I have an intellectual toolkit that I use repeatedly while thinking about social systems. Long time readers probably use many of the same tools, such as the notions of regression toward the mean, nature v. nurture distinctions, bell curves, and so forth. On the other hand, it's pretty clear that these tools are second nature for only a very few people in our society. The articles in major newspapers are clearly written and edited largely by people who, while they may grasp these concepts in theory, do not regularly apply them to the news.
In general, it seems as if people don't like to reason statistically, that they find it in rather bad taste. For example, the development of statistics seemed to lag a century or two behind other mathematics-related fields.
Compare what Newton accomplished in the later 17th Century to what Galton accomplished in the later 19th Century. Both are Englishmen from vaguely the same traditions, just separated by a couple of hundred years.
From my perspective, what Newton did seems harder than what Galton did, yet it took the world a couple of centuries longer to come up with concepts like regression to the mean. Presumably, part of the difference was that Newton was a genius among geniuses and personally accelerated the history of science by some number of decades.
Still, I’m rather stumped by why the questions that Galton found intriguing didn’t come up earlier. Is there something about human nature that makes statistical reasoning unappealing to most smart people, that they’d rather reason about the solar system than about society?
Take another example: physicist Werner Heisenberg and statistician R.A. Fisher were contemporaries, both publishing important work in the 1920s. Yet, Heisenberg's breakthroughs seem outlandishly more advanced than Fisher's.
Take another example: physicist Werner Heisenberg and statistician R.A. Fisher were contemporaries, both publishing important work in the 1920s. Yet, Heisenberg's breakthroughs seem outlandishly more advanced than Fisher's.
A couple of commenters at Andrew Gelman's statistics blog had some good thoughts. Jonathan said:
Physics and mechanics were studies of how God made things work. Randomness is incompatible with God’s will. Newton, Leibniz, even Laplace (“I have no need for that hypothesis”) were quite religious men trying to uncover the fundamental rules of the universe. Statistics is sort of anti-rules discipline, since randomness (pre-quantum physics, say 1930) is not part of the structure of the universe… it’s part of our failed powers of observation and measurement. Gauss realized this and developed least squares techniques, but unless you think “God plays dice,” the theory of statistics was always going to lag physics and mechanics.
R McElreath says:
There’s some history of the perceived conflict between chance and reason in Gigerenzer et al’s “The Empire of Chance”.
Quick version of the argument: The Greeks and Romans had the dueling personifications of Athena/Minerva (Wisdom) and Tyche/Fortuna (Chance). Minerva was the patron of reason and science, while Fortuna was capricious and even malicious. Getting scholars to see Fortune as a route to Wisdom was perhaps very hard, due to these personifications.
As Ignatius J. Reilly says in A Confederacy of Dunces:
“Oh Fortuna, blind, heedless goddess, I am strapped to your wheel. Do not crush me beneath your spokes. Raise me on high, divinity.”
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In order to do good statistics you need good data. I think that could be the big difference between Newton's time and Galton's time: Galton had more and better data to work with.
But Galton collected a vast amount of his data himself, counting attractive women in different towns, setting up a laboratory to measure people with calipers, looking through genealogies -- all made easier by advances in technology, true, but nobody else before Galton seemed terribly interested in what Galton was interested in.
Correct me if my history is off, but didn't Galton develop the idea of regression toward the mean as a way to explain how parents with exceptional characteristics often had children whose characteristics were closer to the mean? The whole idea rests on the premise of inherited traits from evolution. Presumably, before evolution was a fashionable idea, the inheritance of parental traits wouldn't have been a scientific (or at least a mathematically scientific) subject.
There's something that's always been an even greater puzzle to me...
I think a case could be made that Darwinian evolution is the most significant scientific discovery in history, outdistancing any of the work of Newton or any other physical scientist. Yet it has always seemed to me that evolution could have been discovered at any point in the last few thousand years, since its sole necessary assumption is that "like gives rise to like," which was well known to all farmers or animal breeders.
Obviously, the later Modern Synthesis, based upon the discovery of genes, might have come later, but the basic notion of Natural Selection seems like something that could have been explained to any smart ancient Greek or Egyptian in ten minutes. Not so for things in the physical sciences.
Right, Galton was galvanized by his cousin's theory of natural selection.
But, nobody was interested in inherited traits before Darwin?
In general, it seems kind of baffling, like how nobody in Europe climbed mountains or even seemed to notice individual mountains until the Romantic Era of the late 18th Century. But mountain climbing is kind of silly, while statistical reasoning is obviously useful in, say, agriculture.
And, indeed, the rise of scientific farming inspired Darwin who inspired Galton who inspired Fisher to move from the city to an experimental farm.
"but the basic notion of Natural Selection seems like something that could have been explained to any smart ancient Greek or Egyptian in ten minutes. Not so for things in the physical sciences."
Right.
Various British thinkers more or less stumbled upon natural selection before Darwin (Hutton? Smith the geologist?), but never quite got the whole picture together or didn't pursue it. A lot of people such as Erasmus Darwin came up with evolution without natural selection, but some people came up with natural selection but not evolution.
If memory serves, Italian mathematicians were reluctant to discuss probability - after all, it had distasteful, dismal connections to gambling. Who wants to encourage gambling?
Since all of Western Civilization has been heavily influenced by Christianity since at least the 4th century, a number of Christian ideas continued to prosper even when European intellectuals lost interest in it. I think a lot of the interest in determinism and cause and effect comes from a Christian conviction that God created the perfect world, and it's only human beings who are flawed.
The Greeks and Romans had a strong sense of chance and fortune - Lucretius said that we have free will because atoms sometimes move in unpredictable directions - but the Greeks and Romans also had a strong bias against practical mathematics, engineering and other such forms of craftsmanship. Aristotle had an exceedingly low view of Pythias, who was a sculptor whose works were as highly regarded in his day as Michelangelo's are now. Archimedes crafted all sorts of incredible killing machines whose blueprints he never bothered to jot down, because he viewed engineering as being such a vulgar affair. The Ancients valued pure, pristine knowledge, and using your wits to make things was virulently shunned.
From my brief review, it appears that the modern growth of statistics has emerged from getting away from two bias: the medieval bias that the world is perfectly orderly, and the ancient bias that knowledge should be its own end, and not have practical effects.
Heisenberg and R.A. Fisher were pretty much exact contemporaries, both publishing major breakthroughs in the 1920s, but Heisenberg's are so much more outlandishly brain-twisting.
There is also a theme around the study (or theory) of causation. Aristotelian theory of causation (in the thing's nature) was much different from Newtonian (god's laws), which in turn was much different from the Scottish enlightenment (free will implying that future events are unpredictable.) Darwin was heavily influenced by Smith. Before Darwin I don't think anyone thought that randomness (specficall differential reproductive success by random combination, mutation, etc) should be considered causal explanations.
Personally, I found college level statistics to be harder than calculus. I am not sure whether that has anything to do with what Galton did though.
I do think that Steve is on to something though - the high hanging fruit was plucked in this case because of the perceived value. Understand physics, and understand the world so the idea goes. This is expressed in this xkcd comic:
http://xkcd.com/435/
Even though statistics is still math and hence "pure", it does get misunderstood. And there is always that "lies, damned lies and statistics" that causes many a mind to close forever on the subject.
From my perspective, what Newton did seems harder than what Galton did, yet it took the world a couple of centuries longer to come up with concepts like regression to the mean.
No, I don't think the one was "harder" than the other. In some ways regression to the mean is "harder" to come up with - we see gravity in action every day of our lives, but regression only becomes apparent when you analyze large amounts of data.
But people are constantly analyzing other people: the standard example of regression toward the mean is parent-child height, which is quite visible.
statistical reasoning is obviously useful in, say, agriculture.
I don't think it was at all obvious until recently. In fact the field of statistical analysis did not exist until recently, so nobody could have applied it even IF they had realized it would be useful.
people are constantly analyzing other people
You are using the single word "analyzing" in at least two very different ways here. You can say that every time I look at another person - say a member of the opposite sex - I am "analyzing" them, but that's a qualitatively different thing from what we mean by data analysis. In some ways the two things are polar opposites. The entire point of data analysis is to find things which are NOT obvious from looking at people. Regression to the mean is precisely such a counter-intuitive discovery.
"Is there something about human nature that makes statistical reasoning unappealing to most smart people, that they’d rather reason about the solar system than about society?"
I think it's mostly subject matter dependent. One of the main points of Jonathan Haidt's book, "The Righteous Mind" is that when we are presented with some fact or problem, we often have a visceral reaction of approval or disapproval. When this happens, instead of logically examining the proposition, if we disapprove, we ask ourselves if we have to believe it. If we approve, we ask if can believe the proposition. We look for any snippet of fact on which we can confirm or reject, in accordance with our bias. We don't want to statistically analyze the situation and find out that our biases might be wrong. When thinking about society we're far more likely to have a visceral reaction than when thinking about the solar system (unless it upsets our religious beliefs or something, as was the case in the Renaissance. But then again, that makes it social, doesn't it?).
"The entire point of data analysis is to find things which are NOT obvious from looking at people. Regression to the mean is precisely such a counter-intuitive discovery."
People spent a lot of time thinking about good-looking people marrying good-looking people and what their kids turned out to look like.
"The whole idea rests on the premise of inherited traits from evolution. Presumably, before evolution was a fashionable idea, the inheritance of parental traits wouldn't have been a scientific (or at least a mathematically scientific) subject."
Of course people have always known how inheritance works. Farmers knew it, the aristocratic breeders of horses and hunting dogs knew it, parents knew it. The phrase "good breeding" was constantly applied to people. The idea that humans evolved in this way from lower life forms - that's a different story. I'm aware of only one pre-modern instance of it. I remember Bernard Lewis quoting in one of his books a medieval Arabic author who said that humans are descended from lower animals.
It seems to me that for a long time people underestimated the age of the Earth and of life on it. The sort of unnatural selection that farmers practice on sheep isn't going to change sheep drastically over 5,000 years. Natural selection would have an even smaller impact in that time frame. Perhaps if they knew that life on Earth has existed for billions of years, more of them could have imagined us descending from things that don't look like us in the least.
I think I do remember reading ancient Greco-Roman authors referring to what we might call natural selection in humans. They thought that difficult environments (the north, mountains) bred tribes of hard men and that easy environments bred soft men. Tacitus definitely thought that.
Here is Aristotle, in the Physics I think:
Our teeth, for example, come up by necessity–the front teeth sharp, fitted for tearing, the molars broad and useful for grinding down the food–since they did not arise for this end, but it was merely a coincident result; and so with all other parts in which there appears to exist a purpose. Wherever then all the parts came about just as if they had come be for a certain purpose, such things survived, being organized spontaneously; whereas those which grew otherwise perished and will always perish.
I was shocked when I learned how late statistics (state-istics as opposed to Cardano-style gambling probability) arrived on the scene. Maybe prior to that the world just seemed too haphazard?
But maybe it's somewhat the other way around. Classical physics is ultimately about predicting where a cannon ball (of any size) will fly. Now this is important stuff. The odd thing is that in it's own way it's turns into a very simple to understand problem. Just where does that apple fall? And maybe odder still, it turns out that, as hard as it is for college freshmen, who could have guessed that the rules governing so much of the universe were ultimately so simple, so widely applicable, and so comprehensible to the mind of slow-witted man?
i think a lot of this is basically "the wish to publish" versus "the wish to profit". Many of these things were, effectively, white-hot IP of their day. If you knew statistics well, you could make a lot of money doing various tasks (the classic example being the invention of actuarial tables during the scottish enlightenment for setting pensions)
So if you have this tool-kit which is actually really handy in lots of interesting ways, *why on earth* would you disseminate it for free? Remember, Newton only showed the world Calculus when Leibnitz showed up with his own version and wanted the world to know what he had done.
I wouldn't be surprised in the least is stats were known to Venitian merchants, as an example.
the standard example of regression toward the mean is parent-child height, which is quite visible.
I don't think that actually is quite visible. You'd have to examine a fairy large pool of people over a fairly long period of time before you noticed the tendency for height to even out across generations.
And the very conception of looking at large amounts of data over large amounts of time was a huge conceptual breakthrough. It's so central to our own lives that we tend to think it must always have been obvious to everyone, but its a new way of thinking.
It's interesting that economics developed before statistics, since it seems like you'd need the latter to evaluate the theories of the former. Adam Smith was 81 years older than Newton and 99 years younger than Galton.
Maybe in times past man was not so concerned with the origin of things. A simple tale would suffice. His mind was focused on the present and the practical matter of how things worked, to predict the near future.
The main chance was to exploit available opportunity. In agriculture, this mainly meant gains in improving the productivity of available land, or expropriating new land. Large, easy gains in clever breeding had long been gathered.
As populations expanded and margins receded, the enhanced probity of statistics became cost effective, and interesting. At the same time, a theory of origin that carried back beyond one's distant ancestors to non-human creatures also became interesting and plausible.
What do we have to gain in decision advantage from a theory of evolution? For making choices today with immediate impact, or deferred impact, does the knowledge that we descended from single-celled life improve our decision? If not, then how would this knowledge provide us advantage? How is it useful?
Neil Templeton
Yes, probability and regression to the mean don't come naturally to the human mind. But it took the great genius of Daniel Kahneman to discover this, about 100 years after Galton's work. So the order of geniuses goes Newton<Galton<Kahneman.
"In some ways regression to the mean is "harder" to come up with - we see gravity in action every day of our lives, but regression only becomes apparent when you analyze large amounts of data."
I disagree. Except for magnets and electrostatically charged objects the Earth was the only entity that was ever seen attracting anything. The idea that every object attracts every other object isn't intuitive at all. The idea that the attraction increases as distance decreases is weird too. In everyday experience the longer the fall, the bigger the bang.
The regression to the mean in height, beauty, smarts, leadership ability must have been always obvious to everyone. Great kings' children were almost inevitably disappointments. Founders of dynasties were often those dynasties' biggest stars. The ancients didn't quantify this effect, but they must have noticed it.
The simplest answer I can think of is that in a caveman society there was probably limited value in statistical reasoning. Instead we evolved to be physical cause and effect thinkers, eventually leading to mechanics and thought experiments about billiard balls colliding.
Hindu Calvin & Hobbes
Randomness is an equation, a rule, in itself. It's just one paint in the palette used to create the world :)
Cue music now :)
Statistics may be considered as set of math tools to "weigh the evidence." Statistics is not necessary if the decision to be made is obvious. It is valuable when the decision is close.
For many, if not most, "human interest" problems, the decision is close. Not only because we may be connected to affected parties, but also because we typically view the evidence and potential outcomes as impartial, subjective, participants. Because we're human.
The stakes are high, and the evidence is voluminous, detailed, contentious, and ultimately flawed with self-referenced bias. The decision is too close even for statistics.
Neil Templeton
OK, this is from "Islam, the Religion and the People" by Bernard Lewis and Buntzie Ellis Churchill, although I first saw it in Lewis's "From Babel to Dragomans":
"The Arabic language among languages is like the human form among beasts. Just as humanity emerged as the final form among the animals, so is the Arabic language the final perfection of human language and of the art of writing, after which there is no more."
The authors attribute this to "a 10th century Arabic encyclopedic work, probably written in Iraq."
"Emerged as the final form" is ambiguous. Emerged in what way? The quote isn't as surprising as I remembered it being.
The ancients did gather tons of data. Detailed astronomical tables go back to Babylonian times. But that's not very random, not a great subject for statistics. Ancient empires conducted censuses for taxation purposes. In 2 AD the Chinese government counted 57.67 million people in China. The Romans did censuses too, but the results did not survive to our day. I'm not aware though of any of them doing what we'd call statistical analysis of this data.
newtonian physics relates directly to the innate spearchucking/rockthrowing skills of homo sapiens. That is hardwired into us. Statistics is more of a learned as opposed to innate skill.
Until the Industrial Revolution endowed both the aristocrat and the commoner with unprecedented mobility - which also widened chinks first made in the social class system by Enlightenment theorists, most people, even the learned few, subscribed to the class system's prejudices, which admitted no challenges to its stratification of society. Until the class system came into question, no pragmatic value was assigned - or, indeed, was assignable - to collecting statistics about human beings, because one was not expected to rise above one's birth or to descend beneath it.
The word "stock" was applied both to human beings and to animals, even to animals bred by the more primitive methods before the Age of Reason. People came either from good stock, or from common stock, or from peasant stock, or from pagan stock, barbarian stock, &c. - and no one was expected in his life to depart from his class. Under that prevailing taxonomy why would anyone have identified a need to classify human beings by statistics collected about their attributes, forebears, susceptibilities, &c?
I think the answer is animal breeding, and to a lesser extent plant breeding
http://charltonteaching.blogspot.co.uk/2012/03/evolutionary-philosophy-versus-specific.html
It was not until *after* animal breeders had shown how it was possible to *adapt* breeds - mainly for agricultural purposes but also for hobbies (e.g. show pigeons) that the power of heredity became linked with the idea of *change*; and the metaphysical idea emerged that multiple minor quantitative changes might plausibly be assumed to lead to major qualitative change.
But the major evolutionary mechanism, adaptation, was established during the agrarian revolution, which was most advanced in Britain - ordinary people could see with their own eyes the power of selection; more food was one result; and a few people (professional breeders) made a living, made money from doing selection.
(This was, and remains, a metaphysical assumption - used to structure biological research - it was not and has not been a *discovery* of Natural Selection).
The other piece of jigsaw was, I think, the classification of living things from Linnaeus and on - which arranged species in graded and branching hierarchies such that cumulative quantitative change might plausibly be a cause of the species differences.
By this reasoning, Darwin could only come *after* the English agricultural revolution (of the 1700s).
Statistics is sort of anti-rules discipline, since randomness (pre-quantum physics, say 1930) is not part of the structure of the universe
It was Olivia Newton-John's grandfather Max Born who ushered in randomness as being part of the structure of the universe with his statistical interpretation of quantum mechanics.
Later life
Born's position at Cambridge was only a temporary one, and his tenure at Göttingen was terminated in May 1935. He therefore accepted an offer from C. V. Raman to come to Bangalore in 1935.[52] Born considered taking a permanent position there, but the Indian Institute of Science did not create an additional chair for him.[53] In November 1935, Born family had their German citizenship revoked, rendering them stateless. A few weeks later Göttingen cancelled Born's doctorate.[54] Born considered an offer from Pyotr Kapitsa in Moscow, and started taking Russian lessons from Rudolf Peierls's Russian-born wife Genia. But then Charles Galton Darwin asked Born if he would consider becoming his successor as Tait Professor of Natural Philosophy at the University of Edinburgh, an offer that Born promptly accepted,[55] assuming the chair in October 1936.[50]
-meh
Rise of empiricism took longer?
I don't enough about the history of mathematics to say why probability and statistics were late to the game, but this program might cover it: http://www.bbc.co.uk/programmes/b00bqf61
Steve,
As a physicist, I agree that the math behind quantum mechanics (ever looked at quantum field theory or superstring theory?) is harder than the math behind statistics.
However, maybe the ideas actually are harder behind statistics. I remember when I was a kid learning physics I tried to understand what limited how high I could jump – of course, it is energy, momentum, and all that. But, what bothered me was whether there was a sharp dividing line: e.g., could I jump 0.82973 meters high but not 0.82974 meters high. It did not seem plausible that there was a sharp dividing point. It was an epiphany when I realized that the answer was probabilistic: it continuously became less and less likely that I could reach a greater height, without there being any sharp dividing point.
Determinism is simpler than statistical indeterminism. And, then there are all the interpretations of probability – propensity, frequency, strength of belief etc.: as a physicist, I lean towards the frequency approach, but there are areas where this seems not to work.
Dave Miller in Sacramento
"By this reasoning, Darwin could only come *after* the English agricultural revolution (of the 1700s)."
Country boy intellectuals seem pretty crucial to this line of development.
Why would someone think about height reversion to the mean? Unless someone tried a breeding program to get taller humans, they would have not noticed this, only assumed people are roughly this height.
People were malnourished. They were not even hitting their peak heights. Further, most people were subsistence level farmers. You need a big surplus population with time to kill who start asking questions about random things.
Finally, look at 2013. People are forgetting 5000 years of human history and engaging in social and moral behavior that the ancients already knew would lead to destruction—and many of the people leading the charge are among the most intelligent. People today willfully do not see the obvious right in front of their face! So if people today can forget obvious truths and ignore it in their face, is it strange that it took generations to notice the seemingly obvious?
Newton saw himself as a 'natural philosopher' ie he saw his task as trying to explain the phenomena of the natural world by theories that actually worked and had a rigorous mathematical background. Basically, he saw his role as overturning the erroneos theories of the Greek philospohers which held sway for centuries and were treated as if they were carved in stone.
'Statistical science' on the other hand didn't develop from a strictly natural philosophic basis, but from the early insurance companies who were very interested in tabulating life tables in order not bankrupt themselves - the basics of statistics were all there, and the pre-industrial non standardized parts, largely non measuring world of Newton (where virtually all production was done in family workshops as 'one offs'), had no real use for statistics.
The growth of statistical science really mirrored 19th century industrial mass production and the rise in bureaucracy and government monitoring and control of economies etc.
Talking of RA Fisher, one of his dogmatic quotes was "No nation that practices contraception will avoid extinction". He said this in the 1930s at the the peak of the Margaret Sanger/Marie Stopes frennzy, and Fisher himself had many children.
Fast forward 80 years and consider the trendlines for the white nations of the world, and perhaps Fisher was on to something.
There is an entertaining tale of Francis Galton, (who was very interested in HBD), measuring the the bare projecting buttocks of a Hottentot woman in South Africa.
Victorian propriety forbade galton from the direct use of a tape-measure, so the ever ingenious Galton used a sextant from an appropriately 'respectful' distance.
Steve,
You wrote:
>I have an intellectual toolkit that I use repeatedly while thinking about social phenomenon. Long time readers probably use many of the same tools, such as the notions of regression toward the mean, nature v. nurture distinctions, bell curves, and so forth.
Have you ever systematically written up a list of what you consider the most important tools in your “intellectual toolkit”? It would be informative.
For my part, here are the tools that come to mind as the main tools in my own mental toolkit, drawn from physics and engineering (some of these are applicable also to biology, economics, etc., but I have left out concepts from those fields that are not applicable to physics, since others here know as much or more than I do in areas outside of physical science and engineering):
Equilibrium
Symmetry
Linearity/superposition
Stability
Rate of change
Mechanism
Positive/negative feedback
Non-linearity
Frequency domain (music, engineering, quantum mechanics)
Exponential growth
Chain reaction
Collective modes and motions (waves, etc.)
Resonance
Continuous limit of discrete system
Limit of large numbers (e.g., statistical mechanics)
Limiting cases
Levels of analysis (microscopic vs. macroscopic, components vs. system)
Order of approximation
Dave
That's an interesting question as to why Darwinism was an idea that took so long to come up with. After all, as you say, Steve, isn't it obvious that "like leads to like."
The answer seems to be pretty simple. Ordinary evolutionary theory was centered around how an existing species changes over time. Thus, the Romans could speculate about how environment breeds a harder/softer human and breeders can observe how their experiments create new breeds of dog or cattle.
Darwinian evolution is about, well, the ORIGIN of species, it's about how a new species comes into existence. Darwin proposed that the process of ordinary evolution, later discovered as Mendelian genetics and eventually DNA, is the process that leads to the creation of new species.
Why other people never came to Darwin's conclusion is pretty easy to see. Darwin's conclusions are absurd. Basically, Darwin is saying that, over a long enough period of time, a human mother and a human father would eventually give birth to an offspring that was a completely different species from it's own parents and that this would happen on a large enough scale to sustain a population of new-humans that could breed among themselves without producing lethal homozygotes.
Even the more modern interpretation of sexual selection and genes selected randomly from the entire human genome does not allow for a selection of a dormant speciation gene that is activated at random and leading to a new species of human.
In fact,under Darwinian theory, Bigfoot should exist.
In Stigler's History of Statistics, in the section on Leonard Euler and Johann Tabias Mayer. Euler is up there with Gauss, Archimedes, etc., but didn't understand the Law of Large Numbers. Mayer figured out basically you average things, you get better estimates (of planets), while Euler wanted to find n equations for n unknowns, thinking more observations multiplied the errors. Statistics are perhaps a different part of the brain.
Don't the numbers have to be there first? I vaguely remember reading that the early 18th century Utilitarians had a penchant for collecting stats on social conditions. Certainly it had been done before, by the French and especially in the Domesday Book. But I think Jeremy Bentham et al went much further with it.
Wasn't Statistics an outgrowth of that effort? And their quest for the greatest good for the greatest number of people was yet another secular application of Christian charity, or perversion thereof.
"Is there something about human nature that makes statistical reasoning unappealing to most smart people, that they’d rather reason about the solar system than about society?"
Galton did not start start his stat career until his cousin Darwin's theory gave him some grist for the mill, which challenged Christianity in its most fundamental respect - the creation of man.
Perhaps if statistics could be applied to pre-industrial warfare someone would have spent more time on it.
the standard example of regression toward the mean is parent-child height, which is quite visible.
Exactly, so why bother.
Gauss, a genius perhaps surpassing Newton, did not publish all of his work. He was a perfectionist to a fault. Some argue math could have been advanced by decades had he published everything in a timely manner.
TH Huxley's reaction on reading " On the Origin of Species": "How extremely stupid not to have thought of that!"
I think I can shed some light on this question. When Galton and company developed statistics, they had a particular question in mind, that is, they were trying to prove Darwin right, and statistics was the mathematical technique which they created to analyse small variations from population averages that would presumably result in evolutionary direction or progress. Darwin was English, as was Wallace, so this is why statistics was mostly developed in England. Now the reason evolution was developed in England, of course, has to do with the great sea-faring heritage of the English. They were able to compile botanical and zoological data from all over the globe. But they also discovered geology and dinosaurs at home, which no doubt were contributing threads of inquiry. I got these ideas from the Lady Tasting Tea, which is on Steve's list of Amazon reviews, btw.
Steve, your first sentence is missing an "a". It must be either "a phenomenon" or "phenomena".
Biogenesis was proposed by Van Leeuwenhoek 200 years before Darwin and unless I don't understand Darwin's theory, this explanation by Pierre-Louis Moreau de Maupertius from the 1740's already seems to propose Darwinian natural selection as the mechanism:
"Could one not say that, in the fortuitous combinations of the productions of nature, as there must be some characterized by a certain relation of fitness which are able to subsist, it is not to be wondered at that this fitness is present in all the species that are currently in existence? Chance, one would say, produced an innumerable multitude of individuals; a small number found themselves constructed in such a manner that the parts of the animal were able to satisfy its needs; in another infinitely greater number, there was neither fitness nor order: all of these latter have perished. Animals lacking a mouth could not live; others lacking reproductive organs could not perpetuate themselves ... The species we see today are but the smallest part of what blind destiny has produced ..."
http://en.wikipedia.org/wiki/Common_descent#History
LOL, "thinking about social phenomenon" = trying to sound smart with grammar fail in the very first sentence of the post. Learn to read Greek and Latin or continue to be an amnesiac.
http://www.newcriterion.com/articles.cfm/Tanenhaus-s-original-sin-7568
"Yet it has always seemed to me that evolution could have been discovered at any point in the last few thousand years, since its sole necessary assumption is that "like gives rise to like," which was well known to all farmers or animal breeders. "
One thing that wasn't at all well understood or accepted by scientists until just before Darwin was the sheer length of geological time. This was first seriously argued by Lyell, who was only 12 years older than Darwin.
It's really hard to credit evolution of ALL species -- rather than minor tweaks to known species -- without a concept of deep geological time. In fact, it wouldn't even hold water -- without huge quantities of time, all the species we know could NOT have evolved, as we know.
This is actually a point Stephen Jay Gould argued effectively, FWIW.
First of all statistics is probably the hardest course an undergraduate takes. I doubt if this is true at Cal-Tech but it is certainly true for most liberal arts students.
Statistics is taught in many other larger disciplines. I first took it in psychology. Later I took it in the business school and finally in the math department. I taught business statistics at night for five years. It was a required course for several different majors. There were nearly no students who took it as an elective.
My net judgement - although I was a very good stat teacher - is that almost no one I taught ever really understood it. I remember a woman who did in fact 'get it'. I saw it in her eyes the moment she understood. Everyone else had those typical stat class glazed eyes.
Almost all stat classes not taught in the math department are more or less 'cook book' stat. Students learn how to do a t test or calculate a standard deviation but seldom really understand why. This can be unsatisfying for the teacher.
OTOH stat is a good subject to teach because it's so static. After statistics I taught computer subjects especially data communications. But today everything I taught just a few years ago is obsolete. People just are no longer interested in RS-232 pin-outs.
But there have been virtually no new statistical methods and techniques developed since non-parametric stat was developed in the fifties. I read that physicists have discovered the Higgs Boson. I take this as evidence that physicists are working hard on new stuff. But a standard market research tool of multiple regression has not advanced much if any for decades.
So if you wonder why Newton the physicist preceded Galton the statistician, all I can say is that that pattern persists today.
Albertosaurus
Speaking of A Confederacy of Dunces:
That novel was written in 1963. At one point in it Myrna, Reilly's leftist, unattractive "girlfriend" writes to him about having hooked up with a Kenyan exchange student at NYU.
"Ongah is REAL and vital. He is virile and aggressive. He rips at reality and tears aside concealing veils."
The first thing is that Newton's math was doable in Newton's day. In fact, he invented calculus because he wanted to do certain calculations concerning motions of the planets and the like, and when he came up with his calculus he then did them. Himself. All the number crunching. To be a guy like Newton in 1685 a bent for theoretical math wasn't enough, you also had to be able to do large amounts of error free arithmetic, and be able to double check one's calculations all by oneself. With a feather and an inkwell. Until one can do number crunching on an industrial scale, by a machine or an at least an assembly line of clerks, statistics isn't very useful, so why it would be it developed branch later doesn't seem to me to be a mystery.
Galton is pre computer, but I bet he had access to better number crunching tech, (cheap paper and pencils with erasers that Newton could only have dreamed about, and assistants to do or double check his math?). In addition, in order to do statistics you need data, as in statistics. Galton lived in the 19th century where the govt was constantly collecting data on the populace, the govt did not do that all that much in Newtons day. There wasn't as much to work with, and the idea of mathematically analyzing all the data just wasn't in the air because there wasn't any data to analyze.
Statistical theory advanced, and is at some level might still be advancing, all through the 20th century too because of machines capable of doing the number crunching. Newton would have had no trouble understanding the theory behind stepwise regression, but stepwise regression is about as useless as useless can be without a computer to do the number crunching. So Isaac would never have bothered with it.
Probably related, why did elementary game theory appear so late? Why weren't the ancient Greeks who argued over Xeno's paradoxes also thinking about the paradoxical Prisoner's Dilemma game?
Maybe not related, but why is the idea of time travel and associated paradoxes so late to make an appearance? It's all over popular culture nowadays: Harry Potter, Terminator, Back to the Future. Why wasn't there a genre of magic time travel fairy tales? Or was there? (I mean going into the past and encountering potential paradoxes, like meeting yourself, not just falling asleep for 100 years)? There're certainly plenty of you-can't-beat-fate traditional stories (Oedipus, Appointment in Samarra, etc.)
Galton had the advantage of Darwin's theory that minor variations were the engine of natural selection.
Physics and mechanics were studies of how God made things work. Randomness is incompatible with God’s will.
I was thinking something similar: statistics are at odds with free will and the values of the Enlightenment.
Laplace (1749-1827) and Henri Poincare (1854-1912) may be worth thinking about in this question. Laplace proved the Central Limit Theorem that Galton thought so highly of. Laplace's statistics work relates to his work on stability in celestial mechanics; Newton considered that planetary orbits were unstable and in need of divine interventions, but Laplace's higher order analysis tempered that concern. Later Poincare established that celestial mechanics of three or more bodies are chaotic.
Cause-and-effect is a masculine notion in that it is seeking direct and predictable paths of action.
Statistics is much more passive, as in feminine, as the world comes to you in the form of data so one can respond.
BTW, with my own limited exposure to statistics (as distinct from probability), statistics is rules to make better guesses. It is hardly as rigorous and much more empirical than real math.
Maybe it was the influence of Aristotle-ism. Aristotle would observe a few things and then weave grand theories out of them--most of them untrue. This could have become a habit among Western scientists.
Theories are preferable cuz they have a certain purity to them. Reality, in contrast, is messy.
Also, really effective tools of observing reality tended to be rather crude prior to the 19th century. And extensive travel to gather data from all over the world was much more limited in the past--and more about commerce and conquest than about science and research.
So, in Newton's time, there was far less data to work with since far less data had been gathered or could be gathered. So, scientists relied more on theory and logic.
But in Galton's time, British ships were sailing around everywhere and bringing all sorts of collections, data, artifacts, and stuff from all over the world and filling up entire museums and special academic societies. And tools and instruments for observing stuff, from the smallest to biggest, improved greatly. And so, scientists could become more data-based than theory-centric.
In Newton's time, scientists could see only a little and had to theorize a lot.
But in Galton's time, scientists could see a lot more.
Indeed, Darwin and Wallace were only possible in the 19th century because so much data had been collected about specimen from all over the world. In contrast, Newton just had an apple that fell on his head to work with. If Newton could travel all over and have all sorts of fruits fall on his head, he might have been more data-based in his thinking. But he stuck to stuff like math and physics for which he didn't need all the data in the world to figure out. He just needed certain key observations and a lot of logic.
There was evolutionary thinking before Darwin, but it was understood in terms of "ideal types." Variation was considered to be a falling away from the ideal, and thus not something of interest in and of itself.
The notion of ideal type was a major obstacle to any idea of limitless evolutionary change that could give rise to new species. Many pre-Darwinian biologists had grasped the idea of natural selection but they saw it as a form of culling that helped to bring species closer to their ideal. Conversely, lack of culling could cause degeneration or a reversion to a more primitive type.
It took Darwin, and later Mendel (posthumously), to overcome this obstacle to modern evolutionary thinking.
http://www.politico.com/story/2013/03/marco-rubio-rand-paul-foreign-policy-89303.html
Gomer Pyle Rubio is so funny.
http://www.youtube.com/watch?v=XUSDg7NSODw
Newton *had* to precede Galton. You need a pretty advanced conception of natural law in both physics and biology to come up with the idea of using statistics to predict the future or to do out-of-sample inference in general. Without such a concept the idea of an exact mathematical technique for predicting the future from the past, or predicting unobserved from observed phenomena, seems excessively speculative. Indeed we have pushed statistical prediction too far already in many ways it seems.
Except for magnets and electrostatically charged objects the Earth was the only entity that was ever seen attracting anything.
The planet we live on is a pretty big "exception". The (perhaps mythical) story is that Newton was prompted to investigate gravity after an apple fell from a tree he was sitting under.
That the thing called "gravity" existed was always obvious - what was missing were the mathematical tools necessary to properly describe and quantify it. Newton developed such tools with his calculus.
"That the thing called "gravity" existed was always obvious - what was missing were the mathematical tools necessary to properly describe and quantify it. Newton developed such tools with his calculus."
This describes Galileo's work nicely, except for using calculus. What Newton added to this is that terrestrial gravity of the 32.174 ft/s^2 variety is a particular case of the thing that also moves planets through space.
That the thing called "gravity" existed was always obvious - what was missing were the mathematical tools necessary to properly describe and quantify it.
But the problem was that (starting w/ the greeks) people didn't know the cause. They thought that it was in the nature of heavy objects to seek their natural position at the center of the earth (and "light" objects like smoke, to do the opposite). They didn't imagine the attractive nature of matter to itself.
And they thought the planets were set into fixed spheres, not that they were prevented from falling in to the center by their momentum along a tangent.
Until (roughly) Darwin (via Smith noting that freewill and randomness implies NON-PREDICTABLE behavior) became comfortable thinking about randomness as being a causal agent, no one considered it worth studying.
When people began to see that distributions implied predictive power, there was more interest in the supporting mathematics.
http://www.criterion.com/explore/185-william-friedkin-s-top-10
Why weren't the ancient Greeks who argued over Xeno's paradoxes also thinking about the paradoxical Prisoner's Dilemma game?
I think we've probably lost more of this history than we know.
Wasn't there just relatively recent discovery of someone (Archimedes?) that implied they understood more of the idea of infinitesimals (or proto-calculus) than we thought?
Speaking of statistics
King explained his charts to us like this:
It's what I like to call "the most depressing slide I've ever created." In almost every country you look at, the peak in real estate prices has coincided – give or take literally a couple of years – with the peak in the inverse dependency ratio (the proportion of population of working age relative to old and young).
In the past, we all levered up, bought a big house, enjoyed capital gains tax-free, lived in the thing, and then, when the kids grew up and left home, we sold it to someone in our children's generation. Unfortunately, that doesn't work so well when there start to be more pensioners than workers.
http://www.dailymail.co.uk/news/article-2299397/Transgender-male-barred-applying-womens-college.html
Injustice!
Steve:
I've not actually read Galton (so don't know exact words he used) but it seems counterintuitive to have used the words "regression to the mean" instead of "regression TOWARD the mean." The first can be easily interpreted as describing a specific result while the latter is more descriptive of a tendency
(which, I believe, is the more appropriate interpretation).
Nor do I find unusual that there was such a lag as you've posed between Newton and Galton. First of all (and as I tried to explain to you and others at genex.com a few years ago), the concept of "regression toward the mean" is not a mathematical or statistical discovery by Galton. Rather, it's his discovery that a much older law--preceding even Newton--Bernoulli's "Law of Large Numbers"--was applicable to the case of inherited characteristics. If I had to guess at the reason it hadn't occurred to anyone earlier, it'd be my guess that "putting two and two together" had to first, await Mendel's discoveries and then, the rediscovery of Mendel's discoveries. I'd even go further and posit that, were Mendel a buddy of Newton or Bernoulli (or even one of a number of others of about the same time), Galton's recognition would have been made almost instantly.
In contrast, Newton just had an apple that fell on his head to work with. If Newton could travel all over and have all sorts of fruits fall on his head, he might have been more data-based in his thinking.
If it had been a large coconut, falling from a considerable height, well, the whole course of scientific history would have been different.
Peter
They thought that it was in the nature of heavy objects to seek their natural position at the center of the earth (and "light" objects like smoke, to do the opposite).
That's a fairly accurate description of the reality, not a mistake on the part of the ancients.
That's a fairly accurate description of the reality, not a mistake on the part of the ancients.
Of course it is. They weren't stupid. But my point is that this view of causality is not nearly so different from Newton's than they both are w/ Darwin's, ie. natural selection working on random (re)combinations/mutation of genetic material.
And until Smith and the freewill (as a causal agent) arguments against government intervention, Darwin's type of causation (randomness itself) was simply not pursued to the extent that the traditional forms of causation were.
When they realized that there is predictive power in the statistics, they started to systematize it mathematically. I say.
j mct wrote: "To be a guy like Newton in 1685 a bent for theoretical math wasn't enough, you also had to be able to do large amounts of error free arithmetic, and be able to double check one's calculations all by oneself. With a feather and an inkwell. Until one can do number crunching on an industrial scale, by a machine or an at least an assembly line of clerks, statistics isn't very useful, so why it would be it developed branch later doesn't seem to me to be a mystery."
This is really insightful. It reminds me of the difference between most of engineering school work and work in the real world. In exams and problem sets, you use your graphing calculator to solve problems. These days in the real world, you often build a spreadsheet (or commit the data and analysis to computer somehow, e.g. MATLAB) so that you can prove your calculations correct, and change or optimize data near instantly.
Building a spreadsheet simulation to test or design something is a much more advanced technique than chewing through the calculations by hand, but is completely useless without a computer.
Here's an email from a friend:
I haven't looked carefully but both Sailer and Gelman's threads seem
ignorant of the fact that many statistical tools were developed by
early astronomers. Galton was novel in applying statistics to everyday
and human systems, but much more sophisticated things were done long
before his time.
http://ned.ipac.caltech.edu/level5/Sept03/Feigelson/Feigelson1.html
Re: evolution, I don't think most people recognized that there was an
actual problem to be solved -- even Descartes, Newton, Leibniz, etc.
were happy to contemplate a God, Creation, etc., etc. It was only once
some geological and fossil data became reliable that the question of
the origin of species became well-motivated.
####
At the link you will find:
"But it was another Greek natural philosopher, Hipparchus, who made
one of the first applications of mathematical principles that we now
consider to be in the realm of statistics. Finding scatter in
Bablylonian measurements of the length of a year, defined as the time
between solstices, he took the middle of the range - rather than the
mean or median - for the best value.
This is but one of many discussions of statistical issues in the
history of astronomy. Ptolemy estimated parameters of a non-linear
cosmological model using a minimax goodness-of-fit method. Al-Biruni
discussed the dangers of propagating errors from inaccurate
instruments and inattentive observers. While some Medieval scholars
advised against the acquisition of repeated measurements, fearing that
errors would compound rather than compensate for each other, the
usefulnes of the mean to increase precision was demonstrated with
great success by Tycho Brahe.
During the 19th century, several elements of modern mathematical
statistics were developed in the context of celestial mechanics, where
the application of Newtonian theory to solar system phenomena gave
astonishingly precise and self-consistent quantitative inferences.
Legendre developed L2 least squares parameter estimation to model
cometary orbits. The least-squares method became an instant success in
European astronomy and geodesy. Other astronomers and physicists
contributed to statistics: Huygens wrote a book on probability in
games of chance; Newton developed an interpolation procedure; Halley
laid foundations of actuarial science; Quetelet worked on statistical
approaches to social sciences; Bessel first used the concept of
"probable error"; and Airy wrote a volume on the theory of errors.
But the two fields diverged in the late-19th and 20th centuries.
Astronomy leaped onto the advances of physics - electromagnetism,
thermodynamics, quantum mechanics and general relativity - to
understand the physical nature of stars, galaxies and the Universe as
a whole. A subfield called "statistical astronomy" was still present
but concentrated on rather narrow issues involving star counts and
Galactic structure [30]. Statistics concentrated on analytical
approaches. It found its principle applications in social sciences,
biometrical sciences and in practical industries (e.g., Sir R. A.
Fisher's employment by the British agricultural service)."
Much of the work described above (e.g., Bessel and "probable error")
was done before Galton's birth.
Right, but this is just evidence that the heavyweight talent was going into astronomy and physics. I'm a big fan of Galton, but he seems like a gentleman amateur compared to a lot of these guys.
"Now, a theory I've long entertained is that the gay marriage brouhaha reflects a fundamentally healthy movement among gays to push more restrained lifestyles on themselves after their catastrophic debauchery in the 1970s following Gay Liberation caused the AIDS epidemic."
You have some explaining to do. This is enough of a pro-gay marriage statement to make me pull my contributions to VDare. I held my nose when I heard Brimelow took home $378,418 in 2007, but this is the last straw.
If you want to think up "conservative" reasons to institutionalize sodomy, maybe you could write for Pajamas Media or go back to News World Communications.
Sometime in the summer of 1952, three friends and I were fishing (illegally) in a reservoir some distance from our homes (we'd ridden bicycles and hidden them in roadside brush before the 1/2-mile forest trek to the reservoir lake.
Many hours later, after a great day of fishing, swimming, and exploring, we headed back up toward the road for the trip home.
Ed was in the lead, Bill following, Homer next, me in the rear--with about 20 yards between each. Emerging from a forested into a meadowed portion of the route, I called out, "Yo" to Homer and showed him an absolutely gorgeous pear. Immediately, he yelled to the two others and, when they'd come back to where we were, started into a description of how, among the three of us, "Gene has the sharpest eyes and notices so much more than the rest of us. He's usually the one who catches the most snakes (or frogs or lizards or turtles) when we go a-huuting such." It was all true--I was the best at those activities. (And, a few years later, learned to identify and sometimes catch snakes and even lizards by tracks in roadside dust in Texas.)
But I stood there, listening to Homer's praise--and said nothing.
Nor did I ever say anything in the intervening years when Homer would describe the event to some other group--as an example of my skills in that department.
But, after 60 years had passed, I called Homer and told him the truth of the matter--that the pear, quite contrarily to having been an object of attentiveness, came to my notice only when it had fallen squarely on my head!
I still haven't told the other guys. Maybe next year or sometime.
Here is a literal example of why stat took a while to catch on: the difference between getting a lot of data, and getting a lot of error when you get a lot of data.
The linear operation AX = B, where a matrix A transforms a vector X to vector B was well understood by Newton but was not written that way for a very long time still. Such a transformation had a nearly infinite set of applications--but it was a hundred years away from being represented by matrices, at least. The way we organize math makes a big difference in what we understand.
Now, one important application of matrix operations on vectors is the notion of a projection-- take a look at things in 3d space. how do they look if you ignore, say, one dimension, (like z) and see how the points map into the plane. A camera or telescope does this--it maps points in 3d into a plane.
Newton's laws can be written in this form to make these kinds of transformations all the time-- how does the application of a force F change the motion of a particle (x1,y1,z1) to (x2,y2,z2)?
But what if you have X and B, but not A? well, if you collect enough data, you should be able to figure out A from (b1, x1), (b2, x2). As soon as you have enough *independent pairs of points* as the dimension of A, you should be able to solve this.
Every point should have reduced the number of remaining unknowns.
Scientists tried to do this with astronomy at the time. They knew the locations of planets at a time now and a time later, and tried to compute the matrix representing the force/motion.
except every *measurement* they made had an error. So now, instead of decreasing the number of unknowns with each measurement, they were INCREASING them! The error on every point added an unknown amount of error.
iirc, this flummoxed everyone but Newton for a long time, enough to cause them to be unsure how to formalize why the errors could be handled. And it didn't get handled until more than a hundred years later because without the AX=B representation, it didn't make sense how to isolate the errors.
Galton was no real mathematician by any means, but here are among the contributions he made to statistics:
Variance and standard deviation
Bivariate normal distribution
Correlation and regression
The world could use more gentlemen amateurs.
So, this idea of how to handle error wasn't obviously the same as how to handle variance. When you look at a graph of many people and their height vs age, you see variation. But people assume the measurements themselves were perfect. But of course real scientists know measurements have error and that's another source of variance. They understand how to model that now. But then? So when is variance an issue of multiple points on data and when is it an issue of error on an individual datum? It took a LNG time to resolve this confusion. Most undergrads in science never notice it even though they are computing regressions. Many grad students don't get the difference. So it took a lot of years to get the issues separated.
That link to Statistical Challenges in Modern Astronomy dovetails perfectly with another conversation I was having today. I'm under the impression that the majority of the need for dark matter and dark energy to fill in the gaps is based on heavily statistical analysis of whats out there. Now, there's obviously a healthy history of predicted-but-not-yet-observed things in physics. But this idea, that we have to posit the existence of 80% of matter being "invisible" simply b/c we aren't receiving enough light (or other EMR) from places that appear to be under some greater amount of gravitational attraction, is a little unsettling. And it has to be heavily based on statistical analysis of the data.
Now, by no means did I read all of that link, but I think this sentences capture my point: Not only did this lead to confusion in comparing studies (e.g., in measuring the expansion of the Universe via Hubble's constant, Ho), but astronomers did not realize that the confidence intervals on the fitted parameters can not be correctly estimated with standard analytical formulae. (that example actually goes to theory of dark energy, but I think you get the idea.)
And I also understand the entire discovery of the Higgs Boson is just that over how-ever-many-billions of runs there was often enough of a blip at a certain energy location to say w/ 5(6?) sigma confidence that "it's there." And i think it's actually the decay into predicted constituents that actually detected, but now I'[m really talking out of my ass.
Anyway, I sure hope the statisticians in astrophysics are better than the ones in climate science.
Yet it has always seemed to me that evolution could have been discovered at any point in the last few thousand years, since its sole necessary assumption is that "like gives rise to like," which was well known to all farmers or animal breeders.
A few points:
(a) Early science was largely experimental and involved trying to explain how things worked and to create tests to determine if the hypothesis was correct. Evolution by its nature is more of a historical reconstruction, and would have more properly been seen as philosophy rather than science. The idea of science was to actually empirically test the world rather than to try to deduce things from philosophical first principles. With the available tools at the time, macro-evolution is not something that could have been studied scientifically.
(b) Why would someone have thought of it? Things like astronomy sought to explain how things worked or the nature of mysterious things that people could experience. There was a reason to study it. Given that the Bible gave the commonly accepted story of how the world began, there would have been no reason to study evolution unless you were curious as to how life came about; and this would only be an issue for someone who either rejected the Bible philosophically or for someone who discovered something that caused him to doubt the biblical origin story and who therefore needed a mechanistic, or at least a different, theory of how living things came to be.
Put another way, evolution was an answer to a question not many were asking.
(c) Biology in general requires more abstraction in experiments than basic physics. With basic physics, you generally are asking a motion question that you can answer fairly directly. Does a heavy object fall faster than a light one? Do objects fall at a constant rate or accelerate? A lot of biology questions involve things that are not (at least with what was available at the time) directly observable; you're basically looking at a black box and have to figure out the implications of several different models to test ideas.
(d) Physics involves a lot of geometry and algebra, which had been developed long before, so the study was applying and expanding old ideas.
Stats does require a fair amount of computation, and the lack of Arabic notation would have held things back for the ancients.
It also helps to have large, quantitative data sets that may be influenced by multiple factors. For the typical gentleman scholar, what's the smallest quantitative data set that would be interesting, either commercially or scientifically? Galton was out creating his own data sets, but you have to admit he was kind of an oddball.
Insurance? Annuities?
"That the thing called "gravity" existed was always obvious"
Not really. It was obvious that what went up came down, and so forth, but 'gravity'- that that apple was being drawn towards the earth because it was so massive, and that this applied to all objects and explained heavenly orbits (at least until Einstein improved upon it centuries later), was a stroke of genius.
Platonism may have been one big reason, when you think in terms of ideal types and view all variants as imperfect copies of ideal forms whether they be rocks, elephants, or kitchen tables then statistical thinking is probably hard. That was why so many bright biologists before Darwin and Wallace missed natural selection according to Ernst Mayr in one of his last books "What Evolution Is". Cuvier is a classic example, because in many ways he was a much better analytical mind than Darwin or Wallace were, but he perceived Platonism as self-evidently true and never questioned it. A Platonist is in effect trying to ignore variation, because he thinks it is clouding the search for ideal types.
Newton was famous for "borrowing" for others hence his famous phrase about standing on the shoulders of giants.
The idea of evolution in man or human society was quite influential before Darwin, wasn't it?
Hegelian philosophy involved concepts of evolution. The Enlightenment philosophers had a sense of human society evolving towards progress.
"In order to do good statistics you need good data. I think that could be the big difference between Newton's time and Galton's time"
http://www.academia.edu/393769/Vos_P._2005_._Measuring_Mathematics_Achievement_a_Need_for_Quantitative_Methodology_Literacy
It might be worth mentioning that Bayes probably came up with the core idea of what is now called Bayesian statistics in the late 1740s, although his work wasn't published until 1763, after Bayes had died. His ideas were apparently talked about in the late 1740s. There was no particular reason not to publish at the time, perhaps it just wasn't seen as that important.
In 1642 Pascal invented the mechanical calculator, his Pascaline. He made about twenty. He did so because his father had to crunch tax data. No other working commercial mechanical calculators seem to have existed until 1851:
" Thomas' arithmometer, the first commercially successful machine, was manufactured two hundred years later in 1851; it was the first mechanical calculator strong enough and reliable enough to be used daily in an office environment. For forty years the arithmometer was the only type of mechanical calculator available for sale..."
The Arithometer, which could multiply, was a killer app. In 1890 it was still the most produced calculator in the world. It was manufactured until 1915.
Because the first unit was made by a clock maker and took a year to make, I'd guess that to build arithmometers one needed accurate metal machining and tooling that didn't exist until the time. (Apparently a lot of Babbage's technical development also went into the development of accurate machining.)
Thomas needed them for his insurance business and knew how to put on a trade show: "Thomas built a giant version for the 1855 Paris Exposition, and the machine, which resembled a fancy upright piano, won a gold medal..."
Surely this had an effect on statistics. With calculus you can solve a problem analytically, "in closed form". But by its nature statistics needs to crunch (turn the crank on the arithometer) every data point...
Regarding the arithometer, this extract from an 1857 magazine article is impressive:
"A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...
It will soon be considered as indispensable, and be as generally used as a clock, which was formerly only to be seen in palaces, and is now in every cottage."
Numerically accurate square roots of arbitrary numbers in the 1850s in a couple of minutes, yeah, that could change things.
I think the ultimate reason for the required precision of our modern computer floating-point word size (single precision) was the accuracy of the mechanical calculators used in the southern California aviation industry up until the advent of electronic computers in the 1950s.
I can't pass up a reference to the Thomas's Arithometer without mention of the handheld "math grenade", or Curta, which used the same basic principle and "were considered the best portable calculators available until they were displaced by electronic calculators in the 1970s."
Statistics is hard to "touch" or "see".
Up until a few hundred years ago, what our geniuses did was describe things you can directly sense.
That's why the acceptance of the imaginary number (square root of -1) only came into play relatively recently. It was staring many mathematicians in the face for many many centuries, but it simply was too abstract to gain a foothold till about 1800.
Statistics is even less tactile ... and is also burdened with requiring much data gathering to develop, so i see no surprise in Galton lagging Newton by about four generations.
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