Fine-tuned for Interestingness vs. Ramsey's Theorem

by Alexandros1 min read16th May 201119 comments


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I had posted a while back on my proposed dissolution of the Fine Tuning argument. My main argument was as follows:

So the question posed to defenders of the FTA is 'why life'? Why focus on this particular fact? What is it that sets life apart from all the other propositions true about our universe but not other the other possible universes? The usual answer is that life stands out, being valuable in ways that galaxies, iPads, and all the other true propositions are not. It seems that this is an unstated premise of the FTA. But where does that premise come from? Physics gives us no instrument to measure value, so how did this concept get in what was supposed to be a cosmology-based argument?

I present the FTA here as an argument that while seemingly complex, simply evaporates in light of the Mind Projection Fallacy. Knowing that humans tend to confuse 'I see X as valuable' with 'x is valuable', the provenance of the hidden premise 'life is valuable' is laid bare, as is the identity of the agent who is doing the valuing, and it is us. With the mystery solved, explaining why humans find life valuable does not require us to go to the extreme lengths of introducing a non-naturalistic cause for the universe.

In the comments, Yvain came up with a response that I admit took me by surprise, if only because this is not the FTA that I had been exposed to (emphasis added):

The conditions necessary for life are also necessary for iPads: the argument hinges on things like the ability of subatomic particles to come together to form atoms, or the ability of stars to burn. It's not a question of one interesting type of complexity versus another,  but of a vast selection space of universes in which there is nothing complex or interesting, versus a tiny space of universes in which there are many interesting things  like iPads and life.

I admit this explanation lacks a rigorous definition of "interesting", but I think the least that can be said is that our universe is interesting in being a wild outlier in various physical and mathematical characteristics, and not just "interesting to beings with the same value system as ourselves".

I've been pondering how to process that response, and if the argument is salvageable, ever since. Do we really have to explain anthropics and the multiverse to diffuse the FTA?

Today I came across a great article with an elegant description of Ramsey's Theorem:

Expressed roughly, it tells us that complete disorder (in certain situations) is impossible. No matter how jumbled and chaotic you try to arrange certain objects, you will find yourself creating a very highly organized and structured object within it.

As I understand it, positing few 'interesting' vs. the vast majority of 'uninteresting' universes is in direct contradiction with Ramsey's theorem. I put this to the more mathematically educated among this community for feedback. Beyond pushing forward this particular internal dialog of mine, it should have more general application in the fine tuning debate, should someone choose to use it there.


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Nope. Ramsey's theorem says that any sufficiently large colored complete graph will contain a complete monochromatic subgraph that is as large as you like. It says nothing about the Universe and "interestingness". This is because the Universe is a universe, not a colored complete graph.

Ramsey theory deals with more varied objects than colored graphs, though Ramsey's theorem itself is almost what you claim it to be. See for example the Wikipedia article on Ramsey theory. The existence of ordered substructures within huge combinatorial objects is itself more general than Ramsey theory. It requires only a little imagination to conceive of a similar phenomenon producing the apparent rich structure in our universe. (Though I don't think this line of reasoning is very interesting.)

It says nothing about the Universe and "interestingness". This is because the Universe is a universe, not a colored complete graph.

This, so much this.

Alexandros' argument is exactly the kind of utter rubbish you get when you give a mathematical theorem to a philosopher. A delicate, precise theorem that works by exploiting details of one specific situation gets bulldozed into a general principle that couldn't be more wrong.

Reminds me of the argument that rationality is impossible because most numbers are irrational.

Leaving aside the question of whether the universe can be represented as a graph, as I understand it, Ramsey Theory generalises the theorem to structures other than graphs. Is this incorrect?

No, there are analogous theorems about structures other than graphs. But there are not analogous theorems about all structures.

In order to use Ramsey theory to dispute the physicists' claim that "most universes are lifeless" (which is backed up by a technical, though not indefeasible argument), one would have to make a technical argument that

  • identifies counterfactual universes with members of a class C of mathematical objects;
  • identifies life or interestingness with certain features of the members of C;
  • identifies a Ramsey-type theorem for C that has been proven.

I don't imagine this can be done in an interesting way.

On your second point - my definition of interestingness is any distinguishing feature. Anything at all that can be used to tell universes apart. If you think I am talking about life or something like it, you have not understood my argument. It claims that life is an arbitrary feature to focus on to begin with. I don't know which scientists have made the 'lifeless universes' argument and how, but my argument has nothing to do with that.

On your first point - If we accept Tegmark's identification of universes-in-general with mathematical objects, the question becomes whether Ramsey Theory applies or not.

On your third point - Given that theorems exist for coloured graphs, multidimensional grids, and coloured consecutive numbers, (hardly high-level structures), it's not exceedingly far fetched to imagine ramsey-type structure arising in a universe, or our universe being expressible as one of those structures.

Yes, this last bit is speculative, and this is why I asked for feedback.

my definition of interestingness is any distinguishing feature. Anything at all that can be used to tell universes apart.

Oh, your definition of interestingness is kinda sorta the opposite of what I thought it was. "Having a monochromatic complete subgraph of a certain size" is not a distinguishing feature of sufficiently large colored complete graphs, because all such graphs have that property.

It all depends on whether you find very small areas of uniform patterns interesting.

Ramsey Theory, much like Number Theory, Set Theory or Group Theory, is an ongoing field of study which contains many theorems and many unanswered questions. You have to actually give a theorem that applies to universes.

I would also like to point out that Ramsey's Theorem doesn't actually guarantee interesting things, and insofar as it guarantees anything it doesn't guarantee much of it. It asserts that sufficiently large multicoloured graphs must contain monochromatic sub-graphs of any desired size. I don't consider monochramtic sub-graphs to be very interesting, certainly not in the same sense that life is.

Furthermore, the 'sufficiently large' requirement grows exponentially with the 'desired size'. The exact rate of growth is not known but it lies somewhere between 2^(x/2) and 4^x (this is the limit of my knowledge, please tell me if a better exponential bound has been found).

That's just for the complete monochromatic graphs, if you look at Ramsey theory in general you see some even more ridiculous bounds, this is the field that gave us Graham's number.

All this means that the best that representing the universe as a graph will do is prove that some ludicrously tiny portion of the universe has some coincidental property, which may provide a brief 'oh hey look at this' to anyone observing it, but need not have any long term value or interest.

This is, what, 7 years old? Never mind. Read it anyway. Has problems, but what doesn't?. As for the comments. I suppose this is what we get these days, young minds, keen to show what they know, whilst not wanting to contemplate what they don't. Shame really. If universes are likely to display are large number of 'real' constructs represented by a large variety of mathematical objects then, yes, Ramsey-type arguments will come into play. Two things: Ramsey Theory is distinct from Ramsey's Theorem. If you want a 'rule of thumb' then,well, there it is. It is kinda like the helpful anti-demon of what you find in other areas of complexity. Rather than telling you, if you put a particular idea into a certain format that better men have failed, it tells you to look harder, there is something. But it is just about mathematical objects and will always work if your problem fits. It will give huge bounds. But, crucially, these bounds are just the worse possible case: if what you are looking at is purely random. Which is unlikely. There will be rules, otherwise your problem is, well, just a Ramsey Theorem re-statement. So, two things, the 'real' bounds will be lower, likely sharply, if you can find the 'reason'. And, of course, there will be a reason which might lead to all sorts of other interesting things. (Look at the Happy Ending Problem for an example). 'Ramsey-Type' can mean any 'type' of such result. Symmetry Breaking comes from Erdos's work on using his probabilistic method, Turan, loads of stuff.

There's no point invoking Ramsey theory here, because (a) only certain kinds of (not particularly interesting) 'ordered substructure' can be shown to exist and (b) these ordered substructures will occur randomly anyway.

The point of Ramsey theory is that sometimes, even if 'God' is hellbent on avoiding the creation of ordered substructures, if the universe is sufficiently large then He must fail. But since we're not assuming such a 'God' exists, you'd be strictly better off seeing what mileage you can get out of the familiar 'monkeys clattering away at typewriters' argument. (Even if the answer is 'not much'.)

It has been suggested that interesting things, in particular life, happen where there are entropy gradients (I'm thinking of 'Into the Cool' by Eric Schneider and Dorion Sagan). If Ramsey theory could be used to show that most universes are likely to have entropy gradients then that could be used to argue that fine tuning is unnecessary.

The fact that this would only be a tiny part of the universe agrees with the observation that the only life we know about occupies a tiny part of the universe.

Regarding Conway's game of life, it's important to note that it allows irreversible microphysics, and so won't have anything like our thermodynamics.

I'm not sure about this "selection space" of universes, but if we're talking about all possible mathematical constructs (weighted, perhaps, according to Solomonoff's universal prior), it bears noting that even some one-dimensional, two-colour cellular automata - extremely simple systems as far as that goes - have been proven to be Turing complete. Doesn't mean they'll necessarily produce life, as a lot depends on initial conditions, but we know at least that they can, in principle, produce life. Given what else I've seen of mathematics, it seems the space of mathematically possible universes is positively teeming with critters.

even some one-dimensional, two-colour cellular automata - extremely simple systems as far as that goes - have been proven to be Turing complete

Some are, most aren't.

I just love this post and that Ramsey's Theorem. Really.

For I see, there is not a lot of life in the Universe already. A little different tunning could give us more life or less life. Even if there was no stars and planets under a different cosmological constant. We just don't know, we are unable to say 'everything would be dead'. Maybe, maybe not.

So, this FTA is another example of a bad argumentation.

We just don't know, we are unable to say 'everything would be dead'. Maybe, maybe not.

I distrust 'we don't know' style arguments. A Bayesian should always have a guess, and all too often 'we don't know' is just a way to hide an a priori implausible hypothesis behind a wall of unobtainable evidence.

True, we can't examine all possible laws of physics, but we can look at simpler examples and get a good prior from those.

Conway's game of life is a good example, it is an interesting universe which allows for self replicating patterns. You could take the fundamental constants of life, the birth/death conditions, and replace them with almost any other possible combination, to see if you get anything interesting.

I've tried. Most of the time, one homogeneous pattern fills the whole screen, often its just white-space. The rest, you usually just get total meaningless noise that looks like video snow. Occasionally, if you're lucky, you get something with a few curiosities and it keeps you entertained for an hour or so.

I've yet to find anything that looks like it has the slightest hope of producing self-replicators, or anything else remotely as interesting as life.

So, there's your prior. We don't have much evidence to update it, so I guess you'll just have to accept it or find a better one.

Well, if you pick a random sphere of 1 m out of our universe, it will - with a huge probability - be empty. I doubt we have the time/space resources to simulate the equivalent of the resources that our universe employed to produce an iPad. The fact that you could see something interesting in the limited computational resources that you likely put into your simulations might even mean that Conway's game is more interesting than our universe, and more apt to give birth to a mind (after all, it is Turing-complete).

We have never discovered a self-replicating pattern in a random life-field. I once saw a calculation that showed you would need a computer with the volume within a few orders of magnitude of the solar system to do so (not mass, volume). All the ones we have are intentionally constructed.

Most theoretical work done on self-replicators in life works by assuming ultra-low density fields, maybe one live cell per billion at the start (a proportion which immediately plummets much lower owing to the fact that cells need 2 neighbours to survive) so the empty space rule will probably be similar. Even if you use a higher density, most of the space will end up filled with the same mixture of small scale still-lifes, oscillators and high entropy regions, busy but not interesting. Much like most of the empty space in our universe still mostly contains background radiations (I think).

As for the fields I looked at, in general it was quite easy to prove mathematically that they were uninteresting. Interestingness requires a mixture of stability and complexity which even the ones where I couldn't manage a proof lack.

We have never discovered a self-replicating pattern in a random life-field. I once saw > a calculation that showed you would need a computer with the volume within a few orders of magnitude of the solar system to do so (not mass, volume). All the ones we have are intentionally constructed.

Well, per Bekenstein bound, an apple gets approximately 10^41 bits, so I think our universe really has no problem in allocating space for computational resources.