Related papers: The nature of properly human mathematics
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
There are many scientific problems generated by the multiple and conflicting alternative definitions of linguistic recursion and human recursive processing that exist in the literature. The purpose of this article is to make available to…
This article supports the epistemological claim that sound human reasoning about ultimate knowledge is either foundational or circularly justified. In particular, questions which naturally arise in theology, philosophy, and related…
Mammalian brain is one of the most complex objects in the known universe, as it governs every aspect of animal's and human behavior. It is fair to say that we have a very limited knowledge of how the brain operates and functions.…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
The human brain is the substrate for human intelligence. By simulating the human brain, artificial intelligence builds computational models that have learning capabilities and perform intelligent tasks approaching the human level. Deep…
General wisdom is, mathematical operation is needed to generate number by numbers. It is pointed out that without any mathematical operation true random numbers can be generated by numbers through algorithmic process. It implies that human…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
Planning is useful. It lets people take actions that have desirable long-term consequences. But, planning is hard. It requires thinking about consequences, which consumes limited computational and cognitive resources. Thus, people should…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
Objects are a centerpiece of the mathematical realm and our interaction with and reasoning about it, just as they are of the physical one (if not more). And humans' mathematical reasoning must ultimately be grounded in our general…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
Economies are complex man-made systems where organisms and markets interact according to motivations and principles not entirely understood yet. The increasing dissatisfaction with the postulates of traditional economics i.e. perfectly…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
We all are fascinated by the phenomena of intelligent behavior, as generated both by our own brains and by the brains of other animals. As physicists we would like to understand if there are some general principles that govern the structure…