The impossibility of immortality

What is life?

A person is a process. As long as the process runs, as long as it receives data and changes itself and/or its environment in response, it is alive. If that process stops running, either temporarily or permanently, it is not alive. A permanent stop is what we would term death.

Here's an example. I upload your mind to a computer. I run you in a simulated world. You exist, you feel and think in the same manner as you do now. You are alive. If I freeze the simulation, put it in sleep mode where the data and current state of all things, including you and your thoughts, is preserved. Are you alive? You don't think. You don't feel. Hence I say no. The fact that a backup of you exists which, if run, could produce a live you does not change the fact that right now, there is no active version of you running and you are not alive.

(N.B: No you're not unAlive when you're asleep. You're still running, albeit in a different mode.)

What is immortality?

Living forever. Not for a long time. Not for a very long time. Not longer than the universe is likely to exist. Forever. Infinitely. Without any end.

Trivial Impossibility: The speed of light as a constraint on computational complexity

The speed at which causality propagates is limited. This limitation is commonly known as the speed of light, although that is a far too specific name for a more general law. (I think). One implication of this is that there is a limit to the strength of computers we can create, even assuming we had access to unlimited resources. Why? Simple. A computer must transmit data from one place to another. From memory to processor or from processor to processor. Why is this true? Simple yet again. Even assuming we can overcome current limits which require us to separate memory and processors etc..., as long as processors or components have some mass it will be impossible to pack too many in one location lest their combined gravitational pull destroys them or causes a black hole to form, Back to the need to transmit data. As your computer gets larger, the lag/latency arising from communication gets more and more extreme. A Dyson sphere around our sun has a transit time of more than 1.6 second for data to reach from one edge to the polar opposite point. A computer the size of a solar system has even greater latency. Of course you can design around this to some extent with distributed systems, but there's only so much you can do. Past a certain point, increasing the size of your computer will cease to bring increases in strength as the limiting factor becomes not processing power but latency/bandwidth. The law of diminishing marginal returns applies.

1:Past a certain point, you can't make your computer any faster.

The second problem is that older life is more complex life. A living process/person builds up memories of past events. The longer their life, the more memories. The more memories, the more work the computer the person is running on has to do to store those memories and access/integrate them into present decisions/processes in a timely fashion.

(N.B: This assumes processes which do not ignore old memories aka don't have a cut-off point. i.e: possible that alien life integrates memories into basic algorithms determining decision making processes before discarding the rather than keeping them for reference as we do. For a number of reasons, I believe this memory-discarding type of mind is highly unlikely to exist or be comparable to us. If you disagree, assume this article is specific to human minds.)

2: The longer you live, the more computational strength it takes to run you

Hence the conclusion. Eternal life is impossible, at least if the laws of physics hold and my argument is sound.

Serious impossibility: Life as change

Life is change. Life is a process which takes in information and changes in response to it. All your experiences change you, change who you are.  When you gain knowledge, that is change. When you begin to think differently, when you become wiser, that is change. When you love someone and let them take your heart, that is change. Living is accepting change. Without change, there can be no life. This is true in the narrow sense as even forming new memories requires a change in the data you have access to. It is true in the broad sense in that experiences change how you think.

The longer you exist, the more you experience. Every experience changes you and eventually, after enough has passed, you are changed so much that you are no longer anything like your original self. The pattern that now exists traces it's history to you, but it is too different from you to be considered you.