I've noticed a couple posts here suggesting that the "traditional" view of retirement is somehow in contrast to any idea of end-of-life productivity. For those who think that, I'm wondering why they think so?
In my estimation, the original reason for retirement was a loss of productivity- people working in labor-intensive fields eventually lost the strength to do the work, and had to rely on savings, family, community, or government to provide for their existence from that point on. Talking with folks from the Silent, Greatest, and Interbellum generations (people born ~1900-1945), I get the impression that this was the most common perception of retirement for them growing up. Several have told me that they chose their careers precisely because they would not require retirement... incidentally, all of those individuals have since retired.
A second tradition seems to have risen among the later generations, probably fueled by the sharp uptick in both life expectancy and the number of companies that provided pensions, and that's the concept of retirement for out of desire, rather than out of necessity. My father will likely retire while he is still able-bodied, because his pension will provide for it, and his individual retirement accounts and social security will supplement that.
However, in both "traditional" forms of retirement, I don't see most people flipping a switch and giving up productive work altogether. I see it as a sense of freedom, or independce (go figure). Sure, my grandfather can take a random Wednesday and go fishing, or load up the car and drive 3 hours to meet an old friend for lunch, but he can also invest 2 weeks into building a stone wall in his back yard by hand to keep the deer out. And when his knees finally give out and he can't handle the stairs anymore, he doesn't have to worry about how he's going to provide for himself and my grandmother any more. I expect the same will be true of my dad- most days, he'll probably be in his workshop, or the barn, or somewhere else on my parents' 26 acres, fixing things and improving the property. But he's got 4 grandchildren in 3 states, and a whole host of other things he would like to do if he weren't putting in 40 pre-scheduled hours at his day job (where he fixes things and improves properties that are not his).
I expect that if/when I reach FI, whether that's at 40 as I hope, or further down the road, it won't slow my productivity any more than it has my immediate ancestors, but it will certainly open doors and change the format of my productivity. I'm a researcher and a writer first, and a teacher second. But as most people who feel that way can attest, the majority of places that employ people like me expect us to be teachers first, and do our writing on our own time, or wait until we're elligible for sabbatical. While I am sure I will love the classroom, the possibility that I could go into writing full time when I'm in my forties is very exciting. So yes, I have a number in mind, which will allow me to reach Financial Independence, and make it so that I don't have to work, or do anything productive, in order to support myself and my family. But I fully expect to go on being productive because it's what I will want to do. It's a very happy both-and situation, rather than a nerve-wracking either/or.