If pure abstract mathematics can create physical universe, it is not out of nothing, it is out of pure abstract mathematics! And that is something!!

Mathematics is a language for expressing relations. Mathematics exists because relations among entities exist. Remove entities and their relations and nothing exist.

Louis,

Can you demonstrate rather than simply state this assertion ? It does not seem either straightforward nor trivial. A lot of current math (such as wide swathes of number theory) could stand on its own

Issam,

Fair enough, but the question is: can anything else ?

Chris,

I do not believe that something can exist (including mathematics) without being made of relations among existing entities. This image of a mathematical world existing beside the universe reminds me of the image of god existing beside the universe or the image of a sur-natural world existing beside the universe. This is my viewpoint. I cannot prove it. I love my dog but I cannot prove it either.

Louis,

You'd have to admit that this is probably not very satisfactory.

As far back as September 15th, 2007, Newscientist ran a cover story on the big and mounting body of evidence that math (or rather our human apprehension of it) constitutes *the* ultimate reality.

Since then, evidence has kept heaping up and become well-nigh overwhelming. There are very many 1st-rate Physicists out there (oft-cited Tegmark, who featured prominently in the Newscientist coverage, and many others) who take this view, whereas others take the view that math is but a language.

I believe that evidence for the former view is simply overwhelming (even Einstein had owned up to being baffled that nature 'obeyed' math so fastidiously), to address the subject properly however a book-length treatment is needed.

By the way - you can actually quite easily demonstrate that you love your dog - all you need to do is a MRI scan when you think of your dog.

You asked "Can anything else?"

In view of what I said in my earlier post, their are two interpretations to your question and they are both related:

1-your question now become something like this:"can a physical universe be created out of nothing?" There is a thread on RG :

"The notion of 'nothing', is it possible to define it? Is it worth to define it?" by Emauela Matei

https://www.researchgate.net/post/The_notion_of_nothing_is_it_possible_to_define_it_Is_it_worth_to_define_it

Please refer to my last 2 posts in that same thread: "nothing is nothing" and "why stephen Hawking is wrong about God" The first one is from an article published in the new scientist magazine issue no.2001 and the second is a summary of a reply by mathematics professor John Lennox:

http://www.dailymail.co.uk/debate/article-1308599/Stephen-Hawking-wrong-You-explain-universe-God.html

Or your question could be interpreted as:can anything else(other than abstract pure mathematics) create physical universes out of nothing? since pure mathematics is something then anything else that can create physical universes could also be interpreted as something. I don't think you can create physical universes out of complete nothing!!

Chris,

You mentioned an article of Newscientist , Tegmark and Einstein, and in your question you mentioned Shing-Tung Yau in support of mathematics as ultimate reality, or ultimate creator of reality.  But there are other great scientists and philosophers that think otherwise.  The fact that this idea is both supported and opposed by numerous great scientists shows the evidences for one view on this question the scientific/philosophical community is divided ; what is considering as coverwhelming evidence for one group is not for the other group. 

Humans at the time of the first large scale societies invented writing, counting, construction technique, measurement techniques which were later abstracted in the forms of Euclidean geometry, algebria, etc.  A modeling engineering language emerged from this abstraction of the engineering practices and this is the mathematical language.  It was necessary for this language, contrary to the other human languages, that it specifies unambiguously what is being specified within its expression.  Absolutly no subjective references could be allowed within this language.  All other human language are constructed with words which can only make sense through reference to what we see, or touch, or hear, or felel.  So mathematics was totally an objective language for doing engineering.  Science is a reverse-engineering of natural phenomena for prediction purpose.  Solar or lunar calendar systems are such scientific theories.  They are mathematically design clocks.  All science is a mathematical construction projected onto nature that is validated on the basis of its predicting performance of the mechanism.  Science is reverse-engineering in the mathematical domain of aspects of nature that can be reverse engineered in such manner.  Notice that almost none of the aspects of nature that we can easily expressed through natural languages cannot be expressed using mathematics. For example:  ''There is a table in front of me with an apple on it and far away I see a tree''.  Very simple sentence that make numerous subjective references through the words such as ''tree'', ''table'', ''apple'' etc that you easily make sense of because you have experience these objects trrough your bodily experiences and by being enculturated in the English language, you have learned how to translate my sentence in terms of your experience.  None of that could be translated into the mathematical world of science.   These are cultural realities of enculturated humans, easily expressed using our languages.  These realities are not scientific mathematically expressable. Cultural realities are real but not in  an absolute , universal and objective sense.  So there are all sort of realities and what is expressible scientifically, objective scientific reality, is only a small part of reality.

''Pure abstract mathematics seems able to create physical universes ex nihilo. Can anything else ?''

The idea that prior to the universe there where a set of pre-existing mathematic laws is a kind of supernaturalism where ''God created the world'' by another type ''a mathematical realm created the world''.  Both ''God did it'' or ''Mathematics did it'' are capitulation of explaining for creationism.  THe former is a theological creationism, the later is a mathematical creationism.  Can anything else?  Why not an universe that has always existed and evolved.   Why is there a need for a beginning with a specific original state?  Any assumption of a specific original state of affair bring us to back to creationism because the original state of affair cannot be explained from within the theory.   Why is such assumption necessary?  It is not necessary to assume such original state of affair.  We can assume that all that currently exist came from the transformation of was there before.  We do not need to assume that this process had a beginning and that something had to be created ex nihilo.  It is only a problem if you a priori assume that there was a beginning.  

We are human beings and we have a natural tendency to tell stories and each story has a beginning.  All  traditional creation my have beginning, some have a creation god or multiple ones creating each other.  Unfortunatly a scientific universe story can start one upon a time ''Mathematic'' created ....  Unfortunatly a scientific inquiry star from now and search the past and it cannot be a story that begin but only an end telling on how it came to be and it cannot stop at a creative beginning..  If it had a beginning, it would have to be an exnihilo creationism or other type of creationistic absurdities and that is not an scientific explanation.  THe only non absurd scientific  choice is no beginning.  It is curious that we are in a story that always exist and so never began.  We are talking about all the exist and so it this a very special story, normal stories with a beginning are special stories but here the story of '' all that exist'' is not a sub-story, it cannot begin within a bigger story, it is the whole story.

1.So each state of affair of the universe emerged from a previous state of affair of the universe.

2. Assuming that this process is finite, has an origin immediatly created an end to the explanatory process of explaining the universe by the universe (this is a requirement of an naturalist explanation) and create an absurdity. So  the universe has an infinite number of previous states of atfair and has no origin.

3. There is always a change of state of affairs otherwise the universe would have freeze into a state of affair.

Scientists are in the understanding business.  They will by principle refuse to take any state of affair as a stop to the understanding.  God this that is never an answer for them.  THis was originally there is never an answer for them.  Being like , always explaining a state of affair by a previous one, epistemologically force them to have an universe without a beginning.   This is an epistemological choice.