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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).

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Another way to rephrase your question would be "how many different chemical receptors do we have in the nose?". Is it correct? –  Remi.b Dec 17 '13 at 9:28
@Remi.b no, we have 4 types of photoreceptor cells, but our color space is 3-dimentional. –  Anixx Dec 17 '13 at 9:32
Here and here are posts on color perception by the way. Note: Your question might be a good fit for cognitive sciences also. –  Remi.b Dec 17 '13 at 10:42
I really don't know much about this subject… Does it really make sense to talk in terms of dimensions? If we talk about color, then it might seem that there is only one dimension as any color can be define with only 1 number. Could you provide an in-depth explanation of how you apply the concept of dimension to visual perception (and other perception)? This might help. –  Remi.b Dec 17 '13 at 22:48
"any color can be define with only 1 number" - this is not true. –  Anixx Dec 17 '13 at 22:57
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1 Answer

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

In mammals, each olfactory receptor neuron expresses only one functional odor receptor. Odor receptor nerve cells function like a key-lock system: If the airborne molecules of a certain chemical can fit into the lock, the nerve cell will respond. There are, at present, a number of competing theories regarding the mechanism of odor coding and perception. According to the shape theory, each receptor detects a feature of the odor molecule. Weak-shape theory, known as odotope theory, suggests that different receptors detect only small pieces of molecules, and these minimal inputs are combined to form a larger olfactory perception (similar to the way visual perception is built up of smaller, information-poor sensations, combined and refined to create a detailed overall perception).[citation needed] An alternative theory, the vibration theory proposed by Luca Turin, posits that odor receptors detect the frequencies of vibrations of odor molecules in the infrared range by electron tunnelling. However, the behavioral predictions of this theory have been called into question. There is no theory yet that explains olfactory perception completely.

Note: the two competing theories for color sights: Opponent process and Trichromacy

Hope this helps!

I think this question would also be a good fit for cognitive science beta.

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"One color can be describe by one single value (it is unidimensional). This value can be the wavelength for example. " - this is wrong. You cannot describe all possible colors with a wavelength. For example, you cannot describe grey, white or magenta. –  Anixx Dec 24 '13 at 12:03
@Anixx Yes you're right. I updated my answer. –  Remi.b Dec 24 '13 at 17:00
"Therefore, it is nothing else than the number of receptor" - As I already pointed out we have at least 4 types of receptors with different points of maximum. And to be precise there is also a fifth type. So the number of receptor types does determine the number of dimensions of the color space. –  Anixx Dec 24 '13 at 17:22
According to this wiki article we have 3 receptors for the color. But anyway, I don't know much, I suggest something as nobody is giving any answer. Sorry, I can't do better. I added, two wikipedia links that are competing theories of color vision. –  Remi.b Dec 24 '13 at 17:29
unless you know beforehand the color space dimensions, you cannot tell which receptors are used for the color just by counting their types. We know that only three types of receptors participate in color vision BECAUSE our color space is 3-dimensional, not the other way around. –  Anixx Dec 24 '13 at 22:35
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