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.
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.
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.)
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.
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.