Yosemite supplied curl stopped supporting https
I realised what had happened.  I am trying to run BAPS, which requires the Matlab Runtime Compiler, though it is provided with BAPS and an ancillary installation.  Once you install the whole lot you need to let BAPS know where the MRC dynamic libraries are, and the 'recommended' method is to set $DYLD_LIBRARY_PATH to:

export DYLD_LIBRARY_PATH='/Applications/MATLAB/MATLAB_Compiler_Runtime/v84/runtime/maci64:/Applications/MATLAB/MATLAB_Compiler_Runtime/v84/sys/os/maci64:/Applications/MATLAB/MATLAB_Compiler_Runtime/v84/bin/maci64'


That put the wrong libcurl in the way and hosed the system.  So, lesson learned:  figure out how to set the DYLD_LIBRARY_PATH in a smarter way.