Here's the prompt:

Construct an equation or function or machine that is homomorphic with life.

For the purposes of this discussion, we assume that the relevant properties of life are
(1) Heuristical maximization of self-projection onto the time axis (ie. survival).
(2) Nontrivial dependency on variables independent of temporally initial conditions (ie. given a machine M(I) generated from initial conditions I, M(I)(E) and M(I)(E') should result in different survival times for some pair of conditions E and E'). This is to prevent forms of "life" that don't react to their environment.

I think (2) is the only condition consistent with every common interpretation of "life". (1) is debatable, given the non-zero rate of suicide, but it was added for the sake of having some goal that sort of represented the idea of adaptation. I believe it's a goal that "almost all" non-human forms of life have. More importantly, (1) is a property that's very easy to make use of when trying to give some "life" other goals.

Here's the first attempt by Dragor:

integral of all x from x = birth to x = death (amount of endorphins at the current x)

In retrospect, I believe that prompt may not be an accurate representation of the question Dragor had in mind.

2438190
I added explanations for the two properties and tried to clarify (2).

I've heard the "falling entropy" description of life before, and it is a very interesting coincidence that people today happen to want things that lead to lower levels of entropy (burning coal, nuclear power plants, etc). There may be some link between "survival in this universe" and "universe tends towards low entropy", but I haven't yet taken the time to try to find it.

2438769
Yeah, entropy is a bad word, and I definitely misused it in the physics sense in my last post.

That's a very interesting article. I wonder if that idea can be usefully applied to artificial intelligence: create a set of rules that inevitably leads to something that has to either fight the rules or die off.

Edit: I guess evolutionary AI technically does this already by constantly killing off the "weaker" AI. Still, those tend to have a separate goal specifically for killing off AI, and technically that goal changes with the state of the "universe". I wonder if there's any benefit in creating a simple set of static rules that determine whether or not an AI instance lives or not. It might give the program a chance to develop an internal model of the rules.

2437855
That's still pretty vague, some additional restrictions would be nice.

In this general setting I would say we want something like the Bellman equation or the Hamilton-Jacobi-Bellman equation, if you want to go time-continuous. In general, we probably want something from Optimal control theory as this describes our model (even if it's pretty minimalistic ) quite well, I think.

2443122
That... alright, that seems like a valid solution to the question, assuming the machine can perfectly simulate itself and the universe it's in, and assuming the machine may only live for a finite amount of time... and somehow simulate itself and the universe in less time than its existence.

I think there needs to be some kind of lossy optimization for this to be possible. I'll get back to this shortly!

2437944 Sorry for being late. I'm one week behind my feed...

The equation I gave is the one I'm actually using to optimize my own life. Regardless of its practical applications, I don't think it's accurate on an objective level.

Objectively speaking I'd go with
Meaning of life = {}
(there's no such thing as objective meaning of life)

On the other note, I like how you brought in the suicide rate to measure the success of achievement of meaning of life. That does assume however that life itself is the meaning of life.

2438190 What does the Hitchhikers Guide to the Galaxy say about meaning of life?
(Did you mean 42 thingy?)

2478580 I was actually trying to be serious with my equation (it wasn't meant as a joke as 42 answer).

I think you are right. I think I'm misunderstanding this whole group. I feel widely outclassed among you guys. I find new things attractive, but I think I've bitten more than I can chew, when I joined this group. I don't think I have the skills to contribute anything meaningful anymore.

2479352 I studied mathematics for years (granted, it was a while ago and I forgot most of it) and I still feel this stuff is way beyond me. It would take me years to reach your level. I think I'll start with something easier for now, like the science group for instance.

2478486
It's interesting that you're trying to maximize it from birth to death, rather than from present to death. Are you a (bidirectional) time traveler?

That does assume however that life itself is the meaning of life.

I think that's a safe assumption. I was going for a literal interpretation of what you said, and one way of phrasing it is "life is life, now play around with one of the sides".

I think everyone here, except maybe VoidInfinity, feels outclassed. It's definitely the case the everyone is confused. I guess one point of this group can be to make things less confusing? It's a necessary prerequisite for understanding what other people are trying to say, which is necessary to do anything with any logic.

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Well, let me tell you some facts I learned during my studies (of 6 1/2 years, so I hopefully know a little about what I'm saying ):

1. Everybody, no matter how intelligent or gifted at mathematics is "outclassed" by somebody by a wide margin (this even applies to professors).
2. No matter how well you think you understand a subject (even an elementary one), you will always be able to find a problem in that area that will completely stump you, and you will have to struggle very hard to arrive at a solution (if you can do it on your own at all).
3. Mathematics is best learned by a) doing exercises b) talking with people about exercises/problems/ideas (no matter the other person's apparent "knowledge") and c) repeating facts you already know (or believe to know).

So, yeah, "being outclassed" is relative and not a very helpful concept in the study of mathematics.

Maybe we could start some kind of courses here?

That would be cool (I could do pretty much every undergraduate mathematics course there is and a few graduate ones in Analysis and Theoretical computer science). Though with only seven members the interest would probably be... manageable.

2479412
It's your choice, of course (though feel free to come back any time ).

Though remember, if you want to do pretty much any kind of science above a "pop science" level, you need mathematics pretty fast. It's always amusing to see people's faces when I tell them that the physics concept they read about in a pop science book they thought was so simple actually needs the theory of Hilbert spaces as a foundation (that's the case for much of quantum mechanics, for example).

2479782

If you have anything mathematical that seems interesting to you, please consider coming back. I need the exercise dearly, the last two years where literally mind-numbingly boring.

Outside this group there are of course always textbooks (and especially exercises from textbooks) you could do if you're bored, or the Mathematical Olymipad's problems (a lot are actually quite hard!).

2480582 The integral from birth to present is a constant (since it's in the past and we could in principle determine its exact value), so I don't think, I would have to be a time traveler for my formula to work. You can't maximize a constant. What you're suggesting, however, is a valid optimization, but only if you consider the meaning of life of past time to be meaningless (having a value of 0, since only present and future counts). If the latter is true, then the value of meaning of life changes through time and will eventually reach 0 (if not sooner, then when entropy of this universe reaches its max value or every atom gets ripped apart by increasing value of dark energy of empty space).

If this is your view, than I don't agree with it. I don't think there is a distinction between past and future (we're all living in the past; present time is just an illusion). I'd be more inclined to say, that the meaning of life is 0 from the get go (not dependent on current time), than to accept, that objective meaning of life is time dependent.

2479782 2480582 2480608
Thanks for all the kind arguments. Maybe you are right and there's hope for me yet. I guess I can stick around for a little bit longer.

This was originally intended as a joke thread, but I've been looking into neural networks recently and have found some partial solutions that don't require solving potentially intractable max/min problems or explicitly simulating the universe.

Given sets of high-dimensional normalized, centralized inputs, restricted boltzmann machines seem to be reasonable candidates for identifying and discretizing patterns that occur repeatedly in input sets, and recurrent neural networks seem to be reasonable candidates for identifying patterns between input sets. I suspect that a variant of recurrent neural networks can be used to avoid having to normalize/centralize inputs, though I'm still working on wrapping my mind around combining RBMs with RNNs. Simple statistics can be used on top of this to find out which pattern-action pairs correlate with improved survival rate.

This only works as part of an evolutionary algorithm unless the universe can be partially simulated, or unless some heuristics are known ahead of time that correlate with survival. Now if only there were a model for developing a "frontal lobe" to try to simulate the universe... Restricted boltzmann machines can again be used to try to simulate the universe by feeding them action-consequence pairs. Since RBMs are undirected, they can easily be run backwards to generate expected consequences given an action.

2437855 Check it out!

This paper presents a heuristic proof (and simulations of a primordial soup) suggesting that life—or biological self-organization—is an inevitable and emergent property of any (ergodic) random dynamical system that possesses a Markov blanket. This conclusion is based on the following arguments: if the coupling among an ensemble of dynamical systems is mediated by short-range forces, then the states of remote systems must be conditionally independent. These independencies induce a Markov blanket that separates internal and external states in a statistical sense. The existence of a Markov blanket means that internal states will appear to minimize a free energy functional of the states of their Markov blanket. Crucially, this is the same quantity that is optimized in Bayesian inference. Therefore, the internal states (and their blanket) will appear to engage in active Bayesian inference. In other words, they will appear to model—and act on—their world to preserve their functional and structural integrity, leading to homoeostasis and a simple form of autopoiesis.

5435142
That's been an open tab for me for over a year and a half now. I finally got around to reading it. To be fair, I don't think I would have understood its significance if I read it back then.

That is very interesting, though Friston does overstate the findings a bit. It's not clear from that paper that Markov blankets (and free energy minimization) are sufficient conditions for life. The main contributions of that paper seem to be:

1. A mathematical definition of the individuality of organisms as a Markov blanket and its interior.
2. A depiction of how such an individual can adapt to its environment and how it can seemingly perceive its environment through differentials.

The second one I think has been known to most people familiar with machine learning. It's good to see those ideas spread to other fields.

The first one sounds obvious in retrospect, but I had failed to come up with the definition before reading that paper, and it wasn't for lack of trying. It's also remarkably well-suited for grounding otherwise-fuzzy concepts like empathy and hivemind.

Good find.

6361573
Now I feel like I need to get to know you in real life, if you're able to just breeze through and make use of that paper.

6361603
We could meet up. Over the next 6 weeks, I'll be in the Bay Area, Cornell, and the Research Triangle Park, if you're in any of those areas. Otherwise I'll probably be at BronyCon this year. If you want to spend a day hopping restaurants and coffee shops comparing notes on AI, friendship, and ponies, I wouldn't mind flying (within the US) to do so.

6362263
Switching to DM.