:33333 Yay! One of these topics.
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I believe you can, but you will not get them by getting dropped into radiation or bitten by a bat. I believe than inside the human there are superhuman powers, but they are locked away at the second you are born by your conscience, environment, and doubt. Just hiding in an "unreachable" place. They say babies have no worries, but can you be so sure?
If you are ever pinched by a little cousin or just a family member new on arrival, it will definitaly hurt. Because they don't realize their own strength. And who are these? They're only babies. Imagine, if you never ever realized your own strength, ever, and you never had doubts or worries, how strong would you be? Of course, this is dulled out by society and once you grow up more in the human civilization, then you will probably lose this ability in depths. And I don't suggest living on your own in the middle of the Sahara. xDD
I'm not saying that we will be able to shapeshift any time soon. (Though you never know what certain changes could bring, since all animals adapt to their surroundings, including humans.)
But, we could be super strong, if we wanted.