Can We Think About Something We Cannot Imagine?

The very last line of this excellent clip of Carl Sagan explaining the 4th dimension got me thinking:

Can we think about something we cannot imagine? The more direct version of this question is, can we think about something we cannot directly imagine. Since we are almost certainly, in Sagan's example of the cube, imagining a 4th dimensional object without picturing it. We are imagining (and even creating) its shadow, and the rules by which it exists. But suppose there was a thing we couldn't in any way gain a mental hold on. Could we be said to be thinking about it? In the act of thinking about it, do we in some sense imagine it, even if only in a representational way? There's more than a faint aroma of Anselm in this line of thought.

The divide between thought, imagination and reality is one of the most philosophically rich areas for exploration. There are thus many wonderful ways to start a discussion. With older students you might show them this very clip, and ask the question "can we think about something we cannot imagine?". Alternatively one might whip up a small story exploring imagination and reality. For example:

Ebonie whispered to Jen: "I dreamed I saw a unicorn!!!". Jen was not impressed. "So?" she said. Ebonie said "Well, every time I think of something, its real, even if its acting silly. Like when I dreamed of the squirrels dancing". Jen giggled. Ebonie continued: "So, if I can see a unicorn with my mind, it must be real!!!". Jen said: "But you saw it in a book that doesn't count." Ebonie didn't even pause for breath, smiled and asked "But where did THEY see it?"

The video also provides, in its exploration of explaining a 3rd dimension to 2 dimensional creatures, the question of explaining experience. How do you explain the taste of an orange to someone who's never tried one? Can you explain up and down to someone who can only move forward, backward, left and right? How might you do it?

Pavel: "You've never tried pizza, how do you know you won't like it?" John: "It looks yucky." Pavel: "Lots of things look yucky, but aren't. You love oatmeal!" John: "Oatmeal is a good kind of mushy." Pavel: ".... Uh.... yes... a good mushy." John: "What does pizza taste like?" Pavel: "Well...." How would you explain what pizza tastes like to someone who has never had it? What if they've never eaten ANYTHING? Could you explain what taste is to someone without a mouth?

What do you think? What other curious questions might young minds ponder after seeing this video?