^^ your logic makes no sense to me but I don't want to argue about it. Its a scientific fact that larger surface area = faster conductive heat transfer. But you can believe whatever you want that's OK too.
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I agree that there's more heat transferred because of the larger surface area, but each individual receptor doesn't transfer any more heat from the pin than from the screwdriver, they transfer the same amount of heat because the pain receptor size isn't changing, what's changing is how many of them are in contact with the heat source.
Now what makes you think that 12 needles wouldn't be more painful than one since they too would be over a larger surface area. That's really the point I was making. The larger the surface area, the more pain you feel. 12 shots would be more painful than 1. Roughly 12 times as painful, because 12 times the number of pain receptors would receive pain and your brain adds them all up to determine how much pain your body is receiving.
Another way to think of it is that pain receptors are digital. They are either on or off, there's no inbetween. So for instance it wouldn't matter if you heated the pin to a higher temperature, you wouldn't feel more pain, you would feel the same amount of pain. The only way you feel more pain is if more pain receptors are on. That's why I said pain is multiplicative. Your brain multiplies the amount of pain from 1 receptor by the number of receptors that are on to determine the overall pain you feel.