Friday, 25 May 2018

Plagiarism software hardly finds significant overlap between Darwin (1859) and Matthew (1831)

[Update 26.5.2018: Now with control assay (blind sample) at the end, in order to render the conclusion valid.]

Mike Sutton (aka @Dysology, http://dysology.org; aka @SuperMyth, http://supermyths.com; aka @Criminotweet, http://patrickmathew.blogspot.com; aka @OnNavalTimber, http://patrickmatthew.com) incessantly claims that he proved that Charles Darwin (1859: On the Origin of Species) plagiarized Patrick Matthew (1831: On Naval Timber and Arboriculture) by touting similarities in usage in combination with findings that merely show that Victorian naturalists and publishers were connected by less than six degrees of separation. The latter is only to be expected, given that science was a much smaller endeavor back then. Mere connections leading from Matthew to Darwin via acquaintance or citation, along x degrees of separation, does not prove conscious plagiarism by Darwin. Here, I check both books with a plagiarism-detection software, in order to test the claim about similarities in usage proving plagiarism.

The software
WCopyfind is an easy to use software that compares text-files. In order to compare vintage books, like Darwin's On the Origin of Species (1859) and Matthew's On Naval Timber and Arboriculture (1831), you only need to download them as plain text from sites like archive.org, or Project Gutenberg and save them in a format that the program can process (e.g., .docx). The program is very lean, fast and easy to use. The download takes a mere second and getting started a mere half an hour. Just click on the link above and try it yourself.

The interface looks like this.


In the image shown above, the parameters are set to report matching strings with a length of four words or more ("Shortest Phrase to Match: 4 Words"). The parameter "Most Imperfections to Allow: 2" means that, here, the program will bridge up to two non-matching words within a phrase thus allowing for some editing. The parameter "Minimum % of Matching Words: 80%" also allows for editing in that only 80% of two passages or phrases need to be identical and will still be reported. "Fewest Matches to Report: 1 Words" actually means that even 1 matching 4-word phrase (not "1 words") will be reported. This is the lowest bar and one match can be expected by mere chance in book of such length.

Basic check
All the above parameter settings are as recommended by the maker of WCopyfind, except the string-length to be matched. Here, the maker recommends a string-length of 6 matching words for reporting. With this default setting, however, there will be 0% overlap between Darwin's and Matthew's book.


There must be some rounding involved in this reported 0% overlap, because some hits can still be found in viewing both texts side-by-side. But these are entirely fortuitous and would occur in any two texts of a certain length. They signify no plagiarism as the immediate context of the matching phrases shows.

For example, such a search yields matches of the following kind: "we have also seen in the," which Darwin continues with "second chapter" and Matthew with "moss of Balgowan."


Other matches require some more context, in order to get the fortuitous triviality of the match:
"in many cases it is most difficult to" (Darwin 1859) vs

"in cases where it is difficult to" (Matthew 1831).
The green words are the ones that have been bridged and the red words constitute the 6-word match. However, the immediate context of this match is completely different in both books:
"Although in many cases it is most difficult to Conjecture by what transitions an organ could have arrived at its present state yet, considering that the proportion of living and known forms to the extinct and unknown is very small, I have been astonished how rarely an organ can be named, towards which no transitional grade is known to lead." (Darwin 1859)

"Forests of Ficus sylvestris are sometimes destroyed by insects under the bark, in cases where it is difficult to decide whether external circumstances, such as a dry warm season, has been promotive of the increase of the insect itself, or has induced some disorder in the plant, rendering the juices more suitable aliment to the worm." (Matthew 1831)
One actually needs to reduce the string-length down to 4 words, in order to get to the point, where the phrase that Mike Sutton, criminologist of Nottingham Trent University, takes to signify that Darwin plagiarized Mattehew:
"this process of natural selection" (Darwin 1859) vs

"this natural process of selection" (Matthew 1831).
Excluding the word "this," Sutton refers to it as a four-word-shuffle by Darwin. The immediate contexts:
"Therefore, I can see no difficulty, more especially under changing conditions of life, in
the continued preservation of individuals with fuller and fuller flank-membranes, each modification being useful, each being propagated, until by the accumulated effects
of this process of natural selection, a perfect so-called flying squirrel was produced." (Darwin 1859, p. 181)

"Mans interference, by preventing this natural process of selection among plants,
independent of the wider range of circumstances to which he introduces them, has increased the difference in varieties, particularly in the more domesticated kinds and even in man himself, the greater uniformity, and more general vigour among savage tribes, is referrible to nearly similar selecting law the weaker individual sinking under the ill treatment of the stronger, or under the common hardship."(Matthew 1831, p. 308)
It is true, both contexts are evolutionary, but does that prove plagiarism by Darwin of Matthew? The perfect matches amount to 2% of Darwin's book and 4% of Matthew's, most of it the trivial stuff that is clearly coincidental. And allowing for the bridging of words and only 80% matching words in phrases did not change this for the overall matches.


Control assay (blind sample)
The problem with purely random word-salads is that they are not grammatical. That is, two word-salads will show less matches, by pure chance, than two independent texts, because grammar, rules, as well as an era's fashion of speech force language into similar strings of words at times. A blank sample or control assay must, therefore, compare two texts that are from the same time and culture, whose authors did not imitate each other. I assume (with no expertise in English literature on my part)* that Oscar Wilde's (1854-1900) tastes were sufficiently different from that of Amanda Minnie Douglas (1831-1916), author of juvenile fiction like the Little Girl... and Helen Grant... series, and that they did not copy each other. I compared their novels The Picture of Dorian Gray (1890) and A Little Girl in Old Boston (1898) using identical parameter settings as above.

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* I assumed that a homoerotic book by an openly homosexual author would have little in common with the girly romance novel of a spinster.
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Here, the perfect matches amount to 3% in Douglas's book and 4% in Wilde's and, respectively, the overall matches amount to 3% and 5%. This is slightly higher than in the comparison of Darwin's Origin with Matthew's Naval Timber (see above) suggesting that there is no more reason to assume that Darwin plagiarized Matthew than to assume that spinster Douglas plagiarized scandalous Wilde. Surely, the 2% and 4% overlap between Darwin's and Mathew's book, respectively, is within the range of what is to be expected from any pair of books of roughly the same age and culture.

A note of caution to those who are fond of relying on algorithms rather than reading and thinking themselves, the program missed a four-word-shuffle, because it found an overlapping perfect three-word match first. That is, the program overlooked the following matches:
"but it seems somehow" (Douglas 1898, p. 11) vs

"but somehow it seems" (Wilde 1890, p. 14).
Instead, Wilde's sentence is matched with another of Douglas, because of a three-word match that required no bridging:
"Now, it seems to me I never could learn French." (Douglas 1898, p. 99)
"It is a silly habit, I daresay, but somehow it seems to bring  great deal of romance into one's life." (Wilde 1890, 14)
Obviously, neither the perfect three-word match nor the four-word-shuffled match has any significance concerning plagiarism. Apparently, four-word-shuffled matches do occur by mere coincidence at times. One should, therefore, take the occurrence of such a match between Darwin (1859) and Matthew (1831) with a grain of salt.

Some readers might think that the string "natural process of selection" is charged with meaning in a way that "but somehow it seems" is not and, therefore, the former string carries biological significance in a way that the latter does not. However, the first time that the string "natural process of selection" has been used in publication (as far as the digitized record goes) was by Sigmund Spaeth (1829. The Encyclopedia Americana, Vol. 19, pp. 636-639). This entry in an encyclopedia, however, carries no significance concerning natural history. It is about music appreciation and contains the four words in a context that has nothing to do with biology:
"Program music will generally be found easier to grasp than absolute music, and this is again a natural process of selection." (Spaeth 1829, p. 638)

Sunday, 22 April 2018

Why Charles Darwin did not own the Two Essays by W.C. Wells (1818) before the Beagle voyage or after

Tall claims
John S. Warren (2017. Darwin's missing links. History of European Ideas 43(8): 929-1001) claims that Charles Darwin bought William Charles Wells's (1818, Tow Essays: One upon single vision with two eyes; the other on dew. ...) before he even embarked on the voyage of the HMS Beagle. Charles Darwin read Herschel's Premier Discourse at Cambridge, who praised Wells's Essay on Dew as a role model for anybody attempting to do science. Warren promptly concludes:
Darwin required no prompting; he quickly acquired a copy ofWells’ ‘Essay on Dew’.259 The copy in Darwin’s library in Down House is identified in the Darwin Digital Library of Evolution, Bibliography and the ‘Key to Annotations’ as ‘Pre-B’ and ‘Down’: it was in Darwin’s private library pre-Beagle voyage, later located at Down House; that is, since the Beagle sailed in December 1831, the paper was acquired no later than 1831 (Appendix 1).260
259 Wells, Two Essays.
260 American Museum of Natural History (AMNH), 2005. http://darwinlibrary.amnh.org. Accessed January 25 and September 27, 2009. See also Appendix 1.
Appendix 1
The Darwin Library and DDLE are currently accessible on the AMNH website through the following links, as at 13th January, 2017: Darwin Manuscript Project (DMP) Website (darwinlibrary.amnh.org). To go straight to the William C Wells reference, the current URL is (http://www.biodiversitylibrary.org/docs/DarwinsLibraryBibliography.pdf) (Publications in EvoLit.bib p. 23). Excerpt from AMNH, 2005. ‘Darwin Digital Library of Evolution’ (darwinlibrary.amnh.org): web-page listing for the relevant section of the alphabetical letter ‘W’, showing William Charles Wells’ ‘Two Essays’ in Darwin’s private library, with immediately adjacent names. Wells’ book was acquired by Darwin before the end of 1831. The entry for Wells, 1818 is annotated, ‘*’ (the identifier for Darwin’s private library), ‘Pre-B’ (pre-Beagle voyage, but not known on board), and ‘Down’ (Darwin’s library, later located at Down House, Kent): see the Darwin Digital Library of Evolution, ‘Key to annotations’.
Whatever the historical significance of Wells's Essay on Dew (1814. Article IV.—An Essay on Dew, and several Appearances connected with it. The Quarterly Review; London Vol. 12(23): 90-99) the significance for the history of biology of the later published Two Essays lies in neither of the two essays, but in an appended "account of a female of the white race, part of whose skin resembles that of a negro ..." This last account contains an anticipation of natural selection as a means of adaptation of races to their different conditions. That is, Wells did not go as far as to suggest the origin of new species through natural selection, but he got pretty close.

Screwed records
Now, Warren took an information provided by Charles Darwin's Library (at the website of the Biodiversity Heritage Library, BHL) as stating that Darwin owned that book before he even embarked on the Beagle Voyage. (In fact, Warren refers to the American Museum of Natural History, but that link does not exist anymore and the AMNH now relays you to the BHL's Charles Darwin Library.) This would be unproblematic, if the key to annotations had traveled along with the alphabetical list, but it hasn't. Page 84 of this list states: 
The crucial part, here, is that in square brackets: "Down, pre-B, ED." Unfortunately, the Charles Darwin Library or BHL does not give any information as to the meaning of these abbreviations (annotations). While SCRIBD still has a relic of the original list collated by the staff of the AMNH, this only tells us that the key to the annotations can be found in the book Charles Darwin's Marginalia edited by Di Gregorio & Gill (1990, Garland, New York).


Thankfully, Greg Priest (@greg_m_priest) tweeted the key to the symbols and the page with the entry of Wells's Two Essays.

Di Gregorio (ed.) 1990. Charles Darwin's Marginalia: Key to symbols


"ED" seems to be missing from the key to symbols and Warren (2017) simply ignored it. He took the annotation to mean "book located at Down House, Kent" and "book owned prior to Beagle voyage but not known on board," as the key to symbols states for the meaning of "Down" and "pre-B."
However, Warren went further than that. He claimed that Charles Darwin bought the book while in Cambridge and owned it ever since, studiously avoiding the question what that "ED" at the end of the annotation might mean. In my opinion, it hints at one of the many Erasmus Darwin's rather than our Charles. That is, even if Di Gregorio's annotation was correct, it would not mean that Charles Darwin had bought the book before his Beagle voyage and owned it ever since.

However, the information of Di Gregorio, the BHL and AMNH is probably wrong anyway.

The first record
H. W. Rutherford (1908. Catalogue of the library of Charles Darwin now in the Botany School, Cambridge. Compiled by H. W. Rutherford, of the University Library; with an Introduction by Francis Darwin. Cambridge: Cambridge University Press) was the first at Cambridge University, who collated a list of the books that actually did enter their collection of Charles Darwin's books in 1908, and Francis Darwin wrote the introduction to that catalogue.

The first thing to notice is in Francis Darwin's Introduction:
THE library of Charles Darwin has now found a permanent home in his own University, and it is perhaps appropriate that it should be in the Botany School, since it was a Cambridge professor of Botany who, more than any one man, determined his career as a naturalist.
The collection is not identical with that at Down. Thus the books he wrote and some few others from Down are in my own possession. There are also a few books of mine which, for the sake of convenience, are kept in the Darwin library: these are marked with an asterisk in the catalogue. (Rutherford 1908, p. vii, emphasis added) #
#[The books from Francis Darwin's private possession have probably been integrated into the collection by now.] Next thing to notice is the explanation of the abbreviations:
* Books thus marked were not in the Library at Down. ... (Rutherford 1908, p. xiv, emphasis added)
  And, finally, there is the entry for W. C. Wells:
*Wells (William Charles). Two Essays: one upon single vision with two eyes; the other on Dew: &c. 8vo. London, 1818. 24 (Rutherford 1908, p. 89)
Conclusion
The first record by H. W. Rutherford (1908) clearly contradicts Di Gregorio's annotation "Down, pre-B, ED," which has first been adopted by the AMNH and then by the the Biodiversity Heritage Library. While this annotation suggests Down House as the location of the book, the asterisk of Rutherford and the introductory statements by Francis Darwin state that Francis added this book to the collection, which has since been called the Darwin Library. That is, it was not from Down House or, anyway, not from Down House while Charles Darwin still roamed it.

Maybe it came down to Francis Darwin from Erasmus Darwin (either one). Maybe Francis stored it with some other books of his in Down for a while, before they went to Cambridge. Maybe the collator of the BHL's list made some mistake. Whatever the explanation of the screwed-up information at the BHL, it can surely not be taken as proof that Charles Darwin owned Well's Two Essays long before he even went on the Beagle voyage.

Tuesday, 17 April 2018

Darwin's Questions & Experiments notebook. One entry, many interpretations

Here's an entry from page 3 of Darwin's "Questions & Experiments" notebook (1839-46).


The poor performance
A naive and surprised reaction will be based on the fact that the only work on forest trees one usually ever heard of is Patrick Matthew's book On Naval Timber and Arboriculture, because it has some relation with natural selection. Thinking that Matthew was the only source for anything on forest trees will lead to an interpretation as follows:

First Interpretation: The fact that Darwin shows interest in forest-trees and their variability in nursery gardens proves that he had read Matthew (1831).

However, this is not the only possible interpretation, especially if you know something about the pertinent literature from around 1831.

Second Interpretation: There were others before Matthew (1831) writing about forest trees and their cultivation. An interest in the issue does neither prove nor disprove a knowledge of Matthew (1831).

Finally, having actually read and understood Matthew (1831) can even lead to the opposite of the first interpretation.

Third Interpretation: The question whether forest-trees sport more in nurseries than in nature as a consequence of the special conditions in nurseries, like manuring, indicates that Darwin had not read Matthew (1831) or else he would not have asked this. Matthew (1831, 308) had made it clear that the variability only appears to be increased under domestication, because of the lack of natural selection there. For Darwin to get there, it would still take years of studying barnacles and other organisms.
"Man's interference, by preventing this natural process of selection among plants, independent of the wider range of circumstances to which he introduces them, has increased the difference in varieties, particularly in the more domesticated kinds; and even in man himself, the greater uniformity, and more general vigour among savage tribes, is referrible to nearly similar selecting law—the weaker individual sinking under the ill treatment of the stronger, or under the common hardship." (Matthew 1831, p. 308)
One could, then, continue with a useless controversy about this entry and what it signifies about Darwin's knowledge or ignorance of Matthew (1831) or quip something like: "Had Darwin asked whether Forrest Gump sports much in nursery gardens, I'd surely know the answer." However, the entry also provides the chance to do something more interesting.

The historical performance
Let's first look at the context of Darwin's notebook entry. The very first question at page 3 about crossing two halfbred (we'd say heterozygous) animals and their offspring being uniform already shows that Darwin was on the track of hybridizers* in particular rather than on Matthew's general observations about the variability of trees in forests and nurseries.

* [By the way, Gregor Mendel was one of these hybridizers, and he would later answer Darwin's question with a resounding "No." He started from two strains of peas that differed in one trait (e.g., colour of the flowers), but were truebred (that is, homozygous) for that trait. Crossing this parental P-generation yielded a halfbred (that is, heterozygous) F1-generation, which was was uniformly showing the dominant trait. But crossing these halfbred F1 plants with each other yielded an F2-offspring showing the parental traits in the ratio 3:1. Hence, the answer is "No!" to Darwin's first question at page 3: "If two halfbred animals exactly alike be inbred, will offspring be uniform?"]

Furthermore, Darwin's entries at page 21 of the same notebook show that he had a particular problem with trees and inbreeding. He believed that some degree of out-breeding was necessary for the health of organisms but could not understand how that should be possible in in mixed forests. Here, the scattering of trees of the same species should lead to close inbreeding between flowers of the same tree despite insects or wind.
     Darwin even wondered whether fruit trees can flower and their fruit ripen in Scotland—a question he'd never have jotted down had he been in the know of Matthew's writings.
"(2) History of fruit trees far north in Scotland — do they flower — do they live healthily, or does fruit merely not ripen. — The point to attend to is whether good & plenty of pollen is produced. & 2d if so, whether concepcion takes place, — the mere fact of seeds ripening has scarcely any no relation to hybrids." (Darwin's Q&E notebook, p. 21)
     At the same time, experiments by hybridizers, like William Herbert, had shown that hybridization can boost the variability of the offspring generally referred to as "sporting." If trees were inbred in mixed forests, and their out-breeding had similar effects as the hybridizing in experiments by hybridizers, the close proximity of trees of the same species in nurseries should lead to an increase of sporting in their offspring.
     Darwin's further question about the manuring of trees in nurseries ("are the is the ground much manured") hints at another doctrine, which had been well established among horticulturalists and animal breeders of Darwin's time, but has since been refuted. Horticulturalists and animal breeders, like Thomas Knight, believed that conditions of domestication or cultivation (such as an excess of food or shelter from harsh conditions) boost the variability of the offspring. And so did Darwin. Matthew (1831), however, did not subscribe to this doctrine. He did not explicitly refute it, but what he wrote was not in accord with it either. Concerning his personal experience with planting and growing trees he commented in the footnote that domestic trees vary no more than forest trees:
"In fairness, it may be proper to explain, that the greater part of the trees we have thus cultivated have been of Pyrus, although we commenced the practice with common forest trees—yet the pear and apple vary nothing from the oak and ash in the primary stage of life" (emphasis added, Matthew 1831, p. 215, footnote )
That means, had Darwin read Matthew (1831), he might not have asked this question about the effects of domestic conditions on variability in the first place.

The analytical performance
The scan and the transcript provided by Darwin Online are not very good. Let's take a closer look at a better scan provided by the American Museum of Natural History.


The first thing to notice, here, is that the transcription (by David Kohn) has added a footnote "a" after "forest-trees." What does it say? It says: "aDo forest-trees] ‘No’ added over ‘Do’"
Apparently, we must look closer still!


What we see, now, is that Darwin has overwritten the first word, either "Do" with "No" or vice verse. Here are samples of Darwin's "D" and "N" from other pages in the same notebook as well as the Do/No overwrite at page 3 in large.



Taking the question mark at the end of the sentence as an indication that the original sentence must have been a question, the original first letter must have been a "D" in "Do forest-trees sport much in nursery gardens?" That means, Darwin has overwritten the "D" with an "N" and thus turned a question into an answer. He apparently concluded something about the effect of either out-breeding or manuring in nurseries. So here's an interesting project for an accomplished sleuth in trying to find out what this overwrite signifies.

Monday, 16 April 2018

If-by-whiskey... no true scotsman... assume a can opener


A man uses the search and setting options of google, in order to search books.google for specific phrases within specific time-ranges. That is, he sets "search terms" in quotation marks telling google thus to search for the exact phrase, and he chooses a custom time-range from the tools settings. He then claims that he has thereby "invented" a new research method and that google does not want its users to use its search engine in that way. Try doing such a search with any other search engine and you will experience what it is like, if the designers did not mean to build an engine with which digitized books can be searched within customized time-ranges.

It's simply impossible!!!

Nevertheless, our man wants priority rights for having invented a new research method, when in fact, John J. McKay has used the very same method years earlier, in 2009, in order to trace a mammoth literary myth back to its roots. That means that our man is not the first to have invented anything new, but only the first to be foolhardy enough to do the equivalent of claiming that using the lights of a car for searching in the dark off-road is a new invention.

Monday, 26 March 2018

Life of Patrick. A historic comedy of errors about two namesakes

Introduction
Patrick Matthew lived and died long ago (*1785, Newbigging near Errol, Scotland; †1830, Cawnpore, India). The traces of his existence have since been rotting in the archives as of no historical interest. Now, his existence gets linked to the live of his namesake, Patrick Matthew (*1790, Rome farm near Scone, Scotland; †1874, Gourdiehill near Errol, Scotland). Many will wonder who Patrick Matthew of Gourdiehill was, and some who heard of him will, nevertheless, claim his historical insignificance. However, the life of Patrick Matthew from Gourdiehill crossed the path of Charles Darwin, and his ideas crossed the history of the idea of natural selection. He is, therefore, of some intereste to the history of biology.
     Patrick Matthew from Gourdiehill is often said to have anticipated the idea of species transmutation through natural selection in his book On Naval Timber and Arboriculture published in 1831 (e.g., Weale 2015. Patrick Matthew's law of natural selection. Biological Journal of the Linnean Society 115: 785-791). I personally disagree and think Matthew's evolutionary scheme only suggested species transmutation with natural selection in some lateral role, but not as the central force driving the transmutation process (Dagg 2018. Comparing the respective transmutation mechanisms of Patrick Matthew, Charles Darwin and Alfred Wallace. Biological Journal of the Linnean Society 123(4): 864-878).1 Julian Derry even disagrees with that and thinks that Matthew suggested two separate processes—species transmutation without natural selection and natural selection as a species fixing force without transmutation occurring while it is engaged. There you are, already having a hunch of the issues concerning Patrick Matthew's historical significance.
     Now, his namesake from Newbigging also gets significant in a comedy of mistaken identities concerning the (university) education of these two Patrick Matthews.2
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1 If you'd like to know why I think that Patrick Matthew only suggested species transmutation with natural selection follow through the links here. The article linked, there, analyses Matthew's mechanism of species transmutation in detail and compares it with Darwin's and Wallace's.
2 While the following collects the historical facts that clarify these mistaken identities and their education at the University of Edinburgh, or educational leave for a few weeks, or visit of only one experimental fun lecture, respectively, I could never have done it on my own. It is due to a team effort by Anne Carroll, Julian Derry, Mike Weale, and me.
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A family lore turned folklore
One enigma about this Patrick Matthew of Gourdiehill is his education. The only source we really have is William T. Calman (1912a, "Patrick Matthew of Gourdiehill." Handbook and Guide to Dundee and District, British Association for the Advancement of Science, pp. 451-457) stating:
"He [Patrick Matthew] was educated at Perth Academy and at Edinburgh University, but his stay at the latter cannot have been of long duration, for, on his father's death, he undertook, at the age of seventeen, the management of the estate of Gourdiehill, near Errol." (Calman 1912, p. 452)3
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3 He repeated roughly the same in a very similar article: Calman 1912b. Patrick Matthew (1790 – 1874). Journal of Botany, British and Foreign 50: 193-194.
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Ever since, the above sentence about his education has been parroted by almost every publication ever written on Patrick Matthew (laudable exceptions being Mike Weale's and, thanks to him and Anne Carroll, mine). Matthew's university education is now often taken for granted, because this pseudo-replication created an appearance of corroboration that is not warranted.
     Calman (1912, p. 451) only referred to communication with Miss Euphemia Matthew, Patrick Matthew's daughter, in general—a general nod at the memories of an 80 year old lady about a time, when she hadn't even been born, that is, family lore. But Calman did not refer to her as his particular source for the particular claim of Matthew's university education. Unless this communication was by letter and the letters have been preserved somewhere, we shall be unable to check Calman's words.

Excerpt from Calman (1912a). The mistake by May referred to concerns May's claim that the Matthew family was related to Robert Bruce, which Euphemia Matthew denied.

Mike Weale from The Patrick Matthew Project found a first hint that sheds a doubt on the reliability of the communication between William Calman and Euphemia Matthew. The short version is that Pastor Benecke, a relative of the German branch of the Matthew family, told Walther May that the Matthews were descended from a sister of Robert the Bruce. May quoted Benecke on this in a German publication (May 1912. Darwin und Patrick Matthew. Zoologische Annalen 4: 280-311. See here for an English translation). Calman (1912a, p. 452), in turn, denied this in a footnote as follows:
"   * The family tradition alluded to by Professor May, according to which the Matthews are descended from a sister of Robert Bruce, is declared by Miss [Euphemia] Matthew to be quite without foundation."
However, Mike Weale found evidence that Euphemia Matthew owned genealogies that show that the Matthews descended from Robert Bruce in direct line—not via a sister (see section headed "Patrick Matthew's ancient family tree" at this page). And she gave them to A.H. Millar for his book The Genealogie of the Lords Oliphant as it was written in the Castell of Duplin (1890). That is, Euphemia trusted in the correctness of these genealogies. Regardless of the question whether these genealogies were really correct or not, there remains the oddity that Calman claims Euphemia to have declared the family lore about the family link "quite without foundation," when she should only have denied that the link to Robert Bruce went via a sister. This suggests poor understanding between Euphemia Matthew and William Calman.

The misattributed matriculation record
William J. Dempster (1996, Evolutionary concepts in the nineteenth century. Natural selection and Patrick Matthew. Pentland Press) tried to verify Patrick Matthew's training at the University of Edinburgh by consulting its matriculation record. He wrote:
"According to the records in the Department of Rare Books and Manuscripts, Edinburgh University Library, the name of Patrick Matthew appears in the Matriculation Index in 1804-05 and again in 1808-09. His name is on the class list of Professor Gregory who held the chair of medicine. The subjects studied were anatomy, surgery, chemistry, medical practice. In 1808 Patrick Matthew attended Professor Hope's classes in chemistry. There is no evidence that Patrick Matthew graduated from Edinburgh and he appears never to have mentioned in his writings that he had attended Edinburgh University, where his studies were interrupted when he seventeen years old by the death of his father." (Dempster 1996, p. 1, my emphasis) 
Meanwhile, the University of Edinburgh has put its records of historical alumni online (see image below). This online record seems to suggest that the Patrick Matthew in question ran a regular course of studies in medicine and was training abroad, at the Indian Medical Service, from 1807 to 1808. However, it is rather a compound record of two namesakes as will become clear in the following.


A direct look at the records in the library of the university yielded entries for the sessions 1804-05, 1805-06 and 1808-09 (ht Julian Derry). Sessions were beginning 1st October of the first year, say 1804, and running through to summer of the next year, 1805. 
     Anyway, the above record does not fit to Patrick Matthew of Gourdiehill (Gourdiehill PM) for several reasons. First, Gourdiehill PM (1790-1874) would have been 14 in the year that the matriculation record first registered the enrollment. Second, Gourdiehill PM never was in India. Third, this Patrick Matthew (born 20 October 1790) would have been 17 or just turned 18, when visiting the university in the session 1808-09, which began at 1 Oct. 1808. However, the father of Gourdiehill PM died roughly one year earlier, at 1 November 1807.4 Though Patrick Matthew's uncle, yet another Patrick Matthew, was put up to manage the affairs of his deceased brother John Matthew (see here), it seems somewhat unlikely that Patrick Matthew jun. would have proceeded to start a course of academic studies at the university about one year later. He was the only son with five sisters (see section: "Patrick Matthew's immediate family tree" at The Patrick Matthew Project) and a widowed mother to look after. Even without the earlier death of his father, a course of studies including anatomy, surgery, and medical practice would have been a very odd choice.
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4 The church account of the Old Parish Register of Scone records a sum of money taken for forwarding a mort-cloth for a dead Mr. Matthew (no forename) at 8 November 1807.

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     A closer look at all university records (ht Julian Derry, his full data-set contains about 100 photographs of matriculation records, class lists etc. from the university archives), however, shows that the entries for 1804-05 and 1805-06 were by a medical student, whereas the matriculation in 1808 was only for chemistry. Furthermore, this non-medical Pat Matthew seems to have attended only one chemistry lecture of Prof. Thomas Charles Hope, given at 26 October 1808. The class list of that lecture shows that the "Pat. Matthew" attending this lecture indicated that he was not a medical student (see left column "Not med?" in the image below). Hence the above online record is not all of one medical student, but a compound of a medical student (1804-1806) and someone else who did not study medicine.


A day at the University—or a few months at most
That is, Patrick Matthew of Gourdiehill may have attended at least one of the chemistry lectures of Prof. Hope. These lectures were famous for their spectacular experiments and became so popular among the wider population, that was not studying and following a regular curriculum, that Hope, eventually, gave one for the ladies of Edinburgh at 15 Feb. 1826:
"For the first time, [...] the splendid portals of the University of Edinburgh were thrown open to the fair sex [...]. On that memorable day Dr. Hope, the Professor of Chemistry, commenced a popular course of that fascinating subject. That learned lecturer has been long celebrated for his oral instruction, but still more famous for his showy experiments exhibited to the grown-up children of the male sex [...]." (Dr. Hope and his lecture to the Ladies of Edinburgh, The Lancet 6(145): 336-363, 1826)
After toiling with the management of the family estate for 10 months, Patrick Matthew of Gourdiehill may either have needed a distraction or an educational leave for improving his farm management skills. What he did not need was a full-time course of studies for a job, as if he had none yet. He either visited only one of Prof. Hope's edutainment lectures for grown-up children or his stint at the university amounted to several weeks. As he does not occur in any records of 1809 or later, however, the season holidays around 20 December 1808 would probably mark the end of any stint longer than one day at the university. Personally, I do not believe that Matthew attended more than one fun lecture by Prof. Hope, because of the chores of managing the family estate and looking after his five sisters and widowed mother. By his own account in the Gardeners' Chronicle and Agricultural Gazette, he managed orchards from 1807, the year his father died, onward. In 1865, he corrected a claim made in the the Gardeners' Chronicle, that the climate of Scotland does not allow the cultivation of fruit trees, in a letter to the editors as follows:
"I have managed orchards for 58 years; have planted orchards—many thousand Apple and Pear trees in Scotland, Germany, and a small one in Spain; [...]" (Matthew 1865, Gardeners' Chronicle and Agricultural Gazette 25, 16 December 1865, p. 1179

     In conclusion, Calman's account is definitely false. It is chronologically impossible that the death of his father John Matthew in December 1807 forced Patrick to quit studying in Oct.-Dec. 1808. We already know that the communication between William Calman and Euphemia Matthew was unreliable (see Robert the Bruce above). Imagine Calman asking Euphemia a loaded question about her father's university education and Euphemia answering something to the effect that: yes, he did have his stint there in 1808 but, no, he couldn't pursue a full curricular course of studies because of his father's death in 1807...
Calman probably connected the wrong ends once more and construed a story about Patrick Matthew's full curricular course of studies terminated by the precipitous death of his father.

Let the mess begin
The above records for sessions 1804-05, 1805-06, the diploma from the Royal College of Surgeons in 1806, and the medical service in India in 1807 all refer to the other Patrick Matthew, a medical student from Newbigging. Before giving further details that illuminate the existence of this Patrick Matthew, however, a word on the above featured online record of historical alumni of the University of Edinburgh as well as on the habit of Scottish officials in treating fore- and surnames.
     First, the online record includes a typo and an rare expression. "Colleg" must simply be "College" and "Diplomate" was a standard expression for members of the Royal College of Surgeons with a diploma degree. Indeed, the medical student from Newbigging did earn a degree called diploma from the Royal College of Surgeons at 18 April 1806 (thanks to Aaron Fleming, Library and Archive Assistant, The Royal College of Surgeons of Edinburgh for that information).   
     Second, for some reason it was quite common among the Scots to treat the forenames Peter and Patrick as synonymous. Our medical student and his father from Newbigging as well as our orchard owner from Gourdiehill have all been referred to by either name in various documents. Likewise, the same person has variously been called by the surnames Matthew, Mathew, and Matthews in different documents. This is true, for example, for the diploma record of the Royal College of Surgeons, for it spells the medical student from Newbigging with only one "t" in Mathew. The military bureaucracy in India picked up that spelling with one "t" and never corrected it.  

Life of Patrick. Short story of the namesake from Newbigging
Traces of the existence of the other Patrick Matthew from Newbigging can be found in many independent documents. Before piling these historical records, here's the short version:
  • Patrick Matthew is baptised on 16 August 1785 in Errol, son of Peter/Patrick Matthew and Jean McCulloch of Newbigging, Errol. 
  • He studies medicine at Edinburgh University from 1804-05 (first year) to 1805-06 (second year). 
  • The British India Office of Medical Staff appoints him as Assistant Surgeon in 1805. 
  • At 18 April 1806, he earns a diploma from the Royal College of Surgeons and 
  • his appointment as Assistant Surgeon is promptly approved at 14 November 1806. 
  • The Caledonian Mercury, 13 December 1806, lists assistant surgeons P. Matthew and G. O. Gardner among the passenger of the ship General Stuart headed for Bengal.   
  • 16 April 1820, he gets promoted to surgeon. 13 years was quite the normal stretch for such a promotion in the army.
  • He eventually dies, aged 45, as Surgeon of the Hon. East India Company's Bengal Establishment, 15 August 1830, and is buried in Kacherie Cemetery in Cawnpore (Kanpur).
Before that, he marries Margaret McGowan and they have one daughter, also called Margaret. Mother Margaret was born in 1785/6—maybe in Ireland. After the death of her husband, she returns to Scotland with her daughter. She gets on a census record as living in Perth, 13 Marshall Place, from 1841 to 1871, where she also dies in 1873 (aged 87 or 88). Her daughter Margaret is born in Benares (Varanasi), India, on 9 November 1818. At the age of 20, 27 April 1837, she marries John Campbell, junr, Esq of Kinloch, of the Madras Army, in Perth. They return to India and have four sons, all but one born in India. Margaret Campbell (nee Matthew) dies in Jaulnah, Madras, and is buried on 18 July 1844 (aged 26).

Traces of Patrick. Evidence of the namesake's existence
1. Baptism
Here's a record from the ScotlandsPeople website showing that three Patrick Matthews have been born and baptized around the same time and close to each other in Scotland.


Okay, the guy from Udny near Aberdeen is a bit farther off, but the the guy baptized in Errol near Perth is our Newbigging P.M. (see record below), and the third guy baptized in Scone near Perth is our Gourdiehill P.M. known to have been born on Rome Farm near Scone.


2. Family background
The file GD316 of the National Records of Scotland has further information about the other Patrick Matthew's family. This Patrick was the grandson of a John Matthew from Clashbenny and the son of a Peter/Patrick Matthew from Newbigging. The following excerpt is from GD316_16_4, which gives the genealogies of Matthew families other than the one of Gourdiehill (put online by Mike Weale at The Patrick Matthew Project).


As you can see, Peter Matthew of "Newbigging" (red ellipse) was a son of John Matthew (of Clashbenny, this village is given on the next page, which is not shown above) and had a son called Patrick Matthew (third from left), who went to East India and married there. Here's the same excerpt rotated clockwise:


Inside the red ellipse, it says, in the right half (which is the top in the non-rotated version and hence the older half): "Patrick Matthew, went to East India, and married."
The left (younger) half says: "One daughter, married, name unknown." (We actually know that her name was Margaret Matthew and she married Captain John Campbell. See below.)
     Furthermore, the elder brother John Matthew (at the top of the rotated image) also went to East India, and so did the younger brother George Matthew (two below Patrick). The Newbigging Matthews had quite a number of supernumerary sons and quite a family tradition of sending them to India.

3. Transit as appointed assistant surgeon
Here's the list of passengers for Bengal on board of the General Stuart (published in the Caledonian Mercury, Saturday, 13 December 1806).


Again, an ambiguous record. We know that Patrick Matthew/Mathew from Newbigging did study medicine, earn a diploma from the Royal College of Surgeons, was approved as assistant surgeon by the British India Office for Medical Staff, and eventually died as a surgeon in India. Nevertheless, the passenger list can be read in two ways. Either P. Matthew and G. O. Gardner were both assistant surgeons and the newspaper forgot the plural "s," or only G. O. Gardner was an assistant surgeon.

4. Assistant surgeon
However, the following record of both Patrick Mathew (sic) and Gilbert Ogilvy (sic)5 Gardner as assistant surgeons listed in the East-India Register and Directory for 1819 (p. 113) leaves little doubt that both traveled as appointed assistant surgeons in 1806. As already mentioned, the military officials picked up the spelling of the surname "Mathew" with one "t" from the diploma degree of the Royal College of Surgeons and never corrected it in his lifetime.
-----
5 The day these two chaps entered the British military service, two things happened. First, the staff of the British India Office misspelled both their names, Patrick Matthew's as "Patrick Mathew" and Gilbert Ogilvie Gardner's as "Gilbert Ogilvy Gardner." Gilbert's mother was Grisel Elizabeth Ogilvie and Gilbert's second forename was, therefore, Ogilvie not Ogilvy. Second, they were always put next to each other in lists of surgeons or assistant surgeons thus turning Gilbert's unique name into a nice tracer for Patrick's common one.  
-----


5. Promotion to surgeon
In the East-India Register and Directory for 1821 (p. 113), both are listed as surgeons. That is, they must have been promoted between 1819 and 1821.


The dates in the above featured list probably registered the arrival of the soldiers at their current station (e.g. Gilbert Ogilvy Gardner arrived at 17 Dec. 1821 in the Civil station, Bauleah).
     The exact date of Gilbert Ogilvy's promotion to surgeon has been recorded in The Asiatic Journal and Monthly Register for British India and its Dependencies (July to Dec. 1822, vol. 14). Under the heading "Military Appointments, Promotions, &c." (beginning at page 183) it says at page 185: "Surg. Gilbert Ogilvie (sic) Gardner to rank from 19th June 1820, vice G. Campbell, retired."
     Patrick Matthew's career and death in the service has been registered much later by Lieut.-Colonel D. G. Crawford (1930. Roll of the Indian Medical Service 1615-1930. Vol 1, p. 55).
The abbreviations mean:
b.: born;6 d.: died; A.S.: Assistant Surgeon; Surg.: Surgeon; S.A.L.M.B.: Service Army Lists, Medical, Bengal; P.R.: Prize Rolls; M.R.C.S.: Member, Royal College of Surgeons; M.D. Glas.: Medical Degree, Glasgow; R.: Retired.
-----
6 As the baptism of Patrick Matthew was 16 August 1785 (see 1. Baptism), the year 1784 given by D.G. Crawford is a typo, and so is the year 1785 for Gilbert Ogilvie Gardner, who was born 5 February 1788 (see ScotlandsPeople).
-----

6. Death
The death of Patrick Matthew/Mathew, the surgeon, has been recorded in an Army & Navy Pension document of the British India Office and in the above cited book by Lieutenant-Colonel Crawford (1930).

Again, the full record is paywalled.

7. Father
Peter/Patrick Matthew, the father of our surgeon from Newbigging seems to have gone on record as yet another Patrick Matthew in an old tax roll (1797-1798) that is online here. The picture below shows that Peter/Patrick Matthew from Newbigging in the red ellipse:


At that time, Patrick Matthew from Gourdiehill was only 7 years old and surely did not pay taxes for farm horses. Apparently, this Peter/Patrick Matthew from Newbigging also signed the preface of a book by David Young published in 1788, when our Gourdiehill chap had not even been born (see here). And there's even a fourth Patrick Matthew from Sherifftown. (This was the uncle of Gourdiehill Patrick Matthew, who took it upon him to act on behalf of the latter's deceased father, his brother John Matthew, who died intestate at 1 November 1807.)  


As already mentioned, treating the forenames Peter and Patrick as if they were identical has been fairly common among officials in Scotland. Our Gourdiehill Patrick Matthew also got called Peter Matthew in a copy of the Errol churchyard, where he's been buried (ht to Julian Derry):





8. Daughter
The marriage of Margaret Matthew (daughter of Patrick Matthew, surgeon from Newbigging) was announced in the The Perthshire Courier, 27th April, 1837, page 3, column 1. It reads:
"Married, at 13, Marshall Place, on the 25th inst., by the Rev. James Esdaile, John Campbell, junr. Esq. of Kinloch, of the Madras Army, to Margaret, only daughter of the latePatrick Matthew, Esq. Surgeon on the Hon. East India Company's Bengal Establishment."


The first error in this comedy of mistaken identities
Apparently, the lives of the two namesakes have been scrambled together as early as 1831, only one year after the surgeon from Newbigging had died in India, in a vitriolic review of the book by the orchard owner from Gourdiehill (ht to Mike Weale from PMP). The anonymous reviewer of the Edinburgh Literary Journal, or Weekly Register of Criticism and Belles Lettres (2 July 1831, vol. 6, no. 138, pp. 1-4) speculated:
"Mr Patrick Matthew, as we understand, is a small landowner on Gourdie hill, near Errol, in Perthshire, an inconsiderable orchardist, if we may so speak, who has a house, with a garden and shrubbery, where he makes experiments on fruit-trees. Having been engaged, in his youth, in a seafaring line of life, probably as surgeon's mate to a man-of-war, he has acquired some acquaintance with the form and structure of a ship, with a quantum sufficit of naval slang. At one time or another also, it is possible that he may have been under-forester to some nobleman or gentleman in the neighbourhood. At all events, he has now amassed a little wealth; is owner of a couple of sea vessels that trade from Perth or Dundee to the Baltic; and, in a word, he considers himself as fully competent to enlighten the world on “Naval Architecture and Arboriculture.” "
It is true that Patrick Matthew of Gourdiehill owned land with an orchard (big at that) and, later in life, was co-owner of two sloops trading with the Baltic (ht Anne Carroll). He also grew timber on some leased patches, but the stuff about a seafaring youth as a surgeon's mate is probably the first mix-up of the surgeon from Newbigging with the orchadist from Gourdiehill.

Conclusion
While Edinburgh University seems to be a likely source for revolutionary ideas about geology and biology at the time, we have no palpable proof for Patrick Matthew of Gourdiehill having been educated, there, as a regular student. In the shortest case, he went to Edinburgh for one chemistry lecture in October 1808—a form of edutainment. In the longest case, he did spend some weeks, but less than than three month, there for an educational leave serving his self-improvement as an estate manager. He surely did not attend in 1804-05 and 1805-06.
     Edinburgh University's record of a historical alumnus called "Patrick Matthew" (see section: The misattributed matriculation record) is definitely a compound record of two namesakes. Patrick Matthew, the medical student from Newbigging, studied medicine in 1804-05 and 1805-06, got a diploma from the Royal College of Surgeons in 1806, went to India as an assistant surgeon thereafter, got promoted to surgeon in 1820, and died there in 1830. The contribution of the orchard owner from Gourdiehill to this compound record has been detailed in the previous paragraph. As the only son with fife sisters and a widowed mother, he would hardly have gone to study a full curricular course of studies at a university, when he had to manage the family estate.
     Anyway, with this state of affairs, speculating about Gourdiehill P.M.'s tutelage under Prof. Thomas Charles Hope (see Dempster 1996) is mere speculation. Worse still, suggesting a link of knowledge transfer from James Hutton to Patrick Matthew of Gourdiehill via the chemistry professor is spinning a new myth from mere speculation. 

Thursday, 1 March 2018

Comparing the respective transmutation mechanisms of Patrick Matthew, Charles Darwin and Alfred Wallace

The original article has been published at the Biological Journal of the Linnean Society 123(4): 864-78 (2018): https://academic.oup.com/biolinnean/advance-article/doi/10.1093/biolinnean/bly003. [This link brings you to a guest entrance, that is, through the paywall to the full article.] A pre-print version is available here.

The elaborate acknowledgements
I'd like to take the chance to be more elaborate, here, than in the published paper. After a rash rejection by the Journal of the History of Biology, Mike Weale has, for some time, engaged in a ping-pong game of him commenting on the manuscript and me sending him corrected versions back. I also invited Julian Derry to become co-author around that time, but the plan never panned out for various reasons. Nevertheless, Julian's input via e-mail discussions was as helpful as that of Mike Weale.

Despite these important roles of Julian Derry and Mike Weale, the three of us reconstruct Matthew's views differently. (Reconstruction is inevitable for a record as incomplete as Matthew's. It's as if we have a most complete fossil record for Darwin, most of it for Wallace, but only a jaw, and a leg, and a tail for Matthew.) Let me sketch the differences between Weale, Derry and me as aptly as possible. Weale believes that Matthew proposed an early version of species transmutation through natural selection. Derry and I disagree.
    I think Matthew's scheme proposed species transmutation with natural selection also being in it, but not being the central force that does the transforming. On the contrary, Matthew's scheme suggests that natural selection works species fixing except after catastrophes have ripped remnant species apart and thrown them into habitats which they did not naturally occupy before the catastrophe. That is, natural selection only ever works (anagenetically) to adapt a lineage to its environment and the catastrophe does the lineage splitting. Natural selection does play some role, here, during the process of species transformation and lineage splitting, but not the central role that it does play in Darwin's mature theory. In the latter, natural selection and the principle of divergence were sufficient to effect divergence and speciation in symparty.
    Finally, Derry reads Matthew as having >natural selection and species transmutation, separately, but both do not work together in the transformation. Hence, out three different readings of Matthew (1831, On Naval Timber and Arboriculture) can be aptly summarized as species transmutation through natural selection as the central factor (Weale), species transmutation with natural selection playing a lateral role (me), and species transmutation without natural selection playing any role in it (Derry) but getting a species fixing role after transmutation.

The information about the enigma of Matthew's university education reached me via Mike Weale, but he insisted that his source, Anne Carroll then of Perth Library, be acknowledged for it rather than him.* David Lloyd was a peer reviewer who waved anonymity. He and two anonymous reviewers helped to improve the paper a lot, especially on Alfred Wallace. A rant about the second reviewer (there were four in total) could follow, but everybody knows what "reviewer no. 2" means. I must praise the gumption of the editor in chief, John Allen, however. When I challenged the one glib and uncomprehending sentence that constituted the 2nd review, he bethought himself and revised his decision from rejection to re-write. Finally, thanks to Alexandra Elbakyan for literature.


* [A great amount of new information concerning the enigma of Matthew's education has been collected by a team (Anne Carroll, Julian Derry, Mike Weale, and I) and I have collated it in a blog piece lest I forget the links and details. In my opinion, this is a fine example of a person (Patrick Matthew from Newbigging—not Gourdiehill) that has for a long time rotten in the archives as a person of no historical significance whatsoever, brought back to life and linked to a question of historical significance by four accomplished sleuths.]



Abstract 
A comparison of the evolutionary mechanisms of Patrick Matthew, Charles Darwin, and Alfred Wallace highlights their differences. In Matthew’s scheme, catastrophes initiate periods of radiation and speciation until a fully stocked environment gets into stasis. Catastrophes first needed to exterminate competing species before the survivors could radiate into free niches and diversify into new species. In Darwin's early theory conditions of life, such as prevail under domestication, first need to increase the variability of a species, before natural selection can transform it. In Darwin's mature theory competition replaced conditions as the main drive behind evolutionary change and sympatric speciation becomes possible. Wallace’s theory differed from both Matthew’s and Darwin’s. Interspecific competition was neither a brake halting transmutation (as in Matthew’s) nor intraspecific competition a sufficient drive for it. While each theory integrated natural selection with variability, competition and changed conditions in distinct ways, each allowed for species transmutation somehow. The result was similar (transmutation), but the mechanisms yielding that result (the integration of natural selection with variability, competition, change in conditions) differed significantly.

Saturday, 17 February 2018

G.C. Williams and J. Maynard Smith conceived the maintenance of sexual reproduction differently

[This blog post was a mere comment on Sandwalk first, because I thought someone there was confused about the different conceptions of the cost of sex. See this thread, particularly towards the end. The following expands the comment, there, into its own blog post, here. But it just explicates the differences between two historically important conceptions of the cost of sex and does not pretend to offer a resolution. There's also an article here, that also does not pretend to offer a resolution of the paradox of sexual reproduction. But it describes how, despite their different conceptions of the issue, Williams and Maynard Smith were able to communicate with each other fruitfully and amicably. In fact, I find that rather amazing. Often, such situations tend to escalate into a useless dispute with both parties at cross-purpose. None of that ever happened. On the contrary, Williams and Maynard SMith were able to understand each other despite their different assumptions and advance the issue in a dialectic way rather than the contrarian fashion.]


George C. Williams
George Williams conceptualized the maintenance of sexual reproduction as a problem of selection within one species or population. He began by considering organisms that include both sexual and asexual modes of reproduction within their complex life-cycles, for example, aphids & rotifers or strawberries & corals. He conceived the cost of sexual reproduction as the cost of meiosis, that is, the cost of reducing the relatedness with the own offspring from r = 1 to r = 0.5, when these organisms meet the time or conditions for switching from asexual to sexual reproduction. With this kin-selection conception he took the maintenance of sexual reproduction as a problem of selection within a population. Herein, he disagreed with Maynard Smith: 
“I think that the primary disadvantage of sexual reproduction in relation to asexual is most fruitfully formulated as a paradox of kin selection—an organism devotes resources to the production and care of a more distant (r = 0.5) rather than a close (r = 1) relative. This formulation provides a number of advantages. In its focus on genes identical by descent, kin selection is genetically explicit and relates directly to evolution. Maynard Smith’s economic argument (resources wasted on males) makes it easy to overlook the fundamental distinction between (1) the evolutionary problem of sexual and asexual reproduction as alternative character states in a population, and (2) the purely ecological question of competition between a clone and a Mendelian population.” (Williams 1978, ‘Mysteries of sex and recombination. A review of The Evolution of Sex by John Maynard Smith.’ Quarterly Review of Biology 53: 287–289. Page 298)
“I believe that understanding has been hampered by failure to distinguish the ecological from the evolutionary problem of sexuality. In important ways, insights gained from conceptual or experimental comparisons of sexual populations and competing clones (the ecological problem) may mislead in relation to sexual and clonal reproduction as alternative processes in a population (the evolutionary question with which I am concerned here).” (Williams 1980, ‘Kin selection and the paradox of sexuality.’ In Sociobiology: Beyond nature/nurture? Ed. by G.W. Barlow and J. Silverberg. Boulder, CO: Westview: 371–384. Page 372)
The fact that William and Maynard Smith cut the cake differently gets obvious from the way in which Williams treated the maintenance of recombination as not the problem he was at all concerned with:
“I assume that observed chromosome numbers and crossover rates reflect the optimum compromise between maximizing whatever benefits there are in recombination, and minimizing recombinational load. Tighter linkage must reduce recombinational load, but it does nothing to alleviate the cost of meiosis.” (Williams 1975, Sex and Evolution, Princeton Univ. Press, p. 108)
That is, reducing replication-rate by fusing gametes is not alleviated by assuming, for example, a species with a genome consisting of one homologous pair of a giant chromosome and no crossing-over between this homologous pair. [Felsenstein and Yokoyama (1976) modelled this problem.] That would exclude recombination through segregating heterologous chromosomes as well as through crossing-over between homologous chromosomes, but it would not pay the cost of reducing r from 1 to 0.5, or the cost of males, or the cost of fusing gametes, or whatever you conceive the cost of sex to be.

John Maynard Smith
John Maynard Smith conceived the maintenance of high recombination rates (not sex) as a problem of within-population selection between alleles that increase and others that decrease recombination rates. [This differs from Williams's within-population problem of a species with a complex life-cycle and both sexual and asexual modes of reproduction within it.] He accepted Williams's criticism of group-selection arguments for this issue (what he called the "balance argument" of Williams). He agreed that this problem requires an immediate individual-level explanation. But he also maintained that the competition between a sexual population and a genetically isolated asexual clone is a case of between-population selection. At this level, he did allow for long-term or group selection to play some (limited) role.

Anyway, his distinction begins in the preface already:
"I am under no illusion that I have solved all the problems which I raise. Indeed, on the most fundamental question - the nature of the forces responsible for the maintenance of sexual reproduction and genetic recombination - my mind is not made up. On sex, the relative importance of group and individual selection is not easy to decide. On recombination, group selection can hardly play a significant role, but it is not clear to me whether the short-term selective forces I discuss are sufficient to account for the facts, or whether models of a qualitatively different kind are needed." (Maynard Smith 1978, The Evolution of Sex, Cambridge Univ. Press, p. ix)
"It may help to classify the various theories; first, according to the time scale on which selection is supposed to act, and then according to the 'unit of selection' - population, individual, or gene." (Maynard Smith 1978, p. 1)
"I do not find it possible to give an unequivocal answer concerning the role of group selection in the maintenance of sexual reproduction. It has played some role, as evidenced by the taxonomic distribution of parthenogens; but it is not the only relevant force, as will be apparent from the review of the balance argument in Chapter 4, section E. But, whatever one may think of the role of group selection in the maintenance of sex, it cannot explain how it started, and it cannot explain the maintenance of high levels of genetic recombination within sexual populations." (Maynard Smith 1978, p. 6)

And so throughout the book. Maynard Smith consistently distinguishes the maintenance of sexual reproduction from that of recombination, the former being an issue of selection between isolated populations and clones, the latter being one of selection between alleles within one population.

Maynard Smith's support for "some role" of long-term or group selection in the maintenance of sex (not recombination) was also defending his earlier publication from 1958 (The Theory of Evolution, Penguin Books, pp. 138-139). It is often forgotten in potted histories about the paradox of sex, that Maynard Smith did already clearly state the cost of males in this early pop-science writing and also embraced the long-term group-selection explanation of the maintenance of sex.
"If the rate of increase of an animal population were limited by the number of eggs which each female could lay, which in turn depended on how much food a female could eat and transform into eggs, then a population consisting entirely of parthenogenetic females would increase twice as fast as would a population of equal numbers of males and females. From the point of view of reproduction, males are a waste of living material. (This argument does not hold for hermaphroditic organisms, or for those animals in which both parents help to feed the young.)      The compensating advantage of the sexual process is that it increases the range of potential variation in a population, and therefore, its evolutionary plasticity." (Maynard Smith 1958, p. 138)
"Thus the sexual process is a means of ensuring evolutionary plasticity at the expense of interfering with reproduction. [...] Now if the advantage of sexual reproduction is that it increases the range of potential variation in a population, then the advantage refers to the population as a whole, and not to any particular individual in it. It follows that sexual reproduction has been established as a rule, both in animals and plants, because selection has favoured some populations at the expense of others. This forms a contrast to the the examples discussed in the last chapter, in which the 'unit' selected was the individual and not the population." (Maynard Smith 1958, p. 139)

By the way, Ghiselin (1988, p. 16, in Michod & Levin (eds): The Evolution of Sex), reminisced an instance of Williams reviewing one of his papers and telling him about the twofold cost of sex and that he [Williams] had found it in a book by Maynard Smith (1966), which must have been the second edition of the above quoted Penguin book by Maynard Smith (see also Dagg 2016, On recognising the paradox of sex. Philosophy, Theory, and Practice in Biology. DOI: 10.3998/ptb.6959004.0008.003).

The fact that John Maynard Smith never changed his mind about his hedged support for some role of group (between-population) selection in the maintenance of sex is clear from an interview of Richard Dawkins with John Maynard Smith in 1997 (deposited at the Web of Stories in 2008).