Souls and thought experiments

Think about a simple algorithm like insertion sort. It has a distinct definition, it has properties, and it operates.

What if you were to destroy every computer containing a copy of insertion sort, burn every book describing the concept, and if everyone that knew insertion sort were to somehow vanish? Would insertion sort vanish too?

Of course not, it would still be “out there”, it’s a thing whether it’s currently operating or not in any sort of physical way. It doesn’t need time and space to be a thing.

Your mind could be described as a massively parallel algorithm that your meat-brain is currently operating. Every neuron firing off can be captured with an algorithmic, mathematical description, and the sum total could be captured as well.

What’s the difference between our minds and insertion sort then? Do we have a reason to believe that we cease to be a “thing” if insertion sort does not? What makes us different?

I’m not arguing for religion here, or even spirituality, an afterlife or anything I suppose. I just don’t get why it’s wrong to believe we’re a “thing” that much like any algorithm doesn’t require existing in time and space to still be a thing.