Daily Reading Notes

Scale

Day 2

Posted on 2019-12-11

The properties of systems increase at different orders of magnitude when scaled. For example: If an object is scaled by one order of magnitude, it’s area will increase by two order of magnitude, and it’s volume will increase by three orders of magnitude.

The strength of an object is determined by it’s cross-section – it’s area. Therefore, if the area – which determines strength – increase by 2 while the volume – which determines weight – increase by 3, then the object will soon grow too heavy to support itself.

The above strength to weight ration demonstrates why the proportional strength decreases as the size increases. This is why an ant can lift 100x it’s weight while we can only lift about 1x.

Logarithmic scales allow plotting order of magnitude increases within a limited space. Without this scale, the representation of exponential growth would require a giant scale.

Scale