Death and Rebirth of Philosophy. II.

II.Flaws of Laws.

First a few more words about the correspondences describing the change of states in the universe. A correspondence f between sets X and Y is associating to a subset A of X a subset f(A) of Y . We consider the power-set P(X) of X to be the set of subsets of X,then a correspondence f as before may be seen as a map F from P(X) to P(Y). In the model of the universe we proposed in part I, the transition of a state U(t) to U(t’) for t<t’is given by a correspondence so by a map F(t,t’)of P(S(t)) to P(S(t’)). For t<t’<t’’ we demand that: F(t’,t’’)F(t’,t’)=F(t,t”). An existing object O being given by a string of potentials O(t) in S(t),for t in an existence interval for O,with F(t,t’)O(t)=O(t’) thus means that O(t’) has a history in U(t) but not every element of O(t’) has a history in U(t),thus there may be extra new created elements in O(t’). You may wonder why we use correspondences on the sets of pre-things at moments? Well suppose we look at an atom, originally the idea was that an atom was a minimal particle but now we know that these objects contain many smaller sub-objects like electrons,nucleus,protons,…,all the nice subatomic particles and also most of these interact between themselves.So in order to describe an atom, as a string of pre-things we ave to involve the pre-things leading to existing sub-objects and involving both pre-objects and pre-interactions of those internally in the whole potential and even the pre-interactions of sub-pre-things and exterior pre-things. Hence we are forced not to look at maps from S(t) to S(t’) for t<t’ but to correspondences and the potentials containing pre-objects and the one can include also all pre-interactions involving the set of pre-things in the potential with things in or out the potential.It is possible that leaving some elements out does not change the realization of the existing object but for uniformity of our approach it is harmless to assume that starting from the set of pre-objects in a potential O(t)we automatically add all pre-interactions of these with elements of S(t), and call that the “complete potential” for O at t.The definition of existing in terms of time intervals has some far reaching consequences. Let us look for example at the case where T is the set of real numbers with the usual ordering (can be generalized without problem to any finite dimensional vector-space over the real numbers).If we O as realized in the interval (t,t(1)) and view O(t’) as before for some t<t’ and t’ in some existence interval then the potential O(t’) is assumed to be realized in the existence interval (t’,t(1)), That is plausible since the potential O(t) already has been changing under the state transitions between t and t’ and will continu just like the potential O(t’) starting at moment t’(one can also view a more general assumption but we do not go there here).The existence of an object is thus step-wise in a chain of time intervals where the endpoint of one is the begin-point of the next,now since any non-moment interval in the real numbers contains at least one rational number (the real numbers are the completion of the rational numbers at the order topology and so the rationals are a dense set of the real numbers!),one can take the least rational number in each time interval and so define an injective map (so an embedding) from the chain of intervals to the rational numbers which are a countable set (where the real numbers are not a countable set!),consequently if one wants to view the existence intervals as generalized moments then these generalized moments may be counted by the natural numbers. Hence we are almost back at the philosophy of the old Greek scientists,every existing thing is measured by rational numbers. The same arguments can be made by intervals of Planck time length for observed objects.This makes some infinite-handling easier but since even the strongest quantum computer will never be able to write down every natural number the complexity is not necessarily lower now.But there is one important conclusion, in the mathematical description with continuous (differentiable) functions and analytical equations one does use limit arguments,for example letting time go to zero when studying the Big Bang, but in reality with countable existence intervals (generalized moments) there is no limit taking possible,the situation is topologically discrete! Continuous evolution of existing objects in time is then also an empty notion. When we aim to describe existing reality by laws of nature phrased in the mathematical (physical) model using equations and all kinds of differential geometry and analysis, then this cannot work ,unless as a coarse approximation and where limits are being considered it may lead to contradictions! Of course ,if you introduce more general totally ordered time sets the reduction to countable existence intervals does not hold and so there may be more difficult infinities to deal with! In the power set P(X) we always consider the empty subset,so for potentials in S(t) we always consider the empty set as an element of the set of pre-objects of the potential. It is logical to assume that the empty set of pre-objects is not appearing in any pre-interaction and thus the empty pre-object does not influence the transition correspondences and the F(t,t’) takes the empty set to only the empty set. So,if we have a potential from S(t’) with a history in S(t),then the history is not empty. So our basic assumptions (transitions being determined by non-trivial pre-interactions) lead to the conclusion that something cannot come from nothing via the transition correspondences describing the change of states in the universe! Where do pre-things at moment t without history come from, I will talk about our own creative input in the universe in a next section ,but the popping up of new pre-interactions or pre-objects was happening since forever as a continuing creation. Here are obvious links to possible religious theories and beliefs which we may address in the remarks about the rebirth of philosophy. In conclusion for the first flaws of laws we retain that in the reality existing is a matter of countable intervals, for example between two existing periods (generalized moments)there is not necessarily another one different from both ,so the usual mathematical techniques applied to the model do not have correct meaning in “existing reality”!

I repeat, this also follows from Planck units for the observable reality!

Next we shall investigate how causality changes in the new model and that will lead to the breaking of the laws of cause and consequence as we know it.

The set of pre-things in a potential is not arbitrary since it has to evolve into an existing thing and there are coherence conditions on an existing object,these are observed in our abstract world but assumed to have a reality behind them contained in the structure and composition of the object. An existing object is unique,even if there are many iron atoms each one is unique and so it has an identity , a unique position in space and time and we singled it out by observing exactly that one in some time interval of existence.The process of existing in a time interval is not observed but the result is in “generalized moments” which are there because of our bad(too slow)observation method. Existing is like an organism, it consists of evolving pre-things with coherence conditions dealing with forces and energies,the transitions in time induce a creative aspect by the appearing of pre-things without history in substructures with history, the interior activities adapt to exterior interactions which contribute to the process. When we look at society as the organic society of members with all the links between them and substructures (mimicking organs) and clusters (mimicking subsystems like the nervous or lymphatic or the metabolic system) it has the structure of a pseudo-organism with some partial version of awareness in some new definition but also with a moral.An existing object,probably with its complex structure of composing substructures and interactions between these as well as interactions with the outside world, with its unique identity ,with its elements with and also some without history in the existence process, also has the properties of what I called a pseudo-organism, thus the conditions which enable the coherence to be sustained over longer periods combined with the rules of behavior in the sense of the applied physical rules (but that is in our interpretation!) make up an “existing object”-moral of the pseudo organism.I am not tempted to go further and associate a form of awareness to pseudo-organisms (unless it consists of aware members like human society)and in particular to each existing object.In the end the weakening of definitions does not solve any problem it just promotes keeping to the earlier (now wrong) abstract structures in our mind,applied to more general but essentially different situations. for example to say that every existing object is conscientious immediately makes one think it is having some “thoughts”. The process of existing is defined via the connecting of states by correspondences thus by the history of the potentials in a string. Viewing time as a totally ordering of states does allow to distinguish past,future and the moments,where the past and the future are processes before or resp. after the moment, and they may be thought of as existing in the universe (out of time),whereas the moment does not exist . When thinking “out of time” so in the finished universe( as a book which IS but you are not reading it),the moments are the page numbers of the states, they are not part of the content of the book but they do define its structure because pages cannot be shifted (no time travelling!). Now our human cognitive interpretation of the observations of reality noticed the changes and thus the history of some,events is a natural idea for us,the future is not!In our observations we then discover cause and consequence based upon the history of an event. Now in our potential-model the history of any existing thing is described by the string of potentials,so the causes of some so-called present event, where present is now a time interval, are in the pre-interactions in the potentials and the exterior interactions on it. Those pre-interactions can be by non-existing potentials and also from existing inner sub-objects or other objects outside, the uncontrollable aspects stemming from pre-interactions without history appearing in the potentials at some moment in the past. In fact,some pre-existing cause for example outside the potential going to realize itself may realize its existence after the realization of the caused effect. Indeed whereas for objects interacting it is logical that the interacting objects are realized before the interaction between them but for effects of interactions that needs not be, an effect of an interaction is the result of an inner pre-reaction created by some outside pre-interaction,thus of new interaction created by an interaction, like the contamination by a virus creates the immune reaction and the disease symptoms.But if the potential for some kind of virus could already infect something in the stadium of a pre-virus at some level of pre-existence in its process,the effect could be observed before the object causing it can be observed.There may be potentials which never realize their existence but which pre-interact with pre-objects so that that object and the effect of the pre-interactions realize, those potentials will be never observable “interactors”.At the micro-level and dealing with ultra-short tome intervals ,like say in Quantum Theory,it may happen regularly that cause is observed after consequence. As a second reason for failure of causality one can understand that all pre-interactions of some pre-object with all other pre-objects in some state at moment t have to be considered in defining the history of the evolving of some event. However small one might think the effect of such pre-interactions will be for pre-object light years away,the fact that there will be perhaps 10 to the exponent 73 such pre-interactions may actually define a measurable effect on the realizations.In our Physics one rarely would consider hundreds of interactions to “define” the cause. Finally when seeing the effect first then beginning to look for the cause is doomed to be the wrong strategy because after the effect is observed we are trillions of states away from the state where the causal pre-interactions started and we can never “look back” in a past state,not in any state even because a search is in time intervals(!) long after the event. There is a notion of organic causality one can define in reality but we can never observe it, so organic causality may theoretically solve some problems but it will be an abstract solution,say fitting in philosophy not in Physics. Next let us look about the failure of probability and pure coincidence.To be continued.

Born in 1947 .Real name: Fred Van Oystaeyen.Active in Math research, author of many papers and books . Hobby :Blues and plants.