I wonder if someone has come up with an algorithm or some other kind of mathematical structure which, if run (on a computer with infinite memory and unlimited amount of time), or if it just existed physically, would produce conscious being like us or other interesting and kinda similar self-organizing structures.

I want an environment for proofs and/or mathematical explanations, which treats them as a tree or a graph rather than text. More specifically, I want to be able to write proofs like:
* Suppose A
* From A it follows that B
* C can be proved by induction
* Because B implies not C, it follows that A is false

And if you click on "C can be proved by induction", you get a more detailed explanation of how that happens:
* What property exactly we're proving by induction
* How base case is proved
* How inductive step is proved

And there somewhere if you see a logical step and you're not sure what theorems we invoke to prove it, you click on it and see "by lemma 2.2 (ii)"

There's an article by Leslie Lamport (link to article: microsoft.com/en-us/research/u; link to hacker news discussion: news.ycombinator.com/item?id=1)
in which he advocates writing a more structured way of writing proofs, which goes like this:

1. A
2. A implies B
3. not C
4. B implies C, hence not B, hence not A

Proof of 1:
blah blaah


Proof of 4:

What other similar things are there?

workflowy.com/ - a TODO program where you simply have nested lists, and you can easily expand or collapse subtrees

waitbutwhy.com has these circles of different colors in text. Green circles are interesting footnotes, grey ones are boring footnotes. This doesn't allow creating trees of arbitrary depth but the usability of these things is very good in my opinion and perhaps we don't need that much depth.

It seems arbital.com/ has a thing like waitbutwhy, except it allows arbitrary depth.

Philip boosted

🗺️ Our #World in Data: "The #map we need if we want to think about how global living conditions are changing"

>CP-inspired minimal constraint solver
I don't know what that I assume it's a numerical algorithm. Are such things often implemented in languages like Rust? I think that they probably aren't. So perhaps it's better to choose either a project more suitable for Rust or a language more suitable for this project? That way the skills you will get will be more useful in the real world.

@LukasRos I would also suggest to think what will happen to everyone else and what will happen in the future if we do this thing "by means of government regulation I presume". Because usually government trying to change something in economics leads to net negative result (but I must note that this opinion is shared not by everyone). For example want to make poor people better off by increasing minimum wage? Well, that will lead to less low-paying jobs overall, will harm businesses and maybe the poor people too.

@dpwiz That's a possibility, but not 100%, so expected value of your utility function still doesn't exist.

@dpwiz Actually I am not sure how ethics should solve thought experiments with identical lifes and simulations running (or not running) moral patients inside them.

@dpwiz I don't know much about special relativity or about general relativity, so I usually model the universe as Euclidean space, either with another dimension as continuous time (then we need to sum wellbeingmoments with integrals) or as discrete time.

@dpwiz and by thinking about persons and well being of their life problem arise when I think about less exotic (in my opinion) things - like cloning minds, running the same simulation twice, etc.

@dpwiz I guess you're saying here that in practice agents will extremely rarely make decisions such that some pairs of options of the decision looks similar to Repugnant Conclusion. I don't really get why you think so. If the humanity (or whatever humanity will get transformed into; excluding variant with totally alien mind doing whatever it wants with us) will reach extremely high level of technology (I think there's about 20% probability that this will happen), then we might (I hope so) start thinking about how to tile the universe in an optimal way. And then such decisions might happen.

@dpwiz Right now the utility function I like most is as follows:

Consider time to be discrete, for example possible moments of time are 0, 1, 2, ... Utility of a world is the sum over each moment of time over each moral patient existing in that moment of time of well being of this moral-patient-moment.

By population traps do you mean the possibility that overpopulation of the Earth will happen and will cause bad things? I rarely consider such things when thinking about far future because it seems to me other huge changes will happen before that - maybe we will all die, maybe a superintelligence will kill us all and do continue doing its thing, maybe that doesn't happen and we start colonizing the nearby planets, maybe humans will stop living in organic bodies and will rarely produce new humans, etc. So overpopulation problems seem more like a problem of the near future to me.

@dpwiz If physics are in such way that it's impossible to make a bomb that'll go a VERY BIG BIG BADA BOOM, then launch dem Von Neumann probes and nothing might go wrong with them with a large portion of them in one hundred years. In my opinion the probability that we're living in such a universe is nonzero.

>That's it, the problem is in the theorem, not reality.

I wonder if you wrote that to make me angry on purpose.

We can send Von Neumann probes everywhere and tile the universe (not literally the whole universe) with moral patients. Perhaps there will be a decision to send them now with them having very slightly positive average well being or wait a year and increase their average well being a lot. Perhaps due to how exponential tiling of the universe works, if we launch now, we will be able to create much more moral patients before the universe dies. Do all such scenarios seem incredibly improbable to you? They seem plausible enough to me.

@dpwiz Right now I have a decision - to eat soup or to eat potatoes. How does it not impact infinitely many agents who might live in the future? I don't get what you're hinting at by writing 'at "once"'.

@dpwiz So you're thinking something like the universe is ticking and has a nearly constant probability to end with each tick? That doesn't seem reasonable to me.

I think there's a nonzero probability that the rules of physics (the territory, not the map) are made so that it will be ticking forever and it will be possible for conscious being to not stop existing. But in this case the expected utility is undefined.

@dpwiz Repugnant conclusion does not need infinite sets of people. However for the theorem to be applicable as I stated it, finite sets of all sizes must be allowed.

IMO total utilitarianism does have a problem with infinite sets of moral patients.

>all practical purposes
I don't think I know many practical enough purposes where it can be applied. And as they become less practical (like thinking how the future of humanity should be shaped), its problems become more important.

Just to be clear, total utilitarianism is my favorite utility function (even though it is not well defined because of problem with infinite sets). However I prefer to count well being of person-moments and not of persons.

Can you explain what it is you're saying about special relativity? I don't know special relativity theory.

@dpwiz Lol, same planet? Do you even far (and possibly not so far) future?

@dpwiz What is this "usual expected value decay by probability"? If you think it's possible that there will be a countably infinite set of people in the universe (I can't reject this hypothesis because we don't know all rules of physics of our universe) and try to apply total utilitarianism, expected utility will not exist because the corresponding sum over this infinite set will not converge.


Definition 1. World is any pair (P, w) where P is a finite set which represents all people who have ever lived and will live; and w is a function from P to ℝ which represents total well being of people in the world.

Definition 2. Utility of a world (P, w) is defined as
\[ \sum_{h \in P} w(h). \]

Theorem. For any world (P, w) for any positive real number t there exists a world (Q, y) such that the range of the function y does not include numbers greater than t and utility of (Q, y) is greater than utility of (P, w).

Proof is obvious.

So, what do you not understand?

I want to tell you how to form new habits and replace old ones.
Most animals including humans have this thing called Trigger-Action Patterns. It is a habit of if <specific trigger has happened> then <do specific action>. Examples: there's a bowl of chips in front of you -> take one; you open your browser -> click on [you usual first click site]; you have arrived at [specific ttain station] -> go to [specific exit]. The last one often happens to me even when I intend to go in another direction simply because I used to travel that way often when I was studying at university. Basically whenever you making a decision and often even when you are not making deliberate decisions, there's a part of your brain which votes for the action you usually do in similar situations.

Here's how to use it to create Trigger-Action Plans:
1. Identify goal. I want to learn more English words and I have an app on my phone for that.
2 and 3. Choose trigger and new action. Whenever I bring my wallet with bus card to the bus payment device (this is the trigger), I will think whether now is a good time to study using the app.
4. Rehearse. If you can do it physically by getting into situations with the trigger, do it. Otherwise visually imagine you getting into such situation, noticing the trigger and doing the action. Rehearse for 10 times

Google Trigger-Action Plans to learn more.

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