This went way long but I have some apparently counter intuitive conclusions so I fleshed them out. At the top is the summery and and answers to specific question of the OP. Below are detailed arguments if you wish to read them. (Anyone who does so gets a cookie.)
My core conclusions are:
- Methuselah's would have a society based on flexibility, adaptability and change.
- Methuselahs would develop technology more quickly.
- Methuselahs would have a less hierarchal more egalitarian and merit driven society.
- The idea that youth promotes change and adoption of good new ideas is not historically supported. A society of Methuselahs would be not be inherently more static.
- Societies don't change because old people die, they change to adapt.
- Elites cannot control society to prevent change.
If women didn't reach menopause until their 500s or 600s, would large
families be more commonplace?
Simply having one woman fertile over a few centuries instead of a series of women over the same span, would not change the overall birthrate. Humans have regulated birth rates since hunter-gatherer times. People have the children they can support in a given environment with the already extant population. That would be true regardless of how long we lived.
A long lived species of humans would not have much turn over so they would have to limit replacement births. Their populations growth in absolute size would mirror our own, expanding gradually up during the agricultural era when children are important for labor, then a slight uptick at the beginning of industrialization, then a sharp drop off as children began to absorb more resources.
How would the institution of monarchy (or other appointed-for-life
positions, like US Supreme Court justices) be affected by having the
same people in power for centuries?
Not much. The practice is largely followed in countries that still have substantial adherence to common law i.e. historical defined law. Judge's power was checked by the precedents set by previous generations so no other mechanism was needed. The major function of life time appointments was to limit the power of outside actors to influence judges, by influencing their reappointment. That dynamic would not disappear.
If people pursued multiple careers in their lives, they would likely switch to a system we use with US Presidents, a fixed term coupled with an ban against serving again. So, you could be a judge for 50-100 years but then you'd be out of judiciary forever. Judges would be independent while sitting and then have to switch careers.
How would criminal justice be different if it were possible to
actually serve a 600+ year prison sentence?
Bizarrely long but fixed prison sentences are the result of the very strange accounting system used in the criminal justice system. It got really baroque in the 1960s. They are intended to serve as life sentences for accumulations of crimes that individually, for whatever reason, cannot individually warrant a life sentence. Not all societies use them and they used to be rare in American.
The prison is only partially deterrence from loss of freedom. The experience of the last 40 years has shown that the primary good performed by prison lays in simply isolating transgressive individuals from the general populations. That need wouldn't go away in a society of Methuselahs.
If I had to guess, I would say that the Methuselah's awareness of change (see below) would likely lead them to promote capital punishment as a means of avoiding shifting conditions or chance from freeing a dangerous individual centuries down the road.
That happened for real in the 1960s when radical and unanticipated shifts in culture, law and criminal justice theories released large numbers of people who had years or decades before been sentenced life or even death. In some case, individuals sentenced originally to death either killed again in prison or were freed by corruption or accident e.g. Kenneth McDuff, and went on to kill again.
After a few centuries of experience, such an outcome would likely seem more likely than not so executions would seem a more certain form of both justice and prevention.
How would historiography be different if people who lived through the
Crusades, the Renaissance, or the American Revolution were still with
I think the biggest change would be the ability to think of or ask question not on anyone's radar at the time. For example, prior to the 1600s, technology was almost entirely undocumented because no one of the age thought it particularly important. Most of what was documented concerned weapons. We detailed plans and models of on warships from the 1600s but rely on archeology to tell us about merchant ship construction as late as late 1700s.
While providing insight, long lives could also make historical studies more difficult.
Firstly, we have trouble discussing "living history". If the actors of events are still around, especially, if they are still prominent, things get hairy. I spent a big chunk of my life watchings Baby Boomers bob and weave around the Vietnam war even after the end of the Cold War.
Secondly, lot of recollection would be fouled by hindsight bias. Nobody is right all the time or even most of the time. When you read great works of philosophy and science from the past, what you see is 90% flat wrong with a few perils of pretty-close. On social and political matters, everybody would be seriously wrong to point of disgust about something e.g.Lincoln would be considered a hard core racist by contemporary standards.
People writing about their conduct in the distant past would constantly try to reinterpret their actions in modern terms e.g. I'm old enough to remember when leftist declared the idea that being gay was somehow physiological intrinsic was impossible and fascistic and who mocked the the idea that gay people would ever get to marry as right wing hysterical fear mongering. You won't find any advocates for gay rights from the 60s-late 80s, owning up to those then universal stances anywhere today.
Thirdly, people write contemporary they expect to be read in their lives differently than they write accounts they expect to surface only after they are gone. Diaries are different than newspaper editorials. People who lived centuries would likely write with biases assuming that they would be around when all their writing became public.
Methuselah's would have a society based on flexibility, adaptability and change.
Each individual would experience and remember more change and thus be more aware of the need for individuals and societies to be willing to change and adapt.
If nothing else, their view of the natural world would be one of extremely fast and constant change. River courses would whip about like snakes. The sea would visibly eat into the land. Mighty oaks would grow and die like shrubs. They could breed plants and animals over centuries or even millennia which would make life itself seem plastic and shifting. (Someone 500 years old today would remember when most fruits, vegetables, strains of grains breeds of dogs, cattle, sheep and horses etc did not exist.)Every middle-age adult would remember large numbers of superstorms, earthquakes, volcanos, plagues etc.
The cyclic motions of astronomical objects would be readily apparent, as would the cyclic decadal shifts in climate that occur in every region of the earth.
Natural resource bases like game lands, potable water,arable lands, navigable water ways or veins of ore would seem constantly shifting and ephemeral. Likely, they would never develop the concept of a "natural" resource at all since every individual would see many changes in how resources came into being from human effort and how resource use shifted and changed constantly.
In human interaction, they would see more examples of fluke and chance, more lost horseshoe nails loosing battles for example, and would be less likely to see current social structure as something fixed and eternal.
Certainly, the rise of literacy and historical research of all kinds has given us today long artificial memories and made us more aware of the constancy of change and our need to always adapt. Imagine how much more we'd believe this if we personally remembered those changes.
Methuselahs would develop technology more quickly.
Longer memories of individuals would mean greater and faster accumulation of knowledge in pre-literacy times. Until well after the 1600s most technological knowledge was passed directly person to person. A break in the chain caused the loss of the knowledge. People with 1,000 year old memories would not have that loss.
Long life means lots of time to learn new skills explore many avenues of thought. Each individual would have a wide range of skills of all kinds which they could bring to bear on science and invention.
There awareness of the need to change and adapt would create a powerful incentive to look for more new technologies and adapt them.
Methuselahs would have a less hierarchal more egalitarian and merit driven society.
Thinking long term, and much aware of change and chance, when on top, they would value the potential for long term cooperation centuries hence from those currently on bottom when the shoe might well be on the other foot.
Just like the rise of long distance sea trade cause people to worry more about a captain's seamanship than who his daddy was, long term planning for inevtiable change would make them value skill and merit more than the alliance du jure.
More time to learn skills would mean more time to acquire military skills which would make it more difficult for a minority warrior elite, trained since birth, to dominate a large population of craftsmen and farmers. In all known human societies, greater equality of military skill and service has lead to greater social equality while greater inequality leads to the opposite.
The inability to block individuals from rising on merit by force would also contribute positively.
With each individual having the time to learn many skills, society would be less interdependent and more robust against of disorder and disruption. In a pinch, you do without a blacksmith because everyone would know a little blacksmithing. As such, political changes and fragmentations would not present as much as problem as in societies with a high degree of specialization of labor, and a high degree of interdependence.
The idea that youth promotes change and adoption of good new ideas is not historically supported. So, a society of Methuselahs would be not be inherently more static.
Kinda of a modern idea, probably linked to flattery in advertisement and advertisement supported media which is overwhelmingly aimed at the young, because the young respond most strongly to advertising.
Historically, it has no basis. Most science and technology development is done by people 25-35. Most business innovation by people 30-50, and most political innovation by people 45-60. E.g. the Civil Rights movement was carried out by the Greatest Generation and the Great Depression generation who where in their late 40s to early 60s in the 1960s, not the then snot nosed Baby boomers.
Basically, all the heavy lifting or organizing and getting things don is done by people around 50. People who are older wear out and can't keep up more than growing mentally inflexible.
Societies change when their internal or external environments change and they must adapt. When that happens, those with the most existing power and skill implement most of the changes.
Young people play the same role in significant and enduring political and social change as they do in wars i.e. foot soldiers.
To the extent that youth does promote change, its often random as to whether it turns out good or bad. Fascism and Communism were considered youth movements in their heyday of the 20s and 30s. Older people are much better at filtering bad ideas, the majority, and focusing on those that will produce lasting improvements. The effect is even more profound because important changes tend to be rather boring at the time and only people with discipline, experience and an eye for detail can carry them out.
Having longer lifespans would improve this skill as well as reinforcing the need to change and adapt, a relativel lack of young people would have little effect.
** Societies don't change because old people die, they change to adapt.**
By our standards, most historical societies had a higher ratio of young to old yet they remained static for far longer. If young people drove change and old ideas died because the people who held them die off, societies with higher death rates at younger ages should change faster. They didn't and don't.
Every core change in every society occurred because older, wealthier and more powerful changed their behaviors even if they didn't change their stated ideals. From religious reformation to political "revolutions" (really lateral shifts) to Civil Rights, the people that had to change to make the change stick were older, more experience, skilled, and overall effective people i.e. the people who get most of everything important either done or coordinate getting it done.
Methuselahs would be no different. Their long lives would see many changes in nature, technology and society. If they keep trying to act like it was 1300 in Germany the medieval warming period 1777 Massachusetts during the little ice age, they wouldn't last long.
** Elites cannot control society to prevent change.**
Another myth, largely perpetuated by those trying to explain why their particular really, really great and obviously true and perfect idea didn't succeed in radically restructuring society in a weekend.
Far from being inerrant puppet masters or engineers arbitrarily structuring society to their own benefit or whim, elites are historically dullards constantly blindsided by change. This happens because changes usually start small and by the time they appear to be of consequence, it's to late. Social and political change usually occurring owing to changes in the environment or in technology, neither of which elites control.
This is particularly true in the case of technology. New technologies start out about as distinctive as individual tadpoles. Only in hindsight is their rise obvious. Nobody has ever succeeded in suppressing a useful technology despite the fact that every single new technology ever, has threatened some established interest.
So, not only would Methuselahs be more positive towards change, have an less elitist dominated society, they wouldn't be able to stop change even if they wanted to.
Methuselahs probably would have hit the industrial age within a few thousands of years after the end of the last ice age, say around BCE 5000. At our stage of development, they'd probably be planning on nipping on sublight starships. What's a five hundred year stellar voyage to someone who will live to be 1,000?