Let be a basis for a vector space V. Prove that is also a basis for V. Let be n 1 distinct real numbers. Define polynomials by These are called the Lagrange polynomials associated with a0, a1,..., an. [Joseph-Louis Lagrange (17361813) was born in Italy but spent most of his life in Germany and France. He made important contributions to such fields as number theory, algebra, astronomy, mechanics, and the calculus of variations. In 1773, Lagrange was the first to give the volume interpretation of a determinant (see Chapter 4).] 59. (a) Compute the Lagrange polynomials associa
Chapter 13 Personality Ways of looking at the self: Personality ● A person’s individual characteristic patterns of thoughts, feelings, and behaviors ● Persisting over time and across situations Freud ● He “discovered” the unconscious ● People came to him with problems like a numb hand, and he attributed it to the unconscious mind. ● Free association if he had someone freely talk, he would find a hint of the subconscious ● the “problem” was that you had sexual tensions ● His name for his theory and his treatment technique: psychoanalysis ● “Freudian slips” “hello my beheaded, I mean, my beloved” Freud’s Personality Iceberg ● Personality arises from conflict between impulse and restraint ○ Id (pleasure) ○ Ego (reality) ○ Superego (our moral compass) ○ The ego is the mediator Freud’s theory of Psychosexual Stages ● The id is focused on the needs of erogenous zones, sensitive areas of the body ● People can get fixated at one stage ● Stages: ○ Oral (018 months) pleasure centers on the mouth ○ If you did not make it through this stage, you always need a cigarette in your mouth Male development issues ● “The Oedipus complex” boys in the phallic stage develop unconscious sexual desires for their mothers and view their fathers as a rival. ● Resolution: boys identify with their fathers rather than seeing them as a rival Defense Mechanisms (Freud) ● We are anxious about our unacceptable impulses, so the ego represses this anxiety with the help of defense mechanisms (unconsciously distort reality) Assessing the unconscious: ● Freud tried to get unconscious themes to be projected into the conscious world through free association and dream analysis ● Dream analysis ○ Skyscraper = penis ● Projective tests ○ Ambiguous prompts should reveal the inner workings of your mind ○ Ie. thematic apperception test: view ambiguous pictures and make up stories about them ○ Rorschach test: “what do you see in these ink blots” ○ Problem: results don’t link well to traits and different raters get different results (low validity and low reliability) Evidence has updated Freud’s ideas: ● Development is life long ● Peers have more influence on personality ● Dreams as well as “Freudian slips” don’t reveal deep unconscious conflicts and wishes ● Traumatic memories are usually intensely remembered, not repressed ● Few objective observations, few testable hypotheses ● Gender and sexual orientation seems to be more a function of genetics Humanistic theories of Personality ● The “third force” in psychology ● 1st force freud ● 2nd force behaviorism (no free will, you are a product of your environment) ● 3rd force: ○ They studied healthy people and the conditions that support healthy lifesty es ● Maslow: the self actualizing person ○ People are motivated to keep moving up a hierarchy of needs ○ self transcendence ● Carl Rogers ● 3 conditions that facilitate growth and fulfillment ● If our selfconcept is positive, we tend to act and perceive the world positively ● The 3 conditions: ○ genuineness, acceptance, and empathy Critiquing the Humanist Perspective ● Encouraging selfindulgence, self centeredness ● The human capacity for evil ● Rogers saw “evil” as a social phenomenon, not an individual trait ● Humanist response: selfacceptance is not the end; it then allows us to move on and do good in the world and loving and caring for others. Trait theory of personality ● Trait ○ A characteristic pattern of behavior or a predisposition to feel and act a certain way. Ie honest, shy, hard working ● Trait theory of personality ○ We are made up of a collection of traits that can be identified and measured, traits that differ from person to person ● Factor analysis and the Eysencks’ personality dimensions ○ Compass of stable, unstable, extraverted, and introverted ○ Identify statistically correlated clusters of behavior ● Traits; rooted in biology ● Brain: ○ extraverts seek stimulation because their normal brain arousal is relatively low ○ Introverts have too much brain arousal so they seek less stimulation ● Body ○ The trait of shyness appears to be related to high autonomic system reactivity (an easily triggered alarm system) ● Genes ○ Selective breeding of animals, can select for traits (shyness, sociability, etc.) suggesting genetic roots for these traits. The big 5 personality dimensions: ● Conscientiousness ● Agreeableness ● Openness ● Extraversion ● Neuroticism Questions about traits ● Stability ○ Change over the lifespan; not much. With time, personality traits become more stable ○ Everyone in adulthood becomes more conscientious and agreeable ○ Genes account for 50% of the variation for most traits Predictive value: do traits predict behavior ● Conscientiousness grades, healthy lifestyle behaviors ● Extraversion a lot of time spent in social activities ● happiness low neuroticism, high extraversion, agreeableness ● Marital satisfaction The personsituation controversy ● Are your behaviors due to situations or stable traits ● Specific behaviors can vary in different situations ● We change interests, careers relationships ● Averaging your behavior across many occasions does reveal distinct traits ● Personality traits can even predict mortality and divorce
