Your eyes can see the color, but your monitor can't represent it.
When I do lighting installations, I always insist on RGBA fixtures so you can get true warm colors – another thing you can't do with RGB displays.
The Mantis shrimp[1] can see colors in up to 12 dimensions, instead of the pathetic three that we can see.
Further, a study done with mice which I can't find now involved implanting mice with the genes for a third type of color receptor, and they grew up being able to distinguish colors in three dimensions instead of two. In other words, if you add a few genes for more color dimensions, the brain adapts.
To advance the human capability to perceive color, it is probably just a matter of adding a few genes. This kind of stuff is within a century for sure. Our descendants could grow up being able to see visual subtleties we can't even imagine, if we choose to go that way.
All of today's print systems, monitors, etc cover a certain subset of visible colors. I think we can expect the technology to improve toward the year 3000, and there will be new colors that we can't represent today in sRGB. But until then, no, sadly we don't have access to (all) those color palettes.
But hey, the colors we have today are forward-compatible.
http://tools.medialab.sciences-po.fr/iwanthue/
http://www.eigenlogik.com/spectrum/ (OS X 10.7+ app)
Wonder what the purpose of the "Sorry, no Internet Explorer" is.
seems its just cool to post things like that without bothering to test if it, in fact, does work.
One minor suggestion: it would be nice to add a simple tooltip on hover of the different swatches and circles that give the rgb/hex value of that particular swatch/circle.
Generating clear palettes as a result of the palettes discovered would be immensely helpful for designers.