[FOM] John Baez on David Corfield's book

Stephen G Simpson simpson at math.psu.edu
Sat Oct 4 19:32:57 EDT 2003

Alexander M Lemberg Sat, 4 Oct 2003 16:07:01 -0600 writes:

 > exotic R^4, a differentiable manifold which is homeomorphic but not
 > diffeomorphic to the usual R^4. This phenomenon is unique to 4
 > dimensions.

OK, good.  Corfield and others asserted many times that there is lots
of philosophically interesting mathematics other than f.o.m.  I kept
asking for examples, but none was forthcoming.  I am glad to finally
have an example on the table.

However, I don't find this example completely convincing.  

What do you see as the philosophical interest of exotic R^4?  Have
philosophers used exotic R^4 in a serious way to address serious
philosophical issues?  Perhaps you are going to say something about
our 4-dimensional world being possibly homeomorphic or diffeomorphic
to R^4 or exotic R^4.  I don't see that this is a philosophical
question, but maybe you do, and I am willing to be persuaded.


Stephen G. Simpson
Professor of Mathematics
Penn State University

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