to consider the link between nature and mathematics more, however, i cannot say whether i agree or disagree with this statement, as I am not currently sure.
Stewart also discusses whether the mathematical patterns seen in nature are actually by chance, and that they do not represent any significance between maths and nature. Stewarts evidence supporting that humans discovered patterns which are of mathematical significance, and that maths exists within nature, is by implying that early humans noticed patterns, whether or not it was by chance or not, they knew that patterns discovered could be used in future and relied on these patterns. This reliance on patterns and has developed into what we know now as mathematics, as we use patterns and figures to prove or disprove a point.
Stewart also tries to share his view that mathematics is universal by suggesting that aliens would also be able to do mathematics, although not identical to our maths, they would probably also notice similar patterns which they could use to benefit themselves in understanding things
Overall, I have learnt form the article that mathematics is (in my view) a technical way of interpreting things, and a way of knowing and understanding things (as i mentioned above) and is also one tool we use to explain and to simplify things to allow us to understand complex theories.
Tuesday, January 15, 2008
Chloe Chan - Mathematics lesson 1
Baking bread
In this section Stewart considers whether existence is a discovery or invention. Stewart argues that it is not just invention or discovery that makes existence but a bit of both, as suggested by the title, the mixing of ingredients (invention and discovery) make bread, the existence of something. In the case of discovery the item already exists but was just not known to humans in comparison to invention which suggests taking a discovery and playing with it to make something new. Stewart gives us a guiding question of why maths would be so important if it were invented by people and tells us his answer that maths started in reality and in nature and therefore would apply to reality of life. However maths can lead to new ideas and theories can be made which apply to many different things, baking bread for example started out as a discovery from reality and open paths to new ideas. Stewart’s use of language, of questioning, makes the reader feel involved in the topic which in turn convinces the reader of his view.
In this section I have learnt that maths is one of the most basic yet complex things of life as maths started off naturally yet opened up to never ending branches of unknown ideas.
Lottery Illusion
Here, Stewart argues that mathematics is the source of many other subjects such as biology where the petals found on flowers are Fibonacci numbers, which is due to the cells of flowers. With this, he wonders whether mathematics is innate in nature and within us, where we have the natural tendency to detect and try to correlate things into patterns, which supposedly benefit our survival. Stewart argues that it is due to this natural tendency that we come up with many other theories and formulas. Therefore when watching the lottery we tend to think we see patterns in the lottery numbers and the winners but in actual fact this is just an illusion. He also introduces the idea of aliens having their own type of maths which could be similar or different to ours.
This section has made me realise that it is true that we tend to try and correlate things even if we know something is random. Therefore I think maths really is innate.
In this section Stewart considers whether existence is a discovery or invention. Stewart argues that it is not just invention or discovery that makes existence but a bit of both, as suggested by the title, the mixing of ingredients (invention and discovery) make bread, the existence of something. In the case of discovery the item already exists but was just not known to humans in comparison to invention which suggests taking a discovery and playing with it to make something new. Stewart gives us a guiding question of why maths would be so important if it were invented by people and tells us his answer that maths started in reality and in nature and therefore would apply to reality of life. However maths can lead to new ideas and theories can be made which apply to many different things, baking bread for example started out as a discovery from reality and open paths to new ideas. Stewart’s use of language, of questioning, makes the reader feel involved in the topic which in turn convinces the reader of his view.
In this section I have learnt that maths is one of the most basic yet complex things of life as maths started off naturally yet opened up to never ending branches of unknown ideas.
Lottery Illusion
Here, Stewart argues that mathematics is the source of many other subjects such as biology where the petals found on flowers are Fibonacci numbers, which is due to the cells of flowers. With this, he wonders whether mathematics is innate in nature and within us, where we have the natural tendency to detect and try to correlate things into patterns, which supposedly benefit our survival. Stewart argues that it is due to this natural tendency that we come up with many other theories and formulas. Therefore when watching the lottery we tend to think we see patterns in the lottery numbers and the winners but in actual fact this is just an illusion. He also introduces the idea of aliens having their own type of maths which could be similar or different to ours.
This section has made me realise that it is true that we tend to try and correlate things even if we know something is random. Therefore I think maths really is innate.
Monday, January 14, 2008
Norbert: AoK Mathematics 1: Baking Bread and Lottery Illusion
Baking Bread
Steward is exploring the key similarities of discovery and invention. Discovery to him is research in an area which has a specific answer to a question, and invention is trying to gathering ideas to solve a problem but sometimes it might be lost. To prevent this, we always make assumptions to invent the most we could.
He also says 2+2=4, no matter what you are counting, from the smallest of ants to the biggest of planets, no matter how abstract it is, and no one should be surprised if it applies to reality. He thinks however that a discovery is useful; we sometimes will find it difficult to apply to our daily life because it only applies to a specific object. One might argue: what is considered as daily life and what is more abstract ideas. It is different to everyone, and it is factual. A scientist might see law of Mathematics a part of everyone’s life, but we might not have thought to create the things we have, mathematics actually plays a bigger part in our lives than we think it does.
Lottery Illusion
Stewart is claiming the nature has a lot of similarities to mathematics. He used the number of petal a flower usually has to a set of patterns, and from this example he claims mathematics is derived from nature, and we use mathematics to understand nature.. He thinks we also seek these patterns to ‘help us survive’, and that if we didn’t, we would die.
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.
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.
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.
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