CH1 L11: The possible and impossible

    1. After running away from the tiger [1], when the stress hormones dropped and you felt safe, you’d start to explore the environment and see the following thing [2]:


      1. How would you react to it?
      2. You should know that in your world, still, everything was possible. So, there’s a chance that the thing you’d seen before, had moved to the new place (!) [3]. To survive, your brain would actually prioritize the more dangerous possibilities. Then you’d feel a higher level of fear knowing that your last experience with it was painful [4].
      3. A fan of the website questioned the storyline and how related it is to mathematics. The important point in this part of the journey is to be aware that how our brain has grown to realize the impossible which is a crucial insight we need to have while solving problems.
      4. First of all, that’s what I tell my students: “There are two types of mistakes: minor and major. A minor mistake would be saying that 12 × 15 = 170, but the major mistake would be 1800. Because you should be aware that 12 added to itself 15 times can’t reach 300 (12 × 20 = 240) let alone 1800. So if your answer is 1800, it clearly indicates that you don’t have the sense to detect the mistake. Everyone makes mistakes but you must be sensitive to it. If your answer to a question about probability is 1.2, you’re expected to immediately say that it’s wrong [5].” That’s why I am taking you on this journey to show you how we think so we can be aware of its strengths and weaknesses.
      5. Secondly, realizing the fact that our ancestors were in the state of constant fear [6], thus they couldn’t think clearly. But forming civilization which brought a relative safety and security enabled them to think about and develop knowledge and technology.
      6. The third point is we’re usually worried about unlikely or impossible things such as an irrational confrontation that they might happen in future. To protect us, our brain sometimes thinks about the worst case scenario to be prepared for what might not happen at all. So, staying at that level of anxiety can be exhausting and in some cases paralyzing. We should know that emotions come and go like floods and no one can plant in a flooded land [7].
      7. Finally, to answer this question “why do so many students struggle with math and generally learning?”, I started to think and research about the brain. And I’ve realized that apart from the content of subjects, there are many factors hindering students from learning which I’m sharing with you one after another. The fact that not only we’re not aware of our limitations (limited energy [8] and working memory [9]), but also, thanks to the media (especially Hollywood), we might think that our energy and brain ability is unlimited which can create an unrealistic assessment leading to a tragic failure like Don Quixote’s [10].
      8. That’s why I thought that there’s a need to create a reliable foundation to become a thinker first (which is a Herculean task), then it would be easier to think about mathematics or other subjects.
      9. Let’s stop here and as the exercise, I recommend you to continue the thought experiment. How would you react if you thought that the thing was chasing you? We’ll continue the journey in the next post.


Exercise 11:

      1. Think about what Sir Arthur Conan Doyle [11] said: “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”


[1] Link to the previous post

[2] I recommend you to start from the beginning because we started experiencing the thing from the second post.

[3] Jostein Gaarder [Link] in “Sophie’s world” [Link] used the following thought experiment to demonstrate the difference between an undeveloped brain and a developed one that “One morning, Mom, Dad, and little Thomas, aged two or three, are having breakfast in the kitchen. After a while, Mom gets up and goes over the kitchen sink, and Dad—yes, Dad—flies up and floats around under the ceiling while Thomas sits watching. What do you think Thomas says? Perhaps he points up at his father and says: “Daddy’s flying!” Thomas will certainly be astonished, but then he very often is. Dad does so many strange things that this business of a little flight over the breakfast table makes no difference to him. Every day Dad shaves with a funny machine, sometimes he climbs onto the roof and turns the TV aerial—or else he sticks his head under the hood of the car and comes up black in the face. Now it’s Mom’s turn. She hears what Thomas says and turns around abruptly. How do you think she reacts to the sight of Dad floating nonchalantly over the kitchen table? She drops the jam jar on the floor and screams with fright. She may even need medical attention once Dad has returned respectably to his chair. (He should have learned better table manners by now!) Why do you think Thomas and his mother react so differently?”

[4] Link to the post in which you got a puncture wound by a thorn.

[5] Probability of an event is a number between 0 and 1 which will be discussed in the section about probability.

[6] Earlier we discussed that while we’re anxious, our body stops functioning to save more energy for the problem. So metabolism might stop which in a long run can cause stomach ulcer. Link to the post about fear.

[7] For more information, you can check out the link: a talk by Dr. Joan Rosenberg about waves of emotions and how to deal with them.

[8] Link to the post about limited energy.

[9] Link to the post about limited working memory.

[10] Link to Don Quixote. The featured image is Don Quixote by Salvador Dali.

[11] Link


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