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		1.3.8— Biological Implications of Scaling Relationships

		1— No Unique, ''Correct" Value for a Measurement

		The scaling relationship tells us how the value measured for a property, such as length, area, or volume, depends on the resolution used to make the measurement. There is no one value that represents the "correct" value of the property being measured. The value measured for a property depends on the resolution used to make the measurement.

		2— Measurements made at different resolutions will be different.

		The value measured for a property depends on the resolution used to make the measurement. Thus measurements made at different resolutions will yield different values. This means that the differences between the values measured by different people could be due to the fact that each person measured the property at a different resolution. It also means that it is very important to state the resolution at which a measurement is performed.

		3— Importance of the Scaling Relationship

		Our method of analyzing the data must be consistent with the characteristics of the data if the results are to be meaningful. Only if the analysis properly characterizes the data can it give us clues about the nature of the process that produced the data. The measurement of the value of a property at only one resolution is not useful to characterize fractal objects or processes. Instead, we need to determine how the values measured for a property depend on the resolution used to make the measurement, namely, the scaling relationship. This change, from measuring a single value to measuring how the values depend on the resolution is called a change in paradigm.

 

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