2005 Curt Stern Award address. Exploring along a crooked path

Staking out curves is an essential process in construction to ensure the accurate alignment of structures along a curved path. This task involves positioning stakes at calculated locations corresponding to the curve's design, effectively translating plans into physical markers in the field. The process begins by determining the geometric parameters of the curve, including the radius, central angle, and tangent distances. These parameters are critical for identifying key points such as the Point...

In the site survey of a four-sided traverse, internal angles are essential to ensure geometric accuracy. The survey revealed that the sum of the measured internal angles was 359 degrees and 48 minutes, which is 12 minutes less than the expected 360 degrees. This discrepancy signals an error likely arising from measurement inaccuracies during the fieldwork.To rectify this error, the adjustment process involved distributing the 12-minute shortfall equally across the four internal angles. By...

Curvature describes how rapidly a curve changes direction at a particular point. A curve with a small curvature bends gently, while a curve with a large curvature turns sharply. For a space curve, the position of a moving object can be described by a vector-valued function r(t), where t often represents time. The direction of motion is determined by the tangent vector, and the unit tangent vector is obtained by normalizing the derivative of the position vector.The unit tangent vector gives the...

We typically love the people with whom we form relationships, but the type of love we have for our family, friends, and lovers differs. Robert Sternberg (1986) proposed that there are three components of love: intimacy, passion, and commitment. These three components form a triangle that defines multiple types of love: this is known as Sternberg’s triangular theory of love. Intimacy is the sharing of details and intimate thoughts and emotions. Passion is the physical attraction—the flame in the...

During the 1950s, the landmark Robbers Cave experiment demonstrated that when groups must compete with one another, intergroup conflict, hostility, and even violence may result. At the Oklahoman summer camp, two troops of boys—termed the Rattlers and the Eagles—took part in a week-long tournament. During this time, their negativity culminated in derogatory name-calling, fistfights, and even vandalism and destruction of property. However, this work also revealed that such tension could be...

Altered states of consciousness represent significant deviations from one's normal mental state. These deviations can range from subtle changes in awareness to profound transformations in perception, thought processes, and sensory experiences. Altered states of consciousness can be triggered by various factors, including drug use, meditation, hypnosis, illness, or even intense fatigue.
The ingestion of substances like stimulants or hallucinogens leads to chemical alterations in the brain that...