Dear Oliver,

As usual, your posts mean valuable impulses and challenges for me. I think each paragraph would require a whole article to relate it to what I wrote, but still, let me try some brief comments.

Maslow is a psychologist, and as far as I can see their understanding of reality is somewhat different from what a philosopher of science would mean by it: When I sleep I perceive as reality strange things in my dreams (and some people perceive strange things as reality even when awake). But seriously, if by “heuristic approaches” you mean models as heuristic devices to enable understanding of what they model, then, I think, this is only PART of the story that Hawking and Mlodinow (H-M) - and, more generally, those who use the term (sometimes better referred to as representations) in the philosophy of science - have probably in mind. Let me try to explain.

One can use a model (visual, like miniature version of the real thing, or, say, mathematical models) to BETTER formulate and consequently solve some problems associated with the “real thing”. This, I think, is what your examples are about, and this is what I would understand under “heuristic approach” to models.

There are, however - especially as used in contemporary theoretical physics - also conceptual models or rather representations (quarks, space-time, electromagnetic and other fields, state of a physical system, etc) of “physical reality as such” (if you believe in it, without “evidence”, as H-M don’t seem to) that become formally comprehensible and workable ONLY IF dressed in the mathematical language or, equivalently, have BUILT ON MATHEMATICAL MODELS.

It is one of the findings of last century quantum physics (and theories and interpretations that follow from them), that in this second case you need these non-visual representations and mathematical models not only to better your understanding but TO BE ABLE TO SAY ANYTHING verifiable about the physical reality modeled by this kind of physics. Because neither physicists nor philosophers can visualize or describe these findings using only common sense, as it used to be in pre-quantum times. (ctd)

(ctd)
To illustrate the distinction I have in mind, consider the difference between a miniature model of the Cologne cathedral (made of matches, Lego stones or what) to have a BETTER visual perception of the real thing out there, and between a miniature model of an edifice that exists only in the architect’s mind, where the model provides THE ONLY perception, knowledge, of what the architect has in mind.

Your questions in the second-last paragraph are probably answered by this inability to directly visualise concepts introduced in physics to represent situations/concepts/objects where classical physics does not provide any more a universally adequate representation.

Besides, it is the second kind of representations/models that I find applicable in philosophy of religion, where physical concepts are replaced by other abstract concepts (e.g. Trinity), and that of mathematical models is played by anthromorphic, narrative or metaphysical models rooted in culture and evolution (in our “memes and genes”).

In the case of physical reality you can have the philosophically respectable “model-dependent” H-M approach to reality. The same in the case of transcendental reality where you can also have a “model-dependent” approach to this reality, although, it is not a “respectable” expression of religiousity. Of course the problem of adequacy, (closeness to "truth") is even more complicated than in abstract physics.

You can be a scientist without believing in the “existence of model-independent reality” (as H-M’s seem to be), however you are not a good e.g. Christian if you do not believe in the existence of transcendental reality represented/modelled by Chridstianity's tenets

This emphasis on the difference between the two versions of modeling - for practical purposes and for epistemological purposes - brings me far away from your inspiring post. I have to finish, but I might want to continue commenting on your last paragraph, provided you at least are interested.

Especially because you rightly brought into play the human aspect, where our brains and their producst (culture, arts, humanities) when entering as objects of our investigation, much more than in physics, even quantum, inerfere essentially with the investigating subject.

Dear Oliver,

As promised, this is a continuation of my reading of your input, hoping that you are reading it, though I am not sure who else.

>>Yet, it would be unlikely for one to describe a weather system in terms of quarks and isobars would irrelevant to particle physics. <<

The theory that uses isobars as some basic concept, and the theory that uses quarks, do not contradict each other, only for a given system of phenomena one theory is useful, provides verifiable predictions, the other is useless, being either too complicated or inadequate to make relevant predictions.

My favourite, much simpler, example are mathematical models of our Earth: (a) a flat plane; (b) a rotational ellipsoid; (c) a geometric point. For global cartographic purposes (b) is useful, (a) and (c) inadequate. For local mapping purposes (a) is adequate, (b) too complicated, (c) inadequate. For cosmological purposes (c) is adequate, (b) too complicated, (a) inadequate.

>>can something that does not exist still have a “state”. A null state? <<
You could also ask, can something that doesn’t exist be a quark? More precisely, can concepts like state of a physical system, quark, etc. be parts of a meaningful representation/theory/model leading to verifiable conclusion without assuming that these concepts actually represent something independent of the theory used to represent them? Philosophically this corresponds to “can the premises of constructive empiricism (apparently supported by H-M) withstand objections from scientific realism”? That is a question, which I would not dare to answer.

>>What would govern such a relationship? Something, transcendental or is the relationship self-sustaining? <<
I am not sure I understand what you mean, except that the term ‘transcendental’ usually appears in religious contexts and is hence irrelevant when speaking of science explaining physical reality. Maybe you had in mind something like a Unified theory (or "theory of everything") that, if we ever arrive at it - which I doubt - will probably have nothing to do with transcendental reality postulated by religions. (Although the fly in the ointment here is consciousness.) (ctd)

(ctd)
>>perhaps, we have the ability to understand our reality in an elementary way by knowing the connections between mathematics and the mathematical aspects of the knowable universe <<

This is what I meant by the last enigma, namely that in practical situations - dealing with phenomena well described by classical physics and associated sciences, where mathematics can be seen only as “aspects” of physical reality - our commons sense suffices.

>>Maybe, we can even reliably conjecture, from templates, about the unseen universe, say, postulated galaxies beyond the light horizon. <<

I think there is no “maybe” about our universe extending beyond the light horizon. This is what contemporary cosmological theories (or representations of reality) tell us irrespective of whether we postulate the existence of a theory-independent (or "model-independent” in the H-M language) reality. The “maybe” would fit more the postulation of a broad family of universes, i.e. of a multiverse, that (still?) seems to be ad hoc, without any “verifiable” theory that this postulate would be part of.

David G and George,

Thanks for your interesting comments. A bit busy at the moment. Shall reply, as soon as possible, if the World doesn't end.