A metaphorical fugue on minds and machines in the spirit of Lewis Carroll.
Continuing our en-devour of de-mystifying ‘The cognition’ , here is a long read from Pulitzer prize winner author explaining about the strange circularity of life. The real is real real when I say, he proves the true presence of recursion and loops concept by music,arts,mathematics,Physics,Natural language grammar and Computer programming examples. Here most of us say ”That’s enough!’ , ‘Heights of it!’, ‘This is the limit!’ and go on with our real life. ‘I want to know less and be happy is my goal’ lies at logic of such behaviors, but the book facts are bewildering and at same place makes a higher out of box meaning.
Bach is a western music composer. Songs have themes and words with them. The form of communication from the composer to the listener is very fast when only the music is involved,listeners emotions are touched. The singer touches the logical mind of the listener with the voice modulations and tonal vibrations. Bach’s fugue is a contrapuntal composition in which a short melody or phrase (the subject) is introduced by one part and successively taken up by others and developed by interweaving the parts.This is recursion and self-refencing in songs.
He also have given some tunes which have his name hidden inside the themes.How brilliant!
Escher is a western visual artist.In some of his creations he uses mathematics in his drawings where recursion and self-referencing are self-evident.
Godel is a Czech Republic citizen. He has proved
1.If a (logical or axiomatic formal) system is consistent, it cannot be complete.
2.The consistency of axioms cannot be proved within their own system.
The axioms and conjectures of mathematics when proved in terms of mathematics means violating basic logic of proving. Logic says if any thing proves itself its not proved. So if we keep on making a larger and larger set, keep on proving and proving this keeps on being unproved in end.
The above pic is the graph of electron oscillations in a crystal placed inside the static magnetic field.
Natural Language Grammar
Author gives some sentences which are incomplete if taken alone. But does refer to itself when taken with other joined sentence. He tries to explain some of the looping language concepts.
“Is a sentence fragment” Is a sentence fragment.
“Yields falsehood when preceded by its quotation”
Yields falsehood when preceded by its quotation.
The author names such sentences which are having double meaning when repeated with themselves are named Quines. Such sentences are only having that second meaning when read overall along with its better half.
Looping equals the wheel, moves one cycle and another cycle and so on and on.It keeps repeating on and on and when it stops it just stops.
Recursion means wheeling inside or outside,we have to return back when we have to come back to our complete state. This is similar to going in a mesh and coming out from the mesh.
Douglas Hofstadter, the author gives these examples in the sense that these are the form of self-reference and recursion. Such self loops are present in vast numbers in our real life. In nature there is no chaos, there is a higher order of things.To be at the right place and right time is my suggestion by reading and studying this book.
Author says how cognition emerges from hidden neurological mechanisms and finally rests his case to cognition as the sole reason for such self-loops.The analogy of human mind thinking process to the ant-colony natural phenomenon is really nice. The book is heavy and You could not get the mathematics in one single read but there the meaning from other concepts are clear and it definitely is the worthy re-read.
Some people also claim that this book messes with their thinking , but the author cautions before he does so.I self regret for not explaining most efficiently but you go ahead you have the Best Non-Fiction book for you the Non-Technical Readership who like to read science fiction, watch science fiction. You have the future of AI.