The Principle of Scale: A fundamental lesson they failed to teach us at school

...which answers questions such as:

Why do babies need extra layers of clothing?
Why can a flea jump 200 times its own body length?
What led to moore's law?
Why is an elephant the only mammal that can't jump?
Who do babies spend so much time eating and drinking?
Why would spiderman fall off the walls he tries to stick to?
Why are insect's legs so skinny?

This principle was first quantified by Galileo in 1638, and is most commonly referred to as 'the square cube law'. I'd express the principle of scale something like this:

Consider a cube with a side length of 1 unit. How does it compare to an otherwise identical cube with a side length of 10 units?

Side Length
(L)
Cross sectional area
(C)
Surface Area
(S)
Volume
(V)
S/V
(Proportional to rate
of heat dissipation)
C/V
(Proportional to
strength)
116 161
2424 830.5
3954 2720.33
41696 641.50.25
525150 1251.20.2
636216 21610.166
749294 3430.860.14
864384 5120.750.125
981486 7290.660.11
10100600 10000.60.1

(table generated with the world's simplest code generator of course...)

As the cube grew to ten times its original size, we see its properties change drastically -- the rate of heat dissipation decreased by a factor of ten, and the structure's strength decreases by a factor of ten.

This is a funamental and useful principle. It can be quickly derived from simple mathematics that we were taught early on at school. Yet we were never armed with any knowledge of this principle itself.

I would guess that most adults -- even those with considerable education -- are unaware of these basic relations, even though they affect us every day.

(I do remember being taught a corollary: that you can increase the surface area of a reactant [thus speeding up a chemical reaction] by grinding a chemical compound into smaller particles)

at such a tiny size, the lilliputians lungs would choke on water droplets in the air.

Lilliput? Not Likely!

At such a tiny size, the lilliputian's human lungs would be severly hampered by water droplets in the air. And why are they using ladders? Wouldn't they be able to leap onto gulliver's chest unaided? How could such tiny brains create such a complex society?

Attack of the 50 foot woman? Are you havin a laff?

Her puny legs would buckle and collapse under her gigantic mass!

Take this fifty foot woman as an example. Her puny legs would buckle and collapse under her gigantic mass!

In fact, viewed through the smug nerdy lens of the principle of scale, all sorts of books and movies turn from science fiction to pure fantasy. Here's a thought provoking run-through of the physics behind a lot of movies about shrinking, growing, and other scale-related activities: The Biology of B-Movie Monsters. And here's an essay that includes some analysis of Lilliput.

Alrighty, I've pummelled this topic to death already. Have just returned from a two week holiday, after finishing up at Advantech software. I've been sans-computer for all that time (wrote most of this article on paper using a device known as The Pen, I believe.) Read an interesting book -- freakonomics during the break. (blog here) Recommended.

Expect some TimeSnapper updates over the coming weeks!

 

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