Archive for the ‘Uncategorized’ Category

A Hint That Cavalieri’s Name is a Misnomer

July 30, 2013

It seems that plenty of people think that Cavalieri’s theorem is being applied when doing a Cavalieri estimator. It’s not. Cavalieri’s theorem uses a comparison between 2 objects of the same height.

Think about it. When does anyone measure the height of the object that they are studying? There is no need to do that. There is of course an estimate of the height of the object, but no measurement. Cavalieri’s theorem requires two objects to be the same height. Not close to the same height or roughly the same height, but the exact same height.

Back in the 1950s it was well known that the 1902 paper describing the application of Cavalieri’s theorem had been incorrect. That’s long before the term stereology was coined.

Despite it being rather clear that the Cavalieri theorem does  not apply (remember that no height measurements are taken or required) there are still those that incorrectly claim a link.


Failure of the appeal to authority form of argument

April 24, 2012

One of the telling issues with people is when they avoid the facts of the case and instead resort to an argument form called an appeal to authority. This usually indicates that the person making the appeal knows they are wrong and are making a last ditch effort to avoid admitting they have made a mistake.

The appeal to authority can come in many forms:

  1. Prof. Whatchamacallit says that
  2. I read it in a book
  3. I wrote a book
  4. You are not as smart as I am
  5. I’ve got an advanced degree
  6. I saw it on YouTube

In some of the comments to this blog there was the claim that the person was an authority. The appeal to authority was that since they were an authority they must be right. Really? An authority?

If someone writes a book and can’t get simple issues correct such as when something happened, or a person’s profession as clearly stated in the referenced article, or the definition of terms as stated by the author in the article then I say, read the articles. Read the articles and fix the next edition of the book.

So how does an “authority” make so many simple mistakes.

It might be proofreading?

It might be easier to make stuff up than to do actual research?

It might be indifference?

It might be hubrus that prevents someone from checking what they think might be right?

We all deal with these so-called authorities all of the time. It might be a boss, or a clerk, or a sports/politics/movie/scotch/comic book or whatever self proclaimed expert. The discussion should be about the facts and not how pompous someone can be.

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.

Wicksell and the Corpuscle Problem

April 9, 2012

Again, I strongly disagree with your statements and conclusions. You still fail to understand the importance of these works in relation to current stereology practice. Instead, you seem rather obsessed with parsing words. <Irrelevant demands redacted>

So you disagree. Fine. How do you explain the following huge mistakes.

 Wicksell was a Swedish physician interested in quantification of thyroid globules. He realized that counting the number of intersections per unit (Na) on random 2-D planes through a matrix containing 3-D objects provides a biased estimate of the number of 3-D objects per unit volume (Nv). The sources of this bias, which Wicksell referred to as the Corpuscle Problem, are the object’s size, shape, and orientation within the matrix. Though this relationship had been known for centuries, Wicksell was one of the first to make a thorough analysis. For more information on this topic, see my book published by the <removed>

  1. Wicksell was not a physician.
  2. Wicksell did not assist in the study of the thyroid

Wicksell was not interested in the number of profiles as representing the number of objects. A rather cursory read of the article would have told you this.

What I suspect is that you have not read ANY of the relevant material. Nothing. From the outset Wicksell approach the problem from a 3-dimensional perspective.

You claim that a bias, which Wicksell did not consider, or address, was named the corpuscle problem. You might want to take the time to learn what the corpuscle problem is all about. It’s not that complicated.

Here is a hint. In the 1925 paper Wicksell only considers balls. Thus the shape and orientation are moot claims on your part. As I have stated before Wicksell was interested in determining the number of balls regardless of the size distribution.

Please take the time to read Wicksell’s paper. The math is reasonable and interesting. You’ll learn who Wicksell was and what organ he investigated for a researcher at the university.

Comments and Response

April 9, 2012

You seem to be intentionally trying to muddle the situation. As a measure of area fraction (Aoil/ Arock), Delesse cut out and weighted outlines of oil phases traced onto paper (Aoil), and then did the same for the reference area (Arock). He then used a chemical method to determine volume of oil in the rock (Voil), and Archimedes method to measure the volume of the rock (Vrock). The Delesse principle simply show that for a random cut through a volume of rock that contains an oil phase, the area fraction is equivalent to the volume fraction (Aoil/ Arock = (Voil/ Vrock). Rosival and Glagolev used the same approach to show that a similar relationship with volume fraction holds for line fraction (Loil/ Lrock) and point fraction (Poil/ Prock), respectively. Would the blog writer care to suggest a better figure to illustrate this principle? For more information on this topic, see my book published by the <title withheld>

There are quite a few glaring mistakes here:
1.Delesse did not weigh paper.
2.Delesse was studying ores, not oil in rocks.
3.Delesse did not use the Archimedes method in his analysis.
4.It is not known if Delesse used chemical analyses to compare to his geometrical method
5.Delesse did not use random sections. In fact the argument was over what preferential orientation to use
6.He claimed that the area fraction was the same as the volume fraction, but he did not prove it
7.The spelling is Rosiwal
8.Rosiwal did not use a similar approach
9.Glagolev did not show anything about the method he used
10.Glagolev built a device to implement an existing method The method had been in use for years in Europe before Glagolev built his device.

As far as the figure being misleading, the Delesse principle was only applied to macroscopic analysis. The Rosiwal method was only applied to microscopic analysis. Glagolev built a device for a microscope. Glagolev’s device used a single point for a field of view.

I have seen the book and the book repeats these same mistakes. Time to correct these mistakes.

Delesse weighed metal, not paper.
Delesse did not use a reference volume.
Neither Delesse or Rosiwal or Glagolev ever proved anything.

There is not a single paper published using Delesse’s method. Not until Shand published was there a published paper using a geometrical method for modal analysis. That’s over 60 years after Delesse published.

Images that do not reflect the material

March 26, 2012

I was recently chastised by a <name removed on request> about my posts pointing out that the posted online history of stereology is muddled. It is as I have shown in the last 3 posts.

I also noticed that the artwork that goes with these historical posts is also quite off the mark.

Consider the image posted with the Cavalieri comments. It shows an object sectioned uniformly at a distance T. Cavalieri never did that. What is missing that is an essential part of the Cavalieri process is the height of the object shown next to an object of the same height.

Next to Delesse are 3 images. The images are labeled Delesse, Rosiwal, and Glagolev. The lines are straight. Rosiwal used paths and some of them were curved. The lines intersect. Rosiwal thought that his method required that the lines had to be far enough apart to avoid sampling any rock particle by more than 1 line. Finally Glagolev used a single point for his sampling. Glagolev did not invent point counting. He invented a machine to do point counting. In fact, his microscope point counting machine allowed counting rates close to what modern motorized stereological systems can offer.

The Buffon image shows an interesting situation. Buffon was prone to giving solutions without showing the derivation. This parquet floor is one of the problems where Buffon was wrong. His solution for the orthogonal lines is not correct. The correct solution was given by LaPlace in 1814, well after the death of Buffon. LaPlace did not name the origin of the problem so Buffon is not mentioned.

Good images support the story, not add more mud to the waters.

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.

Who needs to use the Proportionator

April 2, 2010

Anyone doing stereology and counting cells needs the proportionator.

  • If you use your stereological equipment more than once a year you need the proportionator.
  • If you have tens or hundreds or more tissue samples to process  you need the proportionator.
  • If you find the the CE is often too large then  you need the proportionator
  • If you have plans to increase your research you need the proportionator
  • If you are moving to a larger experiment with more lab animals you need the proportionator

The proportionator is the stereological tool that makes more effort easier to handle. It is the only tool today that makes it possible to obtain the best results with the least effort. Weibel is quoted as saying “Do more, less well.” The fractionator makes it possible to “Do better, less effort.”

Sampling with equal probability

September 22, 2009

I left off with an issue that is likely to confuse many people. I appear to say yes and no to the equal probability of sampling issue.

The difference is in what infers what. If cells are sampled with equal probability, then it is true that the sampling method could lead to an unbiased answer. There may other factors that prevent the estimate from being unbiased, but the equal probability of sampling is a good start to obtaining an unbiased result.

On the other hand, if cells are not sampled with equal probability it does not necessarily mean that the results are biased.

There are a number of ways in which sampling with unequal probability leads to a biased result. A well known way is profile counting. That is what most people still do today when they count “cells.” In fact, no cells are counted, just profiles seen under the microscope. The thin sections reveal slices through cells. These slices of the cell are called profiles. A number of ways have been conceived to deall with profiles vs cells.
1. Don’t do anything
2. Skip sections to avoid double counting
3. Abercrombie
4. Floderus
5. Rose-Rohrlich

None of these methods leads to an unbiased result.

The proportionator does lead to an unbiased result and makes use of an interesting form of PPS.