How many different smells can a human recognize?
If the space of smells is not discrete, how many dimensions it has (for example, the space of colors is three-dimensional).
As nobody is suggesting an answer I'll give my guess that I already discussed in the comments and give some extra details about ongoing debates on the subject.
We'll start with the sense of color sight in order to make easier. One can argue that we see in 3 dimensions because we use three cells which level of activation inform the brain of the color. I guess that the whole 3D space delimited by the maximum level of activation of each three receptors can be used. Therefore, it is nothing else than the number of receptor that determine the number of dimensions in which we can sense. Now it is assuming that each receptor can send signal of different strength information of the intensity of the light or smell.
According to wikipedia. Mammals have about thousands of genes that code for olfactory receptors. Moreover, the question of how these receptors work is still debated
Hope this helps!
I think this question would also be a good fit for cognitive science beta.