In this article, I am going to link the IB philosophy to Mathematics and go through each criteria in a very clear and precise way. I will also provide a link to an Infographic which is about a lesson idea on ethics, bias and Mathematics.
How does Maths relate to the IB mission statement?
Inquirers: In Maths, we need to research about different methods, ways of analysing and independently investigate different topics.
Knowledgeable: We are continuously developing knowledge and understanding in Mathematics by learning, experimenting, practising and understanding procedures/proofs and theories.
Thinkers: We always think about and evaluate our approaches towards problem solving.
Communicators: Our approach in Mathematics must be communicated clearly in the form of equations.
Principled: We respect the approaches of others and grow from the different approaches.
Open minded: We appreciate the approach of others and grow from the diversity of the approaches.
Risk takers: We take risks in problem solving even if we know that an approach may fail. Trying is more important.
Reflective: Reflect about our work and how we are learning in Maths. We investigate how we can connect Maths to our lives.
I am now going to create a lesson idea by linking a learning profile to an inquiry approach. The following two are the ones selected:
Lesson idea:
Learning profile: Appreciate the moral, social and ethical questions arising from the work of Mathematicians and the applications of Mathematics.
Inquiry approach: Investigate unfamiliar situations, both abstract and from the real world involving organising, analysing information, making conjectures, drawing conclusions and testing their validity.
The full infographic can be accessed on the following link:
This scene together with the ending of the movie are the most intense and thought-provoking ones from the movie. I am going to write down my interpretation of this fantastic scene which is truly inspiring to me when I am fighting my own demons. I am going to take bits and pieces from the interrogation scene and elaborate.
Truth, evolution, and happiness
Joker: I know the truth. There’s no going back. You changed things.
Batman tried to clean the streets and he managed to do it. In this process, while he devoted his life doing the right thing, he made himself into something more than just a man. Deep down, he still wants to get back with Rachel after Dent takes over and fights crime legally. However, is there really a way back? Sometimes, you change so much and understand life so much that it becomes impossible to view life and even enjoy life like a simple person. It’s a price to pay for anyone living a life of high ideals, ethics, and morality. Sometimes, myself, I’d like to just think the world is a nice happy place but the more I observe the actions of people, the less I trust.
The battle of Anarchy and Ethics
Joker represents total anarchy and is a man who is treating society just the way he was treated. In the film, he makes references to being abused by his father and being abandoned by his wife after the mobs treated her badly. Batman represents resilience, ethics, a code of conduct and living as per certain rules. He also represents justice at the expense of himself. When Joker says: “I don’t want to kill you. You complete me”. I see the link between Anarchy (Impersonated by Joker) and ethics (Impersonated by Batman). This is extremely powerful because the only way to deal with the chaos of the world is by having a strong grounding into ethics. The world won’t make sense. The world will beat you down and enjoy watching you down. However, we must live a life we can be proud of, and this can be totally against what others are doing. It’s this resistance to evil which allows us to grow.
Humans, sincerity, and being an outcast
Joker: Don’t talk like you’re one of them. You’re not even if you’d like to be. To them, you’re just like a freak, like me. They need you right now. When they don’t, they’ll cast you out.”
“Their moral code dropped at the first sign of trouble. It’s all a bad joke.”
In the context of the movie, Batman has given so much of himself to Gotham and everyone is now blaming him for the chaos Joker has created. It really shows that people have the tendency to forget easily what you have done for them. The interesting thing is that Joker happens to be the person who truly understands Batman well. For example, Rachel thinks that Bruce did the wrong thing by letting Dent claim he’s Batman. However, as Alfred pointed it out, it’s not about the small lives of the individuals. It’s about doing what is right even if you end up getting hated just like it happened as the Dark knight movie evolved. Who is willing to go to that extent living the right way when you end up being completely alone and misunderstood? Sometimes, I think whether it’s worth doing all that I do for people. However, it’s always about doing the right thing which is not an easy way of living.
As a Statistician/MBSR practitioner who is very passionate about both Mathematics and the mental wellbeing of people around me, I have tried to draw possible links between the different fields as they are complementary aspects of my own weird/unique personality. I also wrote this after sleeping for only three hours.
Importance of Knowledge and its application
Knowledge alongside the will to acquire knowledge for the greater good of oneself and others is possibly the most important skill humans need to have. Knowledge is very important because it enhances our thinking. If we already know about something, our response becomes automatic, and this frees up space in the working memory. Knowledge or accurate knowledge, I should say will also allow people to reason and think in a very critical way. With the current technology we possess right now, it’s very easy to be exposed to information which will enable people to be knowledgeable. Therefore, if technology is used correctly, it’d very possible for people to be very knowledgeable, reasonable, and critical thinkers. The current era is fundamentally an era where there are lots of possibilities for humans.
Role of Mathematics
In this big picture of knowledge creation and application, Mathematics plays an important role in being a critical thinker and taking objective decisions free from bias as much as possible. Given that the systematic way of processing isn’t influenced in any way by personal bias, it becomes the tool which can allow us to make better decisions objectively and create a world free of bias and eventually a world free of conflict. A few ways in which Mathematics can be used in decision making can be found below:
What does correlation mean and how to measure correlation coefficients for different types of data
What does causation mean, how it is different from correlation, and how to prove causation
How to statistically test a hypothesis, and the statistical conditions underlying hypothesis testing
You will also find in the image below the jobs requiring Mathematics skills.
Developing meaning out of Mathematics
However, I’d argue that Mathematics changes humans in ways which are more meaningful and important than the conventional models described above. The essence of solving is about finding solutions to problems. In Mathematics, if we are getting the right solution, the sets of steps don’t matter. In the solving process, creativity gets developed through Mathematics. Furthermore, it develops this resilience to keep trying till we get the desired outcome, and this is an evolutionary thing. As a species, we must push ourselves to be better if we want to survive. So, in that sense, it’s training us to reach that optimum level as a species even if this statement is rather a romantic way of looking at Mathematics.
Biologically, it’s also good for the brain. Recent research by Dr. Tanya Evans of Stanford University shows, “Children who know math are able to recruit certain brain regions more reliably, and have greater Gray matter volume in those regions, than those who perform more poorly in math. Hence, it becomes more obvious that the study of Mathematics is more than just a certain set of skills which are beneficial for certain jobs. It’s actually like another sense given to us to experience the reality around us.
Traits of Mathematicians and emotional well being
Mathematicians are often seen as eccentric, obsessed personalities with a beautiful mind but one which is overcharged. How true is this?
Based on a survey of 557 Mathematicians, the following was concluded:
Mathematicians tend to be predominantly investigative individuals, which means that they are quite inquisitive and curious people that often like to spend time alone with their thoughts. They also tend to be conventional, meaning that they are usually detail-oriented and organized, and like working in a structured environment.
I wrote the term objectivist in the opening paragraph. I will now explore the hypothesis that Mathematics not only improves Gray matter in the brain as Dr Evans pointed out in the paragraph above. It also gives the power to regulate emotions in us. This idea is developed in the following research:
Undertaken at Duke University, the research found that engaging the brain in mental exercises involving mathematics is associated with better emotional health.
For this, 186 participants underwent a type of brain scanning called functional imaging, while solving mathematical problems from memory, and then completed tests for assessing their mental health status and emotional coping strategies. The results showed that the participants had a higher ability to adapt their thoughts in relation to emotionally difficult situations when they activated specific regions of the brain while performing mental mathematic exercises.
Matthew Scult, the main author of the study, says:
“Our work provides the first direct evidence that the ability to regulate emotions like fear and anger reflects the brain’s ability to make numerical calculations in real time.
We can conclude that Mathematics is more than just axioms, proofs, numbers or tools. I’d say that it’s an interesting system which will help us to understand ourselves and the world.
As an objectivist, I have always used Mathematics and logic to make sense of reality and not get trapped in the subjectivity of human perception. I still believe that it’s an amazing tool which can improve communication, bring peace and help humanity by evidence based solution free from bias. In this short article, I will introduce the main philosophies of Mathematics and look at where we are ruining such an amazing system with our own limitations.
Platonist and Non Platonist approaches
It’s important that we try to define Mathematics before we put bias in the equation. There are two categories of Mathematicians: Platonists and Non- Platonists. Platonists look at Mathematics in almost a romantic way. Mathematics is found everywhere and was always present. In fact, Mathematics is the essence of everything. Platonists believe that Mathematics was not invented and the whole existence is in fact digital, in a way. There are so many ways we can support this idea. Particles are probability distributions, there are patterns in nature and human beings are just an operating system using senses that take data, analyse and act. Non-Platonists think that Mathematics is a set of rules created by humans to make sense of the world. For non-Platonists the world would exist without Mathematics.
How do we balance both approaches?
Let’s say we bring a poet, an artist and a Mathematician in a room and we give each of them a sunflower. The poet will write about love, the beauty of the flower and mankind. The artist will appreciate the colors and textures. The Mathematician will conclude that the petals follow a Fibonacci sequence. Is any of the approaches wrong? I don’t think so. They are all ways of looking at the world and valid for the human experience.
Mathematics as the Pure and Impartial study
Let’s consider social sciences and Mathematics. Social sciences are about the study of people and their relationships in a society. It’s cultural and will vary across the globe. In Mathematics, we can solve an equation in any way we want if it leads to the answer. The same differential equation will be interpreted in the same way by all the different people in the world. In this way, Mathematics is a universal language. Mathematics isn’t affected by beliefs, feelings or the culture of a given country. However, there can be misuse of methods. For example, in data analysis, people can choose to ignore outliers or just use the mean and not comment on the standard deviation because it gives the right message. So, the problem is not the Mathematics in this case but the intent of the people using the Mathematics.
Mathematics, Big Data, Algorithm and Human nature
While Mathematics is unflawed, the results we may get after using Mathematics can be biased if the input data is flawed. We use Mathematics and Algorithms to crunch big data and make decisions. Big data is about massive data mined from the internet and analysed so that better decisions can be made based on consumer patterns and what’s really happening in the world. The three main sources of data are social data, machine data and transactional data. All seems perfect so far but let’s look at some results now. I am going to summarise results from Brown’s (2017) article on Forbes
An online ad for “$200k+ Jobs – Execs Only” is shown to 1816 men, but only 311 women.
Ads suggestive of arrest (“Trevon Jones, Arrested?…”.) are far more likely to show up on searches for names associated with blacks, such as DeShawn, than on searches for names associated with whites, such as Geoffrey.
Since the Algorithm only executes based on three sources of data mentioned above, it only suggests that we have an already flawed system with inadequate behaviour patterns as human beings. The machine is mining imperfection and providing imperfect results in a very perfect way. I’d conclude that Mathematics is still pure and impartial and it’s the human nature which isn’t as perfect as the Mathematics.
For the movie’s 13th anniversary, we are going to talk about the dark knight movie. Christopher Nolan’s dark knight movie is considered as a masterpiece by many people including the famous director, Steven Spielberg. Spielberg even said that the movie was a piece of art. The movie had 159 wins and 163 nominations. The movie is so abstract that it will be hard to talk about everything. Therefore, I am going to focus on the ending of the movie which to me is so powerful. I see three important aspects in the ending of the movie. These are the no killing rule, the ability to face the truth and the essence of a great leader/hero.
The no killing rule: Harvey’s death
While trying to save Gordon’s son, Batman accidentally kills Harvey. This scene has been criticized a lot by fans as Batman isn’t supposed to kill. However, it points to something important here. The will to act in adversity is fundamental. When there is an oppressor, violence may be the only way out. For example, if someone tries to break into your house and tries to kill you, you must defend yourself. The US Navy seals go through a process called dehumanization where the enemy is not considered an equal human, and this allows killing to happen in a war. For example, in Iraq, the soldiers were okay with shooting rapists and criminals. In an ideal world, we would not need to kill but in a realistic world, we may need to.
2. The ability to face the truth
“You either die a hero or live long enough to see yourself become a villain”. This is the famous quote from the movie which Batman uses again while talking to Gordon in the final scene. This statement is so deep. The more we learn about the world, the nature of humans and the manipulation that exists, the less we want to trust people. It can make us become like a sort of villain. Do we have the guts to look at the ugly side of life and keep moving positively? If people of Gotham knew Harvey turned evil, they’d lose all hope. That’s why Batman took all the blame. However, Batman says that people need to have their faith rewarded. Sometimes, the truth isn’t good enough. What does that mean? Throughout history, many people killed out of greed for power or because of ideologies. Hitler and Stalin killed so many people. Right now, in North Korea, mothers are selling their children as sex slaves to China because it’s a better life for them rather than die of starvation in Korea. Do we want to wake up to this truth every day? The challenge is about trying to make the world a better place while still acknowledging all of this is happening too.
3. Qualities of a great leader: He’s the silent guardian, the watchful protector and the dark knight
All the actions of batman are guided by the philosophy of doing the right thing for the people of Gotham even if it is done at his own expense. If taking all the blame was good for Gotham, he’d do it. It’s such a great leadership quality when we put others above us. It is also a great act of love, honour and self-respect. How many of our actions have a selfish motive? Thinking about it makes us reflect and really calibrate our actions again. Gordon also mentions that the police will hunt batman and condemn him, but he can take it. This shows the level of endurance, resilience, and inner strength we need to have if we are going to live a life of high ideals and purpose just like the dark knight.
I hope that you found the insights interesting. Much love, Geerish.
Happiness is the one thing everyone is chasing whether it’s through objects, relationships, job titles, external validation, our bank accounts and the list is endless. However, what if we rethink of it in the following way:
We don’t become happy when we acquire. We become happy when we stay significant and let go of desire.
We dont become happy when we feel superior. We become happy by being a great contributor.
We don’t become happy when we criticise. We become happy when we help people rise.
So, let’s redefine happiness. We just live once and happiness is the one thing which everyone wants and deserves to experience.
My own resilience as a person and my willingness to uplift and influence people comes from my time battling illness, depression and manipulation and one thing I can say is that those experiences either break or make you and you do become someone who was made out of these experiences. In this article, I am going to talk about some people who went through some dark times, study their Psyche and analyze how they overcame their tragedies.
The first case we are going to study is Victoria Milligan, a mother who lost her husband and eight-year-old daughter on a speedboat accident in May 2013. In the same accident. she got her left leg amputated and her son who survived had to go through 15 operations to save his left leg.
What saved her?
Support from family, friends and therapists.
Victoria got help from her closed ones and had guidance from professional practitioners too.
To overcome painful events, we need to get maximum support from our close ones and professionals. In some parts of the world, mental health is still not taken seriously or there might be a stigma attached to it. However, no one can function properly if the mental state is not fine and it’s absolutely fine to talk about it with your closed ones or get professional help from therapists who are qualified and have the experience helping people overcome traumatic events.
2. Natural disposition to talk about one’s emotions to others
Victoria talked about how she felt without any embarrassment or fear of being judged. I think that it’s very important to find someone who is a good listener and at the same time someone who will not judge whatever you are sharing. There are actually two sides to this one as only you should get the courage to overcome the tragedy but you should also not refuse the support that you may get from those people who are close to you and actually care about you. One danger of living through tragedy is closing on oneself. No one will heal if we don’t take the thing which is eating us out and we shouldn’t be ashamed and feel embarrassed by what we lived. You will notice that in the intro, I bluntly wrote what I went through because I hardly care about what people might think about it. It’s the truth and I don’t mind sharing such truths if they inspire people
3. Knowing how much love there was in your life before the tragedy
Victoria said that she has no regrets. She doesn’t regret not being able to say goodbye to her daughter and husband a last time. She said that they knew how much she loved them and that is all that mattered. When a person dies, the relationship with the person doesn’t end. It just changes. The human brain is wired in a way that it will remember the sad and painful parts of the past. However, it doesn’t need to be like that. What is important is the quality of the moments which were spent with your closed ones. There should be no regret felt if you have lived your life fully.
4. You can’t get over grief. You get used to its presence.
As per Victoria, the pain never goes. You just learn how to live with it. I believe that the most used phrase that “time will heal everything” is very much overrated. What happens is that we change ourselves in such a way that we learn how to cope with the loss but the loss is real and we will always feel something is missing. However, what happens is that we learn to live with the emotion and we don’t let the tragedy consume our lives.
5. Set small achievable goals and be in the moment
Victoria really took life slowly after her loss. She said that she was not living each day as it comes but living each hour of the day as it comes. She wasn’t overthinking what the future was going to bring and she focused on small aims like saving his son’s legs, learning to walk with a Prosthetic or going to the girls’ sports day. She looked forward to each event as they came and made the most out of them. This is a very important lesson as we are currently going through the Covid-19 virus spread and there may be a tendency to just focus on when everything will be normal rather than take each day as it comes and be grateful for still being alive.
I hope that you found the article interesting. If you’d prefer the same content condensed in a podcast, please refer to the following link:
It’s sometimes very hard to find time to meditate if you have a very hectic lifestyle. The video emphasizes on the one minute meditation practice and explains the “breathing into the fist” practice. Hope you enjoy it.
Along with ethical conduct and Mental discipline, developing Wisdom is an important aspect towards enlightenment.
Mental discipline allows the mind to settle and makes us become more aware. Being aware of one’s thoughts and emotions helps us to understand ourselves and others better.
Once this is attained, we understand deeper truths like Impermanence and no self. In the process, we develop the ability to challenge everything in our quest for knowledge and understanding, even our own beliefs and inner conditioning. We explore in more detail in the podcast attached.
Sila means the ethical conduct and is one of the pillars of Buddhism. The ethical conduct can be broken into right speech, right action and right livelihood. All the three of them are components of the eight fold path.
In the podcast below, the importance of balancing the heart properties with the mind properties in order to create the perfect human being is discussed.
Suuko's Spiritual page 