The Impossible Dream

Is striving towards an impossible but desirable and worthwhile goal a waste of time?

For time out of mind there have been people who strove towards perfect meditative state, achieve world peace, or total knowledge. From a practical standpoint, these people know that their goal cannot be attained, or perhaps attained by them, yet they strove all the same; and what's more, people continue to quest for these goals to this day.

So what do you think? It this a waste of time or is it a worthwhile activity? Should people only work on things that, while they cannot hope to achieve, they may contribute towards the achievement of (a great work)?