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Realistic spaceship warfare
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I was thinking about a bank of lava lamps that one company uses to generate random numbers, or you could take cosmic background noise, etc. Even if a super computer could model a single lava lamp well enough to determine a predictive formula, having a hundred of them should slow it down quite a bit. Heck even having the AI switch to a different pseudorandom algorithm with a different seed often enough should make it really hard to predict.

I suspect actual space battle would be mostly boring until it was suddenly terrifying, and you would either be dead or alive based on the math.
One story I read but can not recall the name of (Brin?) basically had the equivalent of mines-slash-missiles as the ultimate arbiters of space battles. If you didn’t have the correct friend-or-foe countersign, they would lock onto you and simply run you down until you were destroyed. Very stressful and inevitable. Even a near miss from a nuke could zap you with the EMP.
Scatter a million missiles into the area and let them sit there idly for years or decades until someone wanders by. It’s like the landmine problem we have now in former warzones.
In Protector there’s one scene where they swing past a neutron star and Brennan shoots a gun from a hatch. Hours later the pursuing ship gets caught in the resultant blast of radiation caused by the slugs impacting the star’s surface. I think that sort of thing would be pretty common.
I can’t imagine space battles would actually happen much, though. The real issue is planets. Those are the ultimate soft targets. If you start a war, someone just has to drop a big enough rock on your homeworld and boom, instant extinction level event. There’s no percentage in picking a fight if the other side can simply eliminate your entire species with a single asteroid.
Definitely planets are hard to defend. They can’t duck. At least two different series I’ve read have had the enemy pick a rock in the Oort Cloud then accelerate it to something like 0.3c and let it go, or just have a suicide ship going as fast as it can aimed at the capital. If something is coming in at a significant velocity and you can’t dodge then there’s nothing that can be done. Even if you can hit it and break it into pieces those pieces will still hit the planet.

With respect to lobbing heavy objects, the most entertaining description I've read of semi-realistic space battles is in Iain Banks The Algebraist where one strand of the narrative follows an attack group that spends a substantial amount of time (at least decades? might have been longer, need to re-read it) accelerating for part of the force to basically do a flyby at a decent proportion of c.
Not rocks, but at high enough speeds, any vehicle will take so much time and energy to turn away when it gets close enough that it makes little difference. In the book the point was to make a very high speed very precise fly-by capable of launching e.g. missiles at an accordingly high speed to be near impossible to stop, because they had the caveat that when the strike force set out they didn't know whether or not they needed to attack (and FTL gate had been taken out; the force was bringing a replacement at sub-light speeds), so just aiming at the planet was not a solution.
I think in general space battles basically need to happen either at very long timelines and huge distances or at very short distances and relatively low speeds. Either way you're going to be massively constrained if you have squishy humans aboard that you'd like to keep alive. But in fiction having the squishy humans involved is often necessary in order to create tension and danger.

Did you read the other one : What would a realistic alien invasion actually look like ?
https://www.quora.com/What-would-a-re...
That was hilarious !
Books mentioned in this topic
The Algebraist (other topics)Protector (other topics)
https://www.quora.com/What-does-scien...
Dern speed of light limitations, and vastness of space. I found the comments about AI and randomization particularly interesting, although I strongly suspect there are ways to generate true random numbers.