Ord: Spherindricites

< Polybrachs | Introduction

The spherindricites are a derivative of the tetrabrachs, brought about by a mutation that caused repeated cell divisions along the vertical axis prior to limb differentiation, resulting in an elongated (spherindrical) segmented body plan with varying numbers of tetrahedral segments, analogous to the segmented worms which gave rise to arthropods on Earth. The development of segmentation was quickly followed by evolution of invaginations in the body surface to increase surface volume; due to the much higher surface-to-bulk ratio of 4D organisms compared to the surface-to-volume ratios of similar 3D organisms, and the small maximum distance from any point on the interior of a tetrabrach to the surface, small tetrabrachs and early spherindricites had no need for any specialized breathing structures, as liquids and gasses could passively diffuse through the creature from the environment. However, surface pockets which would be alternately compressed and expanded by the creature's movement, thus getting the surface closer to some internal volumes and actively pumping fluid past them, allowed spherindricites to grow to much larger sizes.

The least derived spherindricites, which retain minimal differentiation between their segments, primarily occupy benthic and burrowing niches and are an exceptionally diverse group, just like their close Earthling analogs, the annelids, coming in a wide range of sizes and with a variety of reduced or specialized limb structures. However, one free-swimming group of spherindricites developed encephalization--the fusing and specialization of segments at the mouth end of the creature, which had transitioned from the bottom to the forward orientation, creating creatures with distinct heads and their fronts. The forwardmost set of limbs specialized as mouthparts for grabbing and manipulating food; two of the second-segment limbs specialized as olfactory sense organs, while the remaining two developed more advanced eyes from the terminal ocelli, with ocelli disappearing from the remaining limbs.

One group of cephalic spherindricites, the malakichthys ("soft fish") directly developed a new up-down axial symmetry breaking, with one limb from each body segment specialized as a dorsal stabilizing fin and the remaining three becoming propulsive limbs radially arranged in the sideways plane.

The remaining cephalic spherindricites developed internal mineral storage structures, which would serve as the basis for structural bones. This group further diverged based on three different approaches to developing their own secondary vertical orientation:

1. Polysphenoids dropped two limbs from each body segment, resulting in alternating left/right and ana/kata-aligned limbs, such that the tips of each limb from any two adjacent segments form the vertices of a disphenoid.
2. Trilaterians dropped a single limb per segment to allow planar compression, resulting in adjacent body segments forming alternating triangular antiprisms, with each set of limbs arranged in an equilateral triangle in the sideways plane.
3. Quadrilaterians simply rearranged their four limbs per segment into a square arrangement in the sideways plane rather than a tetrahedron.

All three of these groups would later give rise to different land-dwelling clades which would specialize in different ecological niches suited to their divergent limb arrangements.

Ord: Polybrachs

Introduction | Spherindricites > 

As we saw in the introduction, Ord is a gigantic place. There is enough room on Ord for life to have arisen completely independently several times, and for hundreds of completely unrelated alien civilizations to develop--even though, if they knew which way to walk, they could find each other within a few thousand kilometers.

We will be looking at the development of only one branch of animal-like life. At the highest level, this branch of independently-evolved animal life in Ord's oceans and seas can be split into three groups: sponges, flatworms, and polybrachs. Ordian sponges are much like Earthling sponges--simple sessile colonies of cells which filter food particles from water flowing through them. Ordian sponges, however, are "more spongy"--more porous--than Earthling sponges can be. This is because the four-dimensional space they live in permits qualitatively larger holes, of a fundamentally different kind than exists on Earth. Ordian matter can have linear holes punched through them, just like we can, but they can also have planar holes--and Ordian sponges do, because it allows more water to flow through them from more directions.

Flatworms are spheroidal organisms; they would not look flat to us, but they are flat on Ord, as their entire lower 3D surface can contact the ocean floor simultaneously, and they have very little extent in the upwards direction. These organisms show minimal layered tissue differentiation. Simpler species are completely spherically symmetric, and simply absorb nutrients from stuff they crawl over as they inch their way across the ocean floor. Some more derived species, however, have established a front-back axis specialized for motion; such creatures have more elliptical bodies, and can often be found freely swimming in the ocean bulk.

The flatworms may eventually produce more interesting descendants, but for now the most complex creatures are the polybrachs. These are also spherically-symmetric creatures with an up-down axis, but they have specialized arm structures improving their ability to navigate and manipulate their world. Their symmetrically-arranged body segments and attached arms make them somewhat analogous to Earthling starfish, but with one major difference: while different species of starfish may have have any number of equally-spaced arms, due to the fact that there are infinitely many regular polygons in two dimensions, Ordian polybrachs are restricted to certain fixed numbers of arms corresponding to the faces (or vertices) of different platonic solids, of which there are only a finite number. The polybrachs have further specialized into three major clades based on their early embryonic development: tetrabrachs, cephalobrachs, and dodecabrachs.

In this figure, we can see the 3-or-fewer-dimensional stages of embryonic development from a single egg cell up to 4 or 8 cell structures, which allow the identification of different clades. Tetrabrachs (whose embryonic shape is labelled with a T in the preceding diagram) undergo only two cycles of cell division before adopting a maximally-dense tetrahedral arrangement of cells. The third cell division extends the embryo into the fourth vertical axis, with each tetrahedral segment going on to develop into a portion of the central disk and associated arm. Tetrabrachs tend to specialize in benthic habitats, like symmetrical flatworms, but are capable of much more active lifestyles.

Cephalobrachs (whose embryonic shape is labelled with a C) maintain a more open cellular structure through three divisions, producing a cubical arrangement of cells from which can develop eight distinct equally-spaced arms, corresponding to the faces of an octahedron. Their fourth cycle of division does not produce additional cells associated with an octahedral segment, though; rather, the top cube develops in an entirely different direction from the bottom of the creature, producing a glomular (4-dimensionally spheroidal) head / body cavity. similar to an Earthling cephalopod. Also like cephalopods, many species of cephalobrachs are capable of walking or dragging themselves along the ocean floor, but they are more often found in free-swimming niches.

Dodecabrachs (whose embryonic shape is labelled with a D) maintain an open square arrangement for two cycles of cell division, but then fall into  more close-packed square antiprism arrangement for their third. This third split already corresponds to the division between upper and lower body segments; a further cycle of division could establish cubical/octahedral symmetry, but that is not, in fact, what happens. Instead, several more cycles of cell division produce two joined spherical disks of cells, begin differentiating into distinct organs much later, eventually producing an arm section with either twelve segments in dodecahedral symmetry (hence the name of the clade) or, more rarely, twenty segments in icosahedral symmetry. The 12 vs. 20 choice seems to be easy to flip between as new species of dodecabrachs evolve, but there is a more fundamental division between sessile and medusoid dodecabrachs. In the sessile branch of the family, the body segment extends into a long spherinder (a sphere extruded into the fourth dimension, analogous to a 3D cylinder) which acts as a stalk to attach the animal to a solid surface, with the arms acting to filter nutrients from the water. In the medusoid branch, the body segment instead expands into a wide spherical disk. In some species, the disk remains relatively small such that the arms are free, and swimming is accomplished in a manner similar to an Earthling feather starfish; in most medusoids, however, the upper disk grows large enough to can curve around and enclose the central arm, disk rather like the bell of a 3D jellyfish, allowing jet propulsion by contracting the bell to expel water.

All polybrachs have ocelli (eyespots) at the ends of each of their arms, a feature which is believed to have been inherited from early flatworms before the two clades diverged; spherical flatworms also frequently have eyespots on their upper surfaces, in a variety of regular, semi-regular (corresponding to Archimedean solids) and random arrangements. Within the polybrachs, dodecabrachs appear to be the least-derived clade, with cephalobrachs and tetrabrachs each having split off from a dodecabrach ancestor after settling onto a power-of-two number of arms, which then permitted differentiation decisions to drift earlier in the stages of embryonic development.

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.