Interesting article, but lines like this always make me groan:<p><pre><code> The aliens would, like us, be astonished by
the patterns in our shared cosmos and by the
effectiveness of mathematics in describing
those patterns.
</code></pre>
Why should we assume that any intelligent life form should have a psychology that is human-like in any way whatsoever? You can make the case for mathematical sophistication; but <i>astonishment</i>? I mean, if there are conceptually sophisticated aliens out there (which is a <i>huge</i> "if" that we have no evidence for or against), who's to say that they even have such a state as "astonished"?<p>Maybe they're sitting on their planet right now, and some uninformed and unimaginative journalist in their species is writing in their language:<p><pre><code> The aliens would, like us, take the patterns
in our shared cosmos completely for granted,
and find it utterly unremarkable that mathematics
are effective in describing those patterns.
</code></pre>
Just say NO to humans in funny suits!
"An interesting possibility, which I think should not be dismissed, is that a "true" fundamental theory exists, but that it may just be too hard for human brains to grasp. A fish may be barely aware of the medium in which it lives and swims; certainly it has no intellectual powers to comprehend that water consists of interlinked atoms of hydrogen and oxygen. The microstructure of empty space could, likewise, be far too complex for unaided human brains to grasp."<p>That's a distinct possibility. Further mathematical research might still allow considerable refinement in describing what a correct fundamental theory does NOT imply.
Mathematics is a human language. It reflects the human mind, as well as the human condition, and has already been shown to be less than universal (i.e. that there are true statements which cannot be arrived at via method of proof given axioms).<p>Human mathematical intercourse is generally couched in cliche (since most humans aren't particularly fluent), and is shot through with concepts that other advanced civilizations are likely to find violently stupid (e.g. infinity).