Lolwut?
Dividing the block reward into smaller amounts doesn't fix the problem. It becomes insignificant long before it actually gets to zero.
I was just reflecting on Peter Todd's argument in [1] and thinking what are the realistic possible endstates for Bitcoin in these terms.
The first is along the lines of what Peter is implicitly advocating: adding a tail emission with, asymptotically, a fluctuating supply (because loss rates will fluctuate, for whatever reason). Note "fluctuating" does actually mean it will sometimes go down as well as sometimes go up (though that won't be measurable). Read the article carefully to get the point; if you're not comfortable with first order differential equations, no worries, he explains the point after writing the math. And if you still don't get it, ask me, I can explain.
The second possible endstate is "fuck that" and supply endlessly goes down, *but* we have a mechanism to hard/soft fork such that we divide sats into smaller and smaller units. I think this is what a lot of people hope will happen.
The third one is the funny one: all software changes end (ossification) but supply keeps going down. Sats are worth 10 squillion dollars, but at some point, nobody has any any more.
(of course in reality a fourth option, which we can't envisage, is what will actually happen, but where's the fun in that).
[1] https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
Discussion
I think you misread or misunderstood me. I wasn't talking about changing emission, only talking about infinitely dividing sats so that in a world where 99.9% of the supply is lost, people could still trade with each other using microsats or whatever.
Ah.
Though that's still bizarre. The chance of a sat getting lost is inversely proportional to its value. As more supply is lost, the rate of loss per sat will decrease.
We've got plenty of precision. Especially with L2's.
Inverse correlation seems plausible, literal inverse proportion seems a bit too specific a claim. I guess that's the biggest problem with your analysis here generally; it's basically impossible to know loss rate, and any assumptions about it are just that. I certainly agree it's interesting to think it through, though, starting from the simplest possible model.
Obviously loss rate is a function of value. Not some absolute number. That's why we can be sure that the absolute rate of sats loss will diminish over time.
It's not completely obvious that the function doesn't have some floor/minimum (I don't think I can get to 10^-9 loss per year even if my life depends on it ... or whatever). But generally I'd cede the point that you're mostly right on that.
Sats don't just magically decay. If you have a seed phrase that secures 100 sats, the chance of you losing that seed phrase is no different than a seed phrase securing 1,000,000sats _if_ the price is different enough that both seed phrases represent the same value to you.
...and lightning already supports milisats. So precision isn't a big deal.
Yes the loss rate is not dependent on the numerical sat value, and *is* dependent (inversely) on the economic value. I agree that my message was blurring and confusing these two clearly correct points.
But that dependence on economic value can't be assumed to be some very simple formula such as inverse linear (l.r. = k/value say), albeit that's a sound starting point. It's true that this has a nice asymptote at l.r. = 0 but we don't know if there is some other asymptote/floor; also, we might *think* that twice as much effort expended (because twice as much value) leads to half the loss rate, but .. does it? i wouldn't be surprised to see some exponential component there. it's fascinating to analyze, but it's hard to do more than theorize, because we have a tremendous and, likely, impossible challenge in trying to measure or predict loss rates.