Related papers: The nature of properly human mathematics
Uncertainty enters into human reasoning and inference in at least two ways. It is reasonable to suppose that there will be roles for these distinct uses of uncertainty also in automated reasoning.
Brain science and artificial intelligence have made great progress toward the understanding and engineering of the human mind. The progress has accelerated significantly since the turn of the century thanks to new methods for probing the…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
Time is one of those issues about which many thinkers and scientists have tried to pronounce their finest thoughts, but the discourse about time has remained vague and often inconsistent. In this paper we put forward a conceptual framework…
Human cognition spans perception, memory, intuitive judgment, deliberative reasoning, action selection, and social inference, yet these capacities are often explained through distinct computational theories. Here we present a unified…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
Science and mathematics help people better to understand world, eliminating different fallacies and misconceptions. One of such misconception is related to arithmetic, which is so important both for science and everyday life. People think…
The paper discusses relationships between aesthetics theory and mathematical models of mind. Mathematical theory describes abilities for concepts, emotions, instincts, imagination, adaptation, learning, cognition, language, approximate…
The paper defends the thesis that analysis of time meaning in a context of philosophy of physical and mathematical natural sciences and philosophical anthropology allows to clear basis of human being and to construct special model of…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Introduction: In contrast to current AI technology, natural intelligence -- the kind of autonomous intelligence that is realized in the brains of animals and humans to attain in their natural environment goals defined by a repertoire of…
Neural spikes in the brain form stochastic sequences, i.e., belong to the class of pulse noises. This stochasticity is a counterintuitive feature because extracting information - such as the commonly supposed neural information of mean…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
The view of nature we adopt in the natural attitude is determined by common sense, without which we could not survive. Classical physics is modelled on this common-sense view of nature, and uses mathematics to formalise our natural…
This paper studies the question on whether machines can be rational. It observes the existing reasons why humans are not rational which is due to imperfect and limited information, limited and inconsistent processing power through the brain…
The field of machine learning has focused, primarily, on discretized sub-problems (i.e. vision, speech, natural language) of intelligence. While neuroscience tends to be observation heavy, providing few guiding theories. It is unlikely that…
``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…