Typical errors in online stereology information

Recently an old article of sorts has been spread around the internet. This article makes a number of claims that are not grounded in truth.

Consider the following:

In 1637, Bonaventura Cavalieri, a student of Galileo Galilei in Florence during the high Italian Renaissance, showed that the mean volume of a population of non-classically shaped objects could be estimated accurately from the sum of areas on the cut surfaces of the objects (right). The Cavalieri Principle provides the basis for the volume estimation of biological structures from their areas on tissue sections.

It’s true that Cavalieri did publish something in 1637 and he was associated with Galileo. Most of the rest is quite wrong. For instance Cavalieri was not a student. He was a professor at the same university as Galileo. Galileo and Cavalieri had somewhat of an academic problem since Galileo had his own ideas on the subject called infinitesimals. Cavalieri’s ideas did not agree with Galileo.

The real problem here is the math. The statement here about the work of Cavalieri is completely wrong. What Cavalieri’s theorem does is to compare the volumes or areas of two objects of equal height. Let’s consider only volumes here. Two objects are the same height if two parallel planes touch the tops and bottoms of both objects. Cavalieri goes on to prove that if any parallel plane in between the top and bottom planes intersects the two objects and the areas on the 2 planes are the same area, then the volumes are the same.

The reason that Cavalieri’s name is associated with the estimation or measurement of volumes is due to the same type of misuse of Cavalieri’s work. In 1902, two geologists mistakenly connected Cavalieri’s theorem to volume estimation of crystals observed under the microscope. The name stuck. It’s just a misnomer.

Here is another mistake from the same online article.

In 1777, Count George Leclerc Buffon presented the Needle Problem to the Royal Academy of Sciences in Paris, France. The Needle Problem supplies the probability theory for current approaches to estimate the surface area and length of biological objects in an unbiased (accurate) manner.

The records of the RAS, the Royal Academy of Science, show that Buffon gave his presentation in 1733. His name was not Buffon. That’s another mistake in this online article. The name Buffon was a nickname. It comes from a town his ancestors bought. They owned the town and collected taxes for the King. His name was George LeClerc. None of my research shows he was a count, i.e. French royalty. That is yet another mistake.

If you look online you will see that the date 1777 is common. How did this mistake of 44 years come about? Part of it is poor research by the authors. The other part is a lack of understanding of the date. The person that discovered the work of Buffon was Crofton. He was looking over some books and came across an odd entry in a book by Buffon. In 1777 Buffon published a book on Natural History and added a number of odds and ends to the book. One of the add-ons was a paper he had written years earlier to get into the RAS. That is what the records of the RAS show. Buffon was known for adding all sorts of off topic entries into the backs of his books. Crofton recognized the importance of this work and mentioned it and the date of publication, which was 1777.

Today the date of publication is sometimes given erroneously as the date when Buffon presented the work.

In 1815 LaPlace corrected some of Buffon’s work from his 1733 paper. LaPlace did not name the person who’s work he was correcting. Another little item is that in 1736 Buffon did write his second article on the idea. Finally, in 1780 Buffon died. He had been in ill health and was not developing new ideas in the last few years of his life.

Another mistake is the following:

In 1847, the French mining engineer and geologist, Auguste Delesse, demonstrated that the expected value for the volume of an object varies in directly proportion to the observed area on a random section cut through the object. The Delesse Principle provides the basis for accurate and efficient estimation of object and regions volumes by point counting.

Delesse had a good idea. He did not demonstrate or prove. He developed an idea to estimate volume fraction. He never proved it worked. The method was so difficult to implement that the idea was for all intensive purposes never done. A major misleading suggestion is that the method of Delesse involved point counting.

The article is about as accurate in its content as articles about 2012, and claims that the ancient Egyptians lit their temples with electric bulbs. There is some semblance of truth, but the details are a mess of mistakes.

How can anyone suggest that Delesse had anything to do with point counting, or expected values?

How can anyone suggest that the Cavalieri principle deals with one object?

A fair assumption is that the other details provided are just as unreliable as the other claims. It ‘s largely made up and done with a bit of bravado.


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