Matt Soniak writing for mental_floss goes some way towards explaining why Paper cuts are so very painful.
Firstly, hands are very complex sensory instruments, packed with nerve fibres to sense temperature, pressure and pain. A Paper cut on your leg, Soniak explains, would not send anywhere near as many pain signals to your brain as one on your finger.
Secondly, because we use our hands all the time, the healing of an injury there can be interrupted. When we pick something up, the skin on our hand moves and a wound’s edges can be pulled apart.
Finally, Paper causes a particular type of wound. Unlike a sharp knife which causes a relatively clean cut, Paper will flex a little when cutting and cause more microscopic damage to the skin. Also, because the cut is usually quite shallow, there is little or no blood which means the nerves around the cut are more exposed without a blood clot to protect them. This can exacerbate the pain.
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