I agree that the key has to do with relations -- and that this is related to emergence.
Individual carbon atoms are arguably fairly simple. But carbon atoms in relationship either with each other or with other things form extraordinary structures. In some sense those structures were hidden from us (at least not visible to us) when we looked just at individual carbon atoms (and they may appear surprising when we first encounter them -- one of the less important properties of emergence in my view). Similarly number theory depends on relationships -- such as the addition relation, the multiplication relation, etc. -- that we impose on the individual numbers. Having taken the step to acknowledge the importance of relationships, the next question is: what sorts of relationships does a domain allow. That is, what enduring structures can be imposed on a domain? For the naturals, a structure is enduring if it can be defined. Once defined there is nothing to break it apart. It doesn't deteriorate with time. For physical elements a structure is enduring if it persists without the need to be held together by external imposed forces. -- Russ On Sun, Apr 25, 2010 at 9:53 AM, Marcus G. Daniels <[email protected]>wrote: > Steve Smith wrote: > >> You ask "why", he asks "why ask why", I ask "why ask why ask why". >> > A recursive function definition requires a base case for escape. Doug > provides that case. > > Marcus > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > -- Russ Abbott ______________________________________ Professor, Computer Science California State University, Los Angeles cell: 310-621-3805 blog: http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ ______________________________________ On Sun, Apr 25, 2010 at 10:09 AM, Douglas Roberts <[email protected]>wrote: > string why() > { > while (!why()) > { > why(); > } > } > > > (string theory search) > > > On Sun, Apr 25, 2010 at 10:53 AM, Marcus G. Daniels > <[email protected]>wrote: > >> Steve Smith wrote: >> >>> You ask "why", he asks "why ask why", I ask "why ask why ask why". >>> >> A recursive function definition requires a base case for escape. Doug >> provides that case. >> >> Marcus >> >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> lectures, archives, unsubscribe, maps at http://www.friam.org >> > > > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org >
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
