Four Ways of Thinking

Using mathematical ideas in life

Everything we see or do could be classified as either:

Stable

Periodic - Periodic systems are those which exhibit repeating patterns. Like our daily routines, breakfast, work, lunch, work, dinner, TV, sleep, repeat.

Chaotic - Chaos is our inability to predict if it will rain tomorrow or not. It is the role of a dice.

Complex - Complexity can be found throughout society in a relationship with friends and family. -- Wolfram

Use this framework to have less pointless arguments

There are only two worthwhile arguments:

Class 1 arguments - those on their way to a stable resolution.
Class 4 arguments - those where important new ideas are discussed but might never be resolved.

Avoid:

Class 2 arguments - recurrent bickering over the same contentious point
Class 3 arguments - chaotic, back and forths where we talk over each other

Four ways of Thinking

Statistical Thinking

Class one is statistical thinking - When should you believe in numbers and when should you be skeptical?

The average is the most basic and powerful statistic of all. They tell us the truth about a city.
When comparing incomes, it is common to use the median rather than the mean.
The decision whether to use the mean or the median is therefore a question of deciding what we want to highlight in the data.
The distinction between mean and median illustrates that there are often multiple correct ways of using statistics to describe data.
The maximum likelihood told us the proper way to measure everything from opinion polling of political parties through the rates at which plants grow to our taste for their gherkins and other pickled products. Fisher showed that calculating the maximum likelihood provides a single uniquely correct way of measuring not just the average but the shape of any curve fitted to data. This is the cornerstone of statistics.
Provided you avoid eating too much processed food and you do eat plenty of whole unprocessed vegetables and fruit, it doesn't matter exactly what you eat, all the diets when followed properly, provide these essentials the key to healthy eating as summarized as "not too much, mostly plants" Healthy eating is simply a question of eating your grains and avoiding all the bags boxes and cans of processed foods
When we read headlines about resource studies, we need to consider statistical significance and effect size along with causality. Think about these three aspects: causality, statistical significance, and effect size. All three need to hold for a study to apply to you.

Interactive Thinking

Class two is interactive thinking - uncovering the secrets of our social world.

We should realize there is more than one way of thinking about the world. We act in a certain way and that changes the way others around us act. Equally the actions of others shape how we act and think. Interactive thinking is different from the statistical view of the forest of people. It is more individual, more personal, more related to our everyday experiences. It relies less on data and more on thinking through the consequences of our actions.
In our own interactions the lesson is, if we want to make a change for the better we need to increase the intensity of our interactions. It isn't enough to try something once. We need to build momentum within a group. Once we have that momentum, when we have reached the stable state where everyone is involved then it will be easier to keep on going.
- Often in group settings, at work and school, we find ourselves trapped in a vicious cycle where it seems that everyone is negative all the time and any attempt to be positive is met with further negativity. Simply trying to make one or two positive comments per day might lead you to hearing a few positive comments set back to you, but it won't be enough to change the culture because your low-intensity positivity will be drowned out by the high-intensity negativity. This doesn't mean that it is impossible to change the group dynamic. You need to sit down together and agree to try to change.
- Ultimately the only person that we can truly change is ourselves, but if you change how you respond to others via underlying rules of your interactions then you will also change the outcomes of those interactions. In trying to change our own rules for the better, we need to think very honestly about our own behaviors. Changing your behavior will bring improvements for both you and the person you care about. A small change to your own rules of interaction can make a massive change for everyone around you.
- Class 1 thinking is sometimes referred to as top-down. It starts with a theory and then looks at how well that theory explains the data. Class 2 thinking is more bottom-up. It starts with observations of how we think the world is and generalizes those observations to a set of rules. We then derive the consequences to create a theory. We start by trying to understand the essence of a system and from there we make predictions. It's after we've made these predictions that we test them on data from the real world.

Chaotic Thinking

Class three is chaotic thinking - Helps you decide when you should try to stay on top of things and when you should let go. The harder we try to control our lives, the more unpredictable they become.

Whenever positive feedback is followed by a sharp regulation, chaos can occur. The irony is that it is our attempts to regulate ourselves that are creating chaos. We fall into this trap. We decide not to use social media for a week. We stop drinking alcohol completely for a month, or we decide to get out running and immediately set off our top speed around the park. All these extreme responses are a form of regulation or control, but they are also the exact type of control that generates chaos.
A better solution is to aim to first stabilize and then slowly deflate behaviors we want to avoid. Gradual, carefully planned changes succeed, where drastic measures fail.
We don't need to be in control. Other people are like swirling galaxies. They will continue on their own trajectory, irrespective of what we do or don't do. It makes things easier.
Allowing each point to follow logically from the last is a much more certain path than memorization. Hamilton's solution to avoiding chaos was to take preparation to its far edge. Eight years of planning were needed to secure safety during a few minutes of the descent to the moon's surface. Louis Rose's approach recognized the impossibility of always controlling our lives. He had asked us to accept chaos.
The key is to recognize that trying to control the long term leads to over-regulation and even more chaos. But neglecting to control the short term leads to insecurity and even less order. Getting that balance isn't easy, but recognizing that neither order nor chaos can live without the other is a good start.
Each sliding door we go through on an underground train, each new person we meet, each decision we make to stop for coffee or stay inside because it's raining, each where we stumble over slightly as we speak, introduces tiny differences in our lives. As time goes by, the entropy increases, no matter how well we know ourselves today, we cannot know what the future has in store for us.
Letting go produces a new possibility. The way I've seen the world not in terms of certainty, but as something cleared up as a distribution of possible outcomes.
Distributions describe both what is random and what is typical. Randomness comes distributed in a foreseeable way, providing useful models to outline our observations of the world. Living in Distributions:
- Common Distributions
- Uniform Distribution
- Normal
- Long-tail
- Poisson
Chaotic thinking teaches us that there are always going to be large aspects of our world that are random, that cannot be predicted. Entropy is always with us, created by chaos. We can't predict it and there's nothing we can do about it.
- The first stop is statistical thinking. Know the numbers. But numbers don't usually tell us how we ought to act or how we should interact with others.
- Interactive thinking comes in. We think about how our actions affect others and how you let their actions affect you. You understand why you're stuck in a cycle of doing things you don't want to do or end up in pointless arguments. And see how the underlying rules of your behavior and the behavior of those close to you.
- And that's where chaotic thinking comes in. Decide which aspects of your life you aim to control closely and which ones you want to let go. You cannot control every aspect of your life, not even a small fraction of it. Instead, get ready for randomness. When you do so, when you do decide to let go, do so with humility. If you don't know what's happening around you, ask questions. Don't lose patience with people who are initially difficult to understand. Learn from your mistakes. Remember that you never know what the future holds. Don't blame yourself. Blame never decreasing entropy instead.

Complex Thinking

The more complicated problem is, the more difficult it is to say, solve. A system is only as complex (Class four) as its shortest description.

All of our lives are complicated. We can find a way of measuring how complex something is.
A pattern is as complex as a length of the shortest description that can be used to produce it. - Andrej Kolmogorov
Without people trying to do the explaining, nothing is complex or simple. In 1933, Kolmogorov proposed three axioms for probability.
1. Events cannot have a negative probability.
2. At least one event must have a probability of 100%.
3. If two or more events are mutually exclusive, they cannot both occur. Then the probability that at least one of them occurs is the sum of the probability of each of them occurring.
Complexity is not a property of the output itself. Complexity is the length of the program that generates or describes the output.
The secret then to capturing complexity is to find relatable stories that are both personal and capture variety, then let them grow within the intended audience. We don't need to tell every detail of the story we want to convey.
If you are an influential or popular person, either because of your role at work or through your social status, think about how you can use your physical location to avoid excluding others. The way we interact, inadvertently and collectively, creates hard edges between us. It is your individual responsibility to see where they lie and to soften them. Look behind you when walking with others. Check if someone is left walking on their own. Now and again, sit next to someone you don't know in a lecture and exchange a few words with them.
It is shared social identity which brings people physically closer and creates the positive emotions they feel in crowds. People who identify with each other want to be closer to each other and are happier. This is the reason for gathering, from religious or educational reasons to partying.
A person has a finite life and makes decisions about what they do with their time on earth. Some people will lead boring lives, never traveling, never searching for deeper truths, while some will lead rich lives, always seeking adventure, always learning, and interacting with others. The complexity of a person does not lie in the abstract or the infinite, but in the finite description of what they do with their life. The more complex a person is, the harder we have to work to describe them.
When proving any statement by contradiction, the approach is to first assume that the statement is true, and then show that this assumption leads to a conclusion which we know cannot be true. We should strive for a simple idea that allows a large idea to emerge. We can never fully understand another person. Perhaps we can't even fully understand ourselves.

Conclusions

While there are many problems in life, there are four ways with thinking.

There is thinking based on numbers. How often does it happen to you and to others? Do your research, collect the evidence.
Thinking based on interactions. How do you respond to each other? Find a way of breaking the negative cycle.
Thinking based on chaos. Is it better to let go or take control of a situation? If you let go, then embrace the randomness. If you take control, then prepare your strategy as if you are landing on the moon.
And there are thoughts about complexity. While we can use the first three ways of thinking to handle conflicts with others, remember that we are all part of a much larger social system. Family, work, and society. Try to see everyone as an individual by finding the words that best capture who they are.

The meaning of life, the one that Kolmogorov found, involved enriching his own internal thoughts and engaging with the complex internal lives of others. That is what made his life worthy. Words spoken sincerely to each other, meeting and listening to those near him, looking upwards and forwards to the sky together, hoping and believing that the truth will move just a tiny bit closer.

My distractions