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.)

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".

Hopefully the apparent time limit on the Philosopher's Stone isn't going to get worse over time.

Good point. A time limit of 3:54 does seem too arbitrary to be hard-coded.

Harry also hasn't considered that it may only be good for some finite number of permanent transfigurations. He's going to try to use it many more times than it probably has been used in a very long time.

At least he only intends to use the Stone as a stop-gap measure for fighting death until he is able to properly end the world.

[edited]

Am I missing something? Why is Harry inventing this silly story?

I bet Hermione is just going to love being the center of all the attention and scrutiny this will bring on her.

I sincerely hope I am seeing an excellent parody of extremely irrational SJW attitudes here.

For what it worths, or if it is not the case, the central idea here is self-help for people who suffer. This is certainly missing from this reply. If this is a seriously meant as an SJW response, then I would translate it to that lingo as being hurt by patriarchy, and learning to undo this hurt by adapting to it.

A social, political response, New Athens or New Sparta is NOT a major point here, because for some people like me adapting to society is more important to changing it because we have one life, thrown into society (Heidegger).

But actually what little I wrote about a social-political response was less patriarchy, less toxic mascuilinity and less bullying, so it seems to be a misresponse at that. I think I am being pretty progressive here as a far social change is covered except that I simply don't care as much about social change helping future gens rather than self-help, adaptation for people who suffer NOW.

I think I am in a community of people who don't have very high fertility rates. I actually have a daughter and I have this impression - parenting hardly ever discussed on LW - that most of the community has no children.

From this it seems logical to me that social change is way way less important than self-help. We are not making many people to live in a future society where everything is right. People with 4 kids may sacrifice their happiness for their sakes. For no-children and few-children people and I think it is the case for us, adapting to society must be more valuable than changing it.

The East vs. West aspect sounds valid but only superficially so - relevant only to the letter, not the intent. Obviously it is about Westernized karate - and obviously to everybody who knows these stuff Muay Thay works just as well. One could raise the same parallel with Greek wrestling not training self-confidence (courage) enough and MT yes.

State and local governments in the US have primary responsibility over education, road construction, utilities, policing, the courts, licensing restrictions, zoning laws, and public transportation. The federal government can and does sometimes overrule them in these areas, but they are mostly left to themselves. Federal government action tends to be restricted towards various welfare programs, foreign policy, and the health care system. I would not describe state and local governments as having little power.

Researchers outside the physical sciences tend to be inexpensive in general - e.g. data scientists / statisticians mostly need access to computing power, which is fairly cheap these days. (Though social science experiments can also be costly.)

It appears that you think autistic people are less rational than the average person.

Um, yes for most definitions of "rational". That's why it's considered a disability.

One of the unfortunate limitations of modern complexity theory is that a set of problems that look isomorphic sometimes have very different complexity properties. Another awkwardness is that worst-case complexity isn't a reliable guide to practical difficulty. "This sorta feels like a coloring problem" isn't enough to show it's intractable on the sort of instances we care about.

Separately, it's not actually clear to me whether complexity is good or bad news. If you think that predicting human desires and motivations is infeasible computationally, you should probably worry less about super intelligent AI, since that complexity barrier will prevent the AI from being radically effective at manipulating us.

It would seem to require an unusually malicious universe for a superhuman AI to be feasible, for that AI to be able to manipulate us efficiently, but for it to be infeasible for us to write a program to specify constraints that we would be happy with in retrospect.

Does that stop you regarding a theory as more credible when it's simpler (for equal fidelity to observed evidence)?

It's more credible in the range of data for which it's fidelity has shown it to be more credible. I expect extrapolations outside that range to have less fidelity.

Do you have more specific expectations?

No.

I don't have some grand unified theory.

I just observe that a lot of cosmology seems to be riding on the theory that the red shift is caused by an expanding universe.

Note that I ended my first post with questions, not with claims.

What if it light just loses energy as it travels, so that the frequency shifts lower?

That seems like a perfectly natural solution. How do we know it isn't true?

What would be the implications to the current theories if it were true?