SummaryThe supersymmetry algebra is examined for the (2+1)-dimensional supersymmetricON Georgi-Gl... more SummaryThe supersymmetry algebra is examined for the (2+1)-dimensional supersymmetricON Georgi-Glashow-like model, on the basis of the results of Witten and Olive in the (3+1)-dimensional case. We show that, in the (2+1)-dimensional model, no topological charge, but only an electric one modifies the supersymmetry algebra as a central charge.RiassuntoL'algebra supersimmetrica è stata esaminata per il modello supersimmetricoON di tipo Georgi-Glashow in 2+1 dimensioni, sulla base dei risultati di Witten e Olive in 3+1 dimensioni. Si dimostra che, nel modello in 2+1 dimensioni, solo una carica elettrica (e non anche una carica topologica) modifica l'algebra supersimmetrica come carica centrale.РезюмеИсследуется суперсимметричная алгебра для (2+1)-мерной суперсимметричнойON модели типа Джорджи-Глашоу, используя результаты Виттена и Олива для (3+1)-мерного случая. Мы показываем, что в (2+1)-мерной модели не топологический заряд, а только электрический заряд преобразует алгебру суперсимметрии, как центральный заряд.
Abstract The USp(2) supersymmetry algebra is explicitly calculated for the (4+1)-dimensional supe... more Abstract The USp(2) supersymmetry algebra is explicitly calculated for the (4+1)-dimensional supersymmetric SU(2) Yang-Mills theory with an extended USp(2) global symmetry. An electric charge and a topological one can appear in the supersymmetry algebra as central charges, but each one separately in a different phase of the theory.
We illustrate the logical and meta-logical meaning of the mirror test. We show that passing the l... more We illustrate the logical and meta-logical meaning of the mirror test. We show that passing the latter is a necessary but not sufficient condition for the subject to possess a metalanguage. In fact the test itself can be formally described in logical terms with the law of identity, which however, being purely syntactic, belongs to the object language, and can only be interpreted as self-recognition, not as self-awareness. It is shown that the law of identity is the "crushing" of the axiom of identity from the metalanguage on the object language. The axiom of identity, which is semantic, can be interpreted as self-awareness. The conclusion is that failing the test means that there is no metalanguage, but passing the test does not imply the certainty that there is. In fact the subject (such as a robot) could have been programmed by an external agent. In psychological terms this means that failing the test excludes self-awareness, but passing it does not guarantee that the subject has it. Furthermore, we discuss two other consequences of the lack of metalanguage in children: the absence of Tarski's convention T and that of the "cut" rule. 1. Introduction This work stems from the observation that children are the only mammal cubs to be completely different, especially mentally, from their adult version. A foal is a complete horse even if on a reduced scale, and already behaves like a horse. The same goes for puppies and kittens. We relate to foals, puppies and kittens as if they were horses, adult dogs and cats. Maybe we play more with them, we pamper them more, but communication is practically the same, and their behaviours are already equine, or canine, or feline. Babies don't behave like human miniatures, they are completely different, mysterious, and intriguing. What makes them so different from other puppies? One certainly cannot say intelligence! Sometimes they appear as automatons, waiting to transform ... In fact, they are not yet complete, while the other puppies are. To understand what is the real difference between children and other puppies, we need to investigate the different forms of animal intelligence. Let us consider carnivores, like dogs and cats: they share the "rational" intelligence of the predator with humans (also carnivorous). Instead the horses, which are herbivores, have an "emotional" intelligence typical of prey. So what's different between a child's mind and a kitten's, for example, both carnivores? The kitten can only be a cat, because in addition to this it cannot develop, while the child cannot be a man, because the man is something extremely different from him: he has a metalanguage, which in the child is not yet developed. Most animals, like dogs, cats, (perhaps) horses etc. seem not to develop a metalanguage, therefore between them and their puppies there is not that abyss that exists instead between a man and a child. It could be said that children are the most perfect form of artificial intelligence controlled by man. Like computers, children do not have a metalanguage (at the beginning of their existence) but unlike machines, they transform, evolve, due to the program inherent in their DNA (and most probably in the genoma) and acquire the metalanguage, and consequently, as we will see, the self-awareness. The question is: how does the metalanguage develop over time? It is believed that quantum brain dynamics can be described by a dissipative quantum field theory (DQFT) [1] [2] and recent works suggest that QFT can be interpreted as a (quantum) metalanguage [3] [4]. At this point we make the
We consider the theoretical setting of a superfluid like 3He in a rotating container, which is se... more We consider the theoretical setting of a superfluid like 3He in a rotating container, which is set between the two layers of a type-II superconductor. We describe the superfluid vortices as a 2-dimensional Ising-like model on a triangular lattice in presence of local magnetic fields. The interaction term of the superfluid vortices with the Abrikosov vortices of the superconductor appears then as a symmetry breaking term in the free energy. Such a term gives a higher probability of quantum tunnelling across the potential barrier for bubbles nucleation, thus favouring quantum cavitation. Comment: 7 pages, 2 figures
SummaryThe supersymmetry algebra is examined for the (2+1)-dimensional supersymmetricON Georgi-Gl... more SummaryThe supersymmetry algebra is examined for the (2+1)-dimensional supersymmetricON Georgi-Glashow-like model, on the basis of the results of Witten and Olive in the (3+1)-dimensional case. We show that, in the (2+1)-dimensional model, no topological charge, but only an electric one modifies the supersymmetry algebra as a central charge.RiassuntoL'algebra supersimmetrica è stata esaminata per il modello supersimmetricoON di tipo Georgi-Glashow in 2+1 dimensioni, sulla base dei risultati di Witten e Olive in 3+1 dimensioni. Si dimostra che, nel modello in 2+1 dimensioni, solo una carica elettrica (e non anche una carica topologica) modifica l'algebra supersimmetrica come carica centrale.РезюмеИсследуется суперсимметричная алгебра для (2+1)-мерной суперсимметричнойON модели типа Джорджи-Глашоу, используя результаты Виттена и Олива для (3+1)-мерного случая. Мы показываем, что в (2+1)-мерной модели не топологический заряд, а только электрический заряд преобразует алгебру суперсимметрии, как центральный заряд.
Abstract The USp(2) supersymmetry algebra is explicitly calculated for the (4+1)-dimensional supe... more Abstract The USp(2) supersymmetry algebra is explicitly calculated for the (4+1)-dimensional supersymmetric SU(2) Yang-Mills theory with an extended USp(2) global symmetry. An electric charge and a topological one can appear in the supersymmetry algebra as central charges, but each one separately in a different phase of the theory.
We illustrate the logical and meta-logical meaning of the mirror test. We show that passing the l... more We illustrate the logical and meta-logical meaning of the mirror test. We show that passing the latter is a necessary but not sufficient condition for the subject to possess a metalanguage. In fact the test itself can be formally described in logical terms with the law of identity, which however, being purely syntactic, belongs to the object language, and can only be interpreted as self-recognition, not as self-awareness. It is shown that the law of identity is the "crushing" of the axiom of identity from the metalanguage on the object language. The axiom of identity, which is semantic, can be interpreted as self-awareness. The conclusion is that failing the test means that there is no metalanguage, but passing the test does not imply the certainty that there is. In fact the subject (such as a robot) could have been programmed by an external agent. In psychological terms this means that failing the test excludes self-awareness, but passing it does not guarantee that the subject has it. Furthermore, we discuss two other consequences of the lack of metalanguage in children: the absence of Tarski's convention T and that of the "cut" rule. 1. Introduction This work stems from the observation that children are the only mammal cubs to be completely different, especially mentally, from their adult version. A foal is a complete horse even if on a reduced scale, and already behaves like a horse. The same goes for puppies and kittens. We relate to foals, puppies and kittens as if they were horses, adult dogs and cats. Maybe we play more with them, we pamper them more, but communication is practically the same, and their behaviours are already equine, or canine, or feline. Babies don't behave like human miniatures, they are completely different, mysterious, and intriguing. What makes them so different from other puppies? One certainly cannot say intelligence! Sometimes they appear as automatons, waiting to transform ... In fact, they are not yet complete, while the other puppies are. To understand what is the real difference between children and other puppies, we need to investigate the different forms of animal intelligence. Let us consider carnivores, like dogs and cats: they share the "rational" intelligence of the predator with humans (also carnivorous). Instead the horses, which are herbivores, have an "emotional" intelligence typical of prey. So what's different between a child's mind and a kitten's, for example, both carnivores? The kitten can only be a cat, because in addition to this it cannot develop, while the child cannot be a man, because the man is something extremely different from him: he has a metalanguage, which in the child is not yet developed. Most animals, like dogs, cats, (perhaps) horses etc. seem not to develop a metalanguage, therefore between them and their puppies there is not that abyss that exists instead between a man and a child. It could be said that children are the most perfect form of artificial intelligence controlled by man. Like computers, children do not have a metalanguage (at the beginning of their existence) but unlike machines, they transform, evolve, due to the program inherent in their DNA (and most probably in the genoma) and acquire the metalanguage, and consequently, as we will see, the self-awareness. The question is: how does the metalanguage develop over time? It is believed that quantum brain dynamics can be described by a dissipative quantum field theory (DQFT) [1] [2] and recent works suggest that QFT can be interpreted as a (quantum) metalanguage [3] [4]. At this point we make the
We consider the theoretical setting of a superfluid like 3He in a rotating container, which is se... more We consider the theoretical setting of a superfluid like 3He in a rotating container, which is set between the two layers of a type-II superconductor. We describe the superfluid vortices as a 2-dimensional Ising-like model on a triangular lattice in presence of local magnetic fields. The interaction term of the superfluid vortices with the Abrikosov vortices of the superconductor appears then as a symmetry breaking term in the free energy. Such a term gives a higher probability of quantum tunnelling across the potential barrier for bubbles nucleation, thus favouring quantum cavitation. Comment: 7 pages, 2 figures
We illustrate the logical and meta-logical meaning of the mirror test. We show that passing the l... more We illustrate the logical and meta-logical meaning of the mirror test. We show that passing the latter is a necessary but not sufficient condition for the subject to possess a metalanguage. In fact the test itself can be formally described in logical terms with the law of identity, which however, being purely syntactic, belongs to the object language, and can only be interpreted as self-recognition, not as self-awareness. It is shown that the law of identity is the "crushing" of the axiom of identity from the metalanguage on the object language. The axiom of identity, which is semantic, can be interpreted as self-awareness. The conclusion is that failing the test means that there is no metalanguage, but passing the test does not imply the certainty that there is. In fact the subject (such as a robot) could have been programmed by an external agent. In psychological terms this means that failing the test excludes self-awareness, but passing it does not guarantee that the subject has it. Furthermore, we discuss two other consequences of the lack of metalanguage in children: the absence of Tarski's convention T and that of the "cut" rule. 1. Introduction This work stems from the observation that children are the only mammal cubs to be completely different, especially mentally, from their adult version. A foal is a complete horse even if on a reduced scale, and already behaves like a horse. The same goes for puppies and kittens. We relate to foals, puppies and kittens as if they were horses, adult dogs and cats. Maybe we play more with them, we pamper them more, but communication is practically the same, and their behaviours are already equine, or canine, or feline. Babies don't behave like human miniatures, they are completely different, mysterious, and intriguing. What makes them so different from other puppies? One certainly cannot say intelligence! Sometimes they appear as automatons, waiting to transform ... In fact, they are not yet complete, while the other puppies are. To understand what is the real difference between children and other puppies, we need to investigate the different forms of animal intelligence. Let us consider carnivores, like dogs and cats: they share the "rational" intelligence of the predator with humans (also carnivorous). Instead the horses, which are herbivores, have an "emotional" intelligence typical of prey. So what's different between a child's mind and a kitten's, for example, both carnivores? The kitten can only be a cat, because in addition to this it cannot develop, while the child cannot be a man, because the man is something extremely different from him: he has a metalanguage, which in the child is not yet developed. Most animals, like dogs, cats, (perhaps) horses etc. seem not to develop a metalanguage, therefore between them and their puppies there is not that abyss that exists instead between a man and a child. It could be said that children are the most perfect form of artificial intelligence controlled by man. Like computers, children do not have a metalanguage (at the beginning of their existence) but unlike machines, they transform, evolve, due to the program inherent in their DNA (and most probably in the genoma) and acquire the metalanguage, and consequently, as we will see, the self-awareness. The question is: how does the metalanguage develop over time? It is believed that quantum brain dynamics can be described by a dissipative quantum field theory (DQFT) [1] [2] and recent works suggest that QFT can be interpreted as a (quantum) metalanguage [3] [4]. At this point we make the
Uploads
Papers by Paola Zizzi