# Philosophical Aspects of Astrobiology Revisited

## Abstract

**:**

## 1. Introduction: Metaphysical Preliminaries

^{1}. This means in particular that principal categories of human thought, such as space, time, matter, and so forth, are concepts utilized in order to describe the observable world. They are thus linguistic fixed points in networks of theories—theories visualized then as sets of propositions that are connected to each other by given rules (of thinking). However, these categories are, in practice, either absent or meaningless when we try to conceptualize the ground of the world. This is the difficulty encountered when dealing with speculation. Nevertheless, there is no arbitrariness involved, because the minimal criterion is that speculation must produce at least all that is already known about the observable world. Hence, both re-construction as well as speculation are formulated in terms of a suitable formal language which utilizes metaphorization in the first place: But the former relies on concrete metaphors while the latter relies on abstract metaphors. At present, a bridge from one to the other can be built in terms of modern mathematics which recently developed as a theory of structure and logic at the same time ([7] ancient series, Cf. also [8]).

## 2. Substance-Subject in Formal Terms: The Example of Twistor Space

^{2}. In principle, twistors are elements of a four-dimensional complex vector space called twistor space II that can be defined as a double fibration over spinor space S and its dual S*. Hence, two spinors can be associated with a twistor such that (ω, π) ∈ S ⊗ S* ≈ II. In fact, linear transformations on II that conserve exact sequences of the type O → S → II → S* → O (and their dual) produce the restricted Poincaré group action on Minkowski space. (Here, O is the trivial group.) If in particular, x: S* → II is a section of the fibration, then it defines a motion on S* in II. However, in order to express realistic physics admitting of space-time curvature in terms of twistors, one has to introduce deformed twistor space DII. Space-time with curvature is called DM. It is called anti-self-dual, if it is conformally transformed and a subset of the complexified future infinity of this transformation. In symbolic terms, this is usually expressed as the relation CDM* ⊂ CΩ

^{+}(DM), where C points to the complexification and Ω to the conformal transformation, respectively. It can be shown then that x ∈ CDM* as well as x* ∈ CDM. In other words, a motion on S, say, defined by x, produces a space-time point on CDM*. The converse is not true. The same can be shown for x*. In fact, spaces CDM* and CDM are also called Newman’s heaven spaces H and H*, within different approaches.

^{3}

_{A}′

^{(A}ξ

^{B)}= 0

^{A}= ω

^{A}− i x

^{AA}′ π

_{A}′.

^{A}, π

_{A}′), can be identified with a twistor Z

^{α}. If the conformal group acts on II, then the inner product

^{A}π*

_{A}+ ω*

^{A}′ π

_{A}′

^{α}Z*

_{α}= 2 s, where s is the helicity. (This is because a spinor with 2s indices represents a physical field with helicity s.) Indeed, visualized this way and for a “flat” space, a twistor corresponds to a pair (p

^{a}, M

^{ab}) expressing the momentum and angular momentum of a particle field of rest mass zero such that p

_{a}p

^{a}= 0 and p

^{0}> 0. (All of this being written in the conventional four-notation of relativity theory.)

^{+}(s = $\overline{)\mathrm{h}}$), and PII

^{−}(s =−$\overline{)\mathrm{h}}$). By means of defining representations of twistor wave functions, Penrose can utilize this approach in order to give a table of particle fields that can be directly produced from twistor properties with varying helicities. This deals in more detail with contour integrals on holomorphic functions, which we will not discuss here

^{4}. But the underlying idea should have become clear enough: We have a model here which in principle is able to describe various forms of emergence, of particle fields as well as of space-time points. (Hence, the latter two are less fundamental than the twistor structure itself.) The underlying “attributive motivation” is quite apparent.

^{5}. At the same time, the categories of space and time are still intrinsically available, but they change their connotation, because on the level of twistor space, there is no manifestation of a similar evolution with an unfolding of processes as we have it on the level of Einsteinian space-times. In other words, relative to our observational standpoint, twistor space (and heaven) is (are) eternal, i.e., space and time as we know them, are absent. The absence of potentially corresponding observations could impact our concepts of Life, depending upon its nature. This presents a caveat for categorization of any Life other than that which we know.

## 3. The Emergence of Auto-Catalytic Systems

^{6}. In particular, (physical) space is visualized then as being comprised of autocatalytic autonomous Planck scale agents co-evolving with each other serving at the same time as some sort of crystallization of seeds of classicity (in the physical sense). This is an argument that runs roughly parallel to what is usually called “de-coherence” [34]. The co-evolution of agents takes place according to what Kauffman calls the 4th law of thermodynamics: The maximum growth of the adjacent possible in the flow of a non-ergodic Universe maximizes the rate of de-coherence and thus the emergence of classicity. In the long run, there is a hierarchy of such agents depending on the explicit complexity such that human agents in particular (as constituents of social systems) represent a stage of higher complexity as compared to physical, chemical, or biological systems, respectively. (Games of various types of agents are nicely illustrated by Szabó and Fáth [35].) But on the fundamental level of physics, Kauffman mentions the possibility to visualize spin networks themselves as knots acting on knots to create knots in rich coupled cycles not unlike a metabolism. Hence, they (or their constituents) show up as a sort of “fundamental agents”. We can suppose from this that the intrinsic self-duality of twistor space (as formal analogue of substance-subject) can be translated as a competitive dynamics of games on the observable level of worldly phenomena. This competitive dynamics can be classified according to its degree of complexity. The substratum of the observable world (matter and information) is thus invariant, while complexity increases according to the laws of thermodynamics. Life thus occupies a specific level of this complexity. As compared to spin networks, the various forms of life belong to an elaborated organization within the given range of a hierarchy of forms that have emerged. Hence, Life occupies a special position within this hierarchy, but it does not transcend the general layout of emergent systems.

_{p}

^{2}∫ da ≤ 0,

_{P}is the Planck length.) By the definition of loops above, we clearly recognize that this procedure is not referring to some physically “vacuous” geometrical meaning, but that, instead, this geometrical picture is physically loaded due to the parallel propagator with its gravitational or curvature connotation, respectively, and the explicit group action involved: Hence, with a loop [36] we mean here a closed curve α such that T[α] = −tr [U

_{α}], where

_{α}(s

_{1}, s

_{2}) ~ P exp { ∫

^{s2}

_{s1}A

_{α}(α(s)) ds}

_{α}along α defined by (the s

_{i}being points of α)

_{α}(1, s) = da

_{i}(s)/ds A

_{i}(i(s)) U

_{α}(1, s).

_{i}

^{j}(x) = Γ

_{i}

^{j}(x) − k

_{i}

^{j}(x).

^{t2}

_{t1}dt L(x, x’).

_{J}N(J) Σ

_{e}II

_{f}

_{∈}

_{J}dim a

_{f}II

_{v}A

_{v}(e),

_{K}= <cup|M|cap> with creation and annihilation operations, respectively,

cap: = <b|: V ⊗ V → C,

_{σ}< K|σ > d

^{||σ||}, can be related to the process of quantum computation (similar to the spin network formalism itself). As spin networks are nothing but graphs, the agency in question here is motion on graphs or percolation of energy and information in networks such that phase transitions can be represented in terms of an appropriate cluster formation of connected components. This is what points to a close relationship to cellular automata utilized for the simulation of evolutionary processes (cf. Conway’s game of life or Wolfram’s approach). Stuart Kauffman has associated this with the emergence of collectively autocatalytic sets of polymers, and in fact with the onset of forming classicity with regards to physics. It is straightforward (in epistemic terms) to generalize this (with a view to higher-order agents) to chemical, biological, and other systems.

^{2}that preserve the volume form. Thanks to an e-mail crash course on these matters referring to the Barrett–Crane model and made available online by John Baez and Dan Christensen [42,43], it is easy to understand that constructions in the sense of Barrett–Crane turn out to be invariant under SL(2,C). In other words, we essentially deal with states in C

^{2}which are spinors. And it is from quantum theory and special relativity, especially by the important work of Penrose discussed above, that we know about their relevance. On the other hand, as Baez notes, a state in C

^{2}can also be called a qubit. So “[w]hat we [a]re really doing, from the latter viewpoint, is writing down ‘quantum logic gates’ which manipulate qubits in an SU(2)-invariant [in fact, SL(2,C)-invariant] way. We [a]re seeing how to build little Lorentz-invariant quantum computers. From this viewpoint, what the Barrett-Crane model does is to build a theory of quantum gravity out of these little Planck-scale quantum computers” [44], (p. 42).

↑ em ↑↓ id

SpinF → Hilb

_{γ}dS(Ω) ≥ 0. It is especially the Braunstein–Ghosh–Severini (BGS) entropy in fact which is relevant here: This refers essentially to a quantum field theory on a space Ω ⊆ Σ with H

_{Σ}= H

_{Ω}⊗ H

_{Ω}

^{C}as adequate tensor product of the associated Hilbert spaces such that ρ

_{Ω}= tr

_{H(Ω, C)}|ψ><ψ|. In particular, for the loops of this theory, the appropriate Hilbert spaces are defined by the cyclic functions of an SU(2) connection A. Hence: {ψ; ψ(A) = f(U(A, γ

_{1}) […] U(A, γ

_{L}))}, where |ψ> is a spin network state. The density matrix of the underlying graph Γ turns out to be the Laplacian matrix L(Γ) (essentially the difference between degree matrix and adjacency matrix) divided by the degree-sum of such a graph. In a sense, the “skeleton-of-the-universe view” can be thus visualized as a generalized kind of an algorithmic approach such that the physical phenomena of the universe (i.e., of the observable physical world) emerge as a result of algorithmic procedures that are coded into a procedural space [46] that is logically prior to the action of fundamental quantum computation.

_{n+1}(i) = (1 − ε) f(x

_{n}(i)) + ε/N ∑

_{j = 1}

^{N}f(x

_{n}(j)),

^{2}.

^{7}. More recently, Kauffman has collected all the various aspects in order to present a concise approach to his concept of “constraint closure” [56]. Referring to the work of Mael Montévil and Matteo Mossio [57], he starts from the connectivity of random graphs that eventually leads to dynamical structures and metabolisms [56], (p. 40 sqq.). The results fit nicely the original ideas of the seminal paper on the replication of polymers which at the time was preparing further work about the stochastic onset of network growth [58].

^{8}that starts with the formation of auto-catalytic (strictly self-organizing) network structures from which discrete dynamical systems emerge that can be expressed in turn by continuous differential equations, once the appropriate limit is chosen. The physical beginning of this procedure can be located in the initial co-operation of loops when forming their spin network hexagons that lie at the bottom of space and time proper. But in order to find a reason for the explicit necessity of this dynamical onset, we have to go back to the metaphysical ground mentioned in the beginning. When trying to find a formalized parallel to this ground by means of choosing the example of twistor theory, as we have done above, we can argue as follows: It is the intrinsic self-duality of the spin space construction of the form S ⊗ S* within the framework of this theory that creates an immanent tension which serves as the impulse for the onset of differentiation. Compare this with the theory of de-coherence: At a given order of magnitude (in the nanometer range), the quantum coherence of entangled states is spontaneously broken (in the eyes of the theory, that is) such that a classical world is created. Initial chaos can be compared here with original quantum coherence. This situation is very similar to what we have discussed here: Originally, twistor space shows up as a kind of procedural space containing intrinsic tension. In other words, twistor space is to the observable world what a computer program is to what is being processed and observable on the computer screen. The difference may be that a strict algorithm might be absent. (This is still being discussed.) Once space and time have formed and the dynamics is triggered, evolution accelerates due to the underlying thermodynamics that provides the laws for a necessary strife for diversity—especially according to Kauffman’s fourth law. Remember, however, that this forming, triggering, and accelerating is simply in the picture of the theory developed by those who conceptualize what they observe. (In fact, this comes nearest to the perspective of substance metaphysics from Spinoza to Schelling and further on.) The relevance of this to Life in particular is that it emerges thus spontaneously from a whole bundle of properties and conditions that have been acquired by systems due to the processes involved while translating the implicit structural imprint on procedural space into explicit dynamical phenomena on concrete space-time. Hence, essentially, Life is nothing but an epiphenomenon, perhaps necessary, but in any case contingent. It serves the diversity of what there is.

## 4. Life as We Know It

^{9}. The search for natural laws is a search for the language in which they are written. (The list of lines giving mathematical formulae for a problem in question and the list of lines giving a digital program for this same problem are isomorphic.)

^{10}. Consequently, this is the generic starting point for a possible continuation of such an approach into the detailed micro-structure of material forms. We see from the example given by the Aquarius project mentioned in note 8 that the evolution of interstellar matter defines a motion which can be taken as ground for the further onset of the formation of structure through a generalization of reaction networks of all kinds. (And obviously, the Aquarius project is simply based on a digital program.)

^{11}. Most of these points are compatible with the view pursued here. This is also the case for what Dirk Schulze-Makuch and Louis N. Irwin discuss in their book when for a suitable definition of Life they collect a number of properties common to living beings [64], (p. 7 sqq., ch. 2). But when they also collect exceptions to their list of properties, then we notice that these do not necessarily contradict the principles mentioned above. In Smolin’s definition, the phrase “governed by a program” hides all that we usually connect with the intentional participation of agents in games up to explicitly Darwinian behaviour. If we apply this definition and also assume the existence of the postulated program, then the definition I have given for systems in [2], (p. 27) can be readily utilized. However, in that case the definition is very general, and the Universe shows up as a maximal system that consists of a multitude of sub-systems, essentially a system of systems [65], (p. 130).

^{12}.

^{13}.

## 5. Conclusions: Once More the Meaning of Life

^{14}: We have noticed that, by asking for the emergence, the structure, and the function of Life (the latter deciding about its meaning after all) within the Universe, we are confronted with a constitutive loop of self-reference that closely connects epistemology to ontology. When performing research, we basically ask for the condition of the possibility to observe something. Explaining in scientific terms thus essentially means re-constructing. While science deals with re-constructing processes that can be observed, it is philosophical speculation, metaphysics, that deals with re-constructing processes (or conditions of processes) that cannot be observed. Assuming then that the physical Universe is all that can be observed, looking for its foundations means to actually “leave” it (in terms of reflexion), because the ground is always external to what is being grounded. Although today, we would rather visualize mind as a form of matter, and matter itself not only as bulk matter (stuff) of one or the other kind, but also as energy, the essential point of traditional metaphysics has nevertheless remained valid: We still agree that human beings can only gain access to a part of the world, because their means of observation are limited according to their generic capacity of sensory perceptions. This has obvious consequences for the theories describing the world. For the world as we observe it within the framework of categories like space and time, it is characteristic state transitions that essentially increase the complexity of the systems involved so that, locally, stability decreases tending towards non-equilibria, while globally, it is instability instead which decreases such that the maximal system tends towards an all-encompassing equilibrium in the long run. We typically attribute this to the laws of thermodynamics. The latter form the arena for the dynamics of the world that is emergent with respect to the metaphysical ground. In particular, (physical) space can be visualized then as being comprised of autocatalytic autonomous Planck scale agents co-evolving with each other serving at the same time as some sort of crystallization of seeds of classicity. In a sense, this “skeleton-of-the-universe view” can be thus understood as a generalized kind of an algorithmic approach such that the physical phenomena of the universe (i.e., of the observable physical world) emerge as a result of algorithmic procedures that are coded into a procedural space which is logically prior to the action of fundamental quantum computation. As to consciousness itself, the conventional idea that it is likewise a classical entity emergent with respect to the quantum level appears to be convincing. This viewpoint is strengthened somewhat by the fact that the categories of human reflexion, obviously a product of consciousness after all, such as space, time, material objects and so forth, emerge above a given critical threshold in the order of magnitude rather than prevailing from the beginning on through all orders of magnitude. And this emergence depends on the state of observation (of the human observer), as de-coherence theory has been able to show. This does not however contradict the justifiable assumption that quantum physics is at the bottom of physics altogether. As to the definition of Life then, this implies that its dynamical conditions (based on a network of interacting agents) are coded into the micro-conditions of the observable world as a consequence of its metaphysical ground, but that its specific properties depend on the co-evolution of the chemical material available in terms of the local distribution of matter and information as it can be conceptualized following the results of modern cosmology.

## Funding

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Traditionally, in metaphysics, the foundations of something are called its ground. We follow here the line of Schelling for whom ground is to what it grounds, non-being. Note that this is a direct reference to the Greek (mostly Aristotelian) tradition, with an intrinsic double meaning: ground1 as what cannot be observed, but is basically underlying this which can be observed = substance (οὐσία)—vs. ground2 as what can be observed in principle (but not yet), but is basically underlying this which can be observed at present = subject (ὑποκείμενον). Because at the same time, non-being (μὴ ὀν) carries the connotation of being (the) possible, it is a fundamental demarcation against what is impossible or nothingness (οὐκ ὀν). Both of these states of being are thus included in the substance, but not in the subject. Note also that Greek concepts of philosophy frequently come from the field of judiciary. Hence, in general, their meaning is difficult to obtain, because of their multiple connotations. While “subject” refers mainly to what “is underlying” something, “substance” can mean in turn “essence”, “reality”, but also “ability” and “property”. Even worse, this European style of “substantivating” a verb (making it to a noun) obscures the fact that originally, we should speak of “substance-ness” or “subject-ness”. This somewhat complicates the applications. For more details see Rainer E. Zimmermann: Nothingness as Ground and Nothing but Ground. xenomoi, Berlin, 2014. See also [6]. |

2 | |

3 | |

4 | See in more detail Zimmermann, R. E. Rem Gerere. Op. cit. [29]. |

5 | In fact, the oldest example for such an underlying motivation can be found in the early development of Maxwell’s theory which represents the simplest theory of unified fields. Essentially, electric and magnetic fields show up here as attributes of a fundamental field called electromagnetic which can be associated with a formal concept of substance. We can notice here an implicit influence of Schelling onto Maxwell (probably mediated by Faraday). For more details on the onto-epistemic consequences of this see [33], sqq. |

6 | I am referring here to an earlier manuscript version (sfi working paper 96-08-072) of Kauffman’s book “Investigations”, quoted above [1]. Cf. the address: Available online: https://www.santafe.edu/research/results/working-papers/investigations (accessed on 23 February 2021). In the actual book version, autonomous agents are defined as self-reproducing systems which can at least perform one thermodynamic work cycle. |

7 | A systematic review can be found in [48]. But see also [49]. On the aspect of small worlds see in particular [50]. More recent works on neural nets are [51,52,53]. A different, but very promising approach is also given in a large series of papers that started with [54]. This group should be singled out for further work. Finally, as standard work, [55]. |

8 | The best illumination of formal narratives is by means of computer simulations of complex processes. The Aquarius project e.g. can serve as a useful illustration: Starting the algorithm lets the Universe as we know it presently unfold. Cf. Available online: https://wwwmpa.mpa-garching.mpg.de/aquarius/ (accessed on 13 March 2021). In principle, what we describe in this paper as a formal narrative would be the continuation of the Aquarius simulation project into the detailed micro-structures of the Universe including individual planetary eco-systems. |

9 | It is useful to compare this with the actual procedure applied within the development of so-called Creatures software, when the digital environment of acting game characters represents a type of (simplified) catalogue of “laws of nature”. Obviously, this catalogue is nothing but a list of program lines. Cf. [61]; For the procedural space see in particular ibid., p. 82. |

10 | For technical details concerning interstellar matter see [62]. |

11 | See in this present special Issue of “Philosophies”. |

12 | See in particular [67]. |

13 | A promising alternative would be a structure that can be expressed in terms of a network of one or the other kind. See [68]. |

14 | I thank one of the referees for suggesting to add this short summary to the conclusion. |

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Zimmermann, R.E.
Philosophical Aspects of Astrobiology Revisited. *Philosophies* **2021**, *6*, 55.
https://doi.org/10.3390/philosophies6030055

**AMA Style**

Zimmermann RE.
Philosophical Aspects of Astrobiology Revisited. *Philosophies*. 2021; 6(3):55.
https://doi.org/10.3390/philosophies6030055

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Zimmermann, Rainer E.
2021. "Philosophical Aspects of Astrobiology Revisited" *Philosophies* 6, no. 3: 55.
https://doi.org/10.3390/philosophies6030055