1,720,994 research outputs found
Through the Looking Glass: What Computation Found There
No full textCommenting about the fact that two matrices 1 and −1 in the twodimensional complex space correspond to the identity matrix 1 in the three-dimensional real space, Goldstein (1957) remarks that “such a paradoxical situation plays no havoc with our common sense” as the complex space is entirely a mathematical construction. Focusing on the notion of ‘observability’, this paper aims to entrust the complex space with physical and computational meaning. In the light of quaternions, the efficiency of the Grover search algorithm finds its source in that “paradoxical situation”
Esperimenti mentali e realtà fisica
No full textLa nuova immagine del mondo fisico generata dalla teoria dei quanti mette in discussione la relazione tra teoria fisica e fatti da essa descritti. Muovendo dall'analisi critica dei presupposti concettuali del razionalismo classico, la ricerca di un più soddisfacente criterio di realtà fisica suggerisce di accostare il metodo sperimentale della fisica "galileiana" ai metodi dimostrativi della matematica costruttiva. La visione einsteiniana degli esperimenti mentali come dimostrazioni e l'idea della dimostrazione come esperimento, che emerge dalla riflessione wittgensteiniana sopra i fondamenti della matematica, indirizzano verso una migliore comprensione di alcune questioni teoriche centrali, sollevate dalla fisica del nostro secolo. Di qui la possibilità di individuare nell'esperimento il principio fondamentale per una teoria del significato valida tanto per le proposizioni della fisica quanto per quelle della matematica
Some remarks about knowledge and probability arising from counterfactual quantum effects
No full textCan the mere possibility of a physical phenomenon affect the outcome of an experiment? In fact quantum theory presents us actual physical effects arising from "counterfactuals", that is physical effects brought about by things that might have happened, although they did not happen. How can it be? After a short outline of the quantum-mechanical description of physical reality, the occurrence of such counterfactual effects in quantum theory is illustrated by means of a Mach-Zehnder interferometer. Then these paradoxical phenomena undermining the very notion of physical event and questioning about which knowledge of physical reality can ever be obtained will be analysed using a classical possible-worlds model of knowledge and probability. Finally, a surprising application of counterfactual quantum effects producing a new kind of computing with no classical analogue will be shown
Les relations d'incertitudes de Heisenberg à travers les yeux de Léonard
No full textConsidérer aléatoire un énoncé comme « demain le soleil se lèvera » peut sembler vaine subtilité philosophique, pourtant, en mettant un tel énoncé en relation avec un sujet (pour qui?) son évaluation change radicalement. Même si, en théorie, on pourrait admettre d’attribuer probabilité un « au lever du soleil demain » et donc de considérer certain l’évènement décrit, aucune théorie n’attribuera cette probabilité « au lever du soleil demain pour M. X », qui que soit M. X. Se demander « pour qui », ou décrire un évènement en se référant à un point d’observation, veut dire abandonner la certitude. Cette perte de certitude est à imputer à l’ignorance des valeurs des variables qui déterminent le destin de M. X ou à la conscience de la multiplicité des expériences et des interactions qui donnent forme au destin des hommes et à la signification des théories ? Bien que la « non-séparation » observateur-observé, qui a donné naissance au principe d’incertitude de Heisenberg, reste question ouverte et problématique pour la science contemporaine, dans la vision artistique de la Renaissance, il est possible de reconnaître une de ses clefs de lecture appropriée
Risorse fisiche nella matematica. Dal finitismo hilbertiano ai calcolatori quantistici
No full textSe dal requisito che un sistema formale abbia un algoritmo per controllare le dimostrazioni consegue la possibilità di elencare tutti i teoremi dimostrabili all’interno del sistema, dalla disponibilità delle macchine calcolatrici nella realtà, grazie ai più recenti sviluppi della teoria della computazione, consegue la possibilità che a eseguire l’algoritmo sia un calcolatore. Così, la macchina di Turing, un concetto logico derivato dall’osservazione di una macchina reale – un calcolatore umano –, indica la via per la realizzazione di altre macchine reali: i moderni calcolatori. Ma come possiamo pensare che un congegno meccanico sia capace di controllare la correttezza di una dimostrazione? Quale significato possiamo attribuire a una macchina calcolatrice concepita come un pezzo di materia concretamente osservabile, come un “oggetto fisico”
Special Issue on Hilbert's Axiomatics—Geometry, Physics, Logic
No full textWhat is the meaning of Hilbert's axiomatics? Did Hilbert conceive of an axiomatic system as a meaningless formal structure or rather as a kind of “symbolic form” (like Cassirer)? What was the impact of Hertz's Bildtheorie on Hilbert's view of the axiomatic method? What is the relation between mathematical physics and intuitive geometry?
By discussing conceptual and logical arguments underlying such questions, this special issue aims to focus on meaningful connections and analogies between them as well as to sharpen the more relevant questions
Popper and Turing's Challenge
No full textIn Computing Machinery and Intelligence, Alan M. Turing posed the question "Can machines think?". Popper's answer in The Self and Its Brain is "without hesitation that they cannot", and "Turing's challenge should not be taken up". Why does Popper refuse Turing's challenge? First, we look at what Popper and Turing actually said, in order to put some aspects of the problem in perspective. Second, because Popper's view about mechanical procedures might to some extent match that of Gödel, a glance at Gödel's interpretation of Turing's work may help to find a way through Popper's thought. By this route, we reach the conclusion that Popper fails to see that what Turing was really proposing can be viewed as a genuine application of his own method of conjectures and refutations
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