Infinite and Infinitesimal in Mathematics, Computing
and Natural Sciences
Grand Hotel San Michele
Dipartimento di Elettronica,
Informatica e Sistemistica
Università della Calabria,
Via P. Bucci, Cubo 42-C
87036 Rende (CS),
The Infinity Computer
The goal of the Workshop is to create a
multidisciplinary round table for an open discussion
on modeling nature by using traditional and emerging
computational paradigms. Mathematics and natural sciences offer discrete and
continuous models to describe space, processes, and events occurring in
nature. Very often both approaches use notions of infinite and
infinitesimal in order to create coherent models. It is assumed that it
is possible to work with infinitesimal quantities and/or to execute an
infinite number of steps in algorithms. However, our abilities in
computing are limited and only a finite number of computational steps
can be executed by humans and machines.
The Workshop will discuss all aspects of the usage of infinity and infinitesimals in mathematics, computing, philosophy, and natural sciences. Fundamental ideas from theoretical computer science, logic, set theory, and philosophy will meet requirements and new fresh applications from physics, chemistry, biology, medicine, and economy. Researchers from both theoretical and applied sciences are very welcome to submit their papers and to use this excellent possibility to exchange ideas with leading scientists from different research fields.
Papers discussing new computational paradigms and their impact on natural sciences are particularly solicited.
A special attention will be dedicated to the new methodology allowing one to execute numerical computations with finite, infinite, and infinitesimal numbers on a new type of a computational device the Infinity Computer (EU patent 1728149). The new approach is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks that is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite).
The new methodology evolves Cantor’s ideas in a more applied way and introduces new infinite numbers that possess both cardinal and ordinal properties as usual finite numbers. It gives the possibility to execute numerical computations of a new type and simplifies fields of mathematics where the usage of the infinity
and/or infinitesimals is necessary.
There will be tutorials, discussion sections, and regular presentations.