One of the themes of current scientific progress is getting more and more information out of tiny amounts of data.

I think that if the universe was once a single spot and everything we see comes from there, then the information about everything is everywhere. If we had knowledge of the mechanics and enough computing power we could understand what has happened in the universe since the start just by observing the current state of one atom.

This is because, if we could measure them with full precision, the current position, direction, and speed of an atom (and all other measurements if we could do them physically) are only possible with one and only one specific history of everything else in the universe.

...to what extent can people be re-created from what they've left behind them...

I think us or any other intelligent species that continues after us will control every aspect of our environments. Just like now we are starting to understand the full "language" of DNA and we are in the first steps of cloning, AI, etc., we will also control the planetary weather, solar system level direction and orbits of planets, etc.

In this context it will be very easy to replicate past living beings. The problem is that because they will be operating on a different set of materials (h2o, salts, carbon, etc.) it will not actually be that original person even if it's an exact replica.

Unless there is some sort of entanglement possible, I think that If a person is copied, the copy is not the original person unfortunately, so when we die we will not be back unless its on the same set of materials, which is possible, but very improbable.

EDIT: The above phrase:

This is because, if we could measure them with full precision, the current position, direction, and speed of an atom (and all other measurements if we could do them physically) are only possible with one and only one specific history of everything else in the universe.

Replaced the original sentence:

This is because the current position, direction, and speed of an atom (and all other measurements that can be done physically) are only possible with one and only one specific history of everything else in the universe.

To reflect, as observed in the comments below by lesswrong.com/user/asr/, that "You can measure those things to only finite precision".

Cardinal numbers for utilons?I have a hunch.

Trying to add up utilons or hedons can quickly lead to all sorts of problems, which are probably already familiar to you. However, there are all sorts of wacky and wonderful branches of non-intuitive mathematics, which may prove of more use than elementary addition. I half-remember that regular math can be treated as part of set theory, and there are various branches of set theory which can have some, but not all, of the properties of regular math - for example, being able to say that X < Y, but not necessarily that X+Z > Y. A bit of Wikipedia digging has reminded me of Cardinal numbers, which seem at least a step in the right direction: If the elements of set X has a one-to-one correspondence with the elements of set Y, then they're equal, and if not, then they're not. This seems to be a closer approximation of utilons than the natural numbers, such as, say, if the elements of set X being the reasons that X is good.

But I could be wrong.

I'm already well past the part of math-stuff that I understand well; I'd need to do a good bit of reading just to get my feet back under me. Does anyone here, more mathematically-inclined than I, have a better intuition of why this approach may or may not be helpful?

(I'm asking because I'm considering throwing in someone who tries to follow a cardinal-utilon-based theory of ethics in something I'm writing, as a novel change from the more commonly-presented ethical theories. But to do that, I'd need to know at least a few of the consequences of this approach might end up being. Any help would be greatly appreciated.)

*2 points [-]It's a tempting thought. But I think it's hard to make the math work that way.

I have a lovely laptop here that I am going to give you. Suppose you assign some utility U to it. Now instead of giving you the laptop, I give you a lottery ticket or the like. With probability P I give you the laptop, and with probability 1 - P you get nothing. (The lottery drawing will happen immediately, so there's no time-preference aspect here.) What utility do you attach to the lottery ticket? The natural answer is P * U, and if you accept some reasonable assumptions about preferences, you are in fact forced to that answer. (This is the basic intuition behind the von Neumann-Morgenstern Expected Utility Theorem.)

Given that probabilities are real numbers, it's hard to avoid utilities being real numbers too.