Understanding Calculus

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  Table of Contents

  Preface
  1. Why Study
  Calculus
  2. Numbers
  3. Functions
  4. The Derivative
  5. Differentiation
  6. Applications
  7. Free Falling
  Motion
  8. Understanding
  Derivative
  9. Derivative
  Approximations
  10. Integration
  Theory
  11. Understanding
  Integration
  12. Differentials

  Inverse Functions
  Exponents
  Exponential
  Functions
  Applications of
  Exponential
  Functions
  Sine and Cosine
  Function
  Sine Function
  Sine Function -
  Differentiation and
  Integration
  Oscillatory Motion
  Mean Value
  Theorem
  Taylor Series
  More Taylor Series
  Integration
  Techniques

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CHAPTER 11

Chapter 11 - Understanding Integration

Section 11.5 - Human Applications

Your gut feel = Integrating experience over time

From Funny exam questions

Your gut feel for a situation is essentially the integral of your experiences from your birth till the present moment. The ability to trust your gut is the most fascinating trait of human intelligence. It reduces years of experience and knowledge into a single quantifiable dimension. Understanding the gut can be quite complex as it involves a knowledge of many interacting disciplines, e.g. neurology, psychology, sociology etc. I will not bog you down in complex medical terminology but rather give you a layman's perspective on, 'What does this all mean to me ?'.

While we like to believe the world is black or white , the reality is people are grey. We can distinguish the infinite shades of grey by assessing what our gut feel is for a situation. Why rely on a conclusion based on one piece of information when you can rely on your gut which is based on countless pieces of information?

The gut has many limitations as well, so understanding them will help train your gut better. A lot of current authors have written extensively about the gut's critical role in decision making, as in the following excellent books:

The fundamental principle of the gut is its ability to accumulate information and store it in a distinct location in the brain. We all know it is much easier to recall something rather than remember. For example you will find it impossible to remember all your steps the previous day. However, if you watched a video of yourself moving about yesterday , you would instantly recall each situation with ease. The same goes for places you visit, details of people you interact with, knowledge you read in books etc. While it is impossible to remember the details, you will always be able to recall the details when given a little hint.

So how does this translate to the gut? The brain stores information in containers in your brain. Now the fascinating part is the brain stores both the information and intensity of the information. For example let's say someone told you Hitler was a bad man. Somewhere in your brain that would get filed away in the Hitler department with a score of -1 . Now each time someone told you Hitler was a bad man, that same part of the brain will increment the counter by one .

So if I asked you today what you think of Hitler, your brain will immeadiately fetch the intensity of the information on Hitler and report it to you as a gut feel. That is the remarkable aspect of the gut. While it is fairly obvious that each of us has a Hitler file somewhere, it is not obvious that our brain also stores the intensity of the information as well. Therefore, what is most amazing is this intensity can be recalled on a moment's notice when needed.

Another example that demonstrates how the brain stores increments of intensity of information is through the 'nuisance accumulator'. The phrase explains how the brain collectively logs each recurring nuisance or annoyance. Humans are forced to change when the nuisance accumulator becomes full and needs to be emptied. . For example if you buy a new car, chances are the first year everything seems great. But with time, each minor annoyance starts to grow on you until it becomes easier to purchase a new car rather than live with weight of all the accumulated nuisances in your brain!

Another powerful feature of the brain is chunkification. Essentially it is the ability for the brain to conglomerate details of knowledge into a single conclusion. When this happens the details are forgotten, but the conclusion remains in long-term memory. This is important because it lets your brain just store single pieces of information instead of infinite details. Also chunks of knowledge can be further chunkified into new conclusions.

As we grow older we are basically taking existing knowledge and simplifying them into concise analogies that summarize all the information into a single saying. The gut is then able to probe these chunks. However, the gut is not able to probe the details that contributed to the making of these chunks since that information is forgotten.

A good example that demonstrates this is to pick up an interesting article you read a few years ago. You will notice how all the details are forgotten, but the overall message of the article will seem very familiar and obvious to you. Chunkification explains why most older generations of humans appear to be consciencously ignorant and inferior to later generations. All generations and societies do the best they can with the tools and knowledge they have available. However, the knowledge they develop becomes the building blocks for future generations to build larger chunks of conclusions from.

The same feature that makes the gut feel so powerful also makes it prone to distorted perceptions on life. As your gut feel for a certain piece of information strengthens, your brain goes into a mode where it quickly rejects any information that is in opposition to your gut feel. For example, if someone started preaching to you Hitler is a good man, your brain would not start decreasing your negative gut feel for the man. Instead it would outright reject the information and not change the intensity of the existing information.

This has nothing to do with psychology but is an evolutionary survival mechanism. As we grow older our brains need to be able to act quickly on gut information in order to survive. Furthermore, our brains have to learn to carry out complex tasks with ease. If you have ever watched a professional athlete, you will quickly observe how 'easy' they make it look. The reality is they have conditioned their brains and body through years of training to perform the most complex movements without a second thought. It is impossible to become proficient at a task without building a firm base of fundamental knowledge . Ask any professional and they will all agree.

If our brain was always like clay as a child's brain, then our behavior would constantly be changing . Habits and methods would not develop. Consequentially it would be nearly impossible for us to progress by not being able to build upon established layers of complex systems.

Cognitive dissonance refers to the brain's desire to resist information that would require the individual to act in ways that depart from their established habits. The social animal by Elliot Aronson is an excellent book that uses many interesting examples to explain the concepts of social psychology, including cognitive dissonance.

This is why a child's early development essentially remains the foundations for their personality for the rest of their life. It does not matter what happens to them after maturity, their core self will hardly be unchanged. If you ask any 80 year old how they are different then when they are 17, they will respond " I am essentially the same person, except the things I believed when I was 17, I now believe with far more certainty".

To summarize the following aspects of the brain and gut:

  • The brain stores information and intensity of that information
  • The intensity automatically increases/decreases depending on new knowledge learned until an adolescent's maturity
  • The gut can retrieve the intensity of this information instantly when needed
  • Chunkification lets the brain condense many bits of information into one conclusion to free up space for new information to be digested
  • As you get older the brain autommatically rejects information that goes against the gut feel for that information in the brain

You are probably asking , 'So what does this all mean for me?'. First, since your brain so easily absorbs information like a sponge, spend time reading and learning as much as you can about the world. It does not matter if you can not remember most of what you learn. Rest assured that the information has been processed and filed away in the brain for easy recollection when needed. In other words you are feeding your gut by being a vociferous consumer of knowledge.

By understanding how your gut works you should then learn to trust your gut above any one-dimensional argument. You will gain confidence in your gut's ability to make the correct decision in complex multi-dimensional situations.

Last, you need to be self-aware to not fall into the evolutionary survival trap of rejecting information that goes against your gut feel. Most humans spin in a spiral of a self fulfilling prophecy, whereby they only seek out information that strengthens what they already feel to be true. Therefore, you need to spend considerable time training your mind to be open and tolerant. Obviously you need to strike a balance between nurturing your habits and absorbing totally contrary ideas that can change your established habits.

Next section -> Differentials

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