you mean 32 kbytes.
it's the usual problem with address-space: 32bit can only address 2^32 bytes or twice that many words. that's just 4GB or 8GB or 16GB at most. if you want more, you need 64bit processor. but on the other hand it is not as much of a gain to have 64bit when the 64GB chips take up almost the same space as the whole parallella board, so I guess we need to wait till memory-developers catch up with the new possibilities of 64-bit...
parallella is based on all of the core's memory being directly accessible.1024 cores with 32kb each, that's 32MB used up by them and the rest of the 4GB address-space free for the 2 main processors and whatever other hardware. guess there is some space for improvement, but 64GB wasted by the cores alone would really be overkill -- the way software nowadays is lacking complexity...
btw, 32kb is not really the maximum-program-size for each core, 8kb are reserved for stack, and maybe the program will want another 8kb for storing the data it generates. so better look out for compilers that produce code under 16KB!