Category Archives: Calculus

Chapter XIX: An Individual’s Cycle

Continuing from the analogy of an individual’s cycle being compared to a economic, business cycle, one must assume that time is an important factor.

Below are displayed three hypothetical situations: each case represent’s and individual’s overall perfomance cycle (P) In a ten day period. The vertical axis corresponds to the numerical performance-measuring scale. We can clearly see that individual B follows a regular as the peaks and troughs equates almost. Any one of these curves can never be defined by a function unless the individual follows a very specific pattern.



This is an experimental work in process which shows the plus -minus-five scale (PMFS) model (graph) as tool of measuring cognitive and behavioural parameters.

Chapter XVII: Examining Time


Assuming from we know from Economics, if time was a good, it would be a normal good. Based on their observed behavior, we can deduce the following empirical conclusion: people use wage obtained from hours of work to buy leisure time, which has many possible uses. It is impossible to save it, but possible to “invest it”. The probability that they would spend their leisure time, T­L,  ­on activities payback return (in other words, gratifying accomplishments) like reading, studying or writing. Another optimal choice is activities that generates periodic earnings, but to a certain extent, in which an excessive level of income is undesirable.

From a philosophical, metaphysical or even poetical way, time is reflected in youth’s splendour. From there we can conclude the following thesis: an event in life time occurs only once, if not brought on intentionally; for an event or incident (negative connotation) cannot happen twice, with the exact same circumstances. It is rather obvious that time moves progressively; to move regressively requires an artificially method. This particular method is actually burgeoning, with a highly revolutionary technology, virtual reality.  A consequence of time going backward would, if this statement taken word by word, “make every human being on earth experience their memories once more”. Would that increase marginal utility?  If people can live their most unforgettable life stories once more, by observing they past blunders, we can deduct they will pay attention to their future actions. But that is not yet possible. Time has still yet come…

Speaking of time…

Time is not visible even to the greatest optical instrument; however space is visible. By space we mean the environment, our immediate surroundings. If time is not visible, we want to measure the change in the environment. In Antiquity thinkers understood the concept when they see a very obvious change in weather, observed in seasons. From there, the Time system was created. A full year represents on unit, divided into sub-units. We can therefore deduct that every second correspond to a specific marginal change in the universe. So space depends on time. Space is the aggregation of everything on Earth. How can we divide space? With which possible techniques? Based on countries? Assuming that countries are not equally spread out in terms of land area, there is not a coherent structure for methodic analysis, therefore there is no place for constant linearity. Is surveying a good idea? What kind of sampling distribution it will generate? Instead, we may choose to simply form our research on existing literature and database. To do so the population density per kilometre squared is a good indicator. Unfortunately, this is an enormous range to work with. We might simply use metre-squared for reasonable purposes. And after evaluating this parameter, it seems legitimate that any individuals, with x standard deviations of the normal curve, using height as an indicator would fit well into these descriptive statistics for our results. Also, the Metric System is the optimal tool for this empirical framework. It is important to remind that we are working with a two dimensional space set.

Deriving for above, there is an important aspect to take into account, the Individual perspective, which divide, from eyesight, the environment. Two same individuals can never see the world from the exact same angle. And assuming we use sight to represent the totality of the five senses. Based on these assertions, we can confirm that this is the root of Subjectivity, for two individuals can never agree on everything.  This part is extremely complicated, follow carefully. We know that past experiences accumulates with time, which is equivalent into the number of memories. This variable can be translated into the number of changes in their environment with respect to one’s vision. Let technology be possible. We can fast-forward one’s lifelong journey into a fixed quantity of time, T, and set that to be the model with respect to the average life expectancy. By examining common events in individual’s lives, we can infer additional premises.

In mathematical terms, P(X)≠P(Y), where P stands for perspective, also point of view.

For next chapters/coming:                                                                                                                       Scientific analysis of the cause-effect relationship of music and memories




Pre-work Considerations

  1. Goals
  2. a) Predict individual behaviour by using cognitive analysis.
  3. b) Understanding key factors in human relations
  4. c) Create a universal, numerical-scale based measuring system
  5. d) Improve analysis methods by focusing on structure and patterns
  6. e) Create a systematic solution to categorize abstract concepts
  7. f) Understanding the decision-making process (optimal choice selection)
  8. g) Create a method of quantifying emotion by measuring it


  1. Methods
  2. a) From a sample, generate theories that applies to a whole population.
  3. b) Using economic concepts to
  4. c) Simplify to clarify
  5. d) Detailed Explanation of Concepts
  6. e) Content Analysis of Games


Core concept: Equilibrium

List of Ideas

Strategy, Resource allocation, Opportunity cost, Decision making, Time/Timing (perfect moment/opportunity), Space/Distance, Estimation, Prediction, Aesthetic, Belief, Imagination, Energy (physical, mental)


– To reduce the margin of error, alpha

– To reduce confusion (incomprehensiveness, misunderstanding of human behaviour through cognitive analysis.

– Of the fundamental application of our theorem is to enhance the positive effects of cognitive behavioural therapy





Chap. VII: The solution

We want to predict the future. That’s only thing we want to know.

If dx/dt= the solution to anything, we have found our solution to eternal peace.

Let me explain. We use a simple calculus formulae, the derivative, to produce deductive thinking. If people can predict ahead of time, then their marginal utility could be increased. We use deductive reasoning to have a different way of dealing with problem-solving.

Chap. 2: Interesting Information

A. (Calculus)
  • The rate of change of the gap (disparity) of the individuals’s performances through out lifetime.
B. (Stats)
  • The mean (average or expected value) of the correlations (degree of strength of relationship or link). The correlations has its own probability distribution function (pdf)
  • The mean (average or expected value) number of events that cause another one and their correlation
C. (Microeconomics) Realistic (Alternative) definition of the marginal utility.           Example with apples.
  • The skin represents 0.1% of the apple’s total volume. That additional (marginal or extra) amount of nutritious value . The skin of the apple represents is insignificant in terms of marginal utility, and implicitly the nutritious value.
D. Considering time as a good (resource), as an dependent variable. Leisure time is a good.
  • (Calculus)
    • Other use of the derivative. To measure the words
    • Similarly, using integrals in historical events (the summation,
  • (Stats)
    • The conditional probability is used to represent the cause and effect relationship
  • (History)
    • Analogy between one’s own life time and historical periods
F. (Metaphysics)
  • The materialization of thought.
  • Similarly, the dematerialization of things.
G. Similar to the previous section F.
  • Using the concept of derivatives like in the infinite mirror effect, the reflection effect, to explain a process repeated (iterated) an infinite number of times.
H. (Core)
  • The fundamentals are Link, Categorize Definitions
  • Link. Trying as much as possible to link [abstract] concepts such as derivative, materialization
  • Categorize. 
I.  Brainstorm. List all ideas.
  • Clarity. Subjectivity
  • (Econ), normal, positive, negative, absolute infinite
  • (Calculus)
  • Real, irrational
  • (Psy)
    • Behavior, mood, stamina, judgement, cognition.
  • (Stats)
    • Standard deviation, average, expected value
  • Time, future, value
J. (Calculus)
  • The inverse function, such as f'(x) gives. It is the opposite way of deductive thinking. It is also known as reverse psychology.
I.  (Social)
  • An incentive is like a trap (or a fish rod). It may be a self suggestion.
K. (Calculus)
  • The range (or limits) should be numerical. But they do no have to be cardinal. The ycould be ordinal.
L. (Psychology)
  • A deductive thinking process can be started from an empirical observation.
M. (Metaphysics)
  • Time can be stored. Time is a material. Time exists
N. (Metaphysics)
  • Everything is Binary System Based
O.  Various.
  • A mouse click is an opportunity cost.
  • (psychology)
    • Classic conditioning