Our long, vulnerable childhoods may be the key to our success(spectator.co.uk)
spectator.co.uk
Our long, vulnerable childhoods may be the key to our success
https://www.spectator.co.uk/article/our-long-vulnerable-childhoods-may-be-the-key-to-our-success
7 comments
It seems so. According to https://worldhistorycommons.org/sumerian-school-days:
>This tablet, from ancient Sumeria (as early as 2000 B.C.E.), details a day in the life of a school boy. Students learned by copying lessons on clay tablets, memorizing the lessons, and then reciting them for the school's headmaster (the "school father") or other teachers, monitors, and proctors of the school.
This web page includes a full translation if you want to read it, and cites the paper "Schooldays: A Sumerian Composition Relating to the Education of a Scribe" (https://www.jstor.org/stable/596246)
It makes sense that scribes would have formal education, like other highly-skilled professions imo, but I know nothing about history so who knows!
>This tablet, from ancient Sumeria (as early as 2000 B.C.E.), details a day in the life of a school boy. Students learned by copying lessons on clay tablets, memorizing the lessons, and then reciting them for the school's headmaster (the "school father") or other teachers, monitors, and proctors of the school.
This web page includes a full translation if you want to read it, and cites the paper "Schooldays: A Sumerian Composition Relating to the Education of a Scribe" (https://www.jstor.org/stable/596246)
It makes sense that scribes would have formal education, like other highly-skilled professions imo, but I know nothing about history so who knows!
They also had formal education in ancient Egypt at the time. The math problems given to students at the time aren't trivial either. They need to do stuff like calculate the volume of various 3d shapes. Seems they used 256/81 (3.16) as an approximation of pi at the time.
https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus
https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus
That's an interesting approximation. The error is about 15 times larger than for the well-known 22/7 approximation.
According to Bruno Jarrosson, the Egyptians had a marked preference for some classes of fractions, e.g. those with unitary numerator (so that, for example, representing a quantity as a composition (e.g. sum) of more fractions of the form 1/n was preferred to using single fractions of the form m/n). So, that fraction may have been privileged over others in this framework.
(One immediately notes that 256 and 81 are simple powers. As just a possibility, it could have been found intriguing that (2^8)/(3^4) could "reveal some underlying structure".)
(One immediately notes that 256 and 81 are simple powers. As just a possibility, it could have been found intriguing that (2^8)/(3^4) could "reveal some underlying structure".)
Note that fractions of the form 1/n + 1/m + ... make equity obvious for non-arithmetically sophisticated populations.
Given 3 loaves of bread, and 4 workers eating lunch, we'd probably be fine if 3 of them got 3/4 loaf each and the last got the 3 1/4 slices. To make the fairness of the distribution obvious, the Egyptians might have given all 4 workers the same pair of slices: 1/2 + 1/4.
(Note that for less fungible items, there still might be some practicality in the ancient Egyptian system: if we have 3 5 meter ladders to divide between 4 people, giving everyone one 2,5 meter ladder and one 1,25m would be much fairer than giving 3 people a 3,75m ladder but the 4th three 1,25m ladders.)
Given 3 loaves of bread, and 4 workers eating lunch, we'd probably be fine if 3 of them got 3/4 loaf each and the last got the 3 1/4 slices. To make the fairness of the distribution obvious, the Egyptians might have given all 4 workers the same pair of slices: 1/2 + 1/4.
(Note that for less fungible items, there still might be some practicality in the ancient Egyptian system: if we have 3 5 meter ladders to divide between 4 people, giving everyone one 2,5 meter ladder and one 1,25m would be much fairer than giving 3 people a 3,75m ladder but the 4th three 1,25m ladders.)
Well spotted that they're simple powers; riffing on that idea, if that is the aesthetic behind it, I'd guess that they're supposed to be the same base or the same power, so either (4^4)/(3^4) or (16^2)/(9^2)?
Edit:
Or perhaps (((4^2)/(3^3))^2)^1 and then it feels like an ancient aesthetic-precursor to Euler's identity?
Edit:
Or perhaps (((4^2)/(3^3))^2)^1 and then it feels like an ancient aesthetic-precursor to Euler's identity?
> the aesthetic behind it
It could also have been practical: "Radius to circumference? Easy: double many times, then take thirds a few times".
It could also have been practical: "Radius to circumference? Easy: double many times, then take thirds a few times".
Some more speculation. Have a look at https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplicatio...
Egyption multiplication was (implicitly) based on powers of two. In some sense weirdly similar to modern bit-twiddling.
Note that 4/3 in binary is 1.0101 0101 0101 0101 0101 0101 0101 0101...
So that suggests the following algorithm, expressed in modern day Python:
Repeat this function four times, and you will have multiplied by 256/81.
I have no clue whether they would have done anything resembling this procedure; this is just to show that it's plausible given how their multiplication worked.
I don't know how this relates to 'Egyption fractions'.
P.S. Just for fun the same thing for 22/7:
Egyption multiplication was (implicitly) based on powers of two. In some sense weirdly similar to modern bit-twiddling.
Note that 4/3 in binary is 1.0101 0101 0101 0101 0101 0101 0101 0101...
So that suggests the following algorithm, expressed in modern day Python:
def mul4_3(x):
table = []
while x > 0:
table.append(x)
x //= 4
return sum(table)
Repeat this function four times, and you will have multiplied by 256/81.
I have no clue whether they would have done anything resembling this procedure; this is just to show that it's plausible given how their multiplication worked.
I don't know how this relates to 'Egyption fractions'.
P.S. Just for fun the same thing for 22/7:
def f22_7(x):
y = (x << 1) + x
while x > 0:
x >>= 3
y += x
return y
> Note that 4/3 in binary is
This is consistent with the notion from Jarrosson, because that means that 4/3 can be represented as
The approximated ratio of the circumference to its diameter can be represented by four iterations ( (4/3)^4 ) of infinite series of sums of fractions with unitary numerator.
This is consistent with the notion from Jarrosson, because that means that 4/3 can be represented as
1 + 1/4 + 1/16 + 1/64 + 1/256 + 1/1024 ...
The approximated ratio of the circumference to its diameter can be represented by four iterations ( (4/3)^4 ) of infinite series of sums of fractions with unitary numerator.
> [...] the representation ancient Egyptians are said to absolutely prefer.
Well, they can also represent it as 1 + 1/3.. It's just that I assumed they have an easier time dividing by two than dividing by three.
If you leave it as a fraction, instead of dividing your integers, 1/3 is fine.
Well, they can also represent it as 1 + 1/3.. It's just that I assumed they have an easier time dividing by two than dividing by three.
If you leave it as a fraction, instead of dividing your integers, 1/3 is fine.
Certainly feels plausible, that possibly makes a lot of sense.
And now I spotted the mistake:
> (((4^2)/(3^3))^2)^1
should be (((4^2)/(3^2))^2)^1
> (((4^2)/(3^3))^2)^1
should be (((4^2)/(3^2))^2)^1
Yes, I was thinking about the simple powers, too.
And I don't know whether they had enough math (or cared enough to do all the hard work with the math they had available to them), to figure out what's the simplest good approximation for the real value of Pi.
And I don't know whether they had enough math (or cared enough to do all the hard work with the math they had available to them), to figure out what's the simplest good approximation for the real value of Pi.
They supposedly got it by using an octagon to approximate a circle. Maybe that was a simpler approximation used in education, who knows.
> 256/81 (3.16)
Whoa, trippy coincidence. (16/3)^4 ~= 3.16
Whoa, trippy coincidence. (16/3)^4 ~= 3.16
Despite the math typo, (4/3)**4 is a pretty interesting composition of pi, if only because you get such a fundamental constant out of a relatively simple arrangement of low natural numbers.
I must be misunderstanding something, because based upon my understanding (16/3)^4 ~= (5.333)^4 (or 65536/81) ~= 809.
16^4 / 3^4 = 256 / 81
That is interesting. Not as close to pi as the 22/7 that we were taught in middle school but maybe those exponentials were more meaningful to the Egyptians.
That is interesting. Not as close to pi as the 22/7 that we were taught in middle school but maybe those exponentials were more meaningful to the Egyptians.
Yes and no. Yes in the sense that there was a formal pattern for learning that developed from 3k bc - end (right around 1800bc) which typically included a combination of math (fractions, pemdas, etc, administrative math, enough so you could make a bill of sale) and writing (which meant learning Sumerian as well as cuneiform), among a few other "administrative" disciplines (like calculating the calendar- the Sumerian calendars often arbitrarily added a month or two whenever they felt like the calendar was too far off, so knowing when and how to add those months was critical to maintaining the cultic schedule. fun for archaeologists later to figure out what month it is..). The essential purpose was to prepare you for a life of administration of some kind, whether in a temple or household.
No in the sense that this kind of education was not available to everyone, and I would imagine the vast majority never learned to write.
Here's more Sumerian tablet jokes:
"If a scribe knows only one line, but his handwriting is good, he is indeed a scribe!"
"A scribe whose hand can follow dictation is indeed a scribe!"
"What kind of a scribe is a scribe who does not know Sumerian?"
No in the sense that this kind of education was not available to everyone, and I would imagine the vast majority never learned to write.
Here's more Sumerian tablet jokes:
"If a scribe knows only one line, but his handwriting is good, he is indeed a scribe!"
"A scribe whose hand can follow dictation is indeed a scribe!"
"What kind of a scribe is a scribe who does not know Sumerian?"
Quote: "Yet Hassett knows her stuff – and a lot of that stuff is very interesting indeed. Along the way, she debunks all sorts of received wisdoms. The idea, for instance, that women’s menstrual cycles fall into sync when they live in proximity. Hassett says that this ‘seemingly unkillable myth’ just ain’t so:..."
I'm sorry, but Hassett is wrong on this one. I've witnessed a dorm full of girls in my student years syncing their menstruation in like maximum 2 months after school was started. Multiple years was happening after they came from vacation. My girlfriends at the time were in sync with all other girls in same dorm.
I've witnessed later in life girls I shared apartments with having their menstruation synced just the same.
And fucking finally, my wife and daughter have their menstruation in sync nowadays.
I'm sorry, but Hassett is wrong on this one. I've witnessed a dorm full of girls in my student years syncing their menstruation in like maximum 2 months after school was started. Multiple years was happening after they came from vacation. My girlfriends at the time were in sync with all other girls in same dorm.
I've witnessed later in life girls I shared apartments with having their menstruation synced just the same.
And fucking finally, my wife and daughter have their menstruation in sync nowadays.
You should document this carefully and publish, since scientists have failed to document the effect.
en.wikipedia.org/wiki/Menstrual_synchrony
> my wife and daughter have their menstruation in sync nowadays.
How closely in sync? For how many cycles?
en.wikipedia.org/wiki/Beat_(acoustics)
en.wikipedia.org/wiki/Menstrual_synchrony
> my wife and daughter have their menstruation in sync nowadays.
How closely in sync? For how many cycles?
en.wikipedia.org/wiki/Beat_(acoustics)
I'd really like to know if menstrual synchronization is real, because there's a straightforward explanation: temporal herding. In the ancestral environment, it drew predators, so under the normal dynamics of prey and predators it pays to herd together. Herding in space is easy to see; herding in time, as of oak trees tending to produce acorns in the same year, is also easy to note after awhile. So if our ancestors evolved to all menstruate at the same time as a defense against predation, it seems perfectly straightforward. But all I hear is anecdotes that are promptly attacked, so, is this a real physical phenomenon?
Completely agree - see this in my family as well, even among females under the same roof but not related, IE: step mom and daughter.
+1...but your phrasing, especially of the last sentence, seems a tad indelecate.
This is hard to read. Seriously, both the author of the review and of the book (assuming the reviewer accurately portrays it) seem confused about evolution and have an incomplete or total lack of comprehension of ideas; like fitness landscapes, that evolution is not the result of a design process, and that traits can persist despite being neither adaptive nor maladaptive. Regarding the latter, there's a concept in cancer genomics – passenger mutations – which provides a DNA level example of this on a much faster timescale.
Humans evolved to make up stories. We do that every night when we dream. Here's another one. Rosebud.
Evolution doesn't have a goal or purpose, and it just doesn't make sense to say that 'Humans evolved to...' for anything. You could on the other hand say something like 'human story telling is a consequence of evolution' (though I don't agree).
and it just doesn't make sense to say that 'Humans evolved to...' for anything
I think you’re misunderstanding the GP’s point due to a limitation of language. Verbs (in English anyway) carry a strong connotation of intent for many people. I don’t look at it this way. I read that sentence as “the result of evolution is that humans…”
For example: “humans evolved to walk on two legs” reads as “the result of evolution is that humans walk on two legs”. No intent needed.
Getting to the specific claim about humans telling stories, I think it’s plausible. A lot of morality tales from mythology and religion are actually quite helpful for ensuring survival and cooperation of the group. Of course sometimes it goes wrong and you have things like child sacrifice. But then you don’t see too much of that around today, which suggests that killing your offspring is not adaptive in this environment (it might’ve made more sense when resources were limited and harsh environmental events took place).
I think you’re misunderstanding the GP’s point due to a limitation of language. Verbs (in English anyway) carry a strong connotation of intent for many people. I don’t look at it this way. I read that sentence as “the result of evolution is that humans…”
For example: “humans evolved to walk on two legs” reads as “the result of evolution is that humans walk on two legs”. No intent needed.
Getting to the specific claim about humans telling stories, I think it’s plausible. A lot of morality tales from mythology and religion are actually quite helpful for ensuring survival and cooperation of the group. Of course sometimes it goes wrong and you have things like child sacrifice. But then you don’t see too much of that around today, which suggests that killing your offspring is not adaptive in this environment (it might’ve made more sense when resources were limited and harsh environmental events took place).
I would bet a great part of non-working-in-natural-science-population are geniously persuaded the theory of evolution imply 'intent' from an abstract entity called 'nature'.
It was one of my mind blowing moment during studies and I spoke about it to a lot of 'educated-adults' and they were all adament I misunderstood my book and teacher, and Darwin stuff is about animals developing feature to better survive, and no the other way around : features being aquired 'coincidentally' by random genetic mutation and spread because they allowed better reproduction chances.
It was one of my mind blowing moment during studies and I spoke about it to a lot of 'educated-adults' and they were all adament I misunderstood my book and teacher, and Darwin stuff is about animals developing feature to better survive, and no the other way around : features being aquired 'coincidentally' by random genetic mutation and spread because they allowed better reproduction chances.
“central question in Brenna Hassett’s book, put simply, is: why are our children so very useless for so very long?”
I’m shocked at how obtuse the author must be to not see the value in children, perhaps overlooking the “use” children have in sculpting parents and meeting the needs of children and the net effects that has on society and the economy?
(Or maybe that’s what the book really is about, I haven’t read it.)
I’m shocked at how obtuse the author must be to not see the value in children, perhaps overlooking the “use” children have in sculpting parents and meeting the needs of children and the net effects that has on society and the economy?
(Or maybe that’s what the book really is about, I haven’t read it.)
drewcoo(2)
Whoa - I missed that "paraphrased" bit on first read and mistook this for a translation, which seemed really odd. But even paraphrased it refers to some kind of formal education for young children. Was that present in 1800 BCE Mesopotamia?