This topic has no relation to SEAC, but is a fun exercise on some misconceptions with slowboating it to another star, So you want to go to another star eh? Unfortunately, scientists are stubborn about inventing quicker space travel. Something about physics and Einstein being a kill-joy. Instead of doing it the way we'd like to, we're stuck slowboating it across with current methods. For reference, the closest star is 4.24 light years away, with 5 other systems being less than 8.5 light years away. But why is that a problem? I know our governments are cheap, but what if we assume they're not, wouldn't that help negate the distance problem by going faster? Can't happen.
Let's start with some beginning misconceptions. The most common misconception I'll hear about is a focus on acceleration. Usually something along the line of "If we accelerate at x for y, we'll reach our destination in z years". Nothing seems off at first glance if you're not familiar with the subject, but we measure a rocket's propellant in terms of delta-velocity (dV) for good reason - the total change in velocity is a static number for the rocket and the rate of acceleration is meaningless for the majority of cases. To be clear, the amount of dV a rocket has is what's important for how quickly it can go between stars, and not any other property.
So, the objective is clearly to get more dV into the rocket if we want to get to the star quicker. If dV is propellant, why can't we keep adding more to get to a higher speed? For a rocket, the dV is dependent on the exhaust velocity of the rocket and the percentage of mass spent on propellant compared to everything else. Because we don't have any new rocket engines just now, we can treat the exhaust velocity as a constant. Thus, if we can get more dV by devoting more mass to propellant, why don't we? The easy answer is that the mass not spent on propellant still needs to cover the mass of the engines, containers, and other structural necessities. For a given engine and engineering know-how, there will always be a maximum amount of dV you can put on a rocket.
I can't put more fuel on the rocket. But what about putting more fuel in front of it? On Earth, if I can only carry so many days of supplies, but need to get farther than those supplies allow, I can leave supply depots in-between. If you do the math, it's easy to see that such a strategy takes a lot of extra supplies and time, but it does work. Seems simple to apply a similar solution to rockets. Send out a rocket ahead of time full of fuel. When the main rocket gets to the new one, you can refuel. Get enough of those, and you get tons of extra fuel, wouldn't you? If you're paying attention, I'm betting you already know the answer. (This doesn't work, if you didn't guess)
The primary problem with a strategy of this sort is for the rocket to get the additional fuel, that fuel needs to be at the same location, but also needs a similar speed. You do not want to run into tons of fuel going 1 km/s relative to yourself. It'd make two freight trains colliding look like a gentle accident. Clearly, you'd want to have the supply rocket accelerate to the same speed as the main rocket beforehand. If you're doing that, there's no reason to have it start out farther, so we'd have it start out with the rocket. Instead of having the supply rocket refuel the main rocket, it's simpler to have it fire first, use up its fuel, and then jettison it rather than carry it along. This is effectively how staging/booster rockets work, and they have the same rules as supply depots. It takes a lot of extra supplies for a small boost in distance. This works to an extent, but doesn't allow for much extra dV, unfortunately.
Lastly, remember that even if we accept that it will take hundreds of years to go to another star, the technology isn't there to make it worth anything. A computer that can last that long would be impossible with current tech. Getting a self-repairing computer would be closer to possible, but still far away from what we can do now. Using a generation ship that recycles all its materials is even more complicated, and potentially not doable with our current energy technology.
Hopefully that helps answer some of the questions on why faster-than-light drives are so darned handy.