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Today is the birthday of Agnes Scott born 1894 in Jersey. Scott graduated from Edinburgh University and taught mathematics at Raffles' Girls School in Singapore.
Today's quote is from Alan Turing who said "Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities which we may call intuition and ingenuity."
A parent function is the simplest function that contains all the characteristics of the family that can be formed from it. Examples of equations that form parent functions are: y = x (linear); y = x^2 (parabolic); y = a^x (exponential), and y = |x| (absolute value). The examples I have listed are just a small sampling of the parent functions that exist. The "children" that are formed from these parents are formed by transformations which are translations, rotations, reflexions, dilations, or some combination of thereof. In spite of the transformation that may occur to the parent function to create its "child", the offspring still retains the basic characteristics that defines its parent.
An indefinite integral creates a general antiderivative which when graphed forms a family of antiderivatives. On the graph below, I have depicted a sample of a family of antiderivatives on a slope field.
I have four siblings, one sister and three brothers. My sister refers to us as the Fabulous Five. I have an older brother and sister. My brother is nine years older than I and my sister is seven years older. My younger brothers are identical twins and are a year and a half younger than me. I am sure that my parents remark, as my wife and I do, on the differences that exist among their children and on the remarkable, similar personality traits related to themselves.
I was contemplating the probability of the order in which the Fabulous Five were born; M, F, M, M, M. This probability is the product of each individual probability since each birth can be considered an independent event. I thought that the probability of gender would be equally likely so the P(Female) = P(Male) = 0.5 which would form a theoretical probability of (0.5)^5 = 1/32 = 0.03125. However, nature (empirical probability) adapts accordingly. With some variance due to environmental changes the P(Male) = 0.51 and the P(Female) = 0.49. There are several theories on why the probabilities are not equal. One of the most interesting to me is that nature adjusts the probability slightly due to the survival rate of males past the first 6 months of birth and the historical early demise of males before their female counterparts. Using nature's probability, the probability of Russ, Marilyn, Chuck, Bill, and Bruce is approximately 0.03315.
Another analyzation of family is birth order. The rationalization for the importance of birth order in the development of an individual's personality is a result of the changing interaction that parents have with each successive child. The basic traits of birth order are defined for a family of three with adjustments for number of siblings, gender, and age differences. The basics are defined as follows: The oldest is a perfectionist, a list-maker, well-organized, self-sacrificing, conservative, critical, serious, scholarly, reliable, conscientious, structured, cautious, controlling, loyal, and an achiever. The middle child is a people-pleaser, somewhat rebellious, thrives on friendships, has a large social circle, and is a peacemaker. The youngest is fun-loving, uncomplicated, manipulative, outgoing, an attention-seeker, and self-centered.
Gender, number of siblings, and age differences play an important role in our birth order structured according to "The Birth Order Book" by Dr. Kevin Leman. The first born of any gender is likely to take on first born characteristics. Our family had very traditional role assignments. My oldest brother was assigned outdoor jobs such as lawn mowing, painting, and helping my father. My sister was assigned duties that helped my mother such as cleaning, cooking, and "taking care of the babies". These roles cemented the first born characteristics for each of them.
Age difference is another important factor in my family's structure. When there is a span of more than five years between children, "a second family" is formed. I am the oldest of this "second family" and took on the roles of the oldest, the middle child, and the youngest.
The final spice that added flavor and complexity to our family structure was the birth of twin boys. Usually twins place additional pressure on any sibling close to their age. As twins, my brothers have many characteristics of the youngest. They have a confidence and "swagger" that I admire and envy.
The last part of dynamic that I am focusing on is called "The Sibling Effect". I recently watched a Ted Talk entitled "The Sibling Bond" in which the speaker, scientist Jeff Kluger, makes a pitch on how interactions between siblings model us to what we are today. There are 21 possible dyadic relationships in my family. These relationships will probably be the longest relationships I will have. How impactful were these relationship in forming my personality and how do they impact me now? I don't know. Kluger gives very little science in his talk or his book. I do agree that squandering my sibling relationships is foolish. Recently, my siblings and I have come together in managing my parents' affairs. I found that I leaned on the knowledge and expertise that they have garnered. Our love for our parents is apparent.
Desmond Tutu said, "You don't choose your family. They are God's gift to you as you are to them."
