Ultimately, the two are indistinguishable without a unified theory in hand.

There is no guarantee that if a unified theory is possible, it is expressible in mathematics; or even necessarily in any form smaller than the universe itself. We have been lucky for a long time.

You're right in one sense, in that if #2 is true, then #1 is true in at least some sense.

That is, if the universe is not ineffable - that is, unless there are unknowable components to the universe - then a "worst case" unified theory can be defined as itself. That is, the universe itself is an expression of itself.

That we can express it in mathematics is a given in that case because mathematics is malleable; all you need to do - though it wouldn't be very useful - is to invent a symbol that represents the universe-as-is that by definition acts how the universe would act in a given context.

Obviously that is not very interesting, but the point it makes is that if the universe is not ineffable, then the question is not if a unified theory is possible, because in that case the universe itself is proof that it is, but how much we can compress such a theory, and whether we can reduce it to something simple.

As such whether or not a theory is possible may seem like it doesn't matter, but it's an important point to make, because it means that anyone making the argument that a unified theory is not possible rather than arguing that a simple unified theory is not possible is in effect arguing the universe is ineffable.

This is exactly what I mean when I say physics departments are turning toward theology.

Well, it's exactly the opposite - it is pointing out that rejecting the possibility of a unified theory borders on the religious because it requires the universe to have supernatural qualities.

Nobody asserts that a unified theory is impossible. Obviously, no one can have any way to know such a thing.

But anyone (e.g., I) can fail to discover one, even if given infinite time trying. It is obviously impossible to distinguish (1) the condition of a conveniently-finite unified theory not being possible from (2) simply failing, collectively, to discover one. It is also impossible, in practice, to distinguish (3) a possible universe-sized theory from, e.g., (4) a necessarily infinite-sized one, having neither. We know that the universe itself has always succeeded at discovering a next state, but do not know whether it might at some time, e.g., find the next state incomputable, and stop evolving.

Insisting that a unified theory conveniently smaller than the universe must be possible, having failed to discover one, is religion. Insisting you have actually got that theory, despite being utterly unable to check its correctness, is religion. That is the religion physics departments are flirting with already.

> Nobody asserts that a unified theory is impossible. Obviously, no one can have any way to know such a thing.

The very article being discussed claims the very idea that there "may be a deeper, more unified theory" has become completely discredited. It does not call it impossible, but calling the very idea completely discredited skirts very close to it.

And the message you originally replied to criticised a comment above that called the idea a "false idol" and questioned the very possibility of it.

It seems quite clear that while these people may not entirely and completely dismiss the possibility, they see it as unlikely or not worthwhile. My first reply to you was explicitly to point out that the comment you replied to discussed specifically the possibility, not whether or not we'll find one.

> We know that the universe itself has always succeeded at discovering a next state, but do not know whether it might at some time, e.g., find the next state incomputable, and stop evolving.

If so, then this end-state is part of the computation itself that would itself be part of the model. If the universe is not ineffable, such an end-state must be discoverable from the universe itself, and so does not impact the possibility of a unified theory in any sense.

> Insisting that a unified theory conveniently smaller than the universe must be possible, having failed to discover one, is religion.

With the caveat of the assumption that the universe is not ineffable, such an argument certainly can be put forward in a "religious" way, but there are also a whole lot of approaches that could be taken to try to get an idea of an upper bound without knowing the precise details, and while we certainly can not make that claim in the strongest possible interpretation of "must", we can make that claim in the sense that we have strong enough indicators of compressibility to assign it a high probability.

Consider that "all" we're seeking to do is to unify the forces, and depending on who you ask also explain physical constants, within a single framework, not creating a precise simulation of the universe. As such, we can "subtract" any actual randomness - if it exists - and any constant values. We're looking for a model, not an instantiation.

For us to be unable to compress a unified theory pretty much all matter and energy in the universe would need to be integral to the functioning of the universe itself in a way that can't be abstracted away with less complexity.

E.g. "freezing" the universe and moving a few particles around and "resuming" would need to change not just what happens next but how the universe functions, and would need to do so in an irreducible manner - that is, the relationship could not be constant and universal, because if the positioning matters but is following a consistent set of rules that is in any way reducible, then the positions themselves do not need to be included in the universal theory. In that case we can reduce that part of the theory to "here's how to predict what moving mass around will do to e.g. universal constants or relationships between forces".

Now I will accept that it may be possible that a universe that is not ineffable might be possible where a unified theory would be so complex that the shitty fallback of declaring the universe itself the definition would be the smallest option, in about the same sense I'll concede the possibility of Russel's teapot, but while a general compression algorithm capable of compressing every input is impossible, once you take genuinely random output out of a huge data set, a data set that is not compressible becomes increasingly improbably as the size of the data set increases.

In effect, a universal theory smaller than the universe is possible if we can sufficiently for whatever value of precision you want your model to have, compress any information about the universe including the data needed to specify how to integrate it back into the universe (I'm assuming we agree that any compression here needs to include the complexity of the decompressor, as otherwise a special purpose decompressor that includes the universe as a constant can compress the universe to nothing, which would make the discussion pointless).

Now, of course, the question is how much do we need to be able to compress before we'd agree it was "conveniently smaller". But to me at least the extent to which we can e.g. compress information about gravity alone suggests sufficient compressibility that it would seem to be a truly extraordinary claim that we will not be able to achieve similar compressibility in other areas.

But like Russell's teapot, it's possible.

> Insisting you have actually got that theory, despite being utterly unable to check its correctness, is religion. That is the religion physics departments are flirting with already.

We can maybe agree that many people do have strong feelings of which theories will get there and are invested in them more than they might have justification for, that is fair enough. But I've at least never seen anyone suggest they can know for sure, and a lot of large advances have come from people getting extremely invested in untested theories. As long as people don't all get invested in the same untested theories, we'll keep seeing advances.

Thank you for taking time to explain yourself.

My interpretation of their "discredited" is very different from yours. I did not take it as saying anything at all about the nature of the universe, as such, but only about the purely human activity of hustling Theories of Everything.

Ineffability is an interesting notion. If you have a theory that would work given complete information, but you can never get complete information, even in principle, is that ineffable? If you would need complete information to complete the theory (say, to choose among 10^500 possible variations) is that ineffable? Or just too hard? Can you really call it a difference?