George Gamow: Turning Double Apples into Doughnuts & Inverse Universes

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SUMMARY

George Gamow's book "One Two Three Infinity" details the transformation of a "double apple" into a doughnut on page 56, illustrating concepts of topology and surface manipulation. On page 58, he introduces the concept of an "inverse universe," where a human is turned inside out, prompting discussions on the material properties of the doughnut and the surrounding space. The forum participants express confusion regarding the mechanics of this transformation, particularly the implications of the "FREE" surface that Gamow describes. Understanding these concepts requires a grasp of advanced mathematical and physical principles.

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  • Basic understanding of topology and geometric transformations
  • Familiarity with the concepts of surface manipulation in physics
  • Knowledge of George Gamow's theories in cosmology
  • Ability to interpret complex scientific literature
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  • Research the mathematical principles of topology, focusing on transformations and surfaces
  • Explore Gamow's theories in greater depth, particularly in "One Two Three Infinity"
  • Study the implications of surface properties in physics and their relation to cosmological models
  • Investigate the concept of "inverse universes" in theoretical physics
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Students of physics, mathematicians, and anyone interested in theoretical cosmology and the implications of geometric transformations in understanding the universe.

daniel_i_l
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In George Gamow's book "One Two Three Infinity" he explains on page 56 how to turn a "double apple" with a free surface into a doughnut:
http://books.google.com/books?id=EZ...=X&oi=book_result&ct=result&resnum=2#PPA57,M1
He then (page 58) goes on to explain how the reverse process can be used to make an "inverse universe" where a human is somehow tured inside out.
I'm pretty sure that I understand how the double apple is changed to a doughnut but I don't understand how the reverse process make an inverse universe. It seems as if we just have to change the material of the doughnut itself and not the surrounding space.
Thanks.
 
Last edited:
Mathematics news on Phys.org
Have a look at the surface he demarcates "FREE". What is it bounding in each step? :)
 

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