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Taken.
I've never been completely happy with the "I could make 1M similar statements and be wrong once" test. It seems, I dunno, kind of a frequentist way of thinking about the probability that I'm wrong. I can't imagine making a million statements and have no way of knowing what it's like to feel confidence about a statement to an accuracy of one part per million.
Other ways to think of tiny probabilities:
(1) If probability theory tells me there's a 1 in a billion chance of X happening, then P(X) is somewhere between 1 in a billion and P(I calculated wrong), the latter being much higher.
If I were running on hardware that was better at arithmetic, P(I calculated wrong) could be got down way below 1 in a billion. After all, even today's computers do billions of arithmetic operations per second. If they had anything like a one-in-a-billion failure rate per operation, we'd find them much less useful.
(2) Think of statements like P(7 is prime) = 1 as useful simplifications. If I am examining whether 7 is prime, I wouldn't start with a prior of 1. But if I'm testing a hypothesis about something else and it depends on (among other things) whether 7 is prime, I wouldn't assign P(7 is prime) some ridiculously specific just-under-1 probability; I'd call it 1 and simplify the causal network accordingly.
It seems, I dunno, kind of a frequentist way of thinking about the probability that I'm wrong.
There are numerous studies that show that our brain's natural way of thinking out probabilities is in terms of frequencies, and that people show less bias when presented with frequencies than when they are presented with percentages.
No, that was absolutely not his point. I don't understand how you could have come away thinking that- literally the entire next paragraph directly stated the exact opposite:
I don't think that the following classes are the same:
(1) Facts everyone should know.
(2) Facts everyone knows.
I think the author claims that this is a (1) fact but not a (2) fact.
His claim was:
(a) Everybody knew that different ethnicities had different brain sizes (b) It was an uncomfortable fact, so nobody talked about it (c) Now nobody knows that different ethnicities have different brain sizes
His stated point is about telling things that everybody is supposed to know.
If you have an SD of 35 for an average of 1362 you have no idea about whether the last digit should be a 2. That means either you do state an error interval or you round to 1360.
Human height changed quite a bit over the last century. http://www.voxeu.org/article/reaching-new-heights-how-have-europeans-grown-so-tall . Taking data about human brainsize with 4 digit accuracy and assuming that it hasn't changed over the last 30 years is wrong.
European gained a lot of bodymass over the last 100 years due to better nutrition. The claim that it's static at 4 digit in a way where you could use 30 year old data to describes todays situation, gives the impression that human brainsize is something with is relatively fixed.
The difference in brain size between Africans and European in brainsize in that study is roughly the difference in height between todays Europeans and Europeans 100 years ago.
Given that background taking a three decades old average from one sample population and claiming that it's with 4 digits accuracy the average that exist today is wrong.
His stated point is about telling things that everybody is supposed to know.
No, that was absolutely not his point. I don't understand how you could have come away thinking that- literally the entire next paragraph directly stated the exact opposite:
Graduate students in anthropology generally don’t know those facts about average brain volume in different populations. Some of those students stumbled onto claims about such differences and emailed a physical anthropologist I know, asking if those differences really exist. He tells them ‘yep’ – I’m not sure what happens next. Most likely they keep their mouths shut. Ain’t it great, living in a free country?
More generally, that was not a tightly reasoned book/paper about brainsize. That line was a throwaway point in support of a minor example ("For example, average brain size is not the same in all human populations") on a short blog post. Arguments about the number of significant figures presented, when you don't even disagree about the overall example or the conclusion, are about as good an example of bad disagreement as I can imagine.
The article contains the line:
Average cranial capacity in Europeans is about 1362; 1380 in Asians, 1276 in Africans. It’s about 1270 in New Guinea.
What's wrong here? 4 degrees of accuracy for brain size and no error bars? That's a sign of someone being either intentionally or unintentionally dishonest.
Quick Googling shows that there's a paper published that states that European's average cranial capacities is 1347.
Rather then describing the facts as they are he paints things as more certain than they are. I think that people who do that in an area, where false beliefs lead to people being descrimited, are in no position to complain when they some social scorn.
Source is here. SD for Asians and Europeans is 35, SD for Africans was 85. N=20,000.
What's wrong here? 4 degrees of accuracy for brain size and no error bars? That's a sign of someone being either intentionally or unintentionally dishonest.
...no? Why in the world would he present error bars? The numbers are in line with other studies, without massive uncertainty, and irrelevant to his actual, stated and quoted, point.
Nitpicking, but the quote stated that people who are on neither offensive nor defensive are people you can learn from - it didn't say that people who are on the offensive or defensive are necessarily wrong to do so.
I also dispute this- obvious cases include partial disagreement and partial agreement between parties, somebody who is simply silent or who says nothing of substance, and someone who is themself trying to learn from you/the other side.
(In particular, consider a debate between a biologist and the Pope on evolution. I would expect the Pope to be neither offensive nor defensive- though I'm not totally clear on the distinction here, and how a debater can be neither- but I would expect to learn much more from the biologist than the Pope.)
Actually, one of the sources you just linked (Wikibooks) states that officers were usually promoted from the ranks:
They were generally moved up from the ranks, but in some cases could be direct appointments from the Emperor or other higher ranking officials.
For further sources saying the same thing, see here, here, here, or here. See also this:
The most significant step in any successful army career of a Roman plebeian was the promotion to the centurionate. To become a centurion meant having become an officer. The main supply for the centurionate of the legions did indeed come from the ordinary men from the ranks of the legion. Though there was a significant number of centurions from the equestrian rank. Some of the late emperors of the empire prove very rare examples of ordinary soldiers who rose all the way through the ranks to become high-ranking commanders. But in general the rank of primus pilus, the most senior centurion in a legion, was as high as a ordinary man could reach.
In response to
Why officers vs. enlisted?
Historically, the distinction was based on social classes, but that doesn't explain why every army follows this arrangement, including those in very different societies.
The claim that all societies use this model is inaccurate. The counterexample that springs to mind is the Roman army; I'm fairly certain that there are plenty more.
I don't usually refer to brain drain in my understanding of things. If this is true, I should. But why expect differential brain drain between Africa and Asia, which is what is necessary to explain this.
I endorse Lumifer's reason. Other reasons would include less patriotism (as I understand, loyalties in much of Africa are to tribes/clans/families rather than a nationstate, religion, or ideology, so bringing your family abroad of going abroad to look for money would be less of a shift) and less perceived safety (e.g. apparently 75% of Ethiopia's skilled laborers moved abroad during its famines).
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Not a very good one, though. Most of the ancients that people pay attention to these days are the ones who were well-fed and well-read; it's strongly suspected much of the Flynn effect is population-wide increases in those two variables (as well as similar things like reduced disease load).
You mean well-fed in the sense of "not starving," but that doesn't imply "well-fed" in the sense of eating a healthy diet. There's reason to think that upper-class Romans would have been even more damaged by lead poisoning than the poor, and there's good evidence that even emperors were deficient in iodine.