In this discussion list there were several threads
on what could be the proper description of all of nature.
Typical approaches are that the universe
is to be described by mathematical concepts such as some
special Hilbert space, some special type of category,
or other very elaborate mathematical structures.
There is a little problem however, which I would like to pose
as discussion topic.
All these structures are specialized sets, i.e. sets plus
special properties and specialized relations between
However, I seem to have a simple argument that the universe
is not even a set. In short, it goes like this.
To be a set, nature has te made of elements. Elements
are distinguishable entities.
(We are used to think that points in space or time, or events
in space-time, as well as elementary particles are
However, in the Planck domain, i.e. at scales
around 10^-35 m or 10^-44 s it is easy to show that
two different space-time points cannot be distinguished
from each other clearly, nor two particles, nor even
one from the other.
It takes only a few lines, using the Compton wavelength and the
Schwarzschild radius expression, to deduce this connection,
which is based on the existence of the Planck length and the Planck time as shortest
intervals appearing in nature.
The universe seems to be a set only *approximately*, at energies
or scales which are very low compared to the Planck energy or
And that would mean that all approaches trying to describe
the universe as some complex mathematical structure are doomed.
the universe cannot be described with any structure which contains
a set, or which is built on a set.
It is not clear what the correct structure should be; but
the structure should be very simple, and quite a bit simpler than
a set. If you have any proposals for such a structure, I'd
be interested to hear about them.
PS.I wrote up the argument in more detail in the file
and the preceding
Have a look at my free physics textbook, written to be
surprising and challenging on every page:
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