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  • Determinations of a Substance 3
    sure this dynamical law is ultimately residing in the above mentioned set of atomic species but penultimately it resides in and around the DNA as has been said But we must elaborate on this a little further The set of all atomic species and of each species a not precisely fixed number of atomic individuals that has seen after the fact entered into the organism in the context of a continually going in and going out process originally contains implicitly a multitude of possible dynamical laws But when those atoms are finally organized in a certain way up into the molecular genetic framework of a certain organism we can again after the fact state that a special dynamical law out of the many originally possible has operated and continues to operate resulting in the further formation and maintenance of the organism So the above mentioned set of atoms is the ultimate set of system elements and in this set the dynamical law in question among others resides Penultimately this law and now excluding others resides in and around the genome the DNA of the generated organism But the construction of the organism from the ultimate set of atoms mentioned must be understood as a conceptual construction a conceptual generation of the organism not as a factual one This idea of conceptual generation serves to locate the dynamical law The dynamical law is conceptually found by referring back to some properties of initially freely existing atoms This implies that there is a definite relationship between determinations and Essence be it that these determinations are not those of the Totality in question This relationship is however a very complex one and as far as my knowledge goes not clearly understood The dynamical law cannot be equated with a determination because it is not contained in one special determination but is situated over several determinations i e it involves several determinations which are themselves distributed across several system elements So the ontological status of the dynamical law is different from that of a determination We have expressed this difference by means of a discrimination between the genotypical and phenotypical domain See the next Figure System Elements and a possible Dynamical Law Diagram symbolizing a possible dynamical law red line as it derives from certain properties of the system elements The red line symbolizing this dynamical law should imagined to be interrupted in the spaces between the system elements As one uninterrupted line it symbolizes the one ness of this dynamical law Each system element harbors many properties All system elements participate in the constitution of that dynamical law but not all properties of the system elements do so participate Another possible dynamical law should be indicated by a similar line going through all or some system elements but hitting different regions within each system element Of course the line representing a dynamical law could intersect some system elements twice or more times whereby each intersection corresponds to a certain property of the system element involved So we have in fact the following relationship going from left to right DETERMINATIONS ESSENCE DETERMINATIONS of system elements Dynamical Law of generated Totality The above scheme reflects a very close connection between determinateness on the one hand and lawfulness on the other When some one thing is determined in some way be it per se or accidentally and so possessing a certain feature during all of its existence or just during a certain time interval the acquiring of such a feature is the result of some local process and is as such repeatable over many instances because a process is a regular event i e an event dictated by a certain local law operating at a certain locality of that particular thing or involving the whole of that thing As we have already stated it involves a repeatable interaction of the thing or a part of it with one or another agent or other thing The ontological status of the resulting determination is assessed with respect to the given thing as being either extrinsic or intrinsic and with respect to the latter either per se or per accidens The relation between the Totality and its determinations on the one hand and the ultimate system elements on the other is diagrammed in the following Figure Schematic representation of the Totality as a complete set of determinations and its ultimate system elements containing the Dynamical Law What has been said about organisms with respect to their Essence dynamical law the system elements the elements of the organic Totality and the Totality s determinations is of course no more than a preliminary sketch Much more research biological and philosophical is required to settle the issue in a more satisfactory way The Totality itself In many cases the generated Totality is itself also a dynamical system But this system does not differ essentially from the system that generated the Totality in the first place All this we see in the case of organisms and less so in the case of crystals A growing crystal in a solution or in molten material is a dynamical system because the system elements in the solution or in the molten material are ordering themselves into a regular pattern In the case of a crystal growing in a solution the elements move towards the growing crystal This movement is caused by the dilution of the solution in the immediate vicinity of the surface of the crystal and this dilution is itself caused by the apposition and thus reception of system elements onto the crystal Accordingly the dynamical aspect is in the case of crystallization not so prominent but nevertheless present System elements once being received IN the crystal do not really move anymore but only execute vibrations around their average position We can further observe an attraction repulsion balance between the constituents of the crystal So inside the crystal no generative processes with respect to the becoming of the crystal take place anymore Generally the crystal does not show internal changes except of course in the case of instabilities What is taking place inside the crystal is just the maintenance of what has been formed And because of this we can call such a crystal a more or less static system Also in the case of freely existing atoms and molecules the dynamical aspect only relates to vibrations and rotations of their parts around their average position In some small molecules this dynamical aspect can be relatively significant Of course the expression vibrations and rotations of their parts relates to a physical description A metaphysical description will express those dynamic phenomena in terms of alternating determinations of the atom or molecule in question The case of organisms is as has been said different There the dynamical nature is also after their formation generation well present This is because of the OPEN nature of an organic system to the outside world It is in a state of constant exchange with the environment And now also inside the organism changes are constantly taking place Growth and maintenance of an organism takes place not only in the form of apposition of physical matter like in the case of crystals but also by means of intussusception of physical matter i e the insertion of physical matter made possible by the semi liquid condition of a large part of the body of organisms But even in the case of organisms crystallization processes do occur as is evident in shell bearing animals like many snails and also in Foraminiferans Radiolarians and Diatoms Remark Foraminiferans are unicellular marine animals generating a calcareous shell Radiolarians are also unicellular marine animals generating skeletons consisting of different mineral species dependent on the subgroup to which those organisms belong Diatoms are unicellular vegetable organisms living in fresh or salt water and generating shells of Silica Conclusion On the basis of the foregoing discussions we are now able to characterize the Totality the real being its Essence and its Determinations The Totality is the complete set of all types of determinations When we use classical terminology we have to state that a first Substance is identical to the complete set of all types of accidents But in Classical Metaphysics this statement would be denied Classical Metaphysics considers the first Substance as ontologically something else than the complete set of all the types of determinations accidents The accidents inhere in their Substance The Substance is the substrate of the accidents and is itself considered as an individual instance of the Essence of the thing still according to Classical Metaphysics and this Essence is contrasted with the accidents But Classical Metaphysics considers this Essence as an intrinsic cause of the thing i e the Essence causes the appearance of the thing how it looks like when we abstract from variable appearances NOTE 1 For example Classical Metaphysics considers the Essence of Socrates as follows An instance of humanity where humanity is the common Essence of all humans In the case of Socrates we have to do with a particular instance of this Essence When we were asked to describe this Essence called humanity then one comes up with a definition of MAN It goes like this Man is a rational animal Now Classical Metaphysics considers the Essence of a thing as a principle an intrinsic cause But rational animal is not a principle It is undoubtedly an effect of a principle So following the correct way to characterize the Essence AS Essence one should say that the Essence insofar as Essence of a thing is that intrinsic something that is responsible for the typical structure of the thing i e for how the thing looks like while abstracting from variable appearances and thus responible for how the thing is typically constituted In the case of Socrates one should say that the Essence of Socrates but also of Plato etc is that intrinsic something let us call it humanity that is responsible for the ability to think rationally and this implies a specially structured organic body as the machinery for this ability Expressed in the language of this Essay we can state that the Essence must lie in the genotypical domain and that all the determinations must lie in the phenotypical domain The latter is the domain of the produced generated appearances rational animal is something which is caused produced and so must lie in the phenotypical domain It then follows that rational animal is a determination and thus NOT an Essence Within the metaphysics presented on this website the Essence of a thing is the dynamical law governing the dynamical system that generated that thing And this dynamical law is indeed situated in the genotypical domain it is generative not generated it just inheres in the system elements in an implicit way and still more implicitly in the elements of the Totality and so not concretely visible When we consider one particular determination of the Totality then we can say that this determination accident in Classical Metaphysics inheres in the Totality That Totality which is the complete set of all types of determinations is accordingly the subject of that particular determination or maybe we can state that the complete set of all types of determinations MINUS that particular determination is the subject of that particular determination But see our exposition of the ontological status of the SUBJECT in Part One Now it is possible to assess metaphysically all aspects of the Totality its dynamical law and its determinations in a more or less final way using some terminology from Classical Metaphysics The Dynamical Law in its fully abstract form we could think of a mathematical formulation of it is the Substantial Form This Substantial Form is going to associate itself with matter and ultimately with physical matter as soon as we consider the dynamical law in its concrete but still general i e not individuated form because the concrete dynamical law is immanent in the physical matter namely in the system elements But in conceptually proceeding this way we do not yet include that aspect i e principle of physical matter which causes individuality See for individuality the Essay on The Principle of Individuation We start from matter as not yet definitely delimited How do we conceptually obtain such common matter in the first place We obtain it by means of a conceptual subtraction procedure the subtracted aspect will later be added back again What then remains of the matter i e of the physical matter namely after not considering and thus subtracting that aspect of matter that individuates is because of that no longer physical matter anymore but is the strictly formal aspect of physical matter a non individual matter the common matter Said differently it is in formed matter only and as such Form in a broader sense i e actualized matter Subsequent addition of the individuating aspect of matter renders it physical again Let us further summarize things in the following scheme partly borrowed from St Thomas Aquinas some terms were already considered earlier in this Essay Part One But firstly we will translate some classical Latin terms forma totius form of the whole i e it represents the whole essence forma partis form of the part i e it represents a part of the essence substantial form of material beings materia signata matter as designated materia non signata matter as not designated forma substantialis substantial form of material or immaterial beings materia prima prime matter matter as prime The Essence is the forma totius This forma totius consists of materia non signata forma partis forma substantialis The formal aspect of the dynamical law is as we just saw the forma partis The materia non signata indicates the immanence of the forma partis in physical matter The Essence forma totius is itself not but becomes singular particular individual by virtue of the materia signata i e it becomes individual when matter becomes designated matter The materia signata is prime matter under terminated dimensions and guarantees the here and now individual See again the Essay on The Principle of Individuation The Essence is the concrete dynamical law The forma totius together with the materia signata gives an individual matter form composite The forma partis together with the materia non signata materia signata gives that same matter form composite The forma totius is the non individuated Essence The Essence materia signata is the individual substance s str The Essence generates determinations of the Totality The individuation conditions must to be sure be satisfied but they do not contribute anything with respect to content in the process of that generation The Essence determinations materia signata gives the individual substance s l and thus the Totality It is an individual real being or in short the existing individuum Complete concretization of the dynamical law resulting in its actual operation demands i e implies the presence of an initial system state This initial state is not an addition to the dynamical law this happens only in the case of computer simulations of dynamical systems but contains the formal dynamical law and in a way IS the concrete and active dynamical law said differently that initial state is the concrete dynamical system Remark When the dynamical system is still in its natural initial state the dynamical law is generally not yet the Essence of one or another Totality and this remains the case as long as such a Totality is not yet generated by the dynamical system Ontologically more precisely formulated the initial state contains the dynamical law immanently and because of this the law is now concrete and individual but as such still only implicitly existing and thus although individual it is not an individual not an individuum The dynamical law is as has been emphasized many times inherent in the system elements These are the things which while interacting with each other embody the dynamical system and in so doing generate the Totality in the case of a Totality generating dynamical system The dynamical law itself is accordingly not generated by these elements these system elements must be distinguished from the elements of the generated Totality but IS already present in them Because the concrete dynamical law generates the Totality from an initial state still lacking the Totality it also generates the intrinsic determinations of that Totality These determinations thus are generated by WHAT the Totality essentially IS said differently they are generated by the Essence of the Totality By generating those determinations the dynamical law which is now the Essence of the generated Totality determines itself further and its concretization implies a space time position and only then it can in the form of a Totality that is of a true being exist in the Real World This we can also state in another way With the concretization and individuation of the dynamical law a Totality is generated This Totality is the phenotypical expression of that dynamical law and thus of that Totality s Essence which itself belongs to the genotypical domain or level of the Totality Phenotypical expression is identical with the generation of intrinsic determinations and with it with the generation of the Totality which interacts with the environment This Totality is as has been found out identical to the complete set of determinations Implicitly it contains the dynamical law and it rests on prime matter as its ultimate substrate But this ultimate substrate is only potentially existing It is the potency for receiving any content any form albeit via certain intermediate forms this is why processes always proceed along certain definite trajectories Remark When we speak about dynamical systems in relation to the Essence of a uniform thing we only have in mind Totality generating dynamical systems In addition to these certain dynamical systems do exist which do not generate any Totality They disorganize a patterned initial condition or do not organize any disorganized initial state These systems are not treated of here Remark The classical terms

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  • reductionism versus holism
    e substances first substances as defined in the Essay on Substance and Accident section Substance we will confine ourselves to the static continua As we have stated a continuum is an extensum that is intrinsically ONE First and foremost this is valid for geometrical continua But what about real things i e material uniform things like for instance crystals Are they also continua Although they are extensa they seem at first sight or may be better from one point of view not to be continua because they consist of actual parts A crystal for example consists of atoms ions or molecules arranged in a periodic array But in the Essay on Being and Essence we saw that a uniform thing is always generated by a dynamical system and that the one dynamical law governing that particular system can be interpreted as the Essence or Identity of the thing in question On the basis of this ONE dynamical law we can say that that thing is ONE thing not a collection of many things Of course a dynamical law for instance a particular crystallization law can produce more than one thing more than one crystal but that is only a repeated execution of the same law giving rise to several individual products So when such a thing being ONE thing nevertheless seems to consist of actual parts which seems especially clear in the case of organisms then we cannot interpret these parts as things What are they then what is their status As a hypothesis we could cautiously say that they are properties of that one thing Even when the parts in the thing seem to move we could speak of a variation exchanging of the distribution of those properties over the extended thing the first substance Holistic View and Reductionistic View So when we consider the parts of a thing as properties of one substance because of the one dynamical law then we consider that thing in a HOLISTIC fashion In this way the Whole is ontologically first the parts are ontologically second ontological means according to nature These parts do not exist by themselves but only by virtue of the thing of which they are properties A property as property cannot exist by virtue of itself but only by virtue of the substance A substance being itself an individual uniform thing can and does exist by virtue of itself A substance having different properties and especially properties representing its parts shows according to the location of these parts here viewed not as things but as properties a non uniform or a periodic distribution of such properties over the thing A thing so constituted can then be viewed as a heterogeneous continuum Such a view can perhaps be characterized as a view of the thing at a high structural level But when we consider the parts of the thing in question as actually existing things then we consider that thing in a REDUCTIONISTIC fashion Then those parts enjoy ontological priority

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  • The Universal
    ID exists as ONE identity in the Ideal World the domain of ideal immaterial beings and in its concrete appearance it exists as an individual material uniform thing i e a true being a Totality in the Real World the domain of real material beings or multiplied copied in more than one such uniform things beings Taken as such i e as a formal relation a mathematical structure which is equivalent to the particular dynamical law the Identity cannot exist in the Real World But if we consider the uniform NOTE 1 things Totalities themselves thus the things in their appearance as things NOTE 2 or stated more precisely when we consider the phenotypical expressions of their identities and place them in certain classes on the basis of phenotypical similarity NOTE 3 then we obtain terms which each for themselves refer to a collection of uniform things which are similar terms which are the result of a phenomenological classification This can also be applied to properties and to the things having those properties from the viewpoint of those properties The following example will clarify this The collection of all the individual soldiers living now but also who has lived in the past and who will live in the future is a class a type We place them in the class SOLDIER remember the universal soldier of Donovan because of certain similar properties By establishing the Universal in this case we don t use the term ARMY because an army is with respect to being a soldier only an accidental collection of soldiers established by political and national discriminations and decision making But of course the collection of all armies is a class and is signified by the universal term ARMY A term signifying a class a collection but not an accidental collection implies a one over many one term signifying many items We now can discriminate three cases of signification Each of these signification cases contains however as it seems two subcases a The term signifies some one content and as such it could perhaps signify a universal residing somewhere in the extra or intramental world b The term ultimately signifies a collection of discrete and concrete things In the examples to follow for convenience only two or three significata are mentioned in the case where the reference is not to a universal as such but to discrete concrete things These two or three significata are however not the only members of the collection of things to which the reference is made The reference is of course made to the whole relevant collection which should not be an accidental collection but a whole class that is a class in virtue of intrinsic reasons Let s now elaborate on the three distinguishable cases of signification by a term that is supposed to be related to a universal If such a term on the basis of similarity it is true refers to phenomenologically after all different uniform beings limiting ourselves to these say to crystals of different materials and moreover having different intrinsic shapes for example a Sulphur crystal and a common salt crystal then that which is signified by such a term the significatum cannot be ONE item i e the ONE term does not refer to ONE item The significatum is not ONE in number This means that the term does not refer to something i e to some one thing And this is equivalent to the assessment that such a universal to which that one term would refer does not exist independently of our thinking In this case only the term is universal This term could read CRYSTAL In a classical context such is for example the term HUMAN This term as a sign refers either to Socrates or to Plato or etc But considering a case if the uniform things a multitude thus referred to by ONE term would be phenomenologically identical i e looking exactly the same then it is still the case that ONE term refers to several i e more than one items for instance a NaCl Sodium Chloride common salt crystal and a KCl Potassium Chloride crystal Both can be colorless and both can have a cubic form yet they are essentially different having different identities because their chemical composition differs The term then refers in this case either to the NaCl crystal or to the KCl crystal Also in this case a real existence of a universal an existence independent of our thinking is out of the question because again the term does not refer to some one thing i e to something In this case the universal could be signified by the term CUBICALLY SHAPED CHLORIDE CRYSTAL but as such it is dependent on and residing in the intellect while as a sign referring to many concrete things But if ONE term T refers to several uniform things A B and C all having however precisely the same Identity let us call it ID thus governed by precisely the same dynamical law then T still refers to the Real World and thus the ONE term T still refers to more than one item namely A B and C and thus the term T signifying a universal in the Real World is still out of the question i e whatever T signifies it does not signify such a universal A B and C could for example be three crystals of the same sort the same crystal species say three crystal individuals of NaCl common salt not necessarily looking the same The term COMMON SALT CRYSTAL S then refers either to this crystal pointed to with the finger or to the other one or to etc The term COMMON SALT CRYSTAL S usually refers to all existing having existed and in the future existing common salt crystals but this also is a collection of beings things in this case crystals and thus a multitude of beings But if in this last case case 3

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  • Dynamical Systems and the Metaphysics of Substance and Accident
    system i e the system happened to start just with such a configuration and so is coming from outside the system or such a state is the result of a perturbation which took place at some point in time during the running of the system and so is also coming from outside the system a perturbation of a process state situated higher up in the sequence Thus by actions from outside a current process state itself also being a configuration of system elements can be changed resulting in a new i e other configuration of system elements which then functions as an initial state with respect to the further history of the process So a dynamical system implies a number of types meanings of outside the system A real i e historical or actual initial state is by definition not actually generated by the system It is as it were imposed In this sense it is a true initial condition initial state extrinsic with respect to the system and so also with respect to the Dynamical Law of the system If an initial state is not only not actually generated by the system but also not in any way producible by the system from whatever previous state and thus having the nature of a Garden of Eden State then such a state is even in a stronger degree extrinsic with respect to the Dynamical Law During the progress of the process it is possible that a certain process state is being changed by external factors i e being perturbed into another state And even when the latter happens not to be a Garden of Eden State of the system this injected state nevertheless also has a status of being imposed And in this case such a state also is extrinsic with respect to the system and thus also with respect to the Dynamical Law but it could because it is not a Garden of Eden State during another run of the system and thus starting from a different initial state be generated from one or another state of that run But if the new system state having originated from a perturbation turns out to be a Garden of Eden State of the system then such a state is in a stronger sense extrinsic for the system and for the Dynamical Law because such a state can never be generated by the system itself Stability of a Dynamical System The successive process stadia are when no perturbations coming from without have taken place as succession thus insofar as being a certain succession necessary The succession necessarily follows from the Dynamical Law But as element configuration every process stadium is per accidens with respect to the system because this configuration varies while the Dynamical Law remains constant It depends on the point in time when we happen to observe the system If the process leads to the formation of a relatively stable PATTERN and only such processes are being considered here then the above mentioned perturbations caused by the environment will be damped This is demonstrated by theoretical models and by observations of such processes occuring in reality The system attemps to maintain itself it reverts to its original course This can take place in two ways Before we explain these two ways something must first be said about the status of element With elements coming in from outside the system and therefore quasi elements I mean elements which are not imported by the dynamical system itself but which by accident end up within the active domain of the system If a Totality or more generally a pattern of a higher order than that of the system elements themselves is being generated within the active medium of the dynamical system then it is possible that the elements belonging to that active medium as well as possibly elements coming from without that active medium are going to participate in the formation of the Totality the unified pattern being generated by the dynamical system The insertion into that Totality in this last mentioned case elements coming in from without does not happen by virtue of the Dynamical Law of the relevant dynamical system but is a perturbation from without The present context is concerned with the effect of elements coming from without on the stability of the dynamical system Now we are ready to discuss the above mentioned two ways by which the system tries to maintain itself If the elements incoming from without we can call them quasi elements NOTE 1 which are going to participate in the formation of the Totality ARE OF THE SAME TYPE as those elements which already belong to the evolving Totality then the Dynamical Law which is in operation at that particular moment will not because of that be changed because it is inherent in the relevant properties of those elements Insertion of such new elements coming in from without in the evolving Totality can change the pattern of this Totality and that means that the Totality not only changes in that sense that it is a next stadium but moreover that it also has changed in an extrinsic way It turns out that there are systems whose course of the process and so the appearance of the sequence of the successive states is very sensitive to such changes in such a way that the mentioned change effects a totally different process course totally different from which it would have been had the change not taken place or had another change occurred instead in spite of the fact that the Dynamical Law has not changed Such dynamical systems are called chaotic The system then goes to another attractor that could result in the formation of another Totality But it could also be the case that the trajectory leading to such a Totality becomes very long or that no Totality is formed at all But in all these cases the Dynamical Law stays the same Dynamical Systems lacking

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  • Cellular Automata
    Law for a simple one dimensional CA Thus a CA with a cell grid consisting of one row of cells of which the cells can either be in state 0 or be in state 1 a so called 2 state CA or binary CA a CA with only Boolean variables and for which the update of every cell C is dependent on its own current state and the state of its immediate left neighbor L and the state of its immediate right neighbor R is given here Time t Time t 1 L C R Update of central cell C 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 In the left part of this table all possible 3 neighborhoods are given On the right side we see the Dynamical Law sensu stricto This rule table or look up table must be read as follows If the 3 neighborhood of the cell in question is 0 0 0 then the next state of this cell becomes 1 If the 3 neighborhood of the cell in question is 0 0 1 then the next state of this cell becomes 0 If the 3 neighborhood of the cell in question is 0 1 0 then the next state of this cell becomes 0 etc Then a next cell is examined in the same way and its update determined accordingly till all cells of the grid are thus examined an their update determined The new states which will be attributed to the cells are temporarily stored in the computer memory Only after the whole grid is examined all the new states will actually be attributed to the cells and then the system passes to a new system state The state transition rule the Dynamical Law sensu stricto in this example is 10001101 but it could also in an other example be say 0110100 or whatever configuration In the case of CA s of the type of the example given there is a total of 2 8 2 to the power of eight 256 possible state transition rules and thus 256 different CA s of this type But a large number of them are equivalent with respect to the dynamical behavior because of the occurrence of symmetries in CA s After such a simultaneous update we thus obtain a new cell pattern a pattern of cell states and then at the next time step the same state transition rule is applied again to this new pattern i e to each cell for its new update in other words the new system state cell pattern now serves as an initial condition and to this condition the rule will again be applied And the out of that resulting new system state is again the initial condition to which the rule will again be applied and this will be continued as long as one

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  • Random Boolean Networks
    17 and this means that the update of this cell C 1 thus its state at the next point in time t 1 is dependent on the state configuration of three cells The state of the cell itself C 1 at time t The state of cell C 3 at time t The state of cell C 17 at time t This is accordingly the wiring of the cell C 1 It is wired to itself C 1 to cell C 3 and to cell C 17 Every cell of the grid will be wired and this wiring may differ for different cells But for the moment we first dwell a little longer on the above determined wiring of cell C 1 A neighborhood consisting of three cells k 3 like the neighborhood of our cell C 1 namely C 1 C 3 C 17 can accordingly show 2 3 eight possible configurations of ON OFF cells C 1 C 3 C 17 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 State Transition Rule The Rule State Transition Rule in question for cell C 1 the boolean function to which the cell must conform with respect to its update describes the state 0 or 1 which the cell C 1 must acquire at time t 1 depending on the encountered configuration of its neighborhood at time t The Rule Boolean function could for instance read TIME t TIME t 1 C 1 C 3 C 17 C 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 The Rule right column for cell C 1 is thus 00000001 This means that if the neighborhood configuration of cell C 1 at time t turned out to be 000 then cell C 1 acquires the value 0 at the time t 1 If the neighborhood configuration turned out to be 001 then the value would also become 0 Et cetera So the Rule consists of eight if then expressions In our particular example of a Rule it is the case that cell C 1 at time t 1 only gets the value 1 if all members of its neighborhood have the value 1 at time t We accordingly have the case of an AND function known from Logic if C 1 AND C 3 AND C 17 are ON then at the next point in time t 1 the cell C 1 will also be ON In all other cases it must be OFF In an analogous way we can proceed with the setting up of the system with respect to cell C 2 To this cell we can for example assign a neighborhood with k 2 i e the neighborhood of cell C 2 consists of two cells We accordingly could wire it with say cell C 5 and cell C 7 or as one wishes with itself and say cell C 8 But suppose that we wire it with cell C 10 and cell C 3 The value of cell C 2 at time t 1 is accordingly dependent on the values of the cells C 3 and C 10 at time t 2 2 4 neighborhood configurations are in this case possible C 3 C 10 0 0 0 1 1 0 1 1 Suppose that we assign to cell C 2 the following Rule Boolean function State Transition Rule TIME t TIME t 1 C 3 C 10 C 2 0 0 0 0 1 1 1 0 1 1 1 1 So the Rule for cell C 2 is 0111 This is the OR function known from Logic The total of possible Boolean functions is much larger than the set we know from Logic The Rule just stated in fact means that IF at time t C 3 0 and C 10 0 applies then the value of cell C 2 becomes 0 at time t 1 But if one of the cells C 3 and C 10 or both have the value 1 at time t then the value of cell C 2 becomes 1 at time t 1 Stated in terms of the OR function the rule reads If and only if C 3 OR C 10 is 1 then C 2 becomes 1 In an analogous fashion we can assign a neighborhood wiring and a Rule to every cell of the system thus to the remaining cells C 3 C 4 C 5 C 18 and C 19 whereby the size of the neighborhood and the position of the cells of the neighborhood and the Rule may differ from cell to cell In this way we have set up a NETWORK a dynamical network When we start to run such a network Boolean Network with one or another chosen initial system state i e one or another configuration of 19 ON OFF cells then the system will update all its cells NOTE 2 When this is done and we find ourselves now at time t 1 the process will be repeated and applied to the result i e the result now serves as initial system state producing a new result to which the process is again applied etc etc and as such it is a typical example of a recursive dynamical system When we simulate this on a computer because to do this manually is inconvenient if not impossible we get a succession of system states element configurations which can be displayed on the computer screen But because the neighborhoods and thus the dependency relations are non local meaning that the neighborhood of a cell will not necessarily consist of its immediate spatial neighbors like by the way the non locality in many biological systems we will generally not encounter any system state having a

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  • L-systems
    once Suppose that we have BAB and apply the rule set to it We first apply Rule 1 resulting in B B B Next we must in order to complete the process step apply Rule 2 Rule 2 says that B must be replaced by AB if B is present Accordingly we must apply Rule 2 to the first and third B but not to the second B So the result will be ABBAB and not ABABAB The next process step will proceed along the same lines Each process step consists as has been said of the application first of Rule 1 then of Rule 2 Now we have sufficient knowledge about how to use the rules When we are going to run this Fibonacci L system i e the mentioned prescription algorithm or grammar we will obtain the following process states A axioma B rule 1 A B rule 2 B A B rule 1 rule 2 A B B A B rule 1 rule 2 B A B A B B A B rule 1 rule 2 A B B A B B A B A B B A B etc B A B A B B A B A B B A B B A B A B B A B etc After having applied the set of rules seven times we now have obtained the Product string which reads B A B A B B A B A B B A B B A B A B B A B We can prolong this process as long as we wish to by continually applying the rule set to the preceding result When we now count the number of symbols in each string of the above series of results then we have the famous Fibonacci sequence 1 1 2 3 5 8 13 21 etc This number series starts with two ONES and then each next number is found by addition of the two preceding numbers This number series plays an important role in the morphology of many plants Shrimp In the following I show an example of a much more complex L system that generates a long Product string This string will then be interpreted as a drawing command and the subsequent drawing is given The system is run within a program called L system Parser Mutator available on the Internet Let s see how things unfold L System Parser Mutator v4 0 Copyright C RenderStar Technology BV 1992 1995 Release date Dec 27 1995 386 DOS Sizing memory L system file lsys00n ls Recursion depth 12 This means that the set of rules is applied 12 times consecutively to the last previous generated result Basic angle 10 Thickness 100 Axiom c H AP CD 1 6 U Rule U F 5 U Rule A 1 4 F F 0 6 F 1 7 Rule D 5 F 5 0 1 DGI Rule I ccc Tcc F Occ F Rule G Z 0 9 Z 0 8 Z 0 7 Z 0 7 Z 0 7 Z 0 5 Z Rule P FQ Rule Q cc MN cc MN Rule M F 0 95 M Rule N L L Rule C F R E 5 C Rule E cZ E Rule R cc BL cc BL Rule B F B Rule L cc z z z z z z Rule H S S H Rule S Z S Rule T Z T Rule O Z O Size of string 4068 chars Production product string c Z Z Z Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z Z S Z Z Z Z Z Z Z S Z Z Z Z Z Z Z S Z Z Z Z Z Z S Z Z Z Z Z Z S Z Z Z Z Z S Z Z Z Z Z S Z Z Z Z S Z Z Z Z S Z Z Z S Z Z Z S Z Z S Z Z S Z S Z S S S H 1 4 F F 0 6 F 1 7 F cc F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 M cc z z z z z z cc z z z z z z cc F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 F 0 95 M cc z z z z z z cc z z z z z z F cc F F F F F F F F F F B cc z z z z z z cc F F F F F F F F F F B cc z z z z z z cZ cZ cZ cZ cZ cZ cZ cZ cZ cZ cZ E 5 F cc F F F F F F F F F B cc z z z z z z cc F F F F F F F F F B cc z z z z z z cZ cZ cZ cZ cZ cZ cZ cZ cZ cZ E 5 F cc F F F F F F F F B cc z z z z z z cc F F F F F F F F B cc z z z z z z cZ cZ cZ cZ cZ cZ cZ cZ cZ E 5 F cc F F F

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  • The Mixtum and its Elements
    like the new properties are properties of the mixtum They are identical with the corresponding properties of the elements because there exists a genetic kinship or affinity between the elements on the one hand and the mixtum on the other In this way the elements exist only virtually in the mixtum When the mixtum decomposes those elements become actual again as they were before they were taken up into the mixture before they became elements If we do not interpret the unity in this way then we must allow that the elements do exist actually in the mixtum In that case the elements are things But then there is no unity anymore because now the mixtum IS many things and so is an aggregate Of course all kinds of elements are often clearly visible in a mixtum as its parts and thus as things In such cases we must interpret the status of those elements parts as still existing virtually it is true but very close to actuality little is needed to make them actual We can summarize those ideas which partly go back to P HOENEN 1947 Philosophie der Anorganische Natuur written in Dutch by stating that a mixtum is one in Substance and many in its accidents properties and such a mixtum is a heterogeneous continuum This heterogenity this many in its accidents can include a per accidens heterogenity as well as a per se heterogenity i e specific heterogenity A per accidens heterogenity is caused by external factors and belongs only to the individual in question The per se heterogenity is caused by the retention of some properties of some or all elements or by the newly generated properties of the mixtum This theory could be correct but is not free from all kinds of difficulties To evade it one could suppose or conclude from its difficulties that all the mixta mentioned in the list above with the probable exception of atoms are like the first item in that list NOT strict unities The unity of mixta must then be interpreted as being gradual and never absolute meaning that absolute unities do not exist among those mixta But then they are not distinguishing themselves from aggregates mixtures anymore and obviously they do For example there IS a difference between a mixture of Sulfur and Iron on the one hand and the chemical compound Sulferic Iron FeS on the other This compound emerges when the mixture of Sulfur and Iron is heated Another difference is that chemical compounds show definite proportions of the constituents On the molecular level Sulfuric Iron is always composed of one Sulfur atom and one Iron atom Another proportion either is not possible at all or results in another compound with other properties Aggregates mixtures generally are not constrained by proportions so for example the well known mixture air Also individual organisms do not seem to be just aggregates of chemicals but seem to be unities with STRONGLY INTEGRATED parts So it seems worthwile to investigate the above mentioned interpretation which says that the parts are not a distribution of things in and over the mixtum but a distribution of properties of the mixtum in and over the mixtum With all this in mind we shall first examine chemical compounds and crystals and later on in another Essay the organisms The Molecules of Chemical Compounds as Mixta The atoms in a molecule are bonded to each other They are bonded in an intense fashion as we can learn from the Theory of Orbitals We will give a succinct exposition of this Theory in the Essay on The Chemical Bond The intensity of the chemical bond clearly shows that a molecule is a unified mixtum not an aggregate and persuades us to interpret it as a real Totality a unified being with a specific Identity or Essence If this is correct then the elements of the molecule only virtually exist in the molecule or with other words the atoms are virtual not actual This virtuality is a special kind of potentiality it means not a potentiality for becoming anything whatsoever but a near potency to some specific being in our case a near potency to an atom of a determined species Only as a remote potency that which possesses it is in potency to anything So we can discriminate between a direct near potency and sucessively more remote potencies This is just an expression of the fact that every generation every production process of i e towards something can only proceed along certain lines i e only via intermediates So generally the process reaches this something only through some intermediate products stadia Further elaboration of the general theory concerning the status of elements in a composed being with an application for molecules and crystals When a Composed Being a being resulting from other beings that are going to compose this being appears comes into existence from whatever process a composing process then we must say that its properties originate from the lower level This lower level bottom comprises the things which are coming together while situated in a certain environment So all composing processes are bottom up This must be the case because where else does the composed thing come from WHEN the properties of the composed thing are The same as the properties of the components when they were still freely existing or and Are just summations addition results of the properties of the components when they were still free or and Are just the result of the many ness of the components while they do not and cannot have any meaning for each component in itself THEN such a composed thing will be just an aggregate In this case it is not a unity not a new substance The coming together of the initially free components is not a specific process It does not demand specific proportions of the components The coming together is in this case a process dictated by general attraction

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