Theory of Interaction by Eugene Savov

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Discussion Overview

The discussion revolves around the implications of finite objects as presented in Eugene Savov's book "Theory of Interaction." Participants explore the relevance of traditional mathematical concepts like infinity and infinitesimals in the context of finite physical objects, questioning the necessity of new mathematical frameworks for discrete entities.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant questions the relevance of considering arbitrary large or small quantities if real objects are finite, suggesting a potential need for new mathematics for discrete objects.
  • Another participant argues that the use of calculus is valid and effective in engineering, emphasizing that while infinity and infinitesimals are not physically real, they serve as useful approximations for calculations.
  • A further contribution reiterates that calculus is a mathematical tool that does not necessarily reflect physical reality, reinforcing the idea that approximations simplify complex calculations.
  • One participant raises the concern that incorporating the physics of very small scales could lead to numerous interpretations, each providing a different local description of physics.

Areas of Agreement / Disagreement

Participants express differing views on the validity and applicability of traditional mathematical concepts in the context of finite objects. There is no consensus on whether new mathematical frameworks are necessary or if existing methods suffice.

Contextual Notes

The discussion highlights the limitations of current mathematical approaches when applied to finite objects, as well as the potential for multiple interpretations when considering very small scales in physics.

John274
The real objects are finite as shown in the book Theory of Interaction by Eugene Savov - http://www.eugenesavov.com

Then what is the sense to consider arbitrary large or small quantities?

Is there a need for new mathematics dealing with discrete (finite) objects?
 
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Are you claiming that Calculus does not work? There's one heck of lot of engineering that has been developed using Calculus.

OF COURSE there is no such thing as actual, physical "infinity" or "infinitesmal": mathematicians have been saying that for centuries.

That's completely irrelevant to the fact that approximating very large things (or large numbers of things) by infinity and approximating very small things by "infinitesmal" simplifies the calculation enormously.
 
OF COURSE there is no such thing as actual, physical "infinity" or "infinitesmal": mathematicians have been saying that for centuries.
Calculus (mathematics) is a TOOL. It does not necessarily represent physical reality.
 
If we were to include the physics of the vanishingly small in all calculations, we might encounter an infinity of (or at least, many incompatible) interpretations, each uniquely describing a local physics.
 

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