This is a collection of questions, organized around each section of Mendel's paper, meant to stimulate group discussions and investigations. There are also links to sets of homework questions for each section of Mendel's paper.
In future editions of MendelWeb I will include
links to commentary and further questions by users, and I hope these
discussions will evolve and continue using both the Readers' Mendel and the Mendelroom. If you would like to submit a
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[1]
Introductory
Remarks
Einleitende
Bemerkullgen
Questions for Discussion
1. Here and throughout the paper, Mendel makes clear that his goal is to find "laws" for the formation and development of hybrids. What did the term "law" signify to someone working in science in 1865, and what does it mean today? Were there any known laws in biology (or botany) in the middle of the nineteenth century? Are there any known laws in biology today?
2. What, if anything, distinguishes carefully designed experiments in contemporary botany and biology from those of physics and chemistry? Would your answer be different if the question concerned th practice of science in the middle of the 19th century?
3. One common characteristic of scientific writing, and scientific papers in particular, is the relative absence of the first person singular pronoun "I". Rewrite the introduction to Mendel's paper, as if you were Mendel, but use the pronoun "I" as often as you can (though try to keep the number of sentences almost the same as in the original text). Does this "I" version have a different effect on you as a reader? Is different information communicated in the two versions?
Questions for Discussion:
1. Mendel is sometimes credited with bringing an experimental method to the study of natural history. How is the study of natural history changed by combining observations and systematizing (the traditional taxonomic method) with experiments? Is the distinction between an observation and an experiment a meaningful one? On what grounds can you assume that the laws and principles discovered by experimenting with/on natural phenomena, are the same as those found by observing natural phenomena?
2. If Mendel's plants had met the first two requirements he mentions, but did not produce offspring with constant, or relatively constant, fertility what difference would it have made to his experiments and/or the meaning of his results?
3. How does Mendel's discussion of the species/varieties distinction compare with Darwin's discussion of the issue in the second chapter ("Variation Under Nature") of Origin of Species?
4. For centuries, some mathematicians have claimed that mathematics is free from the uncertainties of the "experimental method", that mathematics is a kind of "pure reasoning." More recently, with the advent of computers, other mathematicians have claimed that experiments are routinely performed in mathematics. If a mathematician wishes to investigate the distribution of prime numbers between 1,000,000 and 10,000,000 (for example), and writes a computer program to help find these primes and analyze their distribution, is this rightly called an "experiment"?
Questions for Discussion:
1. In this section Mendel describes the differentiating characters, and the first cross-fertilization experiments (though he does not give the results until the following section). Before looking at those results, hypothesize about what different forms might occur when plants exhibiting these different character forms are crossed, and what the different hybrid outcomes would lead you to believe about how these forms are inherited in peas.
2. Mendel reports performing "reciprocal crosses" to find out whether it matters, to the form of the hybrids, which parent donates the pollen and which the egg. Since Hippocrates (460-377 B.C.), theories of heredity in humans have taken various positions concerning the importance of the "male" and "female" contributions to heritable form. What was the prevailing view in the early 19th century concerning the relative influence of sperm and egg in the determination of form in humans?
3. Why do you think Mendel chose to describe these experiments, and present their results, in two different sections of the paper? How does the suspense created by this method of presentation compare to that of other narratives (e.g. a "mystery" novel, or a "ghost story")?
4. Compare Mendel's introduction of his experimental plants and the classification of their characteristics with that from another botanical study from the middle or late 19th century (look at Gärtner's Versuche und Beobachtungen über die Bastarderzeungung im Pflanzenreich (1849) if possible). What are some of the differences noticeable in both the design and rhetoric of Mendel's study?
Questions for Discussion
1. Although novels and poems rarely describe scientific theories in detail, they frequently assume or exemplify theories that were accepted at the time they were written. Find examples of novels, stories or poems, written prior to 1900 that you think assume "blending" or "blood" theories of inheritance, and others (if you can) that assume theories of discrete character inheritance like that found by Mendel in Pisum.
2. Do you agree with the statement: "The claim that a blending theory of inheritance is true of all observable characteristics in plants and animals, is strictly incompatible with a Darwinian theory of evolution"?
3. When Mendel finds examples of hybrids taller than the tall parents, he does not consider this to be a "new" form of height, but just a variant on the parental form. Suppose you were performing Mendel's experiments. What criteria would you use to determine whether a hybrid form was parental, or an example of a new form (e.g. how would you react if three of the peas in the hybrid generation were blue)?
4. Mendel studies only structural traits of his plants, but in humans there have been studies of behavioral traits as well. Do you think there are examples of any behavioral traits that are as "simple" as pea color in Pisum? How would you demonstrate or test your claim?
Questions for Discussion:
1. How do the results reported by Mendel in this section justify drawing a distinction between the appearance of an organism (its phenotype) and its genetic composition (or genotype)?
2. In the same year as Mendel was writing his paper, there appeared a book by the physiologist Claude Bernard, entitled Introduction à l'étude de la médecine expérimentale. Of the use of statistics in the pursuit of scientific knowledge, Bernard wrote:
3. In the homework set for this section, the "square-root of n" rule is introduced as a reasonable measure of expected error. Is it a reasonable measure of error? Since it can be shown that, for a binomial distribution with equi-probable outcomes, the sqrt[n] is proportional to two standard deviations, does that make it applicable to Mendel's experiment? How do measures of expected error differ in physics, chemistry and biology? What are the prevalent measures of expected error in the social sciences? How are such measures justified?
4. It is perhaps easy to read too much into Mendel's paper, to attribute more knowledge to Mendel than he possessed. How is such anachronism to be avoided when reading texts from earlier centuries, and particularly scientific texts?
Questions for Discussion:
1. Suppose you wished to explain not only the inheritance of form but the appearance of new species. Would you have to revise some of Mendel's findings or merely add to them?
2. A few historians of science have argued that Mendel did not actually perform the experiments he describes, but created them on paper, based on a smaller set of experiments he did in fact carry out (see, especially, the article by Di Trocchio). While there is practically no evidence for this claim, it raises an interesting question about the communication of scientific results generally. Suppose Mendel actually carried out none of the experiments he describes in this paper. What difference would it have made in 1865? What difference would it have made when Mendel's paper was "rediscovered" around 1900? What difference would it make today?
3. Is the data reported in this section of the paper "better" than in the previous section? That is, are the data closer or further away from the ratios predicted by Mendel's model?
4. What is your reaction to the following claim: "The chief practical use of discovering laws of inheritance is give those with power an opportunity to use this knowledge to keep and increase their power, and in fact knowledge of the laws of inheritance can only result in the deterioration of the quality of life for the great majority of the world's population."?
Questions for Discussion:
1. Does Mendel's notation, in the combination series model, presume a theory about the "internal nature" of the parental and hybrid plants? What alternative representations could he have adopted that would not have presumed this theory? Do all models, whether in the natural or social sciences, presume theories in this way?
2. What is the difference between a mathematical model of a natural phenomenon, a theory about that phenomenon, and a scientific law that "governs" that phenomenon? Does it matter whether that phenomenon is within the domain of physics or biology or sociology? (You will do well to consider particular cases when dealing with this question.)
3. We saw that in reporting the data from the first and second generations from the hybrids, there was a difference between the "ideal" ratios (e.g. 1:2:1) and the actual ratios Mendel found. If we continued to plant and replant the generations from the hybrids, would this difference between the predicted ratios (e.g. those in the table) and those found by experiment diminish or become greater? In Mendel's terminology: "Would the amount of fluctuation increase or decrease?"
Questions for Discussion:
1. Concerning the data presented for the three-character cross in this section, it might be argued that the data are "too good", that they are much closer to the predicted ratio of 1:2:4:8 than they should be, given the number of plants involved. What is a fair method to use to determine whether data are "too good"? How would you explain the notion to someone who finds the idea of natural phenomena fitting theoretical laws "too closely" a bit peculiar.
2. What is the rhetorical significance (or "force") of using numbers in arguments. Is it foolish to talk about a scientist's use of numbers in a journal article as "rhetorical"? Under what circumstances would you consider the use of numbers in an article "merely rhetorical"?
3. What is the purpose of the paragraph, in this section, concerning flowering time in hybrids? What is the purpose of all the calculations Mendel performs using n to represent the number of characters?
4. Mendel begins this section with the claim: "In the experiments above discussed, plants were used which differed only in one essential character." How many varieties of peas would have been required for this to be true? How does the use of "essential" allow us to save the literal meaning of the sentence? How does the idea of not taking all statements "literally" square with your notions and expectations concerning a scientific paper or journal article?
5. Is it possible to find a paper in a contemporary journal that begins with a presentation of experimental results and then presents a model and/or theory to explain those results? How does Mendel's paper compare stylistically to these contemporary papers (besides the fact that it's much longer)?
Questions for Discussion:
1. What did Mendel mean by the phrase "the law of probability"? Were probabilities used in the biological sciences in the middle of the nineteenth century? Were they used in physics and chemistry at that time? Today statistical techniques are used in just about every branch of natural and social science; how has the use of statistics transformed scientific knowledge in both the physical and life sciences since Mendel's time?
2. By the end of this section, Mendel has presented both the data and the descriptions for what are generally considered his two "laws": the law of random segregation (or reproductive cells) and the law of independent assortment. Having read this far in the paper, find a genetics textbook and read the description of Mendel's findings. I hope it sounds familiar! What are some of the differences between the textbook presentation of Mendel's results and Mendel's own presentation?
3. Suppose you were a biologist, or physiologist, working in the middle of the 19th century. Suppose too you were interested in Mendel's findings concerning the production of reproductive cells, and wanted to figure out what it was in the pollen grain that carried character information. What would have been a reasonable hypothesis at that time?
4. Mendel claims that the theory of reproductive cells described in this section "explains" the laws governing the production and development of hybrids presented earlier. Give another example of a scientific law that is "explained" by a theory. What is the difference between an explanation and a description, and how do explanations in the natural sciences compare with those in the study of literature (e.g. an explanation of Hamlet's behavior)?
Questions for Discussion:
1. In his book on the fertilisation of flowers, written in 1873, Hermann Müller wrote of Pisum sativum:
2. If we assume that a trait can be the product of any number of "Mendelian characters" (i.e. characters that behave like those Mendel observed in Pisum), acting in combination, is there any distribution of visible forms of that trait that cannot be explained, provided the number of characters is sufficiently large?
3.In his 1967 essay, "Mendel and the Gene Theory", the geneticist A.H. Sturtevant wrote:
Questions for Discussion:
1. The quotation by William Bateson (1861-1926), in the fifth homework problem, is in some ways comparable to a statement by the philosopher John Dewey (1859-1952), in 1909, about the revolutionary change in thought made inevitable by Darwin's theory of evolution. Dewey wrote:
2. After the sentences quoted in the homework problem, Bateson wrote:"There is no doubt whatever that these laws can be determined." Have they been determined? Is it just a matter of time before they are determined?
3. For the purposes of presenting a collection of foundational papers in genetics, do you think J. A. Peters was right to omit the last two sections of Mendel's paper? Given that little data is presented in these sections, and that the transformation of species was not an issue with which Mendel was primarily concerned, what do you think was the purpose of these sections?
4. In the third homework problem, you are asked to design a set of experiment to discover a "lethal recessive" in mice. Of course it will be difficult to do this without having some of the mice die. Would you feel differently about the question if I asked you to find a lethal recessive in cattle? in cockroaches?
5. A good deal has been written about the lapse of time between Mendel's writing his paper and its supposed "rediscovery" around 1900. In a chapter that calls both the idea of "rediscovery" and "discovery" into question, Augustine Brannigan has written:
6. Having now read Mendel's paper, what are some of the differences between what Mendel thought he had discovered, what those who read him in 1900 thought he had discovered, what current textbooks claim he discovered, and what you think he discovered?