Theory of Interaction by Eugene Savov

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The discussion centers on the finite nature of real objects as presented in Eugene Savov's "Theory of Interaction." It questions the relevance of considering arbitrarily large or small quantities in mathematics, particularly in relation to calculus. The conversation acknowledges that while calculus is a powerful tool for engineering, it does not accurately represent physical reality, especially regarding concepts like infinity and infinitesimals. The participants argue that using these approximations simplifies calculations but may lead to multiple interpretations of physical phenomena. Ultimately, the need for new mathematical frameworks for discrete objects is highlighted as a potential area for exploration.
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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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