ScienceDaily just had an article on fouth dimensional spatial scaling in plants:
one of the things it mentions is how something like an ant, blown up to elephant size, wouldn’t be able to walk. i understand the principles behind this in a general sense, but does anyone know of any actual formulas?
specifically, i’m wondering about a person’s relative strength as he shrinks. logic says it should go up as a proportion to his mass.
so, if – at my current mass – my strength allows me to lift 50% of my body weight, what percentage could i lift if my mass is reduced? it should increase, but along what kind of curve?
A persons (or animal or whatever) mass increases as a cube and strength increases as a square. What this means that if you are 6 foot, 200 lbs and can lift 300 lbs and you are magically proportionaly increased to 12 feet in height, then you would be 2x as tall (12 feet), weigh 1600 lbs (2 cubed=8, 8200lbs) and be able to lift 1200 lbs (2 squared300lbs). You would appear weaker because before you were doubled, you could lift 1.5 times body weight, but now only can lift 75% of body weight.
If this person was shrunk to 1/12 body size, he would be 6 inches tall, weigh .116 lbs and be able to lift 2.08 lbs. He would feel much stronger since he could lift about 18 times his weight.
Weirdly enough, since jumping is a strength activity, strength activities like how high you can jump will cancel out meaning that if this man could jump 3 feet at 6’ tall, he could jump 3 feet at 6" tall. It would appear to him he could jump 6 times his height where he used to be able to jump only half his height.
Of course, he would probably freeze to death quickly at room tempature since he has so little mass.