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Problem Solving

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Mathematics: The Language Of Science
  • According to Galileo Galilei, mathematics is the language in which God scripted the universe.
  • A language, as defined by linguist Noam Chomsky, is a set of sentences constructed using a finite set of elements, being able to represent events and abstract concepts.
  • Mathematics is considered a bona-fide language by many linguists though there are others who disagree and say that it is mostly in written format only.

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Problem Solving

  • A language normally contains vocabulary, meaning, grammer, syntax, narrative and a set of people who use and understand the various symbols.
  • The syntax, vocabulary and grammar of mathematics forms a system of communication which any language must have to qualify as one.
  • It is considered by many as a universal language as it meets all criteria and requirements of the same.

Nouns in math are the Arabic numerals, fractions, variables, expressions, figures, infinity, Pi and imaginary numbers like i.

The verbs of math are equalities and inequalities, addition, subtraction, division, multiplication and many other operatives like Sin, Cos, Tan etc.

The rules of mathematics, like syntax and grammar, are international, with the same structure used universally. Greek and Latin languages are used to denote the various symbols.

  • Many students find numbers and symbols confusing, and using a familiar language to describe an equation makes the subject easy to understand.
  • Solving word problems, where nouns, verbs and modifiers are translated into mathematical equations is a good exercise.
  • As mathematics is universal, it helps people learn and communicate by acting as a common translator language.
Common Causes Of Bad Decisions: Social Pressure
  1. People push their moral boundaries due to incentives and rewards.
  2. No one wants to be kicked out of a tribe or community so they play along.
  3. People do not think through the consequences.
  4. Little things and tiny, overlooked details snowball into something big.
  5. Other people's errors are easier to spot than one’s owns, leading to blind spots and denial of one’s faults.
  1. Many people are unable to put the effort and blindly follow simple calculations with black-and-white outcomes.
  2. Assuming that there is no room for error in the first place, and making a decision based on that.
  3. Underestimating the ability of things to change for the better, and banking on things to remain bleak and static.
  4. Idolizing others who may not be in the same space as you are, and following their actions and decisions.
  1. Inability to predict our response to risk and making knee-jerk decisions based out of fear.
  2. Past success leading to overconfidence and arrogance.
  3. The false assumption of the information on the table being the complete picture.
  4. Taking the wrong lessons from others' success and failures while not able to grasp the complex and diverse set of circumstances.
Improving your idea-flow

A lower idea-flow is this sense that you don't have as many ideas as you used to. Reading more encourages ideas to flow.

You can't create time, you can only re-allocate it. To find the time for improving your idea-flow means that you have to find ways to cut back on other things.

One way to improve ideas is to think of sources of information as being in memetic buckets. If your idea inputs come from the same memetic bucket, your outputs will replicate the same concepts in that bucket. Your thoughts won't be new or particularly interesting.

To combat this:

  1. Reduce the overlap in idea sources.
  2. Go through your social media feeds and see what sources say the same things in different ways.
  3. Pick one or two favourites out of them, and ditch the rest.

When you catch yourself thinking "that's crazy," try to figure out why someone would believe that idea.

People are mostly logical, their starting point is just different. When you try to see if you can find the premises for someone's beliefs and ideas, their conclusions will make more sense. Even if you disagree, understanding where they are coming from will help you better understand your own ideas.

Cut your sources of information so you don't hear the same thing in five different ways.

Realize when you should let go of certain inputs, even if you enjoy them.

Developing good ideas is an active process. The ideas that are starting to form should be coaxed out of you.

  • This is best done by having conversations. It forces you to try to explain them in a moment, realize where they're faulty, then continue refining them in subsequent discussions.
  • Creating is the final expression of an idea. Express your ideas in articles, tweets, songs, paintings, TikToks, to clarify them properly.
Two strategies

When it comes to setting strategy, there are benefits to both popular and loner strategies.

  • Popular strategies are those that are identified by the crowds. The more people that choose a strategy, the better the strategy performs.
  • Loner strategies are those that are identified by only one person. If you want to outperform the crowd, you've got to do something the group isn't doing.
Outperforming the crowd

If you want to outperform the crowd, learn the following two essential skills.

  • Generate ideas by broadening your decision frame.
  • You must be able to distinguish between good and bad loner strategies. It is best done by embracing critical thinking.

When we need to make a decision, we tend to ask "What should we do?" However, it narrows our thinking to one right decision.

If we ask the question: "What could we do?"  it broadens our decision-making frame, because we can consider multiple futures. Could ask what if, what else, and why not.

For example: Ask what would be the equivalent in your industry of something that’s working well in another.

Strategy development and internal reviews often center on precedents, trends, and due diligence. They address"what will happen."  Change the question to "what may happen" :

  • Role-play other parties.
  • Listen to assumptions in the way a strategy is supposed to work.
  • Watch out for confirmation bias, overconfidence, survivor bias, and groupthink.
  • Forecast your competitors' results.
  • Beware of missing pieces in the tools you use.
Daydreaming Is Not A Waste Of Time

Contrary to popular belief, daydreaming is actually an evolutionary trait specific to human beings which harnesses our creative power and enables us to function in an effective manner.

Research shows that a creative distraction like daydreams loosens us form our never-ending stream of thoughts and provides possible solutions to our problems, while enhancing our sense of identity.

Our brains have many regions, like the prefrontal cortex, medial temporal lobes and the parietal cortex cluster, allowing us to imagine and visualize complex scenarios and their possible outcomes inside our minds.

This makes daydreaming a complex and rich phenomenon which we take for granted.

  • We all have imagination at our disposal, a highly complex brain function(though we ignore it), that can take us backwards or forward in time, like a time machine.
  • A comprehensive neuroimaging brain scan analysis shows that dementia patients do not have this brain function of active imagination, and are stuck in the present moment.
  • Similar studies on patients with Alzheimer’s disease showed that they cannot remember past and future events, and are not able to imagine things apart from not having access to their memory.

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