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This is a neat project - the different heatmaps are an intuitive way to present the data. However, I really think these need a date slider or some other way to control the animation. I've made a few projects like this and have come to the realization that animation without a method for "scrubbing" ends up requiring you to wait around to see the data you're interested in - this pretty much makes it just a "cool movie" and not a tool which lends itself to any real analysis.

Adding a date slider would be a pretty simple change that would add a lot to this visualization - see for example http://labs.enigma.io/climate-change-map/

Edit: also just noticed a bug - If you click the animate button, it doesn't turn into a "pause" button. If you click Animate twice, the dates start jumping around strangely.

I'm not so sure about heat maps here. They don't suit the zooming scale at all when viewing the entire map. For example, the first map suggests that Ireland was a major driver of slaving trades at the full-globe scale, which is absurd.
The United States was only slightly green. I would have thought it would have lit up more. It may be because they passed laws in the min-1800s prohibiting importing of slaves.
The lions share of us didn't come to the US, we mostly went to Brazil and other more tropical locations. And you have to remember, that after 1819 or 1820, the importation of slaves into the U.S was banned.
I'm sure the slave import restrictions had something to do with it. There were also the Triangular Trade routes from Africa (rum for slaves) -> West Indies (slaves for molasses) -> Boston (molasses for rum) -> Africa

In doing so, the US benefitted from the slave trade without actually taking part in it.

(well, taking part in that part of it anyway)
I think this is cool, but I think it would be more effective as a directed graph, with edges sized compared to the volume of traffic. It doesn't even have to be on top of the map, just name the edges.
Interesting. Now if they only showed intra-African slave trade, that would be something. Something with a little bit less white guilt...
The data on importation makes no sense at all. There should have been a HUGE drop in arrivals of slaves at US ports after 1808, when importation was banned. The animation shows no visible drop at all, instead showing a roughly flat rate through the Civil War.