Cavalieri is attached to point counting due to a 100 year old mistake

Your posts are ridiculous and simply add unnecessary confusion to the field. “Rosival” vs “Rosiwal” is a joke since languages without “w” use a “v” so the name appears both ways. No one but you claims Cavalieri did stereology, the term was not even invented until 1962, centuries after he died. The work he did forms the theoretical basis for the method used today, in combination with point counting, to estimate total volume of 3-D objects. If you want to be taken seriously, you need to tone down the vitriolic rhetoric, which is out of place for scholarly scientific exchanges.

You have called me a creep multiple times. That is vitriolic.

Rosiwal was Austrian.  The German language has a ‘w’. Not sure what language you are talking about.

I have never stated that Cavalieri did stereology. That is a straw man argument.

Regardless of when the term stereology was coined, stereology was done long before that time. Rosiwal traverses, quadrats, bayonet probes, Shand micrometer, Ford’s device, Glagolev’s device, Steinhaus’s work, and many more methods and devices were in use before the coining of stereology. The term was coined to provide a description of the methods long in use by many disciples.

Cavalieri’s work does not form the theoretical basis for stereology. It has nothing whatsoever to do with point counting. It involves the comparison of objects of equal volume or area. You might want to check with a mathematician to learn why Cavalieri’s theorem is not related to point counting.

Point counting was not developed from Cavalieri’s theorem. It was invented at least 2 independent times, neither of which deal with anything remotely involving Cavalieri. The reason that the name Cavalieri appears in the literature is a mistake in 1902 in which a geological paper improperly applied the Cavalieri theorem in a model based analysis of Manhattan rocks. The name stuck even though it is a misnomer. Chayes explains the mistake quite well. One of the inventions of point counting, the second invention time I am aware of, took place at the NIH. The first invention took place years before Glagolev published his implementation. The first invention was not proved although the mathematician involved with the group had pledged to provide a proof. The second invention has a rather shaky proof. A good example of a proof showing that point counting works is in DeHoff’s book. That proof shows that the estimator is unbiased.

There really isn’t anyway to connect Cavalieri with point counting. Cavalieri compares two objects A and B and then declares that if the comparison holds, then A and B have the same volume or area. That isn’t anything at all like point counting. It doesn’t even have anything at all to do with the Delesse principle or Rosiwal’s work.


6 Responses to “Cavalieri is attached to point counting due to a 100 year old mistake”

  1. Anonymous Says:

    Swedish, for example, did not have a “w” until 2006.

    • stereologist Says:

      It is a non-issue since Rosiwal was not Swedish and he always spelled his name with a ‘w’. Instead of wasting time with ‘w’ not appearing in languages that are not involved such as Mandarin and Urdu you might consider fixing mistakes such as:
      1. Claiming Wicksell was a physician
      2. Delesse’s first name
      3. Proper definition of the corpuscle problem
      4. Suggesting Buffon did sampling
      5. Delesse studied oil in rocks
      6. Delesse used random sections
      7. Delesse used a reference volume

      PS According to the Wikipedia on the Swedish alphabet you are wrong about ‘w’. In fact I think Raoul Wallenberg would be surprised with your claim. Your link states “Words spelled with the letter “W” are rare in Swedish”. To claim Swedish did not have a “w” is false. Did you thin I would not read your link?

  2. Peter Mouton Says:

    Point counting, my creepy invisible friend, is used to estimate the sum of areas (∑A) on the cut surfaces of an object, which is used in combination with the Cavalieri principle to estimate the total volume using V = ∑A • T, where T is the distance between the cut surfaces. Now stop writing about things you do not understand.

    • stereologist Says:

      I know about point counting. I also know that the Cavalieri theorem involves the comparison of objects.

      You might consider actually reading about Cavalieri’s work and learning.
      1. Cavalieri did not estimate
      2. Cavalieri did not use regularly spaced sections

      The Cavalieri principle you refer to has nothing whatsoever to do with Cavalieri’s work.

  3. Anonymous Says:

    You miss the point again. The letters “w” and ‘v” are used interchangeably in many languages, meaning you cannot claim “Rosival” is incorrect spelling of “Rosiwal.”

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