A common objection of AWT opponents, which I can met in discussions, is: "Your theory has no math, so it cannot be a physics at all". Well, at first, no such rule really exists, as here exists a number of physical articles without formal math at all. And the AWT isn't (just) about physics, it can describe the sociological or biological phenomena by geometry based approach as well. And at last, I'm using a logic in my derivations, and the logic is (fundamental) part of math, so it's not even true, the AWT uses no math. At the moment, the derivation of my conclusions are reproducible, the formal math is simply not needed.
The physical models often enable to derive the predictions, which are difficult to handle (or even to express) by formal math, for example the order of Venus phases from heliocentric model (after all, how we can express mathematically the simple information, the Earth revolves around Sun and not vice-versa?). At such cases, the picture of geometry is much more illustrative.
From this point of view it's not accidental, the common illustrations of modern physical theories (like string theory) are mostly quite schematic and pathetic. Such drawings illustrate nothing, but the fact, their authors have no true physical insight into real situation - so they cannot imagine/picture even their own models.
But here are more substantial objections against formal approach in physics. The true is, the consecutive ("step-by-step") logic of formal math describes the heavily parallelized physics of multiparticle systems poorly. Even the gravitational system of five bodies is (nearly) impossible to describe by formal math and the resulting description would be so complex, so that nothing useful can be derived from it. This is the reason, why we have no deterministic description of phenomena in multiparticle system, like the turbulence. This forces the formally thinking physicists to use the probabilistic interpretation instead - like at the case of quantum mechanics - although such system remains deterministic apparently - it's just more complex, then the consecutive formal math can handle (while we know already, we can model the quantum mechanics phenomena by discrete particle models, even experimentally).
By such way, the formally thinking physicists are effectively mentally blocked from understanding, our Universe can be interpreted by multiparticle system for last two hundred years. Their formal math and way of thinking is simply incompatible with this trivial idea - even at the case, the illustrative understanding of such system can be quite simple. This is dual approach to philosophy, which cannot describe some connections by using of formal math, even at the case, such description can be quite simple. It's evident, the optimized approach in reality understanding should involve both strategies (the formal and non-formal one) in balanced ratio.
Of course, the above problem just illustrates the limits of math and formal thinking - not the limits of AWT concept. We should simply face the fact, here exists a wide group of phenomena and geometries, the handling of which by formal math is noneffective with respect to their understanding - that's all. This doesn't say, the formal math is nonsense - it's simply inappropriate tool for deterministic / reproducible description of such systems.
From general perspective, the AWT is extrapolation of free fermion models of string field theories to zero dimension. These models are nothing very new in physics, as some physicists have assumed already, the strings are composed from more fundamental particles (so called preons) already. The one-dimensional strings are just the lowest number of dimensions, which the formal math can handle without problem, while avoiding the singularities. The concept of environment composed from zero dimensional particles is naturally singular from formal math perspective, so the formal math cannot use it. It can be replaced by concept of one or more-dimensional strings partially - but here's a technical problem: such approximation leads to landscape of 10E+500 possible solutions (which roughly corresponds the number of 0D particles involved in this model of observable Universe) - so it's unusable from practical reasons. But the system of many particles can be handled without explicit models, for example by computer simulation:
From such particle model is evident, the system enables the only single way of Aether compactification, leading to dynamic foam of higher-dimensional density fluctuations (i.e. "strings" and "branes") naturally - so no giant landscapes of possible solutions, no ad-hoc assumption of strings, no assumption of (unexplained yet) relativity and quantum mechanics postulates is required here at all - and we can derive all these postulates from geometry of simple particle concept instead. By such way, AWT is highly motivated approach, which follows Occam razor criterion, minimizing the number of postulates in theory.