This comes out of the ethics in belief thread where a number of atheists are speculating that the reason theists believe in an afterlife is fear of death.
Most atheists believe that they will persist through 'their' lifetime.
Even those who are physicalists (or materialists), which is most of them, and know that all the matter in their bodies will be replaced in a much shorter period than most of their lives, still they hold this irrational belief that they, for example, will experience retirement, or that the 10 years old 'they were' was the same experiencer.
These people are all aware, through computer science or use of computers, that it is easy to copy information. That we can even make two copies (or more) of the entire memory of our computer's memories and this does not mean that both of these copies are the original. They know that the matter - which is all that exists in their world-view - is completely replaced in their bodies - is it every 7 years.
Yet they spend at least most of their time living with the delusion of a continuous self - further note: they do not speak or think of a 'sort of me', or a 60% me, even though there are huge changes in mass, memories, habits from a 10 year old to an adult.
Given the speculating without evidence in the other thread, I will now speculate that the reason atheists believe in the continuous self is that they are afraid of the implicit termination - if analogic - in their own world-view. One that comes by degrees much faster than the termination of what is essentially a not at all exact copy in old age.
This is a kind of belief in souls.