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Someone who had removed his strat pickups once asked me how to work out which pickups went in which position. It is a reasonable question, because everyone knows they each sound different. The answer though is that it doesn't matter, because the (original) strat pickups are identical. Even recent single-coil pickups are "reverse-wound & reverse-polarity" in the middle position to help cancel hum, but this doesn't affect the tone at all.
The sound of identical pickups vary in different positions on the guitar because the sound of the string changes along its length. There are variations in tone (the ratio of higher harmonics compared to low), the timbre (the relative strength of different harmonics caused by the position of the nodes of each harmonic) and in the overall level.
The closer the pickup is to the bridge, the sharper the tone (stronger higher harmonics), and the overall level is lower (because there is less string vibration closer to the bridge). The timbre is simply different, and depends upon all the things mentioned in the previous topics.
It is also important to realise that this change of sound along the string is exponential. That is, changes near the bridge are far more dramatic than those near the neck position. You can verify this for yourself by picking the string at different positions. This is best done acoustically, so you can hear the whole string sound rather than the small portion heard by a pickup.
First, pick a string right next to the bridge and notice how bright and "twangy" it sounds, then pick the string at 1 centimetre intervals towards the neck. You will find that the changes at first are quite dramatic, but become less noticeable as you pick closer to the neck.
This illustrates why on a strat, there is less change in tone between the middle and neck pickups compared to the sharp sound of the bridge pickup. Granted, the pickup is angled back on the lower string side to partly offset this effect, but it still remains difficult to get a great sound out of identical pickups with the same EQ settings. That's not to say that there's anything wrong with the design, it is useful for various music and playing styles. A common modification is to simply replace the bridge pickup with a hotter and warmer sounding pickup.
There's one other point to note about the changing timbre of a string along its length. When fretting notes right at the top of the fretboard, next to the neck pickup, it effectively makes the neck pickup sound brighter because it is closer to one end of the string's vibrations. But there are compensating factors here also, such as reduced brightness and sustain due to the shorter vibrating string length.