WHEN SHOULD TWO MINDS BE CONSIDERED VERSIONS OF ONE ANOTHER

What does it mean for one mind to be a different version of another one, or a natural continuation of another one? Or put differently: when can two minds sensibly be considered versions of one another? This question occurs in relation to mind uploading, where one wants to be able to assess whether an approximate upload constitutes a genuine continuation of the uploaded mind or not. It also occurs in the context of the rapid mental growth that is likely to follow mind uploading, at least in some cases — here the question is, when is growth so rapid or discontinuous as to cause the new state of the mind to no longer be sensibly considerable as a continuation of the previous one? Provisional answers to these questions are sketched, using mathematical tools drawn from category theory and probability theory. It is argued that if a mind's growth is "approximately smooth", in a certain sense, then there will be "continuity of self" and the mind will have a rough comprehension of its growth and change process as it occurs. The treatment is somewhat abstract, and intended to point a direction for ongoing research rather than as a definitive practical solution. These ideas may have practical value in future, however, for those whose values favor neither strict self-preservation nor unrestricted growth, but rather growth that is constrained to be at least quasi-comprehensible to the minds doing the growing.