Complex systems are highly sensitive to even minute differences in initial conditions as illustrated here:



You don't even need that 3 minute bus spiel for the systems to diverge at some point. They will do that on their own naturally.

One twin typically gets a 10-20 minute head start. Two or three minutes, if they're delivered by cesarean section. Plus, every time the cells divide, there is a potential variation. Even with clones.

You are implicitly referring to the logical paradox concerning the identity of indiscernibles.

The potential existence of indiscernibles, e.g perfectly identical twins who lead perfectly identical lives, except for their space and location, seems to imply that materialism cannot be reconciled with the subjective concept of self-identification in a way that would be acceptable to a materialist.

The materialist has several options with regards to his understanding of self-identification, but none of the available choices seem to look attractive to him:

1) He could accept the identity of indiscernibles and identify his 'self' as being the possibly infinite collection of physically identical selves that exist at different spatio-temporal locations throughout the universe; each of the physical entities in this collection not only has qualitatively indiscernible experience from one another, but is in fact the same experience, i.e. there is one psychological 'token' of experience shared between many physical lives.

The materialist presumably finds this option barking mad, for not only does it seem a bizarre proposition, but it seems to undermine the whole point of materialism, namely to explain the self as a physical token that is part of the causal nexus, rather than as an abstract and non-causal type of physical entity that is related to the causal nexus via dualism of some sort. It also goes without saying, that this choice also would play havoc with his understanding of science in general.

2) He could accept the identity of indiscernibles as above, but argue that the material universe is such that there are no actual physical indiscernibles. But this seems physically speculative and amounts to neo-Kantianism that goes against the grain of materialist epistemology (should a materialist be deducing materialistic implications from introspective a priori arguments?) This option also completely fails to address the underlying metaphysical problem concerning whatif there were indiscernible selves?

3) Alternatively, he could reject the identity of indiscernibles, by arguing that the spatio-temporal position of an individual is an internal property of the individual's mental state. But in this case it seems that he must either

a) give up the claim that the experiences of his self are explainable by causal laws, for his spatio-temporal position per-se has no causal relevance with regards to his experiential content, or

b) he must reject the Cartesian assumption that selves exist, whereby it is trivially the case that spatio-temporality is an internal property of the self-as-universe. But in this case, what is left of materialism seems dangerously close to idealism and even solipsism, that the materialist presumably wishes to distinguish and distance his beliefs from.