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The tyranny of the rocket equation is, indeed, exponential. Thus, we went to the moon with relative ease, haven't quite "been" to Mars yet, and no one is thinking that a singularity of shoving atomic rockets in the boot is coming to take us to Alpha Centauri in 2027.
Much of theoretical computer science is discovering hard limits on the universe of computation when it comes to scaling. Often times, that big ol' O hides a lot of stuff and is confusing to people. "Why, it seems so easy to run this program on my computer; it's like going to the moon; I just burn some carbon material, and it just works!" But then you just tweak one parameter, and it just breaks utterly.
At the time that we went to the moon, I don't know if people had worked out the theoretical limits of the full spectrum of hypothetical rocket fuels, but we went through a bunch when I was in undergrad. We ignored any sort of practical concern and just worked out, in theory, if you could pretty much perfectly utilize it, what it would get you. Fission, fusion, antimatter, whatever. Yes, we literally did antimatter. The conclusion? None of them give you all that much more in the face of the tyranny of the rocket equation. Certainly not if we're thinking galactic or cluster scale. More? Yes. But in context, underwhelming.
We sort of don't know yet how far this stuff will take us. The achievements to date are seriously impressive. Like literally going to the moon. But we kind of have no clue when the tyranny of some hard limit on computation is going to make itself known. Maybe we'll even go to Mars with ease; maybe we'll go even further. Who knows?
I'm pretty sure antimatter gives you a lot more power than chemical rockets, by any reasonable definition. You can get a decent fraction of c with antimatter.
Also, there's a huge difference between 'bird', 'propeller plane', 'rocket' and 'atomic rocket' in any realistic sense, with regards to what we're dealing with now. Is superintelligence capable of rewriting the fundamental laws of the universe like a real deity? No. Is that necessary to make vast changes to our lifestyle and existence? Absolutely not, just like you don't need intergalactic travel to totally transform our spaceflight scene.
I had said:
Sure, I'd even agree to "a lot more". But "power" isn't necessarily the thing that we care about in rocketry. Nor are you seriously engaging with the exponential.
My brother in Christ, we are not disagreeing; you're just not engaging with the exponential. If we had an order of magnitude or two increase, that could totally transform our spaceflight scene. The moon could be routine. Mars could be like going on holiday. Even further could be an expedition. But the exponential is still the exponential, and in context of the insanity of exponentials and the universe, mere orders of magnitude only push back the hard stop a "little".
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