Are there evolutionary connections between different senses, in such a way that one sense is evolved from the other or from a common root, e.g. the possibility that hearing and touch are derived from a common root? If there are such evolutionary paths, are there any attempts to draw a map between different senses?
Hearing and touch are both examples of mechanosensation, i.e. touch receptors are activated by pressure changes and sensory hair cells (hearing) are activated by fluid motion initiated by sound waves. Therefore, I think it makes sense that they evolved from similar origins.
Vision on the other hand is due to photosensation, which has a very different physiology, so I don't think there's any evidence of a similar evolutionary link, but there may be (almost certainly are) similarities in the way our brains have evolved to respond to the different senses.