It is certainly an open problem of fundamental physics as such, but it is not a defect of string theory.

Besides, there is so little known for sure about points in the landscape, that all debate about whether it is "large" or "small" might better be postponed until it is really understood. It is easy to forget how many simplifying assumptions enter the identification of string backgrounds. One day most of these counting arguments will be obsolete, since they don't properly deal with the mathematics of string backgrounds. This point was made for instance in Distler-Freed-Moore 09:

"We hope that our formulation of orientifold theory can help clarify some aspects of and prove useful to investigations in orientifold compactifications, especially in the applications to model building and the “landscape.” In particular, our work suggests the existence of topological constraints on orientifold compactifications which have not been accounted for in the existing literature on the landscape."

but this kind of careful analysis tends to be ignored these day.

What i meant with pathology was in the context of inferences and the defence of why movement in theory space can be (should be?) seen as a physical process when talking about naturalness. So if string theory offer no solution like a proper inferential theory imo should - ST isnt a proper inference theory. You can still think that string theory is fine for other purposes.

Of course, noone really claimed it was an inference theory. But I see some remote links and its the ONLY merit I personally see in it, but then for sure there are pieces missing. This is not just a technical issue, its much easier to see from the conceptual side.

I seems to me that if the inference scheme associations to ST proves right,then it is likelythat here must is a mathematical way to solve the problems without going via the reconstruction that I have in mind, but it will likely be far more technically complex than necessary, not to mention it seems to be a very non-physical or conceptually akward way, which begs the question of what to use as guidance for coming up with the constraints needed? Its like starting with a description with a massive amount of redundancy, and try to by finding all the constraints extract the real options VS starting with the physical options and then find how that looks like in the continuum approximation.

But i can not follow in details if the former way is viable. I figure people like you are the persons we need to go that route. But going that route i figure takes a different mindset and guidance than i have.

I try to use my intuition about physical inferences and let that guide me to the tools, instead of doing the other way around. String theory to me is an example of an interesting mathematical framework, but it is not really clear what it means and of what use it is for the problem at hand.

It is a myth in the sense that it derives from an a priori Platonic assumption rather than being rooted in empirical evidence or a necessary theoretical consistency.

Naturalness is basically a form of Baysean statistical reasoning. But, there is no scientific source for the Baysean distribution we are drawing from, and Baysean reasoning is particularly weak when there is no meaningful empirical basis for your priors. Baysean statistics exist to not waste existing empirical data points, and is outside of its domain of applicability when you have not empirical data points from which to derive your priors.

Like i said this is unexplored ideas but the solution to your critique here is to consider evolution of law and attach bayesian reasoning to information processing agents. Second associate these information processing agents to matter. This is the direction thinkg i am personally trying to work in.

We should not put in manual priors by hand, this is no good, i agree. The prior is just the current state of evolution. It is a learning schema, NOT a statistical approach based on a fixed probability space. The probability spaces themselves also must evolve.

The scientific empirical support for the prior lies in the interaction HISTORY of the agent, which has carefully selected the prior.

So this is MORE than just simply bayesian probability. You must put the machinery of the bayesian inference in an interacting and evolving context. Then it gets alive.

It doesn't help. Are you saying that there are solutions of general relativity, infinitely many, that are not in any way described, even just in principle, by string theory, since string theory has only finitely many solutions!?

Indeed, perturbative string theory is more constrained than the effective field theories that it reduces to at low energy. The popular discussion of the landscape always gets this backwards: Faced with the landscape of consistent string theory vacua being possibly very large (which is not completely clear yet, since it is so little understood in mathematical detail) people forget that the usual spaces of solutions of plain QFT are much more vast still. Vafa tried to drive home this point with speaking of the vast Swampland surrounding the landscape.

It's like in the children's game of big numbers: One of the 4-year olds cries out "one thousand!" and the others are silenced and awed by the immensity of this number, ignorant as they are. In reality it's the other way around: In physics spaces of solutions generically have the infinite cardinality of the continuum, and something special and noteworthy has to happen to make that become finite.

Your ncatlab.org site is awesome. I can also see your and your co-authors passion for rigour and wish to bring order into theoretical physics field and to explain. There is no question that this is a very important task. Our views also take place at different levels. I am not referring to mathematical inconsistencies at this point.

One core point in there seems to be

this might be, but it is a weak defence to a justified critique towards such a massive investment. A program that with open eyes accepts and builds onto a questionable foundation, made the choice that the foundation is good enough.

The critique is in place because string theory unlike classical GR, is not just a normal theory, its a toolbox for constructing various theories, but the mapping to reality is vauge not only experimentally but also conceptually. Ie. it has traits of an inference system in several ways. First because its a theory of theory, second because it loosely provides a microstructure (strings) whos interactions ENCODE its interaction with the environment, similar to rationally acting information processing players in a game of expectations. I don't execpt that you conenct to this, but what i am effectively saying that there is a possible WAY to see/understand this that is NOT in terms of "geometry", but in terms of inferences. And while mathematically it might well be isomorphic, the intuition is much better in my brain in the inference abstraction, and buy gut feeling is that this is also the right "natural" perspective.

So the critique is also a bit "tough love" because i think we rightfully can have/should have much higher expecations on a theory like this. I personally hope string theorist turn attention to the direction hinted by Heckman, and understand the ST toolbox in new light.