> At this point I'm merely talking about size (which I think is clear from the words I use. I don't think "building a mile tall rocket would be hard" adequately describes the difficulty when we haven't even built a mile tall building.

I was assuming you were using a comical example to illustrate a "nightmare to engineer." The comparison to a building doesn't actually work at all. The practical limitation on how high we can build buildings is how fast we can make elevators. Just making something tall is not a problem.

> Sea Dragon[1] was only envisioned as 490 feet tall, and as near as I can tell even the Super Orion[2] would only have been 400-600 meters tall. And of course, neither of those was even close to implementation. Therefore I stand by my statement that a mile tall rocket is, for all practical purposes, impossible

First, the optimal design for a rocket is not to just keep making it taller, and second, size was not the obstacle to either of these projects not being built. That does not at all prove that it is impossible. What kind of world would we be living in we presumed anything that hadn't already been actively pursued was impossible?

> and thus has a payload to orbit of zero.

My point was that this does not equate to a payload of zero. Surely you wouldn't argue that the weight of this mile high rocket is zero, and therefore that there is some curve for the weight of rockets where making the rockets larger starts to make them lighter. Just as we can calculate the weight for something without actually building it, so too can we calculate the payload, and it can increase far beyond anything we can actually implement.

> If you disagree then add a zero -- surely you agree we can't build a ten-mile-tall rocket?

I agree it would be impractical, but not that it would be so non-physical that we couldn't calculate what its payload capacity would be were it to be built.

> Toy rockets might fail all the time, but the point was complexity, and a toy rocket can be constructed from under a dozen parts. Even larger model rockets have at most a few dozen to a few hundred parts. The part count of the Falcon 9 has to number in the thousands, if not tens of thousands (9 merlin engines with at least several hundred parts each?).

Falcon 9 is a liquid rocket designed to take people into space. That is the source of its part count. You could scale up a solid rocket motor to an arbitrarily large size while keeping the parts count exactly the same. It's probably not the optimal way to make a solid rocket of that size, and you'd be missing out on a lot of capabilities that are important for a real rocket, but if you just wanted a toy no more capable than what you buy in a hobby store it would be no more complicated. Conversely, try to make a fully functional falcon 9 complete with 9 working liquid rocket engines small enough to hoverslam on your desk and you have an immense engineering challenge on your hands.

> But also, to push back a bit, I don't think complexity aggregates the way you're saying it does. A box of hammers is not more complex than a nailgun, even if it has more parts in total.

I concur that part count is not the same as complexity, but that point is in my favor. Making something bigger is like adding hammers to a box of hammers. The quantity goes up, and at some point you're going to need to make some improvements to the box if you want to keep adding more hammers, but conceptually it is simple. Making something more capable, like a nail-gun, is much harder.