Seeking a universal language

Is mathematics a universal language?  Not only is this universality often postulated but also it was said  -- some decades back -- that devices were broadcasting into space the intial decimal digits of pi, expecting that other intelligent beings would surely recognize the sequence of digits.  Robert Gethner examines this arrogance in a poem.

   The Universal Language     by Robert Gethner
                      
                             For G. G.

           “We think we have written the message [on the plaque on the space probe Pioneer 10]     
           in a universal language. The extraterrestrials cannot possibly understand English or
           Russian or Chinese or Esperanto, but they must share with us common mathematics
           and physics and astronomy.”
                                    –  Carl Sagan, The Cosmic Connection: An Extraterrestrial Perspective

   We send out primes, triangles, digits
   of pi---secret alphabets, quirks
   and enigmas of my beloved trade
   ---hoping that some lonely, three-eyed
   traveler from another star will find them
   a million years hence and think of us.
   But I wonder. Even among humans
   mathematics is far from universal. Watch
   this potter, shaping with her sensitive hands
   an inert lump of clay on the wheel
   into sensuous, living ripples. She never liked
   math---as she’s told me ruefully more than once.
   But see the intelligence in those confident
   hands, the focused intention adjusting,
   adapting, yielding to the feel of the clay,
   the delicate progress toward beauty,
   the improbable yet harmonious appositions
   of unequationed surfaces, convex, concave,
   the spontaneous yet watchful groping
   toward some new form implicit
   in the clay---not so different from a
   mathematician's work of molding, shaping,
   reshaping, polishing equations till they sparkle
   with ethereal truth. Imagine the sum
   total of all possible states
   of awareness that the universe
   has to offer (exultation at receiving
   a smile from just this woman
   whose eyes are just this shade of hazel;
   the particular amalgam that we feel, in the first
   Brahms piano concerto, of tenderness
   and troubled majesty…not to mention
   mental states of the three-eyed);
   think of all the different intricate mixtures
   of thought and emotion that sentient beings
   might conceivably experience; think
   of all those states as an immense ocean;
   then surely there are waters
   where we'll never swim, and yet, here we are,
   thriving, more or less, in our harbor,
   while the three-eyed do pretty well in their
   separate seas. They're potters---I forgot
   to tell you that---who never liked math,
   nor had the chance. No Newton, not even
   a Cardano, has arisen to grace
   or trouble their continual state of languid
   half-dream, a distant variant of which
   we experience perhaps once
   a year, when, dozing on a fall day
   with sunshine full on our closed eyes, we hear
   speech in the scratch and tap of an oak leaf
   descending along a trunk. Yet they stay in touch
   across great swaths of space with what we'd call
   radio waves, fashioned as a potter would,
   without the tools of my beloved trade,
   by dreaming, whirling, prodding,
   by shaping space with their gentle, frond-like wings
   not like hands, yet not so unlike, either.

"The Universal Language" was originally published in Mathematics Magazine 82 (2009), 226.