Other posters have pretty much summed it up. Recency.
in the western world, the atlantic slave trade was the last major time of slavery. Post slavery you are always going to remember the last one most of all, for 4 obvious reasons:
1, scale - given technology advances, the last one is always going to be the biggest and most technologically capable. So in terms of pure scale, the most recent slave trade is likely to be the biggest and the worst, and remembered as more because of it
2, being the last - The first world war was described as the 'great' war, until the second happened, when it was demoted to just 'the first world war' by most. Do you think we would remember the first world war more if the second had never happened? Or if there was a third nucelar war, would we still talk so much about the second? etc. The last thing something always sticks in the cultural mind far stronger because nothing comes after it that erases or gets in the way of its memory
3, Those who were freed can tell the story/remember it.
4, technology and recordings, obviously the more recent and technological, the more evidence we have. It makes it all seem far more real then ancient slave trades that we know little about.
3, is a really important one. Imagine hundreds and hundreds of years of slavery, no one talks about it as if its anything but the norm, because its the norm everywhere.. most slaves die, most children born into slavery die in slavery etc.. there is no one to fight for slaves or tell the story of slaves, bar a few religious examples. There is no break in the chain, where slaves can rise to the level of their owners, and then make their case and tell their side of the story.. its just a trap, a repeating cycle. Its only when the cycle is broken that the generations after can actually tell theirs story and reflect on what happened and have the freedom to take action on it.
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My thoughts on slavery are that its perfectly normal to focus more on the atlantic slave trade then all the ones before..
we should also remember though, that the western world, notably british empire, were amoung the first major civilizations to outlaw slavery. In terms of history that is a massive huge step in the right dirrection for the world, that shouldn't be understated. The fact is that slavery was the norm across the world, across amost all civilizations prior to it being ended by western nations. It still exists as a problem today in parts of the world, but in western nations its remained pretty much eradicated. Its a huge leap forward, that is not discredited by the existance of slavery in western nations before it.
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What we do now is harder... I am in favour of the general principle of reperations, that there is an inequality that can still be felt today. I do think there is truth in that. But specific white to black reperations are a practical impossibility and make no sense at all. To start with, what the hell happens to mixed race people(which is most black people in the USA)? A huge number of black people have some white European ancestors, what point is the cut off? How black do you have to be to get repreations? A person who is 1/8th black looks bassically white and would be treated as such.. do they get anything? what about 1/4 black? or 1/2 black.. does your family have to go back to slavery in america, what about the black people who have come since? what about the white families who never owned slaves, or who came since from countries that weren't involved etc.
I would support a general goverment fund to try and help black communities.. fund black-focused charities, and try and fix some of the structural problems inside the communities (schools, lack of fathers, drugs/guns etc), and you could do that in the name of reperations and that would be fine.. but to specifically find some way of taxing white people and giving it to black people? Its absolutly nonsensical.