伽利略在1638年出版的《关于两门新科学的对话》中，通过力学分析论证了人类巨人在物理上不可能存在。[1]他的论证基于面积与体积的不同缩放规律：当物体放大时，其截面积按线性因子的平方增长（强度增加），而体积则按立方增长（重量增加）。[1]以一根梁为例，若将其放大10倍，截面积将增加100倍，但自身体积会增加1000倍。[1]
伽利略据此得出结论：随着身高过度增加，物体自身重量最终会超过其骨骼能承受的强度。[1]他指出，如果希望巨人保持与普通人相同的四肢比例，要么必须找到更硬更强的材料制造骨骼，要么就会面临强度相对减弱的后果，最终在自身重量下倒下并被压碎。[1]这一原理同样适用于缩小的生物，也解释了为什么自然界中的大象、河马等大型动物需要更加粗壮的骨骼结构。[1]
In his 1638 work "Dialogue Concerning Two New Sciences," Galileo presented a mathematical argument proving that human giants are physically impossible.[1] The demonstration relied on a fundamental principle of scaling: while the cross-sectional area of bones increases by the square of a linear expansion factor, the volume and weight of a body increase by the cube of that same factor.[1] When an object is enlarged tenfold, for instance, its skeletal cross-section grows by a factor of one hundred, providing increased strength, yet its mass multiplies by one thousand.[1]
Galileo concluded that a giant maintaining the same limb proportions as an ordinary human would necessarily require either a fundamentally stronger material for bones or would experience reduced strength relative to a person of normal stature.[1] Beyond a certain threshold of size increase, he argued, a giant would collapse under its own weight and be crushed.[1] This principle operates inversely as well, explaining why large animals such as elephants and hippopotamuses require comparatively thicker and more robust skeletal structures in nature.[1]