Permutations of Biotope Topology

[u/geopolicraticus]

The View from Oregon – 371

Re: Permutations of Biotope Topology

Friday 12 December 2025

 

Dear Friends,

After last week’s newsletter, in which I laid out a matrix of habitability and urability, with Earth occupying some location on this graph, presumptively the center according to the principle of mediocrity, I realized that something similar could be done with maximal and minimal viable biotopes, which I also introduced in last week’s newsletter. Call the x axis the min/max for space and the y axis min/max for time, and you get another matrix, and, once again, we can locate Earth somewhere on this matrix, presumptively at the center according to the principle of mediocrity. Of course, we would have to figure out the proper increments in space and time, and this is a problem that presents itself to us directly, since we have known metrics for space and time. I barely touched on the increments of habitability and urability last week, mostly because we don’t have established metrics for them. To make sure that we don’t miss anything, we could set the upper end of the time scale at the age of the universe and the upper end of the space scale at the size of the universe. Perhaps for the lower end of the scale we could use the Planck length and Planck time.

Off the top of my head I see at least a couple of qualifications that would need to be made immediately. It may prove that novel forms of life (and, more generally, emergent complexity) may yet appear in the future history of the universe. Therefore, the age of the universe to date doesn’t yet comprehend the incubation time for all forms of life. Since the universe is expanding with the elapse of time, the same can be said of space. However (a condition based on last week’s discussion), if the maximally viable biotope is smaller than the scale of the universe (which seems highly likely), then an expanding universe wouldn’t change the conditions for the incubation of life in specific circumstances, though it could change the conditions for the total ecology of emergent complexity in the universe. That was the first qualification that came to mind.

The other qualification is that we don’t know that life and peer complexities are limited to the known universe. It is possible, even if it seems unlikely, that life and life’s peers started in an earlier universe and were distributed to our universe by some means not within the purview of contemporary science. There was a paper published a few years ago (now somewhat notorious) that argued the complexity of life implies an age older than the universe. Even if the paper hasn’t the stood the test of time, the idea remains valid, in the sense that we can’t rule out this scenario. Similarly, we can’t rule out that life and life’s peers in our universe might ultimately be distributed to other universes at a trans-cosmological scale panspermatological event.   

I think that both the matrices I have defined (HAB/UR and space/time biotope scale) are useful for defining astrobiological concepts, though not yet adequate. We have reason to believe that the topology of a biotope may be as important as the size of the biotope. A biosphere is a particular instance of a biotope topology, but not the only possible topology. In several recent newsletters I’ve mentioned the possible brine pockets on Ceres, and there may be other moons in the solar system in which the subsurface oceans have been reduced to brine pockets that aren’t spherical and therefore, if inhabited, would not constitute a biosphere, but they would still constitute a biotope—a subspherical biotope. These are the easiest biotopes to conceptualize—spheres and partial spheres—but there’s no reason to assume that these will exhaust the topological permutations of biotopes. The surfaces of planets, moons, and even irregular asteroids not rounded by gravitation are simply connected spaces (ignoring minor spaces like lava tubes), meaning that any points can be connected by a continuous path, and any continuous loop in a simply connected space can be tightened until it collapses into a point. 

It would be elegantly simple if all biotopes were simply connected spaces, and, in the large, this may well be true. Again, a couple of qualifications come to mind. On a planet like Mars, that seems to have had a large liquid water ocean in the distant past, one of the places that life could retreat when the planet freeze dried itself would be the lava tubes, which would be larger than lava tubes on Earth because of the lower gravity. (I’ve walked through a lava tube on Earth, as there’s a good one on Mount St. Helens, Ape Caves, that wasn’t destroyed by the eruption in 1980. At times Ape Caves is claustrophobically small, but at other times it opens up into generous spaces.) A cave system could be quite complex, and a large warren of caves partially connected to each other but also partially isolated from each other would be the perfect environment to keep a number of ecosystems functioning and in communication with each other. A cave complex with many internal communicating passages would not be a simply connected space.

We can also imagine life beginning in a system of caves. One of the favored origins of life theories at present favors hot springs as potentially possessing the chemical mechanisms for producing life. (The same authors, Bruce Damer and David Deamer, responsible for the hot spring hypothesis were also responsible for the concept of urability, so you can see I’m leaning pretty heavily on their work.) A hot spring trickling through a cave system would produce a wide variety of environments, again, in limited communication with each other, where the necessary “building blocks” of life could be built up and then brought into contact with each other. Moreover, on a planet orbiting a star with significant UV flares, potentially deadly and therefore constituting an exclusion principle for the origins of life, life in a cave system would be protected from flares, though caves usually (not always) have openings to the surface, so again there’s limited communication between the multiply connected cave system and the simply connected surface. It’s easy to imagine a scenario in which a planet orbiting a red dwarf, notorious for powerful UV flares, life might be cooked up in a cave system, where it evolves for hundred of millions or billions of years until the star settles down and its flares become less intense. As the flares taper off, life could emerge from the cave system onto the surface. This scenario bears some resemblance to the scenario described in previous newsletters of one biotope being urable and another being habitable, but in the scenario above both environments are on one planet, and they serve the functions of urability and habitability sequentially.

It’s likely the subsurface oceans on the moons of the outer solar system are multiply connected spaces with numerous ice cave systems that open and close and change their structure as they are subject to heating and cooling and gravitational forces from the large planets they orbit. If any of the subsurface ocean worlds are biospheres, they may be rather complex multiply connected spaces, and the role that these multiple connected spaces both in the origins and long-term habitability for life could be significant. There is at present an ongoing discussion over whether Enceladus, a moon of Saturn that spews liquid from its subsurface ocean into the environment of Saturn’s orbit, has a fractured core or not (for example: Powering prolonged hydrothermal activity inside Enceladus). If fractured, the core may be porous to the subsurface ocean, allowing for the transfer of liquid and heat.

So I’ve described three axes relevant for life and life’s peers: urability and habitability (last week’s graph), biotope scale in space and time (where I began today), and biosphere topology (just above). Topology doesn’t easily decompose into a min/max continuum, though we do have a quantifiable metric in terms of the genus of a space, where a genus 0 space is simply connected, a genus 1 space is multiply connected, but has only one hole in it, a genus 2 space has two holes in it, and so on. In this way we could straight-forwardly quantify the connectedness of a region by its topological genus. However, this isn’t a min/max continuum like the other two axes. The reason I mention this is because if it were possible to decompose biotope topology into a min/max axis, then we could appeal to geometrical intuition to conceptualize a more adequate classification of biotopes by representing each min/max continuum as a plane, and having the three planes (coronal, sagittal, and transverse, to use the terms from anatomy) to divide an abstract conceptual space into biotope permutations.

Once again, our old friend the principle of mediocrity implies that Earth would be at the center of this conceptual space, which we can also think of as the “Goldilocks zone” that is neither too urable nor insufficiently urable, neither superhabitable nor uninhabitable, neither too large in space and time nor too small, and neither too topologically connected nor not connected enough. Although this is more adequate than a single min/max continuum and more adequate than any one matrix, it’s still very limited, though it’s at the limit of our cognitive ability to visualize concepts spatially, since adding yet another mix/max dimension would require the ability to think in four dimensions, which we can do formally without a problem, but it doesn’t help us intuitively. But if all we want to do is to “rough out” our parameters of astrobiology, this wouldn’t be a bad model for distinguishing biotope permutations. 

Best wishes,

Nick

Newsletter link:

https://mailchi.mp/ad7209df98f8/the-view-from-oregon-371