Suppose you have some marbles rolling around randomly at the bottom of a box. Now take the box and tilt it so that the marbles roll to one corner. Jiggle a bit so that they come to rest in a reasonably stable pattern and, more than likely, some of the marbles will collect into a "snowflake" configuration such as this:
So how do the marbles show order out of greater order? The orderliness of the snowflake pattern can be measured by counting its symmetries -- that is, how many ways can you rotate it and still have the identical pattern. For example, if rotated five degrees it won't be exactly the same, but if rotated 60 degrees it will be. Rotating the pattern in sixty degree increments (60º, 120º, 180º, etc.) produces identical patterns, thus it has six symmetries. But since you can flip it and then repeat the rotations the actual total comes to 12 symmetries.
The underlying reason for these 12 symmetries is the spherical shape of the marbles. If you started with other shapes, say seven forks or mini Jack Daniels bottles or whatever, they would not have fallen into the snowflake pattern to begin with and thus the symmetries (if any) would be different. So these 12 symmetries arise because of the particular properties of spheres being acted upon by gravity. So how many symmetries do spheres have? Since you can rotate a sphere by any amount and it will still be the same, it has an infinite number of symmetries. Thus, the order seen at the "higher" snowflake level (12 symmetries) is only a miniscule fraction of the unseen order at the "deeper," spherical level (infinite symmetry).
The marble example has a more natural analogue in crystal formation. When the pressure and temperature are right, crystals form in substances such as diamond, calcite or mica. The crystals arrange themselves into a lattice pattern. A diamond lattice, for example, is called a "hex-octahedral group," and it contains 48 symmetries. However, the order of the diamond lattice is but a small fraction of the order found in the carbon atoms composing the lattice. As with the marbles, there is a "spherical" sameness about the carbon atoms that lead to a nearly infinite number of symmetries at the atomic level. Thus, once again, the order that we observe at the higher crystal level is but a minute fraction of what exists at the deeper atomic level.
This idea that the deeper we go in the physical universe the more order we find is repeated over and over again, according to Barr, in such things as naturally occurring geometric patterns (e.g. a nautilus shell), planetary motions and the properties of elementary particles (protons, neutrons, etc.). In every case the observable order is only a tiny surface manifestation of an even greater order at a deeper, more obscure level. Order does not arise from chaos, nor does it arise from nothing. It arises from an even richer order "below."
So from where does the deepest order originate? From a naturalistic standpoint, we don't know because we have yet to uncover nature's deepest laws. However, even if we reveal these laws, the question of why they give rise to such profound order will still remain a puzzle. The pervasive order of our universe appears to go beyond necessity into the gratuitous. "Life could have evolved just as it did even if there had been occasional lapses in the orderliness of nature," claims Barr (p. 108). Life has already managed to survive numerous cosmic, climatic and ecological challenges; occasional small-scale violations of the law of conservation or angular momentum would unlikely have proved prohibitive.
To avoid an immaterial Creator as the ultimate explanation for the universe's deep order, the materialist, argues Barr, must either accept the laws of physics as "brute facts" (i.e. they just are and we don't ask why they are) or he (she) must appeal to chance (usually in the form of multiple universes with variable laws of physics). If ours is but one of an infinity of universes (or possibly "domains" within a multiverse) then simply by chance a universe will arise with physical laws such as ours. While this is certainly possible, a critical point Barr emphasizes is that proposing an infinity of unobservable entities is no more scientifically defensible than proposing a single unobservable one (God). Indeed, sustaining a purely materialistic view of the universe, Barr asserts, requires repeatedly pleading for a multiplicity of envisioned infinities -- of universes, planets, durations, realities, observers, etc. -- a habit that severely undercuts the materialist position.
"...the materialist, in order to avoid drawing unpalatable conclusions from scientific discoveries, has to postulate unobservable infinities of things. How ironic that, having renounced belief in God because God is not material or observable ... the atheist may be driven to postulate not one but an infinitude of unobservables in the material world itself!" (p. 75).
Ultimate questions, such as the ones Barr poses, stand outside of scientific certainty and even if they undermine materialism, they do not immediately or necessarily validate the Christian God or any God for that matter. But I don't take Barr's arguments as religious evangelism. Rather, I take them as scientific evangelism. The spirit of inquiry animates science. That spirit is equally violated whether we stop asking questions out of fear that God might be the answer or we stop out of fear that God might not be the answer. Just keep asking questions and follow honestly where the argument leads.