T H HUNG. HENRY

BLOG

  • About
  • Publications
    • Database
  • Gallery
  • Blog
  • Music
  • Contact

1/23/2018

‘This is a false statement’: is something beyond our logical reasoning? ― A review of Douglas R. Holfstadter’s Gödel, Escher, Bach

0 Comments

Read Now
 
Picture
Gödel, Escher, Bach: an Eternal Golden Braid
Douglas R. Hofstadter
  • Publisher: Penguin
  • Date: 30 March 2000
  • Language: English
  • ISBN-10: 0140289208
  • ISBN-13: 978-0140289206
‘A good poet will usually borrow from authors remote in time, or alien in language, or diverse in interest.’ ― T.S. Eliot, The Sacred Wood
Douglas R. Holfstadter has made an unprecedented move to bond the mathematician Kurt Gödel, the artist Maurits Corpelis Escher, and the composer Johann Sebastian Bach in the common centre of Gödel’s proof on his incompleteness theorem. This proof is targeting the intrinsic logical looseness and limitations in a formal axiomatic system in mathematics.
 
In a nutshell, mathematicians have been fancying exploiting a list of axioms which could give us “all of the mathematics”: it has to be a complete system – that any given statement is both provable and disprovable; it also has to be a consistent system – that a statement cannot be both proved true and false at the same time. However, such completeness and consistency are inherently contradictory – for example, ‘This statement does not have any proof in the system of Principia Mathematica (PM)’: if this statement is provable, then PM would be inconsistent (PM is self-referentially contradicting); if this statement is unprovable, then PM would be incomplete (the PM lacks the internal proof for it).
 
The mathematical ground of Gödel’s proof itself is a stand-alone masterpiece, but it also steps further to reveal the epistemology of any formal system science – theorems are the branch-outs developed from an axiomatic trunk, extending towards the vast space of truth while some being unreachable, at its counterpart, negative axioms provide the basis of all negations of theorems, also leaving some falsehoods unreachable. Coincidently, this reminds me a Chinese counterpart: Yin Yang Theory, and the symbol itself would give you the intuitive thought of its similarity with Gödel’s proof (Figure 1).
Picture
Figure 1.    The Symbol of Yin Yang Theory
​(image from Wikipedia)

The book is precious in the presentation of such rigorous and complex ideas. First, the dialogue at the beginning of each chapter unveils the limitations that we may come across in our daily lives – such opening encores with the dialogues in Plato’s Symposium. It successfully rings a bell among the readers, preparing the laymen to digest the mathematical and logical paradoxes. Second, the author’s imagination is far beyond mathematics alone: he traces back the connections from Escher and Bach with the Gödel’s theorem, offering a highly vibrant repertoire of aesthetics that is engraved in any field of knowledge. For example, Bach’s canons and fugues are often self-referential to deliver ambiguous perceptions to the listeners. In the meanwhile, many of the Escher’s artwork seem unreal and challenge our intuitive perception of space. Third, at the final portion of the book, it brings out a twenty-first century grand challenge of artificial intelligence, and how it may shed light on resolving the complex systems of self-reference, offering valuable insight to the futurism.
 
This book is definitely a classic that any learners at all stages of knowledge and truth inquiry should read, for the most underlying structure of how we learn and perceive.

Share

0 Comments



Leave a Reply.

Details

    Author

    T. H. (Henry) Hung
    Radcliffe Scholar in Interdisciplinary Bioscience, University of Oxford
    Events Committe, British Ecological Society
    Fellow, Zoological Society of London

    hung.studio
    ​

    Archives

    April 2020
    July 2019
    February 2019
    January 2019
    May 2018
    March 2018
    February 2018
    January 2018
    October 2017

    Categories

    All
    Book Reviews
    News
    Opinions
    Publications
    Stories

    RSS Feed

We live in a world where there are enough reasons to separate us. Yet I choose to connect to people with music and science.
© T H Hung. 2020.
Photo Courtesy. Matthew Smith, from Unsplash.​
___
PAGES

Home
About
Publications
Gallery
​Blog
Music
Contact
___
EXTERNAL LINKS

University of Oxford
University College, Oxford
Department of Plant Sciences, Oxford
Oxford Interdisciplinary Bioscience DTP
British Ecological Society
OxHKScholars Association
  • About
  • Publications
    • Database
  • Gallery
  • Blog
  • Music
  • Contact