I'm wondering why East is left and West on the right of the celestial sphere if you look at images of it?
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You're viewing the celestial sphere from the inside looking outwards, as opposed to maps of the Earth's surface which are viewed from the outside looking inwards.
Imagine drawing a map on a sheet of glass. When you view the map from the other side, it will appear mirrored.
Maps of the sky are being used to actually get to know the sky. Thus you take the map and hold it above your head (as opposed to a map of the Earth's surface where you look down on Earth). Thus East and West are switched between that two types of maps, so that directions match actual directions when viewing the map.
Both comments are perfectly valid. For clarity I would describe it this way, now that I understand it.
You have to imagine being inside the celestial sphere look outwards. From within the sphere you have (counter-clockwise, starting at the top) North, East, South and West. But if you view the sphere from the outside then of course East and West are swapped. And that is precisely because the coordinate system that is used to find the location of any specific point, on the surface of the sphere, is still used viewed from within the sphere.
Just another way of describing it, thanks for the other answers. Hope this helps.