FOM: Reuben, did you really mean this?

[JOE SHIPMAN, BLOOMBERG/ SKILLMAN]

   "Once a mathematical entity is invented, it has definite properties which we
are not free to choose, and which may be difficult or impossible for us to
discover."
   Did you really mean "impossible"?  That would seem to spell defeat for your
position, for how can they be definite and yet impossible for us to discover
unless their reality is something other than social?  Or did you mean impossible
for *us* but in principle discoverable by a future generation of mathematicians?
   Last night my 9-year-old son asked me "what is the first digit of  2 to the
googolplex power?".  (googolplex=10^(10^100))  This looks like an example of a
definite property (of the invented entity 2^googolplex, namely its first digit
in its base 10 form) which is impossible for us to discover.  In what sense
does my son's question have a definite answer?
    Regards,
    Joe