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MATHEMATICAL HIERARCHY. “Even quite simple physical theories such as, for example, Newtonian mechanics of point particles interacting just by gravity, are complicated from the viewpoint of logic and foundations of mathematics; simply because such theories use mathematical apparatus (for example, calculus) that is ‘high up’ in the deductive chain from basic logic and set theory.” https://lnkd.in/dMm_YkR View in LinkedIn

UNRESOLVED CONFLICT. “The fact that general relativity treats matter classically, and gravity as curvature, while our best theories of matter are quantum theories using a flat metric, is enough to show that some sort of reconciliation is needed.” https://lnkd.in/dMm_YkR View in LinkedIn

SETS AT THE HEART. “By concatenating such deductions with judiciously chosen definitions, one shows in effect that all of classical pure mathematics can in this sense be deduced from the theory of sets. This remarkable result, showing how large an expressive power can be obtained by applying this small stock of logical operations to a small initial family of predicates, is the source of the traditional philosophical restriction to considering just these logical operations.” https://lnkd.in/dMm_YkR View in LinkedIn

THE WORLD OF PROBABILITIES. “Quantum theories are conceptually very different from classical theories: in particular, the state of a system does not assign real-number values to physical quantities but only probabilities for obtaining such values if appropriate measurements are made. And, though they share with general relativity the assumption that it is appropriate to coordinatise space and time with real numbers, they do not treat gravity as curvature of the corresponding spaces: they use either Newtonian spacetime (which corresponds to a degenerate spacetime metric), or the flat metric of special relativity.” https://lnkd.in/dMm_YkR View in LinkedIn

“QUANTUM THEORY is not a theory per se but is rather a certain mathematical and conceptual framework within which specific theories are constructed. Typically, these deal with various kinds of matter and the forces they exert on each other, including the fundamental forces other than gravity: the electromagnetic, weak and strong forces. “ https://lnkd.in/dMm_YkR View in LinkedIn

ON GRAVITY AND NEURONS. “The above synaptic connection among the neurons, in the excitatory regime, is analogous to a gravitational interaction among particles. Therefore, such a setup represents a most naive way of bringing a gravity‐like dynamics into the neural networks.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

THE GOAL. “Finally, we would like to comment that our main goal is to reach a maximal energy efficiency of the memory storage, as well as, the efficiency of the response to the input external patterns. We shall not be interested in implementation of the learning algorithms and other computational tasks in the quantum neural networks.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

INSPIRED DEDUCTION. “The above dictionary gives us a rough idea that in a neural network designed by the above rules, we should encounter a state of an enhanced memory storage capacity in form of a state in which some of the lowest threshold neurons are highly excited. As we shall see, this is indeed the case.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

NEW LEXICON. “To summarize, we establish the following dictionary: Particle momentum mode Neural degree of freedom; Oscillator energy gap Excitation energy threshold of neuron; Mode occupation number Excitation level of neuron; Gravitational interaction among particles Excitatory synaptic connection among neurons; Black hole state Critical state of highly excited low threshold neurons.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

Gaudi, the architectural genius behind Barcelona’s Sagrada Familia also created works out of wood and metal, all of course with extremely organic themes derived from nature, like this beautiful door panel. View in LinkedIn