I am sitting alone in the small seminar room on the tenth floor. This is known as 'Harry's room'. I am at the head of a long oak table, working at a laptop computer. The door is at my back and the single window at the other end of the room sheds a thin, early evening light. There are glass-fronted oak cabinets along the walls, left and right. On the shelves are rows of display jars containing specimens of human brain, each suspended in a liquid the colour of watery piss. This is Harry's collection. The specimens are arranged according to pathology: tumours, cerebrovascular disease, degenerative disorders, and so on. There are whole brains, half brains, and parts of brain, sliced and segmented. Close to my right shoulder, there swims a cerebellum.
The room is ineffably still.
'I could be bounded in a nutshell and count myself a king of infinite space,' said Hamlet, 'were it not that I have bad dreams.' The infinite space was within the shell of his head. And so, inescapably, were the dreams. But looking around now at these dead still, grey-beige objects it is hard to see them as erstwhile progenitors of infinite space. They each represent the opposite: a singularity. A point at which the universe has collapsed.
(Paul Broks, Into the Silent Land).
From our perspective, it takes a finite time for other people to die. Each death represents the end-point of a mental world-line in space-time, a type of mental singularity, as Paul Broks puts it. Perhaps, however, there is a sense in which we can use a well-known psychological phenomenon, and the mathematics of conformal transformations, to rescue the dead from these singularities.
It's a familiar truism that time passes more quickly when you're concentrating on something, and more slowly when you're bored. The more you think, the less subjective time appears to elapse, and the less you think, the more subjective time appears to elapse. A greater amount of thought corresponds to greater brain activity, a higher rate of information processing, whilst a smaller amount of thought corresponds to less brain activity, and a lower rate of information processing.
Taking the limit in which the amount of brain activity, and therefore the rate of information processing, tends to zero, as one approaches death, the amount of subjective time which elapses becomes infinite. Thus, subjectively, we never die.
We can retain the general relativistic representation of physical space-time as a 4-dimensional manifold, equipped with a metric tensor of Lorentzian signature, but for each worldline γ representing a physical system with a mind supervening upon it, we can introduce a subjective time tensor. Let τ denote the proper time along the worldline; this is determined by the metric of the physical space-time, and a finite proper time will elapse along the worldline of any mortal. However, if we let dI/dτ denote the rate of information processing along the worldline of a mental system, then the reciprocal of this (dI/dτ)-1 measures the lapse of subjective time, and we can treat this as a conformal factor Ω which enables us to define the subjective time tensor as follows:
-Ω(τ) dτ ⊗ dτ ,
Ω(τ) =(dI/dτ)-1(τ) .
The conformal factor Ω blows up towards the end of the worldline of a mental system, providing such a system with an infinite lapse of subjective time, even though, to an external observer, a finite time lapses before the death of that system.
Possible objections? Well, for a start, one needs to explain why the years seem to pass more rapidly as we get older. And presumably, there is a lower threshold on the rate of information processing which a brain is capable of, below which the continuum approximation tacitly assumed by this use of calculus breaks down. Below this lower threshold, the brain has ceased to operate. Moreover, an infinite lapse of subjective time, in which a vanishing amount of experience is possible, seems to constitute something of a living purgatory...
How to live forever Paul Broks Conformal Death