I’m preparing to teach genetics again, and as usual, I’m trying to rework some of the lectures, because I don’t care to say the same thing every year. I had one odd thought that I’m probably not going to squeeze into the lectures this year, but thought I’d bounce it off people here.
Evolution and genetics were on parallel tracks in this very interesting period of 1860-1910. While the American Civil War and the Franco-Prussian War and the Boer War might have been distracting most people, biologists had their own obsessions. Charles Darwin published in 1859; Gregor Mendel in 1863. Darwin had immediate popular success, while Mendel was basically ignored and neglected. I was contemplating why the difference was there, and had a random idea.
Darwin started with a phenomenological and largely descriptive foundation, no significant math anywhere in The Origin. Mendel’s brief paper was little more than a mathematical hypothesis, with limited qualitative description — it was just peas, one model system, and the traits weren’t even particularly interesting, except for the fact that their inheritance was so discrete.
Evolution took off fast, and rather erratically. There were so many bad hypotheses built on the framework of natural selection (for instance, all of Haeckel’s work) that by the end of the 19th century, Darwinism (and in this case, that was an appropriate name for it) was fading, and people were finding flaws and poking holes in the idea. The absence of a quantitative basis for analysis was killing evolutionary theory.
Meanwhile, Mendel’s laws of inheritance weren’t getting any attention, but there was all this foundational qualitative work getting done — cell theory was being established, microscopy was taking off (instruments were reaching the physical limits of optics), Weismann had worked out the limitations of cellular inheritance, Sutton and others were publishing all this tantalizing stuff about chromosomes. When 1900 rolled around and Mendel was rediscovered, everyone was primed for his statistical/probabilistic theory of inheritance. We could do math on it!
Also, evolution was rescued by it’s happy marriage to genetics and in particular, population genetics. We could do math on evolution, too!
Everything is better with mathematics, is my conclusion. Except maybe individual success — before 1900, someone could come up with a hot theory and get it named after themselves. Afterwards, there’s too much detailed quantitative thinking going on for any one person, and eponymous theories went out of style, being regarded with suspicion, even.
Along comes SMBC to correct me:
OK, OK, it’s not just mathematics, it’s thinking precisely. But isn’t that what math is? How do you think precisely without the application of math and statistics and quantitative reasoning?
The real key thought to get out of the SMBC cartoon above is that it is quite frequently math abuse to apply math to imprecise things. We’d greatly mitigate the techbro / libertarian douchebag / nazi atheist problem if we could get miscreants to understand this.
I think it is more that science deals with discrete observations that then require a continuous relationship to explain as a phenomenon. Math simply provides a fundamental relationship that gives a continuous means of organizing the discrete observations so they can be predicted.
There is also a huge difference in the circumstances of the two men. By 1860 Darwin had been a member of the Royal Society for more than 20 years, having been elected at 29. He was the author of a long series of well received natural history books based on his time on the Beagle and observations in Britain, on topics from coral atolls to worms. Mendel was a studious monk who had failed his exams to become a high school teacher and published his work in a local science society journal. His religious duties increased after he became abbot of the monastery interrupting any followup research. It is entirely possible that no one capable of understanding the importance of his discovery ever saw his paper while Darwin already had an influential audience waiting for his next publication.
Did Mendel publish his findings in English or German?
Going further than John Watts #4
Mathematics is in many ways its own language. Philosophers often talk about how natural languages suck because they are ambiguous and sloppily grammared etc. and try to create new ones. They fail. The Klingon-language does not fail. Because in order to do the main survival thing for humans, you need the slop. People grow up learning to communicate that way in which there are five definitions for a word that sounds like ‘right’ (rite, wright).
People who think precisely -and these are not philosophers- do math and suddenly there’s new symbology that always means the same thing all the time. If you’re brain is not set to understand a new code-system this is a challenge. If it is, it is a lesser one. But that’s the thing: talking precisely to people gets you into godsdamned trouble. Science requires standing on the shoulders of giants, so you need to talk so other people will listen. Surviving day-to-day involves going to the grocery store and not getting your head chopped off by someone who’s better at swinging (hopefully) metaphorical swords at you than you can sharply talk.
Of course Mendel got ignored.
German. That shouldn’t be a factor, though, since German science was esteemed.
@John Watts #4:
German. While that was the commonly used language for scientific communication in Northern Europe at the time, it does seem unlikely that a journal published in a distant, small regional capital ever made its way to the Royal Society or to any of the major British universities. Even as Darwin’s ideas spread in the 1860s and 70s no-one in Brno seems to have considered a connection with Mendel’s work, and as time went on it was increasingly less likely that anyone who had read it would remember it.
I’ve become known as the language police in several companies–imprecise, “we all know what we mean”, language has caused too many production delays. It is particularly bad in biotech where multiple domains have to come together–and while it is usually clear whether we are talking about the pathologist’s “sample”, the instrument manufacturer’s “sample”, or the statistician’s “sample”, that isn’t always true.
More than once I’ve seen heated arguments come to quick and amicable resolution once those involved realized they weren’t actually talking about the same problem.
Evolution was something that had been debated long before Darwin and Wallace came up with natural selection and sexual selection. Everyone knew evolution was occurring but was puzzled over the exact mechanism. Part of the key to that puzzle was discovery of geology of the immense age of the planet. Mendel was doing something new and was not well known in the evolution debate, and was published in an obscure journal.
Rich Woods @ # 7: … it does seem unlikely that a journal published in a distant, small regional capital ever made its way to the Royal Society or to any of the major British universities.
Can’t recall just where I read this, but apparently a copy of the journal in which Mendel published was found in Darwin’s library.
Printing at that time entailed long sheets of continuous paper, and readers had to use scissors or knives to separate the pages. Though Darwin could read German in a limited way, he had not applied any such tool to this particular publication, so we know he did not read it.
Imagine how scientific history might have changed if he had …
On precision and math, I thought of Kepler and Brahe, where Brahe provided the precision and Kepler the math. (I haven’t actually read the post yet, just looked at the pictures. I think that causes more problems…)
Dear PZ, First of all, I know you are diligent and like to review your work and refine it. But, don’t run yourself ragged trying for ‘fresh content’ (that’s just a stupid pop culture idea). Remember, only those who are repeating your classes will know if it is the same as last year.
You said, ‘Everything is better with mathematics’. I agree that is generally true. However, That just doesn’t add up (every time). There are ‘artistic’ endeavors that are not precise or mathematical and yet they can still be masterpieces.
No miracles! And, it’s more than just thinking precisely, it must also be rational, or you are wandering back into the swamp of miracles again. Don’t create an endless ‘logic loop’.
And, to mix topics, we ‘observe’ that the tRUMP is trying to make the united states ’empirical’ again. And, that was a disaster the last time it was tried.
Stay sane, PZ.
Oh, and by the way, I notice there are a lot of ‘new faces’ in the comments. I don’t have the data, but it seems you are gaining quite a following (and that is appropriate). Just don’t go crazy for followers and turn this blog into another disgusting muskrat xhitter.
@10 Pierce R. Butler
https://www.nature.com/articles/s41437-019-0289-9
Fairbanks shows that Mendel on the other hand may have had some familiarity with Darwin’s views.
See too: https://www.pnas.org/doi/10.1073/pnas.2122144119
Renowned Darwin biographer Janet Browne and Andrew Berry write:
So what about Mendel’s approach to Darwin’s work? From Berry and Browne in PNAS above:
So Darwin was ignorant of Mendel, yet Darwin was percolating through Mendel’s brain? Fairbanks from the Nature link above:
And so on…
Fairbanks really pushes the idea of Darwin’s covert then overt influence on Mendel. He was involved in a Darwinized translation of Mendel’s work that leans toward this view. I don’t have the background to critically evaluate such an idea, but I will link it here:
https://pmc.ncbi.nlm.nih.gov/articles/PMC5068835/
But then B. E. Bishop:
https://academic.oup.com/jhered/article-abstract/87/3/205/908553
So…
Darwin was wealthy. Mendel was not.
It’s easy to promote a theory or one’s scientific work when you don’t actually have to work for a living and equally important, your wealth allows you access to the people who will be interested in your work and who might actually use it.
Gregor Mendel was a monk who did not come from a wealthy family. Even though the abbey provided, everyone in it had to work.
Ask anyone who has ever poured blood, sweat & tears into a passion project how much time it took. The ones who have to work for a living usually have to take far longer to get the thing done.
Meh. Everyone was rushing to stamp their own interpretation of evolution on Darwin, so I don’t see much point in arguing whether any old 19th century guy was pro or con.
Meh? Meh?
Mendel wasn’t just “any old 19th century guy” per any pro or con views he had on Darwin. There are far worse ways to spill too much ink than reflecting on Darwin influencing Mendel, since the opposite direction is clearly off limits.
Okay, how about a parallel take on it?
Discus how Boolean mathematics was originally designed by George Boole in 1854, but was considered more of a curiosity rather than having practical uses, although some famous people played around with it. At least until Claude Shannon realized it had a real-world application in 1937 for optimizing telephone switching relays. (Note: I just read this on wiki. It was new to me but relevant. Of course I know who Shannon is, but I didn’t realize his first suggested use of boolean logic was on telephone relays.)
The lesson is that sometimes the math has already been created, but until science or technology develops to the point where the math is useful, it may just remain buried in technical papers. Innovation does not occur because a lone, rogue, scientist is working on “Things Man Was Not Meant to Know!”, but because the work of many people collaborate. Sometimes whole groups of people head down the wrong path (remember N-Rays?). But, because science, all science, is collaborative, the process will eventually reach an greater understanding of the universe.
There are probably other examples beyond Boole. Maybe other commenters can think of some?
“Though Darwin could read German in a limited way, he had not applied any such tool to this particular publication, so we know he did not read it.”
Apparently quite limited. He seems to have depended on his wife, Emma, for some of his German translation (women of her class were typically educated in modern languages while their brothers were taught the classical languages necessary for admission to Oxford/Cambridge). Their daughter wrote “My father often said that where she [Emma] failed in making out and translating a sentence for him in German, a non-scientific German would generally also fail.” (EMMA DARWIN: A Century of Family Letters https://darwin-online.org.uk/converted/published/1904_EmmaDarwin_F1552/1904_EmmaDarwin_F1552.1.html) The daughter also wrote that Emma knew French well and also a fair amount of German and Italian.
The poet thing bothered me.
There’s no precision in art? No math?
fishy, that bothered me as well, as I remember an aphorism that inspiration without technique yields incompetence, but technique without inspiration yields sterility. You do not usually find artists completely lacking in one or the other, but find them with qualities of both. (And in my own case, one of the harshest criticisms I remember receiving as a young student was along the lines that my technical skills were secure but where were the big ideas?)
“Talking precisely about precise things” is more plausibly a description of logic than it is of mathematics. Mathematics, the axioms of set theory, the structure provided by the principle of induction are much more substantive than simple logical precision.
Sorry to burst your bubble but math does not work more often than it does.
You can keep adding one apple to one orange but it won’t make two pears.
One plus one equals two only in very specific conditions.
Nice interesting post, I think. And to rietplum, isn’t being clear about the specific condition for which 1+ 1 = 2 an example of the precise thinking we need to do when we apply math?
@Jack Krebs #26 – There are no such conditions in math itself. In math, one plus one equals two unconditionally.
Of course, I posted #25 more or less jokingly, but the point is that math is not applicable in different fields of study by some sort of miracle. We have to do something to make it applicable. People are forgetting that when they say it’s astonishing how it just works in so many areas.
Hemidactylus @ #s 14-16 – I sit corrected.
So many details, so many devils.
Maths is like sex. If you know how, it’s much more fun doing it than talking about it.