Reality revealed: The ultimate fabric of the universe (video)

http://www.newscientist.com/blogs/nstv/2012/10/reality-revealed-the-ultimate-fabric-of-the-universe.html

by georgecmu • 14 years ago

11 4 14 years ago

DaNmarner2• 14 years ago

Empty set is not equivalent to nothingness. Therefore mathematics can not be constructed from empty set. So reality described by mathematics is not based on nothing.

tambourine_man• 14 years ago

“0 is particularly nice. It's the class of sets equivalent to the set of all objects unequal to themselves! No object is unequal to itself, so 0 is the class of all empty sets. But all empty sets have the same members—none! So they’re not merely equivalent to each other—they’re all the same set. There's only one empty set! (A set is characterized by its membership list. There‘s no way to tell one empty membership list from another. Therefore all empty sets are the same thing!) Once I have the empty set, I can use a trick of von Neumann as an alter- native way to construct the number 1. Consider the class of all empty sets. This class has exactly one member: the unique empty set. It’s a singleton. “Out of nothing” I have made a singleton set—a “canonical representative” for the cardinal number 1. l is the class of all singletons—all sets with but a single element. To avoid circularity: “1 is the class of all sets equivalent to the set [ I I I.” In words, 1 is the class of all sets equivalent to the set whose only element is the empty set. Continuing, you get pairs, triplets, and so on. Von Neumann recursively constructs the whole set of natural numbers out of sets of sets of sets of nothing.”

http://books.google.com.br/books?id=R-qgdx2A5b0C&pg=PA14...

DaNmarner2• 14 years ago

Yes, number of subset of an empty set is 1, therefore an empty set is not equivalent to nothing.

Thanks for the quote!

Udo• 14 years ago

Math is not the ultimate fabric of the universe. Mathematics is a set of formal languages and concepts that can be used to describe the nature of reality really well. Those laws and phenomena that can be described using math are the "fabric of reality". A language is not equivalent to the things expressed with it.

The frequent invocations and interweavings of human concepts such as consciousness into this muddled mess of an explanatory video serve little purpose beyond giving the whole thing a vague New Age vibe that isn't really warranted and the whole thing could have been avoided by not intentionally mixing Math [the human construct] and Things-Described-By-Math [the inner workings of the universe].

Reality revealed: The ultimate fabric of the universe (video)

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