Aristotle (384-322 BC) already advises us to be cautious when applying pure mathematical averages to human daily life:
By the mean of a thing I denote a point equally distant from either extreme, which is one and the same for everybody; by the mean relative to us, that amount which is neither too much nor too little, and this is not one and the same for everybody. For example, let 10 be many and 2 few; then one takes the mean with respect to the thing if one takes 6; since 10-6 = 6-2, and this is the mean according to arithmetical proportion [progression]. But we cannot arrive by this method at the mean relative to us. Suppose that 10 lb. of food is a large ration for anybody and 2 lb. a small one: it does not follow that a trainer will prescribe 6 lb., for perhaps even this will be a large portion, or a small one, for the particular athlete who is to receive it; it is a small portion for Milo, but a large one for a man just beginning to go in for athletics.
Aristotle, Nichomachean Ethics, Cambridge, MA: Harvard University Press.
He wasn't published by Harvard University Press either! But I think it is interesting and relevant to the discussion how the modern English aspect was overlooked whereas the imperial unit triggered his anachronism detector.
I had looked up some of the ancient Greek units (I had almost posted more information and a link to the Wikipedia article; but figured the truly curious would do the same search), and there is a listed unit that is within a few % of the modern customary pound.
It is very likely the translator did a simple substitution. Given the interconnectedness of the Greek trading world, it's likely that the unit variations were small to negligible in the eastern Mediterranean at that time; probably even less so that during the Renaissance when city-states were vying and fighting each other for commercial dominance.
Having read vol 1 of Braudel's book on the Mediterranean world in the 16th c, units used in commerce varied widely in the 16th century (at least for shipping), and Braudel doesn't even bother in most cases to translate them to modern units, he simply leaves them and compares magnitudes with a few asides to anchor the terms.
"The libra (Latin for 'scales / balance') is an ancient Roman unit of mass that was equivalent to approximately 328.9 grams. It was divided into 12 unciae (singular: uncia), or ounces. The libra is the origin of the abbreviation for pound, 'lb'."
The actual unit Aristotle used was the "mna". A mna was 100x as heavy as a drachma. According to Wikipedia (which is always right except when it's wrong) the most commonly used standard in ancient Greece made a drachma weigh about 4.3g, in which case a mna would be about 430g, compared with 454g for a pound weight. So "pound" or "lb" is a pretty good translation for "mna".
(The "mna" has rough equivalents in other ancient Near Eastern cultures. There's at least one "mina" in the New Testament, and in the famous "writing on the wall" at Belshazzar's feast -- MENE MENE TEKEL PHARSIN -- "mene" is basically the same word as "mna".)
I was unable to find a definite answer to this, but seeing he was Greek I guess he should have not used it.
I understand this is a translation, but changing actual facts in a script then addressing it to someone seems like too much creative freedom to me.
> For example, Quetelet showed that the average rate of suicide was relatively stable from year to year. While this would hardly be startling news these days, in the 1830s suicide was seen as a highly irrational private decision that could not possibly conform to any deeper pattern. Instead, Quetelet showed that suicides occurred with reliable and consistent regularity. And not only that: He claimed that the stability of the occurrences indicated that everyone possesses an average propensity toward suicide.
I must admit this is really interesting. If all people are individuals, it's not obvious that the suicide rates should be stable.
I didn't downvote it but I know why it's downvoted.
The downvotee could clearly imagine this being unintuitive if he were inclined to be so creative. The entire comment evals to "I inherently grasped statistical thinking from birth, what's wrong with you that you didn't?"
To borrow from a Hacker School post a long time ago: it's feigning surprise[0] at the ignorance of others. If you're on HN you probably work in an environment where learning is a non-optional part of your every day. Getting to the point where not knowing things isn't a blow to your self-esteem can be a pretty big professional hurdle for people.
Unless the downvotee was born with an inherently sound understanding of statistical thinking and also has some trouble empathizing with other humans then his comment was just going out of his way to tell a fellow human that their moment of learning and realization was remedial.
Edit: After explaining it and rereading the downvotee I decided to downvote as well. The clincher was following up with the implication that the original poster was not only remedial but poorly educated.
The hover text is especially applicable: "Saying 'what kind of an idiot doesn't know about the Yellowstone supervolcano' is so much more boring than telling someone about the Yellowstone supervolcano for the first time."
>> Unless the downvotee was born with an inherently sound understanding
This part? I meant "was born" as made the jump from being a fetus to being a baby, not "borne" in the sense of being carried, although I guess that works in a bit more poetic sense.
(Also thanks for the comment either way, always happy for feedback and corrections)
Whoops, did you edit that? I could swear I read "the downvote" rather than "downvotee", but then it doesn't make sense in context anyway. Brain fart, I guess, sorry.
While total ignorance of statistics might lead you to expect suicide rates to be wildly unpredictable, and knowing a bit of statistics might make it obvious that they shouldn't be, knowing more statistics should make it not-obvious again.
So, from a position of total ignorance you might say: suicide rates are the result of lots of individual freely made decisions, and should therefore be completely unpredictable.
Then if you know a bit of statistics you might say: no, the population's suicide rate is the average of the individuals' suicide rates, and averaging things reduces their variance so we should expect it to be quite predictable.
But if you know a little more statistics, a few other things will occur to you. The first is a red herring: averaging things only reduces their variance when the variance is finite. Standard counterexample: mount a gun or laser or something on a swivel mount with a 180-degree range near an infinitely long wall. Point it at a random angle and see where it hits the wall. This gives you a position with the so-called Cauchy distribution, and the average of a million of these has the exact same distribution as a single one. (That doesn't mean you can't extract information from having lots of samples; e.g., the median is nice and informative. It just means that taking means isn't the way to do it.)
Why is that a red herring? Because an individual's suicide-or-not during a given year can only take the values 0 and 1, and therefore its variance can't be larger than 1/4 (and in particular can't be infinite). So averaging together lots of these should give you something well-behaved, right?
Not so fast. Those individual suicide-or-not random variables may be correlated (e.g., when Goethe published his gloomy book "The sorrows of young Werther", whose protagonist -- SPOILER WARNING -- kills himself at the end, a wave of copycat suicides swept across Europe). And they may depend on something that varies with time (the same example will do nicely, but you might also consider economic conditions, weather, polluted water supplies, etc.), and there's no reason why that something (or those somethings) shouldn't swing around wildly.
So no, it isn't altogether obvious to anyone who knows some statistics. It shouldn't be a big surprise if in fact suicide rates are pretty well behaved, but I think if you think it's obvious then you're not thinking hard enough.
The default psychological view (if you can call it that) in 1830 was Romantic Individualism.
The default psychological view in 2016 is that objective statistical trends are the rule across populations, not the exception.
There can be arguments about which statistics apply, and whether or not they're accurate and not measured poorly, or impossible to replicate, or even deliberately dishonest and politically motivated.
But there's no argument that in principle it's perfectly scientific to use statistics to identify and measure behavioural trends.
The shock in 1830 was discovering the latter fact. The idea that something personal like suicide might fit a measurable statistical trend was completely novel - perhaps because it directly challenged beliefs about heroic personal self-determination.
The fine details of the distributions don't matter. The fact that statistics can be used at all shocked people in a way that it doesn't now.
I think this article is less about "normal" and more about "average" person. The history of normality and curing/fixing abnormality has been dissected by Michel Foucault's "Discipline and Punish: The Birth of the Prison" and "The Birth of the Clinic: An Archaeology of Medical Perception".
It's interesting that Quetelet Index aka BMI is arguably 'wrong' as it's comparing volume of something with one dimension ^2 instead of one dimension ^3. There are reasons it's valuable in human health as square cube law scaling has negative consequences. Still, it's interesting just how 'old' that measurement is.
The BMI is more right than wrong. The strength of a physical object varies with cross-area, so the strength of your heart varies as height squared. The amount of work it has to do varies as mass, which does tend to scale as height cubed.
From my very anecdotal perspective, BMI is only used when addressing obesity or anorexia as a first-order approximation, or rather illustration and a way to find out where you are in relation to peers of the same sex/height/age. Do other formulæ fare better in those use cases?
> Quetelet’s invention of the Average Man marked the moment when the average became normal, the individual became error, and stereotypes were validated with the imprint of science
I wonder what would have happened had he used a statistical mode instead of the mean. He was coming at the problem from the experience of correcting error in astronomical measurement, but it seems like there were some mental gymnastics required to equate individual measures of humans as errors.
This was likely more a result of the European tradition of a Platonic ideal of man, and the Christian doctrine that man ought to be virtuous. The two intertwine, and you have a Platonic ideal of a man who is both naturally and spiritually virtuous. Many scholars spent their careers showing that spiritual impurity effects natural deformity and vice versa. Not only bodily defects were understood to be errors, they were thought to be either a natural result of the person's viciousness, a deserved supernatural punishment, or a Jobian trial. Either way: ideal = good, deviant = not good.
So it makes sense that there is an ideal physical form of a man, which is definite (quantifiable) and unchanging (i.e. no evolution). I have never heard of Quetelet, but I doubt he did anything more than put a series of numbers to this preëxisting notion.
>Many scholars spent their careers showing that spiritual impurity effects natural deformity and vice versa. Not only bodily defects were understood to be errors, they were thought to be either a natural result of the person's viciousness, a deserved supernatural punishment, or a Jobian trial. //
You implicitly suggest this comes from Christian doctrine (?) which is strange as it's recorded in the New Testament (https://www.biblegateway.com/passage/?search=john+9&version=...) that Jesus was asked who had sinned in order that a blind person had become blind and he responded that no-one had, that it wasn't the result of sin.
Now, scholars who wanted to control the people's behaviour might find it beneficial to promulgate a position that sin caused deformity but it seems quite at odds with this NT account of the position of Jesus on the matter. Moreover the greater message from Jesus is to bring succour to those who are weaker, and that we are all sinners deserving of God's wrath.
I don't doubt that your suggestion matches the position of some Christians, but that does not make it a Christian position - it seems more derived from societal superstition than from Christian theology.
Hold on though, statistics actually work in real life. If you're taking into account base-rates based on measurements of "normality" or "regularities" you will win more on average. It doesn't matter how you choose to carve up some ideological category of "normal", probabilities are conserved, and taking that into account will improve your decision making.
But you have less obvious non-representative means: average # of sex partners (Pareto distribution), average life expectancy (bathtub curve), average autism-spectrum quotient (camel curve). In all these cases the averages obscure, rather that elucidate.
I mean if you intentionally increase the entropy of your model, sure. But knowing the average person has 1 testicle and 1 ovary is still better than if you really didn't know anything about that before.
This is a great read. I'm especially surprised about what it means to be an "Average Person".
"Average" or an "Average Person" now (at least amongst my social circle) is actually a bad thing, something that people will put effort into _not_ being. Describing something as "average" (or just "av" in conversation) is a way to describe something as disappointing.
So strange how the meaning has pretty much completely flipped on its head.
"Average" also means safe, solid, ideal, normal. This happens when avoiding risk:
* probabilistic estimate of future risk (there is evidence that averaging multiple faces renders a face more beautiful than the rest): average mate => higher probability of average (viable) offspring
Where do you get that number? All the statistics I've seen from dating sites indicate that while women have an 80% cut off men have a 50% cut off (i.e. truly average).
In other words, while women consider any men below the 80th percentile "below average", men's opinions reflect the actual average (i.e. considering any women below the 50th percentile "below average" and above it "above average") rather than (as you seem to say) considering any woman above the 20th percentile "above average".
This applies to all sexually-reproducing species, not just humans. The male strategy is optimized for low cost, so males prefer to mate with a fit female, but will settle for "anything with a pulse". In humans, this is evidenced by virtually all women having babies.
I don't know what the actual ratio is, and it will probably be different depending on the fitness of the male and how near the bar's closing time. The salient aspects are that the division is asymmetric, the strategy complements the female strategy, and that there is a hard cutoff (some of the females are so unfit they will never be considered).
Sure, but the interesting part is that we like to think such animalistic traits are beneath us. We're not rational creatures, we're just ordinary creatures that happen to be capable of ratio sometimes.
A lot of the social discussions we are currently having in tech likes to portray humans as entirely rational and intentional when in fact the problems we're trying to solve are engrained in our biology, not part of our culture. Doesn't mean we can't (or shouldn't) work around them but it means you need to do more than just pin all the problems on the majority and assume that once the power dynamics shift the problems will go away.
Another interesting bit of etymology: the article mentions the field of statistics arising with the need for governments to manage information on their citizens. The word "statistics" literally comes from "state", a fun factoid for anti-statists to chew on.
I'm not done with it but so far it's been an epistemological history lesson that has me thinking a lot about how the current era of Big Data / rising ubiquity of mechanical objectivity (esp photography — from WWI photojournalism to google earth) has been altering humanity on all fronts, from the sciences to the arts to the justice system... particularly how seeking truth is seemingly no longer a burden when everything is recorded by computers, yet at the same time there is still the very real burden of communication (presentation/interpretation) when said data is given an audience.
Interesting article! I'm a little skeptic to the final paragraph, though, specifically the notion that this research prompted the birth of stereotypes.
Stereotypes might not have existed in their modern form previously, but they're akin to the notion that people have an essence, assigned to them by nature. Platon's ideas about comparing an individual's essence to a metal is a good example (bronze people are good at this, iron people good at that). And I definitely think we'd fool ourselves thinking that the individual held a stronger position in society prior to the early 19th century...
I think they're really talking about scientific stereotypes.
It's this kind of thinking that starts to give rise to so-called scientific explanations of why certain races are "inferior". The average man concept lets you compare races and genders and all sorts in a way that can appear scientific - in method at least - whilst ignoring the fact that there are so many variables to account for in the human condition, that any result must be taken with a lot of skepticism.
But people in general, particularly around the time, were astounded by the leaps and bounds that science had been making. So anything "proven" in a scientific enough manner, must be true. No skepticism to be found.
As products and services became increasingly standardized, conformed, and repeatable in the industrial age, so did the users. This dynamic is changing in the electric age where products and services are becoming increasingly customizable to the individual needs and desires of the specific user.
E.g. if you have a set of things which vary in many dimensions (even if each element is no more than a set "distance" from normality), very few elements will belong in the "centre" (normal on all dimensions) and most will belong on a spike (wildly extreme in 1 or 2 dimensions).
Depends on the time and region you select your sample from. In some provinces of China at different times, the average person might have six tenths of a penis.
Because before recently, the world was divided up into "royalty" and "people who mostly didn't matter." Maybe add a caste for soldiers or for farmers or for merchants, depending on how enlightened the society was.
The article's about statistical averages, and their implications for the modern social sciences, not about historical classes and castes.
Indo-European society probably had three castes: medicine men (responsible for law and justice, good relations with the gods, and magic; "wizard-priests" would also work as a description of their role, but feels too flattering for such an early, primitive society); warriors; and commoners. India split commoners into two classes (artisans etc., and laborers); Europe and Persia grouped skilled and unskilled commoners together. Europe and India both saw intense competition between the two top estates -- roughly speaking, magi and knights -- to determine who would rule society; in Persia, the magi more or less won without a fight (and sacralized the knights), thanks to Zoroaster.
In short, it wasn't nearly as simple as royal versus non-royal, at least not in the Indo-European world -- and the high-ranking estates had obligations as well as privileges.
By the mean of a thing I denote a point equally distant from either extreme, which is one and the same for everybody; by the mean relative to us, that amount which is neither too much nor too little, and this is not one and the same for everybody. For example, let 10 be many and 2 few; then one takes the mean with respect to the thing if one takes 6; since 10-6 = 6-2, and this is the mean according to arithmetical proportion [progression]. But we cannot arrive by this method at the mean relative to us. Suppose that 10 lb. of food is a large ration for anybody and 2 lb. a small one: it does not follow that a trainer will prescribe 6 lb., for perhaps even this will be a large portion, or a small one, for the particular athlete who is to receive it; it is a small portion for Milo, but a large one for a man just beginning to go in for athletics.
Aristotle, Nichomachean Ethics, Cambridge, MA: Harvard University Press.