

Reality revealed: The ultimate fabric of the universe (video) - georgecmu
http://www.newscientist.com/blogs/nstv/2012/10/reality-revealed-the-ultimate-fabric-of-the-universe.html

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Udo
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].

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DaNmarner
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.

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tambourine_man
“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...](http://books.google.com.br/books?id=R-qgdx2A5b0C&pg=PA147&lpg=PA147&dq=construct+all+mathematics+from+empty+set&source=bl&ots=Njv-
XEuF8q&sig=z9C0SiZF1DQ7X8YF1fOBYxptW88&hl=en&sa=X&ei=WURyUIKUFpOG9gTH3IHIBg&ved=0CDAQ6AEwAw)

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

Thanks for the quote!

