In particular, I find it odd that a newborn baby is given a "length" whereas I as an adult am given a "height" even though the same dimension is being measured. The difference in use seems to be that a baby must be measured lying down whereas my height would be measured standing up. If I were measured lying down, would my height or length measured, most likely we would still say height.
The difference between is height and length is based on context rather than perspective. Basing it on perspective would imply that it would depend on a person’s view and could vary. A baby’s recorded measurement is its length due to the fact that it must be taken lying down. With length being the measurement from end to end, it applies here. This is not due to the perspective of the doctor or nurse, but due to a systematic approach that was decided for consistency as well as taking in other considerations (such as the baby’s safety in attempting to make it stand when it's not physically able to). A person, barring physical or mental impairments, can be reasonably expected to stand. With height being the measurement from base to top, a person would have their measurement taken down as height.
Perspective - Cambridge Dictionary
A particular way of viewing things that depends on one’s experience and personality
Length - Wikipedia.com
In geometric measurements, length is the most extended dimension of an object.
Length may be distinguished from height, which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length.
Source link: https://en.wikipedia.org/wiki/Length
Length - Merriam-Webster’s Dictionary
The distance from one end of something to the other end : a measurement of how long something is.
Source link: http://www.merriam-webster.com/dictionary/length —
Height - The Free Dictionary
The distance from the base of something to the top.
Source link: http://www.thefreedictionary.com/height
Height is the distance from the base to the top whereas length is always the longest of the three dimensions, height, length, and width.
I would superimpose an assumed restriction for inanimate objects of being in a stable position for statistical categorization.
There are two related but distinct meanings of height here: (1) the measure of the principle dimension of an adult human, and (2) the tallness of something in the direction of a gravitational field.
Which one is used depends on the particular context. If you were lying down in a bed, your height would be meaning #1. If you were lying down on a train that was about to go through a tunnel, your height would be meaning #2 (that is, the height of the highest part of your body at that particular time).