The whole is not always the same as its parts

You are going to buy a new home.  The house is 2000 square feet on a 3/4 acre lot.  You hire Rich (the termite inspector) to check it out before you buy. After all, no one wants to buy a house with termites. 

  • Good news!  The house passed.  No termites.  Thus, you buy the house.
  • Bad news!  A month after the sale closes you discover - termites.  

What?  How could this happen?

 
You go back and look a little deeper in the method of inspection Rich relied upon.  You find out his methodology was to only check "one square inch" of the floor in the house.  When he did not find anything wrong within the "one inch" he assumed everything else was also termite free.
 

How do you feel now?
 
A part of something does not always represent the whole. Determining how many termites are in "one square inch" of a house does not really answer the question whether you have a termite problem.
 
The termite inspector committed what logicians call the all things are equal fallacy.  This occurs when when it is assumed, without justification, that conditions have remained the same at different times and places.
 
The same danger is present when attempting a forensic measurement.  For example, in a typical DUI case where a blood sample is taken, the lab will test less than a M&M size sample of blood.  However, in Arizona the legal definition of an alcohol concentration is grams per 100 micro-liters. Translation, the legal definition of an alcohol concentration requires multiplying the results of the "one inch" by about 1000 (assuming the M&M is about 100 micro-liters).
 
The danger is assuming the rest of 1000 micro-liters (or 100 milliliters) has a proportional amount of ethanol in it.  Small errors multiplied by 1000 can easily mislead you to believe that a person's alcohol concentration is above a legal limit when it is not.
 
Like the termite inspection, it is up to the crime laboratory to prove their justification for assuming using such a tiny amount below the legal definition of an alcohol concentration answers the question - is the person above the legal limit?  After all, no one wants termites...or people being wrongfully convicted.
 
 

Measuring and Counting

 MEASURING

Measuring is the assignment of a number, and all the uncertainties of that of that number, to something.  The purpose of assigning a number is to give meaning to the object measured.

  • Uncertainty: A bag placed upon a scale shows its weight to be 41 pounds.  If the bag must be less than 50 pounds, then the number produced by the scale indicates it meets this requirement.  However, you must know how far from its true value might the 41 pound number be off by?  Uncertainty is the amount of doubt (e.g. the amount of possible variation) you should expect that number might be off.
  • Fit for Purpose: Assume there are two scales.  The same bag weighing 41 pounds is place on both scales.  However, it was determined that Scale A produces numbers that can be off by as much as 30 pounds.  It was also determined that the number produced by Scale B merely off by as much as 3 pounds.  Knowing the amount of uncertainty contained in the number helps distinguish counting from measuring.  Knowing the uncertainty allows you determine if the measurement is fit for the purpose of determine if the object exceeds 50 pounds.

Measuring relies upon estimation.  The choice of data, the methodologies employed, and level of quality measures used tells you how confident you can be in the estimation.  Once you have a reliable estimation of how close a number may be (or not be) to the true value, you can make informed decision as to what purposes the number can be used - and not used.  

 

COUNTING

Counting is not the same as measuring.  However, the two are often confused.  Counting is usually a technique within a measuring process (methodology).  Counting can result in an exact number.  However, measurement will never claim to represent a true value. Measurements are merely estimations.

Counting an exact amount of something is often not possible or practical.  The thing you are intending to measure (the measurand), the matrix it is found in, or the level of accuracy required may make counting impossible.   Thus a system is needed to provide a reliable estimation which you can rely upon.  

Some things to take into account when making an estimation:

  • Distinguishing: Some molecules are so similar to others that it is often impossible continuously distinguish them from each other.  Thus, they cannot be easily counted.
  • Location: Some substances are contained in places we cannot practically enter to count them.  The best way to know how much alcohol is affecting a person's brain at a particular time would be to take a sample of brain tissue.  However, society has not yet determined such a procedure falls outside the protections of a person's 4th Amendment rights.
  • Gas Chromatographs: The results of a gas chromatograph are often used to determine whether a person's alcohol concentration is above a legal limit in DUI cases.  However, the machine does not measure a person's blood alcohol concentration.  If properly used, the machine merely counts the number ethanol molecules in a gas portion of a headspace vial.  Thus, it indirectly counts a microscopic amount ethanol from a tiny sample.  

A measurement based upon a machine's indirect count of a substance results from combining it with algorithms, numerous assumptions, and historical data regarding the past performance of the machine (and software) used in the process.  This is known as an uncertainty calculation.

In this manner, measuring requires much more than counting.  Measuring requires more than merely assigning a number to an object.  More importantly, one can assign a number to an object but not create a measurement.  When this occurs it is not a measurement.  It is a misrepresentation.

 

Counting is what you do to get a number.  Measuring is what you do if you want to know the truth about the number.