http://popups.lib.uliege.be/1373-5411/index.php?id=1164 Publications of Auteurs Arturo Graziano Grappone fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4677 Dimensional analysis permits us the rigorous comprehension of physical quantities by its reduction in terms of mass M, length L, time T, electric charge Q, and temperature Θ. E.g., speed is LT-1, force is MLT-2 and so on. However, Saumont has observed that it is no rational to give dimensions to constant quantity and not to give dimensions to variable quantity. Also, standard dimension analysis implies an evident hyper-cubic topology MnLpTpQrΘs that isn't incompatible with (hyper)incursive systems that have hypersphere or torus topology. Finally, Grappone has proven that anticipatory systems, in terms of set inclusive networks, are equivalent to first order theories in mathematical logic, i.e. polyadic or cilindric algebras that haven't a simple hypercubic structure. This paper is an attempt to start the solving of these problems. Mon, 14 Oct 2024 16:15:47 +0200 Mon, 14 Oct 2024 16:15:54 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4677 http://popups.lib.uliege.be/1373-5411/index.php?id=3867 Algorithmic topology is the spanning of an algorithm on a topological structure. The common calculus with paper and pen shows that all the recursive functions can be spanned on Euclidean planes. It is known that two topological structures are identical if and only if cut-pasting operations don't need to transform one in the other. Dubois' third stage (identification of incursive algorithm last row and column respectively with its first row and column) gives to incursive algorithms a spanning only on a torus that can be transformed in Euclidean plane only by cut-pasting operations. Thus incursive algorithms couldn't reduce to recursive algorithms and Church's hypothesis couldn't be true. Now, observe the affinity between topologic cut-pasting operations, Dubois' third stage and quantum entanglement. This last one can be considered either two "entanglements" in incursive algorithms or a cut-pasting operation on Euclidean plane on which such an algorithm is spanned to transform such a plane in torus. Is quantum entanglement simply the inadequacy of algorithms that can be spanned only on Euclidean plains to represent quantum mechanics? The same question could have value for some complex biological systems. Mon, 30 Sep 2024 14:20:43 +0200 Tue, 08 Oct 2024 14:43:38 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3867 http://popups.lib.uliege.be/1373-5411/index.php?id=3531 This paper describes the possibility of science hyperincursive integration by construction of a formal theory which becomes a universal language for the sciences and where it is possible to build their integration process. After this integration any scientific theory assumes all the data and ideas that can be useful for it from the other scientific theories. Dubois' incursive algorithm scheme permits a good two by two integration process of all the sciences but the continous making of new scientific ideas and data in the outside environment of the integration process implies the necessity to can change it during its execution by opportune control parameters which represents the new scientific data and ideas which we can introduce. Thus we have really an hyperincursive process to integrate the sciences among them. Tue, 24 Sep 2024 10:19:55 +0200 Tue, 24 Sep 2024 10:20:05 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3531 http://popups.lib.uliege.be/1373-5411/index.php?id=3357 This paper would like revaluing Albert Einstein's famous sentence : God does not play dice with the Universe, in quantum mechanics by unification of measure and probability concepts in a complete Boolean representation of quantum mechanics. Mon, 16 Sep 2024 10:41:04 +0200 Thu, 10 Oct 2024 10:33:45 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3357 http://popups.lib.uliege.be/1373-5411/index.php?id=1452 This paper describes the possibility of incursive proof in classical formal theory. Fri, 12 Jul 2024 14:22:57 +0200 Thu, 10 Oct 2024 10:33:12 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1452 http://popups.lib.uliege.be/1373-5411/index.php?id=1159 This paper proves that the Boolean connectives and the recursive functions -i.e. the rational order- are generable by hyperincursive algorythms -i.e. 'chaotic' phenomena- as the above Hesiodus' verse affirms. But, for the archaic ancient Greeks, chaos -the space that is enclosed between sky and earth [χάος = χά(ϝ)ος =cavus = cave?]- does not mean disorder. Were they right? Fri, 05 Jul 2024 15:06:08 +0200 Fri, 05 Jul 2024 15:06:15 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1159