The Earth is made of cubes

Pythagoreans, Platonists and Lego fans, rejoice! It turns out the Ancients were right... sort of.

You'd be tempted, at least initially, to imagine something like what was presumably the same kind of mystical reverence, an almost unbounded sense of awe, felt by the original interlocutors of geometrical relation resulting from this relatively new and dramatic discovery. The universe has at last confirmed beyond a shadow of a doubt its most tantalizing of hints - that a simple underlying mathematical framework links numerical possibility with the physical structure of the material world. There has been almost no other story of progress through the ages.

Yet at the same time that underlying mathematical framework is ever more subtle and altogether more prosiac. Consider that iron (Fe, number 26 on the periodic table) is the most common element found on Earth by mass, and that it makes up the majority of our planet's inner and outer cores. Since iron is a metallically-bonded element with a cubic crystal system (BCC or FCC, depending on temperature and pressure), you would expect to find distinctive larger-scale expressions of its intrinsic material properties when found in large quantities, even when bonded with other elements. Chemical composition obviously has a direct effect on the way any material behaves at the macro scale: whether or how it may fracture, flow, bond, solidify, become a vapor, rapidly oxidize (that is, explode), etc.

So is it really all that surprising that terrestrial material (and in turn the material from which the solar system itself was formed) tends to cleave along boundaries oriented, roughly speaking, at 90° angles - precisely in the manner of cubes? A quirk of the local chemistry. Nothing mysterious. 

Actually the picture is just slightly more complicated. Like carbon, iron is an oddly versatile element when it comes to atomic packing arrangements. Not only does iron spontaneously switch from a Body-Centered Cubic (BCC) to a Face-Centered Cubic (FCC) system and then back to Body-Centered Cubic again when heated to high enough temperatures and pressures, under conditions of extreme pressure it will even assume the Hexagonal Close-Packed (HCP) structure that, like FCC, is the tightest of all possible packing arrangements given proportional size of spherical elements. It is thought that the interior of Earth's core, under immense pressures at the center of our planet, might consist of an iron alloy bearing this hexagonal arrangement, known as hexaferrum, or ε-Fe. 

The trouble is, atoms aren't really spheres; consequently, the Earth can't really be made of cubes. At any scale. The most we can say is that nature is a process by which certain definite regularities are seemingly endlessly approximated, but never precisely duplicated or permanently fixed. It is as the whole of physical law amounts to one giant counterfactual, an empty set: a looming void of non-being to which the reality of any given situation may approach as closely as one may wish, but never enter.. hold on... wai ta  min  ute .we 'r e br eaki n g  u  p  .. .. ...u     m .. . t   h    i     s    i  s  h  ar d ...     t     o      .  . .      d         o  o  o    ooo  o      o .   .  .   ..  .    ..    ... . . .       .   .    .     .