Does Square Cube Law always hold? [closed]

Question

There is a video that has been doing the round for a few years of an MIT lecture that has become a topic of debate in another forum I am a member of.

The lecture by Prof Walter HG Lewin discusses Galileo's square cube law and then measures femur bones of mammals increasing in size. The mass of the bones do not scale up in the way predicted. The uploaded video presents the findings as disproving the law and also opening the possibility of giants.

Some have argued that; SC Law does not apply to bio mechanics and this lecture proves it. The MIT lecture has successfully debunked the law and proven it doesn't always hold. Elephants have proven to break the law as their bones have not scaled up the way that the SC law would predict. Therefore giants are possible as the SC law has been proven wrong, there is no upper limit to animal size.

Others argue: SC Law is pure math and not been been debunked. It applies to every three dimensional object, including in biology. Elephants do not "break" the SC law. Animal's bones are not expected to scale up perfectly with increasing animal size and this isn't relevant to the SC law. Saying otherwise is a false assumption. The SC law does not in itself disprove the possible existence of giants or give an upper limit to animal size, but when applying other aspects of bio mechanics problems arise which do indicate an upper limit to animal size

I would appreciate any thoughts on this, thank you.

https://www.youtube.com/watch?v=qzq710aOHjE

Answer 1

The square cube law will be perfect for mathematical objects such as, sphere, cube, pyramid etc.

Biological objects are often, or maybe even generally, fractals.

Mathematical objects have three dimensions, but biological objects may exist in 3 dimensions but actually be better described by fractional or fractal dimension.

Fractal objects will not follow the square cube law generally.

To find out more about this then a high level article is here with lots of detail.

An example of this sort of thing for a 'mathematical fractal object' consider the Koch snowflake fractal. This object has finite area, but infinite perimeter. The equivalent object in 3D will have finite volume, but infinite surface area.

Finally, thinking about the elephant/other bones - the structure inside the bone will be some sort of honeycomb type (most likely fractal) structure. So although the outside of the bone may not be fractal, the effect of the internal structure will be that the mass does not scale as expected, thus breaking the expected square cube law.