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Numerical Infinity and

The Infinity Computer

The problem

  • Nowadays physical limits (speed, miniaturization) of traditional computers have been almost reached. Current attention of the industrial and scientific communities is dedicated to new computational paradigms and areas of their possible applications.
  • In spite of huge investments, there do not exist on the market general purpose unconventional computer architectures ready for a broad implementation and production. For instance, industrial quantum general purpose computers do not exist (D-Wave is not general purpose).
  • Traditional computers work with finite numbers only. Numerical computations with infinities and infinitesimals are impossible due to: 1. the presence of indeterminate forms such as ∞ – ∞, ∞ / ∞, ∞ · 0. 2. the impossibility to put infinite numbers in the finite computer memory.
  • There exists an insuperable wall in performance beyond which traditional computers are not able to go and all kinds of divergences and usage of infinitesimals can be studied only analytically by human beings.

Grossone® Infinity Computer

The Infinity Computer is a new kind of a supercomputer able to execute numerical computations with finite, infinite, and infinitesimal numbers using a new numeral system with the infinite radix called Grossone® and expressed by the symbol ⓵

  • An analogy: Ancient Romans did not know about existence of zero and negative numbers. As a consequence, they were not able to execute computations requiring these numbers and such expressions as V-V or III-X were indeterminate forms for them. In modern computations 0 is indispensable and the work of traditional computers is impossible without zero and negative numbers.
  • The Infinity Computer makes a similar thing thanks to Grossone® making possible the passage from finite numbers to infinities and infinitesimals and allows consumers to work numerically with different infinities and infinitesimals as with finite numbers giving so to the consumers an unprecedented level of accuracy and power of computations that does not exist on the market.

Reviews published in International Journals

Prof. Adamatzky about the Infinity Computer

Article, MIT Technology Review, 2012

Computational Management Science, 2007, vol. 4(1), pages 85-86, written by Prof. D. Trigiante

Cybernetics & Systems Analysis, 2006, vol. 42(6), page 183, written by Prof. V.P. Shylo

Optimization Methods and Software, 2006, vol. 21(6), pages 995–996, written by Prof. O. Prokopyev

International Journal of Unconventional Computing, 2006, vol. 2(2), pages 193-194, written by the Editor-in-Chief Prof. A. Adamatzky

Journal of Global Optimization, 2006, vol. 34, pages 157–158, written by the Editor-in-Chief Prof. P.M. Pardalos

News

On February 6, 2020 the Book Y.D. Sergeyev “Arithmetic of Infinity” was Best Seller #2 on Amazon.com among books “Infinity Mathematics”

Prof. Sergeyev is Member of the Editorial Board of the international Journal of Industrial & Management Optimization, American Institute of Mathematical Sciences

Special issue of the journal Soft Computing dedicated to the 3rd international conference “Numerical Computations: Theory and Algorithms – NUMTA 2019” has been published

Prof. Sergeyev was included in the list TOP 100 computer scientists in Italy by the rank Guide2Research

Prof. Sergeyev was included in the list “Top Italian Scientists, Mathematics”

Prof. Sergeyev was elected Corresponding Member of the Italian Accademia Peloritana dei Pericolanti

Intervista al Prof. Marco Cococcioni

The paper of D. Rizza is among the most read in the Journal: Rizza D. (2018) A Study of Mathematical Determination through Bertrand’s Paradox, Philosophia Mathematica, 26(3), 375–395.

https://www.numericalinfinities.com

The Infinity Computer presented at the Johnson Space Center, NASA, Houston

A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic

Article, ПОнедельник, 16.01.2018

Intervew to Russian national TV Channel “Culture”, 14.03.2017

La nuova aritmetica dell’infinito: GRAVITÀ ZERO intervista il Prof. Davide Rizza

Interview to Russia Beyond The Headlines

Articolo del Prof. G. Lolli per “Newton”

Articoli divulgativi del Dott. Walter Caputo

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