# On the Explicit Function of Life within a Physical Universe

^{1}

^{2}

^{3}

## Abstract

**:**

## 1. Introduction

- How does a difference arise in physical structures?
- How can a difference be made in physical structures (triggering a difference in its configuration that subsequently leads to new ways of interacting with its environment)?
- These questions are elaborated and discussed in the following so that the inherent question in the title about the meaning of functionality in different environments can be addressed in the discussion.

## 2. Results

#### 2.1. How Can a Developed Physical Difference Make a Difference by Functionality?

^{2}= W/m

^{2}]) or intensity related available energy. Subsequently, properties important for interactions with fields such as the one that caused the alterations are altered. Those properties comprise absorption, transmission, reflection and the complex medium property refractive index (RI). The RI is mathematically defined as the relation between traveling speed of the phase (in the case of the electromagnetic field being the wave field under consideration: the speed of light in vacuum, c) and the traveling speed inside the medium, v. RI~c/v, and in most known naturally occurring media, it is smaller than 1. The micro-dynamics behind the effect of the RI of a medium on an incoming wave are quantum mechanical by nature and are not delved deeper into here, but a simple macroscopically observable detail is helpful for visualization: Remember that we discussed interference with interference being the main mechanism of altering the intensity distribution structure of a wave field. In classical optics, what is important in a wave field for the average intensity (incoherent relative phase) or the diffraction pattern (coherent relative phase) spatio-temporally “coded” intensity distribution transmitted to a screen is the front hitting the screen at a distance to the field’s source, called the wave front. When a wave front hits a screen, depending on the complex RI of the screen material medium, part of the wave front will be reflected, part of it will be transmitted and other parts of it might be absorbed. In reflection, as in other cases, classical optics uses the model of the so-called Huygens’s elementary wave mechanism. The details can be found in any physics textbook comprising classical optics and are worth deeper study, but for the discussion here, the important message from the model is that it is possible to construe any part of a wave front as a source for an elementary, i.e., spherical wave (in three dimensions). This is valid for the original wave front as well as for its reflection after it hit—and possibly interacted with—the medium. This is the crucial point. If the medium in interaction altered the phase of a reflected wave, the intensity at that point of the medium as a source for the reflected wave front might be altered due to interfering with interference, compared to the wave front that came in. In the case of light, when the light goes from a low-RI medium to a high-RI medium (air to glass), the reflection undergoes a 180-degree phase change. When the light goes from a high-RI medium to a low-RI medium (such as glass to air), it does not undergo a phase change. This is analogous to the case of a vibrating string (from footnote 7) as an example for the generation of a standing wave: At an edge of the medium that is held fixed (i.e., the point is not allowed to displace at amplitude as every other point in the medium), the reflected wave flips over (corresponding to a 180-degree phase change). At an edge of the medium that is free to displace, the reflected wave does not flip over [30]. This becomes relevant at any point in the medium where there is a sufficiently large region of altered RI while the wave is propagating through. Especially interesting is the case of the incoming wave interfering with its reflected “copy” since this is an example for a coherent relative phase, and the interference defines the image of the reflector, i.e., the incoming wave as a reference wave plus the modulation on the phase done during reflection. In a first summary, it can be said that:

- Linear interference influences the intensity distribution between and local observability of frequencies of a given spectrum.
- Depending on the relative phase, the intensity of frequencies inside the given spectrum can at a screen at a certain distance to the source of the wave front attain an average value or an image of the primary source modulated by a reflector9(and possibly a noisy transmission medium, e.g., air) at that frequency as a diffraction pattern.
- When a wave front transmitting a diffraction pattern as a spatio-temporally “coded” intensity distribution in the field hits a target surface which is sensitive for some of its frequencies, energy is not simply transmitted but is transmitted with information.

#### 2.2. Making a Difference by Non-Linear Wave Guiding and Mixing between Frequencies

_{1}and f

_{2}), new frequencies are generated and can be perceived. When the new frequency which is the difference between the two non-linearly mixed frequencies is slow enough, humans do not hear it as a tone but as a periodic oscillation in the sound intensity of the summation tone, i.e., as a beating. When above ~20 Hz, the human auditory threshold, the difference frequency is heard as a tone too, and the frequency mixing becomes observable. The two similar sine waves oscillating at f

_{1}and f

_{2}(colored blue and green, respectively, in Figure 1) are linearly superposed. Due to constructive and destructive interference in their dynamically evolving phase relation, the amplitude periodically increases and decreases and does so with a frequency (colored orange in Figure 1) that is the sum frequency of f

_{1}and f

_{2}. As long as no non-linear medium is distorting the superposition, no signal is generated at the sum frequency. The Fourier transform of the time domain to the frequency domain only shows the two original frequencies f

_{1}and f

_{2}, and thus this is no new acoustic signal yet. Likewise, the difference frequency (colored red in Figure 1) is not appearing in the Fourier transform, just the intensity oscillation in the time domain. To arrive at the generation of a sum and a difference frequency signal, a non-linear distortion needs to occur as is shown in Figure 2. The mathematical function describing the mixing in the non-linear medium, the so-called transfer function, needs to be of quadratic order or higher; that is, it must contain exponents that are at least quadratic.

#### 2.3. The Importance of Non-Linearities

_{kin}) mv

^{2}, or qr

^{2}, amount to the same average value, given as proportional to k

_{B}T (equipartition theorem; K

_{B}being Boltzmann’s constant) [36]. Total energy is then equally distributed over all (excitable) energy levels and associated degrees of freedom (dofs) of motion. This makes temperature T of a medium proportional to the mean kinetic energy of its particle motions in thermodynamic equilibrium. Inside an ensemble of a closed system (i.e., which is not coupled to a surrounding system with a different average value (different T)), many different isoenergetic configurations of the ensemble of particle motions, so-called microstates, lead to the same temperature value. Although microstates of ensembles of chemical molecules have more degrees of freedom (dof) than a cyclically periodic sinusoid wave and the phase space thereby becomes accordingly more complex, the analogy between the incoherent relative phase in a spectrum of waves leading to an average local intensity on a stricken screen and many different configurations inside a closed ensemble of particle motion leading to a common average E

_{kin}is astonishing. The influence of the relative phase altering the distribution of intensity in space on frequencies thereby not altering the (theoretical) average energy per length of a frequency’s period transmissible to an area of impact but completely changing local availability of energy is pictorial for imagination. Transmitted total energy is the same, but locally there are differences from the average which forms a global intensity distribution pattern (interference pattern). The statistical probability measure of thermodynamics distinguishes microstates (of independent motions in physical phase space) from each other in energetic terms. The distinction of energetically equivalent different relative phases, in contrast, is possible by the image of their intensity distributions on a stricken surface, i.e., the spatio-temporal pattern given to the energy of the field. When non-linear processes come into play—as in the described emergence of solitons and mixing processes between superposed frequencies—equipartition is counteracted in a locally and temporally limited way. The spectrum and most certainly also the average value of the ensemble is altered. Thereby—limited in time and space—anisotropic distributions are compatible with and thus functional for maintenance of the structure of the medium. It is trivial to mention that the other accounts on function would not distinguish the physical process from transmission of a random pattern and thus treat anisotropic media not differently from isotropic media regarding their properties to partly store and re-emit received wave-field information.

#### 2.4. Information in Its Most Basic Physical Representation

^{2}] can be given by the maintenance account. The function of the otherwise immaterial image is a contribution to the maintenance or repeated generation of distribution functions similar to “itself”. One special property which wave transmission of pacing for local energy availability has is its potential independence from the type of medium it is transmitted by. Naturally in transmission from one medium into another, details of the information of the energy pacing are lost, but the natural relation between electromagnetic waves in the electromagnetic field and moving as well as resting charges (as described by Maxwell’s equations) facilitates cross-medium transmission. Information should be—at least in principle—quantifiable as the amount of discrete possibilities to distribute probability for selection.

_{pot}? It behaves complementary to kinetic energy in that it comprises the position of mass and charges in relation to accelerating influences that potentially can be transformed into kinetic energy during relaxation into their resting position. E

_{kin}and E

_{pot}are sufficiently known from physics, but is it possible to logically relate them to the amount of possibilities to choose from for differential acceleration, or, the position of differentially accelerating influences? The soliton wave can conduct energy and the length of its period: if a series of solitons is excited, power and frequency are transmissible in a stable form. The condition for a signal, a wave function that can itself be a discrete sinusoid or comprise discrete elements stable in form, is given. Form stability in waves would have to be translated as stability in energy per frequency. As is widely known, Planck’s formula for quanta of black body radiation (E = hf) gives the smallest unit of discrete waves of stable energy/frequency, the constant h. Interestingly, the physical quantity E/f, that is, E*τ (with τ being the duration for a process from a starting point to an endpoint), has meaning for physics. It is called action (therefore Planck’s constant h is called the quantum of action) and is the main quantity in a natural principle, called the principle of least (in strictly non-dissipative systems replaced by “stationary”) action (PLA). Processes without dissipation according to the PLA happen along trajectories that are the shortest path (in traveling light this can be taken literally as shortest in time) that connects starting point and endpoint, so-called geodesics.

_{kin}and E

_{pot}, quantified in a single number as the Lagrangian temporal integral functional over (E

_{kin}-E

_{pot}) [39], changes, physical action changes, and the trajectory deviates from the geodesic. The thrilling fact that this quantity, physical action can be expressed using the units of classical translation (distance and time) as well as of classical wave motion (wave number and frequency) is a detail that has been keeping physics busy for quite some time [41,42,43] and that most certainly will be of great relevance for insights regarding physical information processing in evolution. An important question in this context is the importance of the connection between linear and non-linear dynamics for evolution. If the group of Annila should be right with the theory of a connection between the Second Law of Thermodynamics and the PLA, delineating dispersal of energy along the steepest directional descents in evolution [44], implications for the understanding of natural processes can hardly be imagined.

**can be stored**(as a relative phase in a field or as in a configuration of chemically bound particles) and which can

**influence selective processes**(differential acceleration, enhancement, delocalization or more generally differential support or weakening of fluctuations present in the receiving system).Translated into action of information on the mechanically relevant kinetic and potential energies, there is:

**Kinetic information**, which is connected to information contained in kinetic energy. It is the differential enhancement of coherence between mutually independent particle motions in phase space, that is, waves in a relative phase in a wave forming a motion structure with a (communicable) spatio-temporal pattern of interference “coded” intensity related values. In a (projectile) motion of single-particle objects, where N

_{ensemble}= 1, speed and direction of propagation are also given by kinetic information, I

_{kin}. If E

_{kin}occurs without I

_{kin}, it plainly transmits an averaged intensity value anywhere into a stricken target, i.e., it is thermalized.

**Structural information**14 is connected to information contained in potential energy. It amounts to relative position inside a potential as well as to the basic units of potential, charge and mass. Relative position in space and in relation to accelerating (positively or negatively) influences organizes potential energy of correlated densities of mass and correlated densities of charge into spatial networks of distinct geometry. Thresholds for the spatial constraints are defined by topologically influenced restoring forces and local potentials. Subthreshold impacts of energy are reversible due to restoring forces. E

_{pot}without I

_{Struc}is hardly possible. Even the densest packing of mass or charge defines a spatial structure and threshold energies. Collapse into a point is forbidden by the Pauli principle. Maximum random dispersion into free space under thermalized E

_{kin}, splitting all relations that define elementary structure would minimize I

_{Struc}but also E

_{pot}.

_{Struc}, cannot inform a receiver unless the receiver is coupled to it via a field or motion containing I

_{kin}. Sensory functions that can receive information about structure from signals in the field in a structure can improve the transmission.

#### 2.5. Selection Regimes Guiding and Defining Functionality

_{struc}17 and a very slight form of self-referentiality between frequencies excited and spatial frequency of cavities in the canal structure that define the fundamental and its harmonic series. Nevertheless, this slight form of self-referentiality in differential enhancement of amplitude for frequencies inside a non-linear process is based on a principle that allows much stronger basic physical self-referentiality in evolution: the linear generation of a pattern or average value in local availability of energy per period and area coupled to a non-linear differential enhancement of amplitude of frequencies in a spectrum.

_{kin}and I

_{Struc}. In this paper, the focus has been on the maintenance functionality of the latter, since stability of matter is known from everyday experience. The maintenance account can assist in understanding the contribution of structural dispositions to the coupling between I

_{kin}and I

_{Struc}in the process of evolution. Storability is the basis for the original background of Bateson’s famous quote18 where the difference that is made can do so as it leads to a change in the receiver’s mindset. With the evolution of robust means of information storage and processing, genetic storage, the human mind and its brain came into existence.

## 3. Discussion

^{43}Tc, causing rareness of those isotopes. The human cultural selective regime found a use for, e.g., the radioactivity and its effects; therefore certain isotopes (e.g.,

^{97}Tc) including synthetically generated radioisotopes (e.g.,

^{95}Tc) of the element are produced. The maintenance account thus can support the tool-use-function argument, since the probability for being reproduced (maintenance in this example cannot be influenced selectively) increased in comparison to pre-human selective regimes and radioisotopes which in environments of planet Earth before human culture and technical capabilities developed to that point could not emerge now occur due to regular artificial production. By adding non-negative self-referentiality to the relational functionality, the maintenance account can examine the development of effects of structural dispositions which initially proved detrimental for their maintenance in the course of evolution. Atoms and molecules show non-negative self-referentiality in many variants of structural dispositions. The maintenance account can explain their primary maintenance function as well as a secondary evolving maintenance of structurally disposed properties or structural dispositions when the selective criteria in the environment are changing. Mechanisms of compensation for negative effects by environmental influences can change non-functional properties into functional ones or enable effects that are only coded together with detrimental effects in a structural disposition to outweigh the disadvantage. Detrimental effects of maintained structures are certainly an important selective factor; maintained means functional due to maintenance account. In living systems, it is important to consider the difference between functionality for maintenance of a disposition or for maintenance of the bearer of that disposition. The best way of detecting this difference is asking whether a detrimental disposition that (potentially) is life-threatening for its bearer could become functional and how. Three possible situations are considered.

- The recognition of such an effect of a function might occur too late to enable negative selection by the Darwinian natural selection mechanism. One example would be a propensity for using up resources. Another example would be a propensity for (accidentally) rendering impossible the survival of an important compensator of negative effects in a system. A propensity very common in living systems is to locally accumulate metabolical waste products that show threshold toxicity for the species. In an ecosystem with functional biological detritus utilization cycles and enough space, this property is not harmful, with toxicity below the threshold. Nevertheless, in case the recycling system slowly and unnoticeably weakens, the carrying capacity of an ecosystem for waste accumulators can reduce in favor of propensities to non-randomly dispose of waste. All three propensities can appear as neutral or economical to the individual as long as the resources, or, the producers of resources and space to evade problematic effects, are abundant.
- The environmental conditions prevent the negative action of the function by compensation for its effect (hiding by compensation). The biggest difference to functionality in 1 is that life-threatening propensities hidden through compensator action can (in principle) be recognized by systems. Compensated detrimental propensities different from temporally hidden ones can be immediately effective every time the compensation temporarily stops.
- The structural disposition for a functional effect is invariably coupled to a non-functional effect (side-effect) so that there is hardly an alternative to accepting/adapting to the coupled detrimental effect. A famous example is sickle cell anemia which is a negative effect when maintained in the system since circulatory disturbances occur frequently. A positive effect of this deformation of blood cells is malaria resistance. In environments with high infection rates of malaria, side-effect functionality of sickle cell anemia is evident. Another example would be a firecracker or explosives in general: being a functional source for local, short-period thermalized energy in idm, selective regime lets its abstract structural information (in form of recipes) be maintained and lets its structures be repeatedly reproduced. Functional is a certain way of dissolving its structure under energy input.

_{kin}motion structure possible in almost any type of medium if there is a structurally disposed non-linear differential amplification property in balance with dispersion. The soliton I

_{kin}for its special properties is deliberately generated and used in the idm selection regime as a tool. According to the maintenance account a functionality of the I

_{kin}has evolved there.

## 4. Conclusions

## Funding

## Conflicts of Interest

## Notes

1 | When v. Uexküll spoke about environments or “Umwelten” of animals, he pointed out the individual character and relative invariance of it as perceived by the animal [11]. The environment is more defined by being a source of perceivable conditions than by its location. |

2 | Selective environments, that is, environmental selection regimes, are discussed in Section 2.5. |

3 | Functional adaptations for being maintained, not-detected and stably transferred during life cycles by hosts. |

4 | See footnote 2. |

5 | Or alternatively, wave diffraction: wave packets propagating in a linear medium have a natural tendency to broaden in time (dispersion) and space (diffraction) [19]. |

6 | Respectively, the speed of the water flow dragged by the ship which continued propagation after the ship suddenly stopped—in the case of Russel’s observation. |

7 | In the simple one-dimensional case of waves on a string, differential excitability of frequencies is easily observed: try exciting even multiples of a fundamental (frequency) in a string that is fixed at one end and free to move on the other—it is forbidden by nature. The decisive factor is the form of the fundamental in the given space (the string), namely how nodes (minimum amplitude) and antinodes (maximum amplitude) are distributed at their boundaries. |

8 | Another common intensity-related measure of available energy from an impacting field is radiance L(r, ω). It is defined as the power radiated at a given point r in a given direction ω per unit of projected area perpendicular to that direction per unit solid angle (in steradian or square radian, sr) for a given frequency [W/m ^{2}sr] [29]. |

9 | More generally a re-emitter, since the process could be a reflection as discussed here or similarly absorption and re-emission or transmission and transition into a medium with an altered RI. The principle is the same. |

10 | For mathematical reasons, the sum and difference frequencies are (f _{1} + f_{2})/2 and (f_{1} − f_{2})/2, respectively. In contrast, the audible intensity beating frequency (f_{beat}) is double the difference frequency, i.e., f_{beat}=|f_{1} − f_{2}|, since, for intensity oscillations, it is irrelevant whether the amplitude is above or below the baseline. For readers who are interested in more details: The mathematical reason for a multiplicative mixing occurring when the non-linearity has an exponential, at least quadratic characteristic at least for a technical mixer which includes diode elements can be easily explained. There the sum of two input signals is applied to a diode, where an output current is generated that is dependent on the input voltage, i.e. it is a relational function (f(x)) of the input voltage. When the input thus appears as an exponent in the calculation of the output, the exponential can be expanded in a Taylor series and for small inputs, the series can be approximated by the first terms, that is _{output} $\approx $ (_{input a} + _{input b}) + ½ (_{input a} + _{input b})^{2}. As is known from the binomial theorem expanding the square term yields a multiplicative mixing of _{input a} and _{input b}: (a + b)^{2} = (a^{2} + 2ab + b^{2}). This is the critical point in understanding the contribution of the non-linearity to mixing. |

11 | Heterodyne is the name given to a signal frequency created by non-linear mixing of two other frequencies using a technique called heterodyning, and it is a term used in communication engineering, e.g., in modulation of radio signals. |

12 | A more detailed answer than that mixers use one or more diodes and rely on their non-linear relation between voltage (V) and current (I) to provide the multiplying element would be helpful. Which property of the semiconductor (diode) accounts for the non-linear relation in the IV characteristic? |

13 | Both acceleration and enhancement are meant to be understood in a neutral, analytical way, i.e., positive as well as negative. |

14 | The author keeps the term structural information as proposed by Stonier to honor his work and also because the term potential information is already in use with a different definition. Stonier in [38] proposed equating I _{struk} with E_{pot}, which is not adopted, since his argument of thermodynamic improbability does not hold for potentials and E_{pot} in general [18]. |

15 | Thus showing a kind of relational zero function, f(x) simply being the keeping up of thresholds against irreversible distortions. |

16 | Intuitive thinking often is recognizing affordances or mechanism components inferred by analogy (see introduction). |

17 | I.e., relational zero function, i.e., physical maintenance of I _{Struc} keeping up thresholds for structural constraints to dissolution. |

18 | Although Bateson’s “(...) make a difference because the neural pathways along which it [elementary unit of information] travels and is continually transformed are themselves provided with energy.” Elementary unit of information viewed from an evolutionary perspective represents a unit of information inside a system that is already at a very highly evolved level of energy-fueled capacity for signal excitation and information processing: the human mind. |

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**Figure 1.**The superposition of two sine waves with similar frequencies f

_{1}and f

_{2}(blue and green) linearly causes an interference frequency sinusoid at the sum frequency (f

_{1}+ f

_{2})/210 (orange) and another sinusoid which is the envelope of (f

_{1}+ f

_{2})/2 modulated at difference frequency (f

_{1}− f

_{2})/2. The Fourier transform contains only the two frequencies f

_{1}and f

_{2}. Picture taken from [31].

**Figure 2.**A non-linear distortion happening inside a non-linear medium can generate a perceivable signal of the non-linear frequencies: (

**a**) out of the beating between f

_{1}and f

_{2}under the influence of a non-linear distortion in the medium (

**b**) the non-linear frequencies can emerge: The sum frequency (f

_{1}+ f

_{2})/2 (dark blue) and the difference frequency (f

_{1}− f

_{2})/2 (red) modulating its envelope. The modulated frequency (f

_{1}+ f

_{2})/2 is the carrier frequency of the modulating frequency. The Fourier frequency domain contains only the two non-linear frequencies (f

_{1}+ f

_{2})/2 and (f

_{1}− f

_{2})/2. Pictures taken from [31,32]. Source: Mike Run.

Selective Regime/Evolving Frame of Reference | ||||

Physical | Physico-Chemical | Metabolico-Genetic Biological | Intentional Decision Making | |

Drives for transformation processes inside selection regime | Second Law of Thermodynamics and principle of least action linear and non-linear combinations | Delocalization of charges and energy; minimization of Gibbs free energy | Darwinian natural selection: fitness and evolvability; individual’s felt deviation from homeostasis at possible relative minimum | Leading a good life that makes sense; making things easy but keeping them interesting |

Impossible properties that mark transition to subsequent selection regime | Reproduction; autocatalysis | Autopoiesis; search for gradients | Teleology | Breaking physical law? |

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Grathoff, A.
On the Explicit Function of Life within a Physical Universe. *Philosophies* **2021**, *6*, 59.
https://doi.org/10.3390/philosophies6030059

**AMA Style**

Grathoff A.
On the Explicit Function of Life within a Physical Universe. *Philosophies*. 2021; 6(3):59.
https://doi.org/10.3390/philosophies6030059

**Chicago/Turabian Style**

Grathoff, Annette.
2021. "On the Explicit Function of Life within a Physical Universe" *Philosophies* 6, no. 3: 59.
https://doi.org/10.3390/philosophies6030059