Related papers: Human being is a living random number generator
Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given 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…
Surreal numbers are created recursively, with the "birthday" being the depth of the recursion. Birthday arithmetic describes how birthdays of surreal numbers are transformed by standard arithemetic operations. This paper shows that birthday…
The theory of rational choice assumes that when people make decisions they do so in order to maximize their utility. In order to achieve this goal they ought to use all the information available and consider all the choices available to…
When presented with information of any type, from music to language to mathematics, the human mind subconsciously arranges it into a network. A network puts pieces of information like musical notes, syllables or mathematical concepts into…
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…
The rapid advancement in machine learning has led to a surge in automatic data generation, making it increasingly challenging to differentiate between naturally or human-generated data and machine-generated data. Despite these advancements,…
We live in a world brimming with uncertainty, where we constantly have to make a lot of decisions under incomplete information. We are firm believers that our subjective belief cannot be computed by rigorous mathematical formula; instead…
Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only…
Consider the fundamental problem of drawing a simple random sample of size k without replacement from [n] := {1, . . . , n}. Although a number of classical algorithms exist for this problem, we construct algorithms that are even simpler,…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
The world has seen the emergence of machines based on pretrained models, transformers, also known as generative artificial intelligences for their ability to produce various types of content, including text, images, audio, and synthetic…
Random number generation is crucial in many aspects of everyday life, as online security and privacy depend ultimately on the quality of random numbers. Many current implementations are based on pseudo-random number generators, but…
One of the most compelling problems in science consists in understanding how living systems process information. After all, the way they process information defines their capacities to learning and adaptation. There is an increasing…
Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be…
Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one specific example of an absolutely normal…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
This paper introduces a simple method for producing multichannel MIDI music that is based on randomness and simple probabilities. One distinctive feature of the method is that it produces and sends in parallel to the sound card more than…
The human brain can be considered to be a graphical structure comprising of tens of billions of biological neurons connected by synapses. It has the remarkable ability to automatically re-route information flow through alternate paths in…