Essay Abstract

Starting with a non-anthropomorphic definition of intelligence, this essay leads to the conclusion that the critical property driving the universe away from chaos is the tendency for particles to connect to each other, forming associations with new properties and as big as possible. The intrinsic relationship with processes of intelligence, both inorganic and organic, is explained. Considering a model for Earth's past temperature that fits isotope and biological data, it is shown that such a tendency and the consequent processes of intelligence led to the formation of molecules like DNA and to a much better understanding of life evolution. Given that thermodynamics concerns only systems with non-connecting particles, a theory on systems with connecting particles seems to be of utmost importance to explain the evolution of systems, from the inorganic ones to human societies.

Author Bio

I was very young when I started my quest to understand the universe; later, as a teenager, I concluded that I had to focus on foundational questions. This is a life-long project, and requires a specific methodology. By weighty reasons, I decided to choose Engineering as my profession, instead of Physics, and to do my research autonomously.The draft papers I published in arXiv and viXra deserved several complimentary emails, mainly from mathematicians. I have also been invited to present a contribution for a book by the main Portuguese science publisher.

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Indeed we are short of a theoretical framework to empower the analysis of systems of complex interconnected particles/components. ThermoDynamics is good for star's interior and kinetic collisions but is not adequate for the real complex world.

    I think that such a theory on the properties of systems with connecting particles is one of the two theories required to model the evolution of the universe in all its aspects - life included. They represent a new frontier.

    Dear Alfredo Oliveira,

    Thank you for your gracious remarks. You note that our essays complement each other, and I agree that each overlaps in ways that expand the topic. You discern 'intelligence' in the universe, and begin by clarifying the concept of intelligence. Whereas I define intelligence as consciousness plus logic, you exclude consciousness and define intelligence as "the ability to solve a new problem".

    First you do assume 'mind' and note that the easiest way to find a solution is 'table lookup': you already possess the answer - find it. The problem arises when no previous solution exists; the problem is new. You then formalize 'wandering to a goal' in terms of 'generating hypotheses' and 'selection processes'. The intelligence involved in solving new problems then consists of generating hypotheses (potential solutions) and applying a selection process (does it solve the problem?) Generators of hypotheses can be random or algorithmic. "Physical" intelligence favors random variation or mutation, while "physical" selection is Darwinian survival. Thus at the basic level of matter you defined "intelligence" and demonstrate its presence. Interestingly you do not claim that this leads to consciousness, merely that it exhibits intelligence as an inherent aspect of the universe.

    Of course a very large part of your solution is keyed to the fact that as the systems of particles grow larger and acquire more degrees of freedom, they expand the repertoire of potential 'hypotheses', while at the same time acquiring a greater susceptibility to temperature. You weave these threads together exceedingly well.

    My definition of intelligence related more to mental aspects as indicated by the definition: consciousness plus logic. The consciousness represents awareness of the problem. The logic enables algorithmic constructions, counting, and comparison. The consciousness must be aware of the 'match' of solution to problem. And the awareness of 'match' of solution to problem in mental space is analogous to 'survival' as solution to the problem in physical space.

    So I agree with you that our essays complement each other in a significant way. I enjoyed the many details in your essay, linked to the concept of expanding space [I didn't realize the moon had been shown to have an expanding orbit. I guess those laser reflectors we left there have paid off.] In other words I enjoyed your entire essay, but I most enjoyed your working definition of intelligence without invoking consciousness.

    My very best regards,

    Edwin Eugene Klingman

    Dear Alfredo Gouveia Oliveira,

    Please excuse me for I have no intention of disparaging in any way any part of your essay.

    I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

    Only nature could produce a reality so simple, a single cell amoeba could deal with it.

    The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

    A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

    Joe Fisher, Realist

    Dear Edwin Klingman

    You perfectly summarized the essential points of my analysis with that clarity that seems to be a distinctive characteristic of your work.

    I excluded consciousness from the quest because I concluded that trying to explain consciousness from basic matter properties is like trying to explain the entanglement of particles from those properties. Furthermore, during my life I had a set of experiences that in no way I can explain by known matter properties or by coincidences; as I am an empiricist, I cannot deny them, and I had to conclude that the universe is a much more mysterious place than we can imagine and that consciousness is just one manifestation of that unknown side of the universe. But I understand also your approach to the problem, the best one I know if we exclude the possibility of it being consequence of unknown properties. We are just beginning to discover the universe, there is a long way ahead.

    Yes, the reflectors on the Moon are of the utmost importance!!! On allowing measurements with enough accuracy to detect the evolution of the universe, they are a kind of "time microscope" and open a new frontier, as did the optical microscope or the telescope. Science and Technology are interdependent.

    I want to say that I have the greatest respect and admiration for the work done by scientists. As I see it, the quest for understanding the universe starts with a basic model, a set of properties, i.e., a paradigm; on it we base the research, obtain new data, organize it in theories; then, when data is enough, we have to go the other way: to obtain from that data a new hypothesis on fundamental properties, i.e., a new paradigm. So, the discovery process, in whatever field, is a repetitive two way process, paradigm to data (P-D) and data to new paradigm (D-P). All theories are only steps in the process, none is "right" or "wrong". A common mistake in police investigation is, after hypothesizing that someone is guilty, to neglect contrary evidences due to the lack of preparation to do the "data to paradigm" process. A process for which we are not naturally suited (i.e., not at the reach of our mental "search-engine"; one has to use the "idea-engine" and that is not easy). You know, Sherlock Holmes used drugs to find the solution of the crime, by the process you describe in your essay; many creative persons are skilled in generating "good ideas" and Connan Doyle was one of them.

    Current scientific system is exceedingly good on the P-D process, but while the importance of the "data to paradigm" process is not understood, Physics will keep dependent on "geniuses". Some physicists say that geniuses only anticipate what "normal" science would discover, but that is just a convenient illusion. In my essay I mention also something about the D-P process.

    Sincerely yours

    Alfredo G Oliveira

    Dear Joe Fisher

    You start with a finding: all our eyes see from the outside world is surface. Ok. Then I was expecting that you developed the reasoning, go beyond what eyes can see. But I did not find that. The universe is not just what we see, or touch, or ear or taste or smell. Our senses gave us an initial information and our aim is to find what is behind that. That is what allows us to predict how systems evolve; and when we predict it correctly, we assume that to a certain extent we have approached the reality.

    Therefore, here you present your starting point; now I would like to see the continuation.

    Best regards

    Alfredo Oliveira

    Nice essay Oliveira,

    Your ideas and thinking are excellent for eg.,

    Therefore, there is a huge capacity in nature for generating associations of particles with new properties. And we can go beyond molecules and think that even a human society is an association of particles potentially able to continuously acquire new properties.

    Thus, the universe is a giant H generator! However, in order to have an intelligence process, an S process is also needed. As far as I can understand, what is selected in physical systems is what lasts longer under environmental conditions. This is expectable, of course. Therefore, Selection in physical systems is "natural ...

    .............................. At this point I want you to ask you to please have a look at my essay, where ...............reproduction of Galaxies in the Universe is described. Dynamic Universe Model is another mathematical model for Universe. Its mathematics show that the movement of masses will be having a purpose or goal, Different Galaxies will be born and die (quench) etc...just have a look at my essay... "Distances, Locations, Ages and Reproduction of Galaxies in our Dynamic Universe" where UGF (Universal Gravitational force) acting on each and every mass, will create a direction and purpose of movement.....

    I think intension and intelligence are inherited from Universe itself to all Biological systems

    For your information Dynamic Universe model is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other.

    Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

    With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

    Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

    Have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

    http://vaksdynamicuniversemodel.blogspot.in/

    Best wishes to your essay.

    For your blessings please................

    =snp. gupta

    Hi Oliveira

    I like the definition you have proposed for intelligence, "the ability to solve a new problem". It is somewhat similar to the definition of Legg and Hutter (2007) which is presented in Mohapatra's essay (Informational Unification) submitted on this forum, "Intelligence measures an agent's ability to achieve goals in a wide range of environments".

    The objective measure I have arrived at for separating intelligent systems is rather different. I have constructed a model for extrinsic intelligence (Constitutional nation state) and use that to arrive at the objective measure. The measure proposes to check whether the system has a capacity to 'nurture' the root elements of the system. I could be wrong on this, but I think this measure is generic enough that it just might be applicable across multiple types of intelligent systems.

    It is also interesting that you speak of 'quantification' of intelligence. My model offers that as well if you look at the first para in the last page. However, I did not develop the concept further as the essay's guidelines wanted only an objective measure for separating systems that were intelligent.

    Warm Regards, Willy

    9 days later

    Dear Alfredo,

    I like your essay for its attempt to formulate and answer some big questions. Although I do not consider your answers convincing, they are interesting, and this is already important. Below I am sharing with you some ideas which came to my mind while reading your essay.

    1.

    "...just one function that we can ascribe to Intelligence: the ability to solve a new problem, i.e., one with no solution stored in the database of the mind or obtainable from a source accessible to the mind. "

    It looks as a circular logic to me, since not only "mind" and "problem", but "database" already imply "intelligence".

    2.

    "A Hypotheses Generation (the random paths) and a Selection procedure (the paths that do not lead out of the maze are rejected). "

    This reminds me similar schemes of Poincare and Compton, see e.g. http://www.informationphilosopher.com/freedom/two-stage_models.html

    3.

    "Is nature able to generate by itself something with new properties? The answer is yes, of course."

    This I do not understand. How can you know that with certainty? If you said that you believe in that, I would understand; however, if you wanted to claim it obvious, I would disagree.

    4.

    "From the above it seems that the key for the apparent intelligence of the universe is the tendency of particles to form ever larger stable associations, each of them with specific properties. "

    The problem is that these long molecules are not just long, but they are specially ordered, and the order is important. They are like long meaningful texts, not just like long arbitrary sequence of letters.

    Well, I think, I would rather stop here, with a hope that my remarks sound not quite unreasonable for you and at least a bit helpful. As I already said, I appreciate your efforts to truth and your feeling of mystery, so I give your essay rather high score.

    All the best,

    Alexey Burov.

      Dear Alexei

      Thank you very much for your comments and your vote. Your doubts are certainly the ones of others and your comments give me the possibility of clarifying important aspects. A Portuguese writer said "Do not affirm the error of a truth before changing its context. Unless it gives you joy to be stoned." Unhappily, the short size of this essay has limited my capacity of changing current context. So, allow me to try to do it now.

      The classic definition of Intelligence is just a useless description of human mind, grounded in the belief of our exclusive nature.

      Do you think your computer is "Intelligent"? I think your answer is "no". But why? A personal computer has memory, it can play music, make calculations, answer questions by finding the answers in the net - some can even talk with you. So why is not the computer "Intelligent"? The reason is that it cannot answer a question like: What killed the dinosaurs? (it can present current hypotheses, but that is not the answer, just hypotheses); or "does dark energy really exist or is just an ad hoc parameter?"; or "how to do a non-polluting and inexpensive car"?; or "how life was created?"; etc. That is the capacity computers do not have (yet).

      Now, lets see your questions

      About my definition of Intelligence you say:

      1 - It looks as a circular logic to me, since not only "mind" and "problem", but "database" already imply "intelligence".

      From the above I think that now you understand that what you say is wrong. Database is the content of memory; your computer has databases, a book can have databases. Intelligence uses them but they are not Intelligence, in the same that you use the computer but the computer is not you. And also a problem is not Intelligence, of course.

      2- about your mention of Poincare, of course that Poincare has influenced me. As it happened with Einstein, by the way. I read it more than 30 years ago. It is not only with Poincaré or Compton that you can find resemblances - also with Darwin, as I detailed explain. In this case, it is Darwin that has inspired me the most.

      3 - ""Is nature able to generate by itself something with new properties? The answer is yes, of course."

      This I do not understand. How can you know that with certainty? If you said that you believe in that, I would understand; however, if you wanted to claim it obvious, I would disagree. "

      I explain: take an electron and a proton; they immediately converge and form a Hydrogen atom. This atom is something new with new properties, is not so? And these atoms then can merge and form other atoms, with new properties. Therefore, the answer to the question is obviously yes, of course. I explained in the essay why I say that.

      4 - "The problem is that these long molecules are not just long, but they are specially ordered, and the order is important. They are like long meaningful texts, not just like long arbitrary sequence of letters."

      Again you are not correct and in two ways. One is that I don't claim to explain the creation of life, just the appearance of the long organic molecules it requires - molecules of the kind of DNA and with the capacity of auto-replication. The other is that the order is not so important as you seem to think because there are (or were) many thousands of different types of bacteria, presenting a huge diversity of DNA, and these are just the survivors of a still much larger set of previous cells. Now you have to consider the huge number of those large molecules that were produced in the described Earth early environment during near one gigayear - it's an astronomical number, making the possibility of obtaining specific sequences a reasonable value.

      When we see something different of what we are used to think, the first reaction is to consider that the author is wrong; the possibility that he/her is correct is so low that we do not consider that possibility. But it can happen.

      Once again, I thank you very much for your comments. I hope that I was able to clarify your questions, which are consequence of the short size of a text that had to analyze such a complex subject.

      I hope to ear from you again, this is a fruitful discussion.

      Alfredo Gouveia de Oliveira

      Hi Alfredo,

      On my first reading of your essay, I passed it by, because I could not figure out what it was about. On my second pass ( a few weeks latter), I find it quite good. Here is what I agree with:

      A purely material explanation was here presented for the appearance of molecules like DNA. However, when we consider more complex systems, namely life, we can no longer explain the illusion of a goal by simple mathematics.

      Your essay is excellent, I think the abstract confused me. Question for you: Do you think "global warming" is just a minor glitch in the scheme of things? Please answer on my blog and while there take a look at my essay.

      Thanks for your essay,

      Don Limuti

        Dear Don Limuti

        Thanks for your comment and king words about my essay!

        In this adventure for understanding the universe, there are steps we can aim to do, and others that we are still too ignorant to even try. In my essay I describe some important steps - for instance, concerning life, for the first time it is presented an explanation for the formation of molecules of the kind of the DNA with no obvious drawbacks; and also an explanation for how life evolved from the link between climate and proteins. This link is so strong that one can predict the main occurrences in life evolution. In the viXra paper that I mention, there are much more about it.

        These, however, are just simple aspects of life. A cell is something of utmost complexity. I think that the amount of information required to build one of our cells is much more than the one required to build a human from the cell. And I do not even know whether life is just the result of the properties of matter - nor me, nor anyone, although some seem sure that it is not, and others that it is.

        I will answer your question in my comment to your essay, as asked.

        Thanks again for your kind attention to my essay.

        All the best

        Alfredo Gouveia Oliveira

        Dear Alfredo,

        Thanks for your reply...much appreciated.

        I was very interested in your graph showing the earth's temperature on a monotonic decline since the beginning. And there was speculation in at least one of the essays in this contest that the world will end in ice.

        Since this is such a "hot" topic these days I wanted to get your thoughts on the question: Is our concern about global warming just a temporary condition, and the cooling will start again?

        This was not part of the contest...just curious.

        Thanks,

        Don Limuti

        Dear Alfredo,

        I did get your comment on global warming! And yes please send me more info.

        Also, thanks for visiting my website...and your favorable remarks.

        My email can be found on my site www.digitalwavetheory.com in the about the author section. It is don.limuti@gmail.com

        Thanks,

        Don Limuti

        In the above post I misquoted Lev and Alexy Burov. They did not say

        "Physics does not make the assumption that the laws are simple."

        Instead they said:

        "Physics does make the assumption that the laws are simple."

        I apologize to Lev for misquoting him. It does not change the sense of the above post, but it means that Lev and Alexy agree more closely than I implied. In other words, they are in agreement with my final "proof".

        And this does not change anything about the masterful quotes attributed to Alfredo.

        Edwin Eugene Klingman

        Alfredo,

        A very good essay, well written with a good proposition, logical argument, and even a few dinosaurs! (which beats my tiger!). I agree most all, indeed employ similar concepts in a different way, with different scale 'layers' of your; "ever larger stable associations, each of them with specific properties".

        I also agree and think it well expressed that; " we can solve a problem if we have a generator of hypotheses able to generate the solution and a selection procedure independent of the generator of hypotheses." Which I see as equivalent to the 'feedback loops' I discuss.

        I even like your title, as I find 'decoding' the noise in an information channel allows us to derive intelligence (I discussed with the IQbit in the 'It from Bit' essay) I also now identify a classic QM solution so if you do get to read mine don't try to rush through it!

        One question; Do you see gravity as the fundamental force promoting the ever larger connections between entities?

        If you disagree with my suggested analysis it seems we have a number of parallels. I also found nothing I disagreed with, and it was a pleasant read.

        Best of luck in the contest.

        Peter

        Dear Alfredo Oliveira,

        There many fascinating threads in this contest. Another thread dealt with "the unreasonable effectiveness" of math for physics, and you made some excellent points which I quote below.

        I have addressed Wigner's quote in my ref.5. The key physical fact underlying our metaphysical reasoning is that the universe behaves logically. This can be exemplified by the creation of 'logic gates', AND and NOT, and subsequent sequential operation of these gates to construct all (finite) logical structures. In his 2009 FQXi essay Marcel-Marie LeBel noted that

        "Maths are the metric extension of logic. Logic is therefore more primitive, more fundamental than mathematics."

        It is not difficult to show that from logic gates one can easily construct counters to produce [finite] numbers, and comparators to test for relations (less than, equal, greater than]. From Kronecker we have reason to believe that, given the numbers, all else follows. Grossberg's mathematical model of neural nets allows us to construct similar logic and to sequence it, and to do so with 3-D structures. Given consciousness [!!] we become aware of these math relations, but without awareness of the material source of the logic, we may do as Robert Godwin says:

        "One begins by abstracting from concrete existence, and ends by attributing concreteness to the abstraction."

        Instead, Alfredo Oliveira notes:

        "Mathematics is a logic language, strictly logic; however, to where it leads depends on the hypothesis and assumptions on which it is applied. Because it is logical, it leads to 'understandable' models provided that the hypotheses and assumptions are "understandable"...

        "Mathematics has also the possibility of fitting whatever set of data - it is just a matter of considering enough parameters." [... such] mathematical models are usually "not-understandable", they present logical inconsistency and parameters that obviously cannot represent a physical entity."

        "However, many consider that these models of data are correct models of reality, and so they consider that the universe is "non-understandable". That seems to be the case of Wigner,..."

        I believe that Oliveira has perfectly stated the situation.

        I try to further clarify "the unreasonable effectiveness" as follows: My vehicle was to teach a robot how to derive a theory of physics from measurements. The general approach, group the numbers via inter-set and intra-set distances to derive feature vectors, is summarized in my endnotes. Thirty years later Schmidt and Lipson applied this theory via pattern recognition algorithms to

        "automatically search motion tracking data captured from various physical systems..."

        Whereas I had treated little more complicated than trajectories of rocks, etc, Schmidt and Lipson treated complex systems such as weights on springs and the double pendulum, systems with predictable regularity. Based on their pattern recognizing robot they found:

        "Without any prior knowledge about physics, kinematics, or geometry, the algorithms [the robot] discovered Hamiltonian's, Lagrangians, and other laws of geometric and momentum conservation."

        This agreed with my theory. However what I found most fascinating was that the 'type' of law that the system found was determined by what variables were presented (to the robot observer). They discovered:

        "... if we only provide position coordinates, the algorithm is forced to converge on a manifold equation of the system's state space. If we provide velocities, the algorithm is biased to find energy laws. If we additionally supply accelerations the algorithm is biased to find force identities and equations of motion."

        I find this absolutely fascinating. This comment does not address life or consciousness. The consciousness is in the mind of the programmer of the robot and the designer of the pattern recognition algorithms. Yet the result is one that I had not expected, namely that the type of data determines the type of physics in the derived model. It makes sense when one thinks about it, but it's still an impressive fact. It addresses the question of the "unreasonable effectiveness" of mathematics, and falls on the side of "complete reasonableness" of mathematics, as it depends from logic, which can be demonstrated physically. To dispute this I believe requires that one demonstrate physically something that is not logical. And such a demonstration should not depend upon mathematical structures that have been projected onto physical reality, as described in my essay.

        While this in no way detracts from the beauty of mathematics, or the mystery of life and consciousness, it does, I believe, remove some of the mystery from mathematics as applied to physics.

        I thank you, Alfredo, for so succinctly stating your arguments above.

        Edwin Eugene Klingman

          Dear Edwin

          I thank you your kind words. A real surprise to me!.

          What you mention is fascinating. An exercise that I did when young was to answer the following question: what are the possible mechanical physical laws? That gave me important insights on why they are as they are.

          I commented your essay in the respective page. Really interesting your work!

          All the best!

          Alfredo

          Dear All

          On my essay I did not made clear what I think about consciousness; it seems that there is also some misunderstanding in relation to what I say in relation to the origin of life. I see now that it is important to clarify these aspects.

          I am an empiricist; I strictly follow Descartes method. I question every piece of knowledge, every experimental result. My knowledge is composed of only what surpasses all my scrutiny.

          Everything that surpasses my scrutiny is accepted as valid, no matter how unexpected it may be. That is the case of a set of experiences that I had during my life and that in no way can be explained by known physical properties or by coincidences or hazard. And as I do not deny them (it would be against my methodology), I know that in the universe there is much more than what can be measured and, therefore, at the reach of Science.

          In relation to consciousness, I do not know whether it results from the properties of matter or belongs to that different level where I place the above mentioned experiences. That is why I do not analyze it in my essay.

          Concerning life origin, although I present an improved explanation for the appearance of molecules of the kind of DNA, in no way I explain the origin of life. Between these molecules and a living cell there is very long way, as anyone with a minimum knowledge of biology certainly knows. It is true that in many texts and videos about the origin of life, this one is reduced to the appearance of first organic molecules as if life was a necessary and trivial consequence of those molecules; but we all know that it is not so.

          I would like to say a last think. As is explained in the Bible (namely in words of Jesus), God, whatever He may be, does not interferes with physical laws. His "kingdom" is another! Of course that many persons need to think that there is a God that interferes with everything, but we are obliged to have a better understanding of all this. Namely in relation to the origin of life, we cannot think that God build life from clay, or the universe in seven days; this are just images, of course. Instead, we have to consider that the material components of life were produced in accordance with physical laws, whether life has divine origin or not. Physics and Religion address different levels of the universe. Which, by the way, I learned from those experiences that it is so more complex than we imagine... but what we have to do is to keep understanding it as much as we can. And we must hurry, by the way...

          If you want to question me on these subjects privately instead of leaving here a comment, just send an email to alf.g.oliveira@gmail.com; I will answer the best I can.

          All the best,

          Alfredo