Content warning: This is a baker’s dozen not a regular dozen, in case anyone clicks through expecting to find twelve and is mildly and briefly perturbed.
The scary thing is that yea we can see these in 2D and maybe 3D. But ...
usually there are more than 2 or 3 columns in our data :(
It's clearly hard, but there are tools for doing exploratory visualization of high-dim data. GGobi http://ggobi.org/ and all the ones that arrange points but try to get local neighborhoods correct (t-sne, umap, et al.).
Yeah, but still "scary" because you have to be really careful to not fool yourself and pay attention even with those algorithms. For example, a good demonstration with tsne
https://distill.pub/2016/misread-tsne/?hl=cs