IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-030-50273-7_5.html
   My bibliography  Save this book chapter

The Physical Numbers

In: Artificial Mathematical Intelligence

Author

Listed:
  • Danny A. J. Gómez Ramírez

    (Instituto Tecnológico Metropolitano (ITM), Research’s Labs Center Parque i)

Abstract

A detailed cognitive analysis of the most outstanding forms of “understanding” the natural numbers is presented. In particular, the fundamental formal features and intuitions of this ancient numerical system are classified into physically supported parts and meta-physical (or mental) ones. A new numerical system consisting of the physical numbers is proposed which has an initial and a final element, and is essentially grounded in the physical realm. Semantic foundations and an initial seminal axiomatization for the physical numbers are offered, as well as a canonical correspondence between them and the natural numbers. The classic act of counting numbers is reduced in terms of doing physical partitions in a sequential way. Additionally, a pragmatic ontological clarification of the notion of infinity is presented in terms of the (physical) concept of immensity. Finally, based on the former constructs, a paradigm-shifting (bottom-up) meta-perspective is shown for understanding the causes of the high level of difficulty that the solutions of a large number of problems in classic elementary number theory possess.

Suggested Citation

  • Danny A. J. Gómez Ramírez, 2020. "The Physical Numbers," Springer Books, in: Artificial Mathematical Intelligence, chapter 0, pages 67-89, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-50273-7_5
    DOI: 10.1007/978-3-030-50273-7_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-030-50273-7_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.