It's very difficult. We can look at the fact that the US imprisons more of its population than any other nation, and if prison is a working deterrent, this would mean that the United States is a phenomenally lawless and criminal society barely held in check by the fear of the USA's notoriously harsh judicial system. Is the USA a phenomenally lawless and criminal society?

There are studies that try to evaluate the deterrence effect of prison. Some conclude yes, some no, but the weight of evidence appears to indicates that on the whole, it's a pretty ineffective deterrent. You can google as well as I can so I won't list a bunch of google hits.

"Our culture considers those barbaric (but not prison somehow.)"

Now that is interesting. I meant a detention system that actually works; that actually is applied with the intention of turning criminals into good citizens and making a better society. I assume that you don't consider that "barbaric", so I'm guessing you thought I meant something like state-sanctioned torture or other such physical abuse, or cutting off people's hands, or public executions in the town square, and all that sort of thing. So our cultural gap is so big that the first thing you thought of to deal with detention as an ineffective deterrent wasn't an effective detention system, but harsher punishments, whereas I thought of stopping trying to use it as a deterrent and do something useful with it.