If human height were quantized in 1-cm increments, what would happen to the height of a child as she grows up: (i) the child's height would never change, (ii) the child's height would continuously increase, (iii) the child's height would increase in jumps of 6 cm, or (iv) the child's height would increase in 'jumps' of 1 cm at a time?

Key Concepts

Quantization

Quantization refers to the concept that certain properties, such as energy or height in this case, can only take on discrete values rather than a continuous range. In the context of the question, if human height were quantized in 1-cm increments, it implies that height changes would occur in fixed steps rather than smoothly. This concept is often discussed in quantum mechanics but can be applied to other scenarios involving discrete changes.

Discrete vs. Continuous Growth

Discrete growth means that changes occur in distinct steps, while continuous growth allows for gradual changes without fixed increments. In the scenario presented, if height changes in 1-cm increments, it exemplifies discrete growth, where a child's height would only increase in whole centimeters rather than any value in between. Understanding this distinction is crucial for interpreting how the child's height would change over time.

Incremental Change

Incremental change refers to the process of growth or change occurring in specific, measurable amounts. In this question, the height of the child would increase in increments of 1 cm, meaning that each time the child grows, her height would increase by exactly 1 cm. This concept is essential for determining the nature of the child's growth pattern and understanding the implications of quantized height.