This text I rescued from my drafts, 2002 (almost twelve years ago). At the time did not publish because, certainly, at that time few would understand what was actually dealing with. The Internet had not even gotten more intensively in the universities. They are fragments of readings and conversations with authors, many should have been cited, but not longer remember the precise origin. A fragment of it was published somewhere on the internet that do not remember.
Gilson Lima. Sociologist of science. gilima@gmail.com
Contemplate the heavens and the earth. the sea, all that shines on them or on them, everything that crawls or flies, or floats, all forms have because everything is number. Remove them and nothing will be the number ...Question what you dance to the delight and the number respond: "I'm here!" Examines the beauty of bodily form, and discover that everything is in place thanks to the number. Examines the beauty of body movement, and see that everything is in due time thanks to the number. St. Augustine.
There is in contemporary science two great currents of thought that, after running parallel for a long time, begin to take seductive channels that point to your future convergence. The circumstances of this meeting will determine which one will be later seen going forward as a mere tributary of the other.On one side is the belief of physicists in the "laws of nature," associated with the symmetry, the first as the basis of logic in the universe. These symmetries are linked in this case the representation of space and time as a continuous indivisible.In contrast with this view, there is one in which the abstract computing instead of symmetry, which appears as the most important of all concepts.In this image of reality, it is considered that the digital logic that is based on your rules something discrete rather than continuous universe.The unresolved enigma, which is in the future, will even have to decide what is the government's most fundamental representation of the world: the symmetry or the computer.So, say, the universe is a cosmic kaleidoscope, or a cosmic computer? A standard or a program? Or neither? Or rather, are the rules that govern the process of computing that states that laws of nature are possible?The decision in this case also will - therefore - we know if the laws of physics control the computing capacity of the abstract. The laws of physics impose limits its speed and range?Before showing how little we have to say about this decision, should be careful with it in itself. Let's see.Throughout the history of human thought existed dominant paradigms of the universe. Often these mental images tell us very little about the universe and more about the society that was engaged in his study. For those ancient Greeks who developed a teleological perspective on the world as a product of the first systematic study of living things, the universe was a great body. For others, who thought that the geometry should be revered above all other categories of thought, the universe was a perfect harmony of geometric shapes. Later, at the time they became the first mechanical clocks and mechanisms of the pendulum, the image of the post-Newtonian universe as a mechanism became dominant, and a thousand ships set off in pursuit of apologetic Cosmic Watchmaker. For the Victorian Industrial Revolution, the dominant paradigm was the steam engine and the physical and philosophical issues that she raised with respect to the laws of thermodynamics and the ultimate fate of the universe at that time bore the brand of machines. So today, perhaps the image of the universe as a computer is nothing more predictable than the last extension of our habits of thought. Tomorrow may be another paradigm. What? There will be some profound and simple concept that is behind the logic, as well as the logic is behind the mathematics and computing?At first glance, the notions of symmetry and computing seem very far apart, so that the choice between them would have to be exhaustive. But the symmetry down the possible changes and the "laws" that result can be seen as a kind of software that runs on some hardware - the hardware material of our physical universe. This representation - implicitly - is one of particular visions of the relationship between the laws of nature and the physical universe by almost dogmatic modern Western knowledge.See nature and the universe (nature and culture) as separate concepts, independent. Symbiosis has fatal consequences of this approach. Ends the mechanical process of disciplining, complete with technical expertise perital without reflexivity, ending the idea of man without Symbios with nature.Thus, we could also imagine the software being run on different hardware, the-symbiotic dualism. This representation seems to lead us, therefore, a potential conflict with the belief in a theory which breaks the conditions of existence of even the elementary particles and their laws that govern it.At first glance, the success of the reductionist view continuist knowledge of the mechanism that "explains" the physical world seems to oppose the discrete computational perspective. The logical waged a war of attrition against the notion of a continuum of numbers over the past 80 years. The same concerns and fears that have taken some mathematicians who defined the introduction of irrational numbers as just a convenient myth that artificially simplifies the laws of arithmetic and physical objects which are entities postulated causal rational, and simple rounded by the flow of existence are added Now new fears about the forward recursion computational causal symmetry, linearity, sequentiality, ....
Where is the IQ of the BIT [1]?
The computation is the most basic aspect of reality? To this we would find that the universe only makes things computable.The field demonstrations of mathematical analog of the universe would have to be limited to the jurisdiction of the Constructivists. This is the penalty payable by the abandonment of continuous and computable aspects appeal to the world as the basis for the explanation of the whole.We've found, however, many of the same mathematical operations that are not computable, and we have many of them peeking.In the study of quantum cosmology, we find several examples in which the listing of the areas required are operating a non-computable and can not be carried out systematically by means of a finite number of computational steps of the Turing machine type. There is need for a new element to generate each member of the set. It can, of course, there is another way to calculate the observable quantity in question and that does the realization of this operation is not computable, but it may not make it there and in fact less likely to computability.If we examine partial differential equations describing the propagation of waves of some kind, whether quantum or gravitational waves that propagate through the geometry of spacetime, we find the same problem. When the initial profile of the wave is described by a continuous function, but non-differentiable twice, there is no solution can computable the wave equation in two or more spatial dimensions.The crux of the problem is the irregularity of the initial profile. If this is twice differentiable, all solutions of wave equations are computable. But if, in the most fundamental level, things are discrete and discontinuous, can be victims of the problem of non-computability.The solutions of these difficulties lie certainly a broader concept of what we mean by computation.Traditionally, computer scientists define the computing capacity of any computer, either the real or imagined, as idealized Turing machine. Since the world is fundamentally a quantum system, any attempt to explain its inner workings in terms of a computational paradigm must be founded on a misunderstanding of what sound is in fact quantum computing and what it can accomplish and the Turing machine does not. The computational paradigm has many affinities with the quantum view of the world. Both are discrete, both have dual aspects as evolution and measurement (compute and read). But it would be possible to provide even more arguments in favor of the relationship between the quantum and symmetries of nature.Almost a century of detailed studies of physical amalgamated the two in indissoluble union. What position would the computing paradigm come to occupy after a similar investment of reflection and energy?
The Unknowable: Stop quoting and show what you know. Ralph Waldo Emerson.
Why the world would be mathematical or geometric? But then again, it is true that most things we encounter in day-to-day seem anything but math?The mathematical description is relegated to a peculiar structural world, simpler than those that participate in day-to-day. Furthermore, we found no mathematical relation to emotions. How, then, when we speak of a mathematics confidence. What are the things that can not be included in this physical design? It seems that they exist, but most often are excluded under the pretext of not being scientific. An explanation is not very different from the infamous Master of Balliol [2] who was said "do not know what he is not know."The gap between the two cultures - science and humanism - has widened considerably since the beginning of the century. We realize that there are most sacred precincts of the temple of science in which Symbios is not invited to participate (both sides). Those people did their cults devoted to political opinion and consciousness dominated by self-reflection made by beliefs and ideologies romanticized feelings of love are considered adept at missing a chatter of intellectual activities and practices as ends in themselves, loosely constrained by the requirements of knowledgecomplex.However, the Symbios, we have a trained mind to act and react in certain ways to particular types of multiple and simultaneous inputs missing from this contradiction.So while the information "logic" is a ready-made structure that could be accommodated with the symbiosis information, it does not resist compression broader facets suggestive. Our brain is not good at making algorithmic details, because we are similarly permeated by chemical seasonings and emotional about the information and facts available to us when they happen to the world. Some branches of experience lend themselves to this sublimation clearly better than others.In the sciences pejoratively coined as "hard", the most important feature in favor of the compression algorithm is the existence of idealizations complicated concrete phenomena.A typical star like the Sun, allows an excellent approach to this view.Treating the Sun as spherical and having the same temperature throughout its surface is evidently absurd proportion. No star is thus exactly spherical and isothermal surface. All the stars are so that you can not make several idealizations of this type and the resulting descriptions of them will be very inaccurate.Then, slightly relaxing the idealizations, we can proceed towards a description which admits the presence of small non-esfericidades. This sequence step by step approaches are less understood by operations "computable" in the sense of Turing. In contrast, many of the sciences "soft", which seek to apply mathematics to things like social behavior, riots in prisons or psychological reactions, can not produce a considerable body of sound knowledge, because the matters they deal with do not allow idealizations obvious and fruitful. Complicated phenomena, especially those aspects that are not amenable to algorithmic understanding are inherently unpredictable because they react to the act of research, can not be replaced by simple approximations.It is easy to imagine how one could model a "rough society" or a "paranoia approximate." These phenomena do not allow the effective use of the most successful instrument of the mind to make sense of complexity.In practice, it can express the failure of our minds to find the right way to go in search of idealizations, or may be the consequence of some intrinsic incompressibility to the phenomena in question.Science feels more at home when facing technical problems that require deep insight that claim. For technical understand the systematic application of a sequential procedure - a recipe. The fact that this approach is often fruitful world attests to the power of generalization. Nature uses the same basic ideas over and over again in different situations. The mark of such reapplication is its mathematical character. A search of that technique whose application would be able to decode the message of nature in all circumstances is doomed to failure.The lessons learned from the theorems of Gödel, Church and Turing on the scope and limitations of logical systems are often forgotten in everyday scientific production. The most accessible and quantifiable in the world have the property and computable procedures are set to decide on this.But the truth is not one of those properties of things kind of a prime number or a set of subtle properties that can only be listed.The most logical systems have the property to be listable but not computable and all its theorems can be listed, but there is an automatic procedure to examine a design and decide whether or not it is a theorem.If the mathematical world had not Gödel's theorem, all property of any system that contains arithmetic would be listable. We could write a program set to perform each activity. Without the restrictions imposed on the Cliurch and Turing computability, all property in the world would be computable.Decide if this page is an example of Portuguese written according to the rules of grammar is a computable problem.Words can be confronted with a reference dictionary and syntactic constructs can be checked sequentially, but the page still having no meaning for a reader who does not know Portuguese.All though this time with the player could go learn Portuguese and a growing number of elements of this page would be meaningful to him. However, the property is therefore listable meaningfulness, but not computable. So, decide if this page is something that the reader will want to write in the future is a property listable but not computable.Not all features of the world can be classified as listable or computable.For example, the property of being a true in a system mathematical formulation is not particularly listable or computable. What we can do is to approach the "truth" with increasing accuracy by introducing an increasing number of rules of reasoning and adding other axiomatic assumptions, but we can never fully capture it by a finite set of rules.Beauty, simplicity, truth, are all forward-looking properties. There is no magic formula that you can use to generate all possible varieties of these attributes. They can never be fully exhausted. No program or equation can generate all the beauty or ugliness.The forward-looking properties of things can not be captured in any theory of everything. Also no explanation of non-poetic reality can be complete.The scope of computable theories is huge, but limited, are necessary parts of a full understanding of things, but far from sufficient to uncover all the subtleties of a universe like ours.The computability of electrons microphysics is informational bits or pixels, is the infogene and their biochemistry, nano is macroscósmica or may contain elements that are beyond our current view of the compartmentalized nature of modern Newtonian ingredients, but still are limited and our world contains attributes prospective .There is no formula can give us the whole truth, all harmony, all simplicity, as to see through all the things of all for a logical switch would leave us without seeing lots and lots of things out of it.No theory or understanding may be a theory of everything and will never allow a full understanding of everything, whether we like it or not.
[1] Bit As everyone knows is the language of computing, is the unit of information expressed as a choice between two possibilities (for binary digit, ie binary digit). Play on words between it (impersonal pronoun) and bit, something like "the essence from the bit."
[2] Balliol is one of many schools forming Oxford University was established around 1268.
