Posts Tagged ‘science’

Why Cavalieri and Buffon were not stereologists.

April 10, 2012

Cavalieri was a mathematician that was trying to solve a number of problems involving volumes and areas. He never did any work that is employed in stereology unless you want to consider crediting him with an initial attempt at calculus. Like many other contemporaries such as Galileo and Roberval he was attempting to come up with a theory of infinitesimals. He and others understood that there were problems with their approaches.

Buffon solved a number of problems involving geometry and probability. Unlike previously solved probability problems his work involved continuous values. Cards, dice, and coin flips are discrete events with a countable number of outcomes such as 6 outcomes for the roll of a die.

Neither Cavalieri or Buffon applied their work to areas considered in stereology. Later mathematicians saw how these ideas could be applied. Steinhaus and Tomkeieff and others extended the ideas.

Delesse and Rosiwal produced ideas but the implementations were onerous. They did not prove, but were pretty sure their ideas worked. Most of the rest of the geological community was skeptical.

It would take the Shand recorder to provide the first usable instance of a stereological procedure. You might say that Shand’s device marks the start of actual stereological research. With his device comes the first published works using what are recognized today as stereological methods.

Continued exploration of the muddling of stereological history

March 26, 2012

Here is another part of the muddled history of stereology.

In 1847, the French mining engineer and geologist, Auguste Delesse, demonstrated that the expected valuefor[sic] volume fraction of an object varies in direct proportion to the observed area fraction of the object’s profile on a random section through the material containing the objects of interest. Today, by point counting, a derivative of the Delesse Principle, provides the basis for accurate and efficient estimates for object and regions volumes.

The first obvious muddled issue is the name. The first name of Delesse is Achille, not Auguste. The name Auguste is the first name of Rosiwal. Is this part of the confusion?

Delesse was  interested in what is known as modal analysis. He wanted to know what fraction of the rocks were of a particular type of mineral. He developed a technique so arduous to accomplish that he only performed it a few times and no one else did it.

Delesse did not use random sections. One of the big questions was the orientation that should be used. Those same issues would be discussed well into the 1950s by Chayes.

Is modern point counting a derivative of the Delesse principle. Not really. Point counting had an independent origin. The work had nothing to do with modal analysis. The original work was not even related to volumes. The mathematics might look similar and there is a mathematical relation, but the fact is that point counting was not derived from either Delesse’s work, or Rosiwal’s work.

Digits of precision and software

March 22, 2012

One of the basic notions that kids are taught in school is digits of precision. Even going back to elementary school kids are taught as early as grade 2 about approximate numbers. This is done using rulers that are marked out in units of inches or centimeters. The student has to pick the closest line on their ruler. Later on reading dials covers telling time. The distance and time issues are extended to measurements of volume and even surface area.

The idea is covered again and again especially as the arithmetic is advanced. Computations involving measurements are reduced to the significant digits.

Somewhere along the line this concept is lost as computers are used to perform the calculations. It is unfortunately all too easy to find journal articles which report numbers with 5 or 6 digits of precision. The numbers are copied out of whatever software is being used and pasted into the article being written.

Most stereological work is limited to 2 digits of precision. There might be 3 digits at times.

The measurements themselves are limited to 3 digits. If the measurements are taken from a computer screen, then the screen is often limited to about 1000 pixels. That limits the precision to 3 digits. Due to imaging issues the number of significant digits might be less than 3. Slices and sections cut with a microtome are limited to 3 digits at best. The thickness measurement is limited.

Stereological estimates are often done to a CE of .05. That limits the precision of the results to less than 2 digits.

Report values properly. Do not copy and paste from the software.