A chart from the book.
"To ‘see’ something, we need to expose it to light of wavelength similar to its size; thus, small objects require small wavelengths of light, which have high frequencies and energies of vibration; these are most able to perturb the system under investigation. This catch-22 situation is expressed by the famous Uncertainty Principle first discovered by Werner Heisenberg. It states that we cannot simultaneously measure the position and the speed of something to ever-increasing accuracy, no matter how perfect our instruments. A measurement of the position of a small object necessarily results in its position being disturbed by the radiation used in the measurement process. It is this consideration of the disruptive effect of the measurement process that distinguishes what is meant when a physicist says that something is ‘small’ rather than ‘large’. ‘Small’ sounds like a totally relative adjective. ‘Smaller than what?’ is our response to someone telling us that something is small. But the absolute dividing- line between large things and small things is picked out by asking whether the act of observing them with perfect instruments has a negligible, or a significant, impact on their states.
An important lesson from these simple considerations is that the sizes of things in the Universe are not random. They lie in the ranges they occupy because they are manifestations of balances between opposing forces of Nature. Their locations are determined by the inflexible values of the constants of Nature that express the strengths of those forces. This is the explanation for the things that are seen. As for the things that are not seen, the existence of black holes and the Heisenberg Uncertainty Principle exclude a vast range of mass-size combinations from the view of any observers. The cosmic inventory is neither the result of some process of natural selection, nor of an attrition of the set of all possibilities; and it is not merely haphazard—it is at once a matter of balance and censorship." - John Barrow
Our size is not an accident. It is, within quite narrow bounds, imposed by the invariant strengths of the forces of Nature. But the consequences of our size for our development, our culture, and our abilities are deep and wide. They shed light upon how we have outstripped other living things in controlling natural resources.
The battle between strength and size is displayed by a simpler struggle: that waged between volume and the surface area enclosing it. Watch a rolling snowball as it accretes snow and grows bigger. Its radius increases; so both its volume and surface area grow as well. But, whereas its volume grows according to the cube of its radius, its surface area increases only in proportion to the square of the radius: its surface area cannot keep pace with the growth in its volume. This losing battle that surface area fights with volume as size increases imposes many vital constraints upon the sizes of living things. As your volume increases with growth, so your heat-generating organs increase in volume and energy output. But your ability to keep cool depends upon how much heat can escape from your exposed surface. Small creatures have a relatively large surface area for their volume; large creatures possess a relatively small one. In cold climates small creatures will therefore be at a disadvantage, unable to generate enough heat from eating to keep warm.
it is wrong to believe that all Nature’s solutions to the problems posed by the environment are optimal. They may not need to be. Nor might the range of variations available for natural selection include the optimal case, because of other constraints on what can happen,
(Perhaps the solution is answering to a different objective function and a set of constraints)
Here's something done with AI on top of the above chart to show the key dominant forces on each level:
Followed by some comments by AI
Reading it from the bottom up, the ladder of "who's in charge" goes like this. At the atom, the strong force holds the nucleus and quantum mechanics fixes the electron cloud's size — and just below sits the ℏ wall, where an object's Compton wavelength outgrows the object itself and it stops being localisable. Step up into the long teal stretch and one force — electromagnetism — runs everything, but it wears different costumes at each scale. Around DNA and bacteria, bond energies are only tens of times kT, so thermal jitter jostles molecules constantly (Brownian motion) and, for anything swimming, viscosity so overwhelms inertia that water feels like tar — Purcell's "life at low Reynolds number," where a bacterium coasts less than an atom's width after it stops beating. A little larger, at the insect, the crossover you named arrives precisely: the capillary length of water is about 2.7 mm, so below a few millimetres surface tension beats weight and a strider stands on the pond. Chemistry is still the boss all the way up through us — bone and muscle are electromagnetic bonds, and Galileo's square–cube law (strength ∝ L², weight ∝ L³, so strength-to-weight ∝ 1/L) is what caps the height of trees and the thickness of an elephant's legs.
Then comes the one transition that matters most on the whole diagram, the teal-to-red boundary near the asteroid: gravity overtakes electromagnetism as the force that decides an object's shape. Below roughly 500 km, chemical bonds hold a body in whatever lumpy form it was born with — hence potato-shaped asteroids. Above it, self-gravity crushes the lumps smooth and you get spheres; that's essentially the physical definition of a planet (hydrostatic equilibrium). Push further up the red band and gravity does something even more dramatic — it compresses matter hard enough to ignite the strong force, and a ball of gas becomes a star.
This is the deep asymmetry of the chart: small things are ruled by contact (electromagnetism), large things by gravity, and the changeover happens right around the asteroid–planet line.
We sit near the top of the electromagnetic stretch, just below the handover — still creatures of chemistry and strength, but the first scale at which gravity begins to be felt as a genuine rival rather than a rounding error. And the galaxy floating off the band, low and to the right, is the coda: it obeys none of this. Its density is a trillion-trillion times below solid matter because nothing touches — it's bound by gravity reaching across near-empty vacuum (with a great deal of dark matter doing the reaching), which is why it falls clean off the line of constant density that organises everything else.
