The Natural History of Ord: Introduction to the Universe

Introduction

The Polybrachs
The Spherindricites

Ord is an inhabited world in an alien universe with 4 spatial dimensions rather than our usual three. It's a different bubble of stabilized space in our eternally-inflating multiverse. This has wide-ranging effects on geometry and physics, and thence on biology. Planets like Ord don't orbit stars in closed ellipses, and they don't have well-defined axes of rotation. From atoms up to galaxies, the entire universe is organized differently from our own. What we are mainly concerned with is the middle scale: how living things develop in four-dimensional seas and on three-dimensional continents. But it will be useful to investigate some high-level features of the universe those creatures are developing in, and the world they are developing on.

First, we will establish a scale. Comparing sizes between universes with different physics, let alone different dimensionalities, is a tricky thing; 1 meter here doesn't inherently mean anything on Ord, and units can seem to match up in different ways depending on what specific things we are comparing. Lets suppose we wanted to somehow "import" a human explorer from Earth to Ord; their normal 3D body would completely fall apart in a 4D space. We would have to somehow re-arrange their bits and pieces into a 4D form. But however we alter the body, we will want to keep the mind--and thus, the neural connections--intact. So, every neuron will need to be accurately mapped and reconstructed--and the number of neurons in an Earth human and an Ord human can be assumed to be the same. Since that will give us some idea of the level of biological complexity necessary for civilized life to arise on Ord as it has on Earth, let's adopt that as the basis for our standard of comparison: we'll declare neural cells to have the same linear size on Ord as they do on Earth. Human neuron bodies are around 100 microns across on average. If we deconstruct a human into individual cells, adapt each cell for Ord's universe, and then re-assemble in a stable 4D arrangement, the resulting explorer would be between 14 and 16 centimeters high--but composed of tens of thousands of times more atoms per cell!

Simply equating atoms between Earth and Ord does not accurately reflect the needs of biological systems. Four-dimensional Ord cells have a much larger proportion of their mass bound up in 3D surface membranes than we do in 2D surfaces, and thus a lower proportion available for interior structures and functions. Thus, on average, they do require thousands of time more atoms to achieve the same functions--we couldn't build an body capable of supporting our explorer's intelligence just by using the same number of atoms on Ord as we do on Earth. However, when it comes to linear measurements, atomic radii are much more precise than average biological cell sizes. Thus, in order to compare the sizes of organisms with the planet they live on, we can declare than Ord's four-dimensional atoms have the same range of radii as our three-dimensional atoms (although their internal compositions can be quite different)--exactly 1 angstrom.

To retain heat and maintain geological activity over geological time scales, Ord would need to have about 4/3rds as many atoms between its surface and its core as Earth does, to maintain the same surface-to-volume (or area-to-bulk) ratio, and thus the same heat loss rate. Earth is about 6.378x10^16 angstroms (average atomic radii) in radius, or 3.189x10^16 atomic diameters. Ord, it turns out, is about 8.5x10^16 angstroms in radius--which means it has about 2.37x10^17 times more atoms in its 4 dimensional bulk than Earth does in its 3 dimensional volume! In terms of atomic mass units, Ord is about 1/4 to 1/3 as massive as our entire galaxy! Fortunately, between a totally incomparable gravitational constant (it has different units in Ord's universe than in ours), gravity following an inverse-cubic law, and flexibility in how we measure units of time, all that extra material still only results in surface gravity comparable to Earths!

Now, about time... cesium atoms and quartz crystals don't exist on Ord (atoms with the same nuclear charges have radically different chemical properties), and pendulums depend on gravity and on our somewhat arbitrary choice of how to measure lengths, so it would seem that there is no really good method of establishing a correspondence. Furthermore, 4D brains are more tightly packed, so nerve signals travel faster, and thought occurs faster than it would in the same neural network "squashed" into a mere three dimensions. Nevertheless, we'll acknowledge the 4D brain architecture as natural for Ord, and declare that what our transposed human explorer perceives as 1 second passing (e.g., when mentally counting out "one Mississippi, two Mississippi," etc.) is one second, and everything else can follow from that. We note that objects seem to fall at a normal-feeling rate, and objects on the scale of our 15-cm-tall explorer's body seem to take normal amounts of effort to push, pull, and lift, and the gravitational constant and inertial mass units can be calculated from those observations.

Now, how much surface does Ord have? Using our angstrom equivalence, it comes out to about 2x10^28 cubic kilometers. Compare with Earth's approximate 5.1x10^8 square kilometers. Or, 2x10^37 cubic meters, compared to Earth's 5.1x10^14 square meters. Directly comparing a 3D surface volume to a 2D surface area is a bit tricky, but that's about the same volume as a sphere of space 23 AUs wide--larger than Saturn's orbit in our solar system! When intelligent creatures like our universally-transposed can be a mere 15 centimeters in height, that's a lot of space for life to fill!

From that, you may guess that Ord's universe is much more densely packed with matter than our own universe is--and you would be right! It has to be, or, with that whole extra dimension to move around in, nothing would ever run into anything else, and nothing interesting would happen! It's almost a blessing, in fact, that two-body orbits are unstable--that forces matter to collapse into interesting structures despite the extra room to expand in. And Ord does not orbit a single star; but, it does have a somewhat chaotic orbit through a globular (or glomular) cluster of stars along with many other such planets, with days and nights distinguished by which side of the world is closer to the brighter, denser center of the cluster. The space-filling distribution of matter in the cluster produces an effective potential with a lower exponent--not quite a harmonic potential as it's not completely uniform, not exactly inverse-square, not even exactly an integer or even completely constant--which, in combination with close encounters with individual other bodies, produces the chaotic nature of Ord's motion. Some day, Ord may fall into the core and be burned up, or be ejected as the cluster evaporates, but for the functional equivalent of billions of years it is mostly-stably bound, wandering through a space of roughly-constant illumination.

Many of the stars in Ord's cluster are not a whole lot more massive than Ord itself, and may someday cool down to become additional planets. How can this be? Well, that requires looking way down at the other end of the size scale, at how atoms are built. The difficulty of fusion in Ord's universe follows a much steeper curve than in ours. In fact, monoprotium can fuse at near absolute zero, if the density is high enough to make collisions probable! This is because, while the atoms of Ord's universe are made out of close analogs to our own protons, neutrons, and electrons, they are put together quite differently. When there is only one electron, it exists almost entirely overlapping the proton, controlled by the interior harmonic potential. With 4 spatial degrees of freedom and 3 quantum spin states for electrons, elements up to duodecium, with twelve protons and electrons and no neutrons in the lightest isotope, are all chemically inert and nuclearly sticky! Only at atomic number 13 do we encounter an atom with an external electron orbital and a nucleus with a distinct positive charge with can repel other nuclei. Ord's chemical equivalent of hydrogen is thus as heavy (in terms of atomic mass units) as our carbon-13 isotope, and much smaller than that in terms of nuclear to atomic radius ratios. With many more orbitals available for electrons to fill (e.g., there are 4 rather than 3 p-orbitals, each of which can hold 4 electrons in different spin states) Ord's periodic table is significantly stretched horizontally, with many types of atoms and bonds that have no analog in our world--and with nuclear-internal electrons and supplies of easily-fusible duodecium isotopes around, Ord has many more elements with higher atomic numbers than we do for chemistry, and biology, to play with.