The Scientific Problem with String Theory (With Lee Smolin): Maths and Reality (2)

In his book, The Trouble With Physics, Lee Smolin puts the case against string theory when he says that

“we must conclude that string theory has nothing to do with nature, because every single one of [the theories that are known to exist] disagrees with experimental data”.

It must also be said that elsewhere Smolin concedes that string theory does indeed have its own predictions. However, “[t]he few clean predictions it does make have already been made by other well-accepted theories”. Not only that. When string theorists say that there are “extra dimensions” and that “all forces are united into one force, and that there is super-symmetry”, Smolin also states that all these “are independent of string theory”. Thus “finding evidence for any one of them does not prove that string theory is true”. Nonetheless,

“[i]f we learn that there is no super-symmetry or no higher dimensions or no unification of all the forces, then string theory is false”.

All these factors – one must suppose - are within the domain of the evidential, experimental and predictive. Thus they run free of the unique claims of string theory. In other words, when string theory offers us something new or original, it's that which disagrees with experimental data.

More specifically and on the subject of this piece, Smolin explicitly comments on the maths/reality connection when discussing Albert Einstein and the German physicist, Hermann Weyl. He quotes Einstein's response to one of Weyl's theories:

“'Apart from the [lack of] agreement with reality, it is in any case a superb intellectual performance.'”

This clearly shows that there can often be (at least in principle) a complete disjunction between mathematics (or mathematical physics) and reality. This isn't a surprise because that link has often been either underplayed or completely rejected (by mathematicians and philosophers) throughout history. The quote above also stresses the mathematical virtuosity-for-its-own-sake problem which has particularly beset string theory.

Smolin again puts the case for this maths/reality disjunction (this time with direct reference to string theory) in the following:

“The feeling was that there could be only one consistent theory that unified all of physics, and since string theory appeared to do that, it had to be right. That was the stuff of Galileo. Mathematics now sufficed to explore the laws of nature. We had entered the period of postmodern physics.”

Prima facie, it can also be inferred that not only can there be a maths/reality disjunction - there can also be a unified theory/reality disjunction too. In other words, unification – or at least the intellectual desire for unification – might sometimes have run completely free of reality. Particularly this may still be the case if reality is messy, random, chaotic, non-symmetrical, ultra-complex, dynamical, etc. In other words, wouldn't a unified theory be difficult – even impossible – if the world were truly messy?

Even before string theory, many writers have commented on the physicists' “rage for order”. This is Kitty Ferguson on this theme:

“The diamond shapes in a sunflower seed-head were lop-sided. One had to give tree-trunks the benefit of the doubt in most cases to call them cylinders. The earth bulges and is not a perfect sphere. As for mirror symmetry, one side of the human face is not the true mirror image of the other.”

She goes on to say:

“The things we build and the art we create exhibit much more geometry and symmetry than we can find in nature. Are we bettering nature, imposing rationality on a less rational universe....?”

Of course none of Ferguson's examples above are from the world of physics; though physics is of course indirectly connected to every example she cites. It can also be said, prima facie, that symmetry and order are perhaps more likely in the world of physics than in the world of “medium-sized dry goods” (to use J.L. Austin's phrase). Symmetry (even “supersymmetry”), particularly, is a very important aspect of string theory.

However, physics doesn't fair very well either. As Smolin himself points out in the following:

“... we had learned that nature lacked a certain symmetry – that of parity between left and right. Specifically, all neutrinos are what is referred to as left-handed (that is, the direction of their spin is always opposite to that of their linear momentum). This means that if you look at the world in a mirror [as mentioned by Ferguson above] , you will see a false world – one in which neutrinos are right-handed. So the world seen in a mirror is not a possible world.”

Thus can't that “bettering [of] nature” fixation also be applied to string theory and even other theories in physics? Is string theory attempting to “exhibit more geometry and symmetry than we can find in nature”? Is string theory also “imposing rationality on a less rational universe”?

This thirst for order appeals to mathematicians. It also appeals to mathematical physicists. And it especially appeals to string theorists.

It's also the case that string theory satisfies (or at least attempts to) the mathematical side of mathematical physics. Some experts think it does so with flying colours. Indeed string theory's mathematical virtuosity and dexterity is what appeals to many people – especially those experts who have less knowledge of physics than they have of mathematics.

So it can be concluded that maths can run free of physical reality. Or at least there has been a long debate about this. On the one hand, philosophers and mathematicians - dating back to the ancient Greeks - have stressed the tight link between maths and physical reality. Other philosophers and mathematicians, on the other hand, have denied the importance - or even relevance - of that link.

Maths and Reality Disjoined

It's easy to see how the maths of string theory can run free of reality. However, how would non-experts know if that were the case? It may also be the case that string theorists have no sure (i.e., philosophical or non-mathematical) mechanisms which can show them that they're disappearing up their own mathematical backsides.

As Smolin puts it, the maths of a particular string theorist may simply be his personal “toy”. He tells us that such a person (though in this instance he's not talking about a string theorist) “may simply have invented a theoretical toy that has nothing to do with nature”.

The string theorist will of course say that his theory does indeed have something “to do with nature”. How would we know that this is the case? The string theorist will also say that his mathematical theories describe reality or – at the very least - the way that reality may be. Again, how would we know? We'd need to be in Sherlock Holmes's situation in which we literally have to go through the entirety of the string theorist's mathematics and thus replicate his own labour and results. To re-quote William Poundstone's passage (already quoted in Part One of this piece):

“... William Shanks, a mathematician of our fair island, has recently computed pi to 707 decimal places. It took him twenty years. His result filled a whole page with quite senseless, random numbers. Should anyone doubt Mr. Shank's result, he would have to budget an equal amount of time and duplicate his work. In that case also, verifying the answer would be precisely as difficult as coming up with the answer in the first place – the very antithesis of an 'obvious solution.'....”

In terms of the dearth of experiments, observations and predictions in string theory, that's presumably why some string theories leave us in a position in which “there is no evidence either way”. And if there's no evidence either way, then, again, where does that leave us? Of course a string theorist may hint at evidence. He may even suggest actual or possible experiments. (That is, he may say that in such-and-such a situation one would observe this-and-that.)

Smolin doesn't seem to have a problem with this kind of talk about hypotheticals/conditionals (at least when talking about “doubly special relativity”). When referring to such a theory, Smolin writes:

“The idea is an elegant one.... We don't know whether it describes nature, but we know enough about it to know that it could do.”

Could we say the same about string theory – or about a particular statement within string theory?

Thus let's take it as given that a particular string theory is “elegant”. In that case, we still wouldn't know that “it describes nature”. Would we know that “it could do”? We can conclude by saying that there's one thing which is the case: mathematical elegance alone will never be enough.

Does Maths Correspond With Reality?

Smolin recalls a conversation he had with João Magueijo (the Portuguese cosmologist and theoretical physicist) in which he seems to say that there should never be an absolute disjunction between maths and reality. Smolin writes:

“João said that everything to do with physics could be understood without the fancy mathematics. Giovanni argued that it was easy to talk nonsense about these theories if you weren't careful about which mathematical expressions corresponded to things that could be measured.”

This depends on what that understanding of physics amounts to. It can be argued that there is a kind of understanding without the maths; though not a full understanding. (This is parallel to the use of images, metaphors and analogies in quantum mechanics.)

Nonetheless, the link between “mathematical expressions” and the demand that they “correspond to things that could be measured” seems to be very strong. So is that meant in the same sense that each word in a natural-language sentence must correspond with a thing? In terms of language, this is obviously problematic from a philosophical point of view. Some words don't correspond with things. Indeed some words don't even correspond with anything – not even with abstract entities. In addition, a word gets it meaning (or role) from its context within a sentence (or statement). Perhaps this is also true of the mathematical expressions in a mathematical theory (or statement). Again (as with a sentence), why should all mathematical expressions correspond to anything at all? The mathematical expressions in pure maths don't need to correspond with anything (which is a point that Wittgenstein and the constructivists often stressed). However, surely the same can't be be said of the maths in mathematical physics or string theory.

The other point (in reference to the quote above about “fancy mathematics”) is that even if mathematical expression x corresponds to thing y, and then that thing y is “measured”, then isn't measuring itself a mathematical process or function?

The astrophysicist and science writer, John Gribbin, also seems to put a similar point. He does so, however, in terms of what he calls a “physical model” of “mathematical concepts”. He says (in his Schrodinger's Kittens and the Search for Reality) that “a strong operational axiom” tells us that

“literally every version of mathematical concepts has a physical model somewhere, and the clever physicist should be advised to deliberately and routinely seek out, as part of his activity, physical models of already discovered mathematical structures”.

Yet even in Gribbin's case, it's still clear that a “mathematical concept” comes first and only then is a “physical model” found to square with it.

Many Theories about x

One problem with the possible divorce between maths and reality is that many theories – perhaps an infinite amount of them – can be constructed precisely because of that freedom. More specifically, many theories can be formulated to deal with the very same evidence, data or experiment. This is certainly true of string theory (or string theories in the plural).

There are many problem with this multiplicity of theories and their possible parallel lack of a connection to reality. Smolin tells us (though specifically about “unified-field theories”) that “[r]ather than being hard to find, unified-field theories were a dime a dozen”. What's more, “[t]here were many different ways to achieve them and no reason to choose one over another”.

Nonetheless, there may not be a huge problem with many theories fighting for the same space. It may even be the case that all these rival theories are in fact “complementary” (or at least some may be). Why assume that the different theories about the same x must mean that not all these theories can be useful? Indeed why assume that only one can be true or correct? Moreover, why should a multiplicity of theories about a given x hint at a break from reality? Why not be a pluralist about such theories?

John Gribbin (again) is such a pluralist (as are many scientists and philosophers). Gribbin, in the following, specifically talks about quantum theories:

“I stress, again, that all such interpretations are myths, crutches to help us imagine what is going on at the quantum level and to make testable predictions. They are not, any of them, uniquely 'the truth'; rather, they are all 'real', even where they disagree with one another.”

This is heavy stuff. Of course what's true of quantum theories/interpretations (or “myths”) may not be true when it comes to mathematical theories or theories in other disciplines. However, the above is certainly problematic for string theory for the simple reason that Gribbin talks about such theories/interpretations making “testable predictions”.

Philosophy of Mathematical String Theory

One can of course say that the maths of string theory must have a connection to reality for simple Aristotelian reasons. As Aristotle himself put it (in his Metaphysics) when talking about the Pythagoreans:

“All is number. The principles of mathematics are the principles of all things.”

In other other words, if the principles, theories or statements of mathematical string theory are true/correct/accurate; then, by Aristotelian definition, they must match “all things” - they must match reality.

There's a distinction, however, to be made here.

It can be said - in loyalty to Aristotle - that the maths in string theory can't contradict anything in reality and reality can't contradict anything in mathematical string theory. But does that also mean that the maths of string theory must also describe or explain given aspects of reality - or any part of reality? Nothing in string theory may contradict the “principles of all things”; yet a given string theory may not have anything to do with any aspect of reality.

In that sense, what's true of maths generally is passed over to mathematical string theory. That is, if the maths in string theory is true/correct/accurate, then nothing in it can contradict reality. Still, string theory may not describe (or explain) any aspect of reality. More specifically, it may not describe such things as extra dimensions, branes, multiverses and even strings simply because such things don't exist in reality.

We can also bring in Galileo here. Galileo famously claimed that “the book of nature is written in the language of mathematics”. Thus, again, if the maths of string theory is true/correct/accurate; then – by definition - it can't contradict anything in nature or reality. Still, it may not describe (or explain) anything in nature or reality either.

We can go further here and say that a “false dichotomy” has been set up with this talk of maths or reality. It may even be the case that maths and reality is a false conjunction.

What I mean by all this is that many people say that “physics is maths”. (Though not that “maths is physics”.) Therefore can't we also say that reality/nature is maths (along with with Galileo)? And if that's true, if the maths in string theory is true/correct/accurate, then it simply must be about reality. Though, again, this distinction must be made here:

i) String theory does not contradict reality.

ii) Does string theory actually describe or explain reality?

In criticising what can be seen as string theory's over-dependence and over-reliance on maths, we also face another problem.

Physics is nearly always utterly dependent on mathematics. The science writer, John Horgan (in his The End Of Science), puts it this way:

“Numerical models work better in some cases than in others. They work particularly well in astronomy and particle physics, because the relevant objects and forces conform to their mathematical definitions so precisely.”

Horgan goes further than that. He says that many of the entities, fields and forces of physics are entirely mathematical in nature.

Firstly he tells us that “mathematics helps physicists definite what is otherwise undefinable”. Then he cites an example:

“A quark is a purely mathematical construct. It has no meaning apart from its mathematical definition. The properties of quarks – charm, colour, strangeness – are mathematical properties that have no analogue in the macroscopic world we inhabit.”

This isn't necessarily to say that quarks are nothing other than maths or the numbers which express their nature. (Otherwise why use the words “their nature”?) It's to say that we couldn't say much – or indeed anything – about quarks without the requisite mathematics.

This may also mean that mathematical physics not only describes nature: it also – in some sense - creates it. This may also mean that the entities, strings, dimensions, etc. which string theorists postulate may make much more sense than we think. In other words, if we've no grasp of reality that's separable from the maths of mathematical physics, then how can we even so much as question what string theorists are saying? As with quantum mechanics, we may have no independent ground to stand on.

Thus surely we can follow on from all that and question if there really is something beyond the mathematical formulations which express the nature of strings and quarks. In other words, what's left after we take the maths away? Nothing or just a little something “we know not what”? What can be said without the maths? And what if what's said without the maths is highly misleading in that's it's purely analogical, metaphorical or imagistic in nature? Indeed perhaps we would be better off – in both string theory and quantum mechanics - without the analogies, images and picture-painting. 

A Digression: Wilder on Constructivist Maths

We can compare string theory with mathematical constructivism in the sense that the latter is deemed to be unchained from reality and the former may well be too.

The constructivist theory of mathematics (which includes mathematical intuitionism) has it that rather than maths being chained to reality, it is actually free to journey wherever it likes. (This parallels - at least to some extent - “free logic”.) That's because mathematics is said - by constructivists - to be a human construction and thus each “mathematical concept” is an individual mental construction.

The American mathematician and anthropologist, R.L. Wilder (1896 to 1982), saw this mathematical freedom in terms of developments which came to fruition in the 19th century. In his book, Introduction to the Foundations of Mathematics, he wrote:

“Following the 19th century developments, the mathematical world came to feel that it was no longer restrained by the world of reality, but that it could create mathematical concepts without the restrictions that might be imposed by either the world of experience or an ideal world to whose nature one was committed to limited discoveries. ”

What we have here is the ancient battle between what we can call “empirical maths” (which can, of course, be seen as an oxymoron) and “Platonic maths”.

In the Platonic scheme, to quote Wilder again, mathematics was seen as “a description of an ideal world of concepts existing over and above the so-called real world”.¹

The question is whether or not the maths in string theory is also (at least partly) Platonic or constructivist (if only by default) in nature. (The large distinctions which can be made between mathematical constructivism and mathematical Platonism don't matter in this precise context.)

Wilder's own position is very different from both Platonism and constructivism. He offered us what may be called a conventionalist - or even an anthropological/“materialist” - view of mathematics. He wrote:

“Mathematics derives its concepts initially from the existing world of reality and uses them as a way of dealing with this reality…”

The traditional view was that it's indeed the case that mathematics can be used “as a way of dealing with” reality (though not necessarily that it also “derived its concepts… from the existing world of reality”). In the case of string theory, the primary question here is about its descriptions or explanations of reality; not whether maths of string theory is “derived” from reality. However, if mathematical concepts are derived from reality (if only initially), then it's not surprising that they can also be applied to - or deal with - that reality.

Wilder then explicitly puts the anti-Platonic or constructivist position. He says that the concepts of mathematics

“were [in the 19th century onward] no longer embodiment of an independently existing realms of ideas, having an existence before and after the fact of their discovery, but only of a world of concepts continually under construction and having no existence until conceived in the minds of the mathematicians who created them”.

More relevantly, we can rewrite the passage above in the following manner:

Mathematics is no longer the embodiment of an independently existing realms of ideas, having an existence before and after the fact of their discovery, but only of a world of concepts continually under construction and having no existence until conceived in the minds of the mathematicians who created them.

The above only stresses the case of mathematical string theory being opposed to mathematical Platonism (with its abstract world full of abstract Forms). String theory may also run free of concrete reality too. Again, to rewrite another passage from Wilder above:

String theorists came to feel that string theory was no longer restrained by the world of reality, but that it could create mathematical concepts without the restrictions that might be imposed by the world of experience.

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Note

1 This freedom from “the world of experience” (or from physical reality) may make one think in terms of a Platonic conception of mathematics. However, if one is a Platonist, one must be equally committed to Plato’s “ideal world” which would inevitably “limit [one’s] discoveries” (to use phrases from Wilder). It's no wonder that philosophers have said that Platonic conception of mathematics is also implicitly - or even explicitly - committed to a correspondence theory of both numbers and equations. That is, mathematicians must be both committed to - and make their numbers and equations correspond with - the abstract mathematical entities in Plato’s abstract world. As one can see, this is just as much of a limitation as making one’s mathematics abide by the dictates of experience or the physical reality. It was no wonder, then, that some mathematicians rejected the infinite, never mind Georg Cantor’s infinite infinities. They did so because they believed that there are no actual infinities in the physical world or in the world of experience... at least not until 20th century physics.

*) See my 'The Scientific Problem with Panpsychism & String Theory (With Lee Smolin) (1)'. 
To follow: 'Experiments and Predictions', 'What is a Theory?', 'The Aesthetics of Theory-Choice'.

The Scientific Problem with Panpsychism & String Theory (With Lee Smolin) (1)

[The words “string theory” are used in the following. One of Lee Smolin's main arguments is that there are many string theories. Not surprisingly, some/many string theorists dispute that.]

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Lee Smolin's book book, The Problem With Physics, is relied upon in all the parts of this piece . It's relied upon because Smolin's views parallel (at least in part) my own on panpsychism. However, I certainly wouldn't have relied on Smolin's book if it weren't for his strong and detailed emphasis on string theory. It's this emphasis on string theory which ties in strongly with my own positions against panpsychism.

I personally don't have a firm position on string theory. I certainly don't adopt Smolin's strictly scientific positions on it. That's primarily because any position (at least of a scientific nature) on string theory must – almost of necessity - involve complex mathematics. Yet I'm neither a mathematician nor a physicist. Indeed I'm not even an “amateur expert” on string theory. However, it's also the case that nothing said in the following depends on my knowing the complex mathematics required for string theory. Everything I say should stand without such scientific and mathematical knowledge. Despite saying that, I'm well aware of the possible objections – from string theory acolytes - to my position. Smolin himself brings up such objections. He writes:

“Some string theorists prefer to believe that string theory is too arcane to be understood by human beings.... One recent posting on a physics blog laid this out beautifully: 'We can't expect a dog to understand quantum mechanics, and it may be that we are reaching the limit of what humans can understand about string theory. Maybe there are advanced civilizations out there to whom we appear as dogs do to us, and maybe they have figured out string theory well enough to have moved to a better theory...'...”

The Czech string theorist (or perhaps I should say physicist), Luboš Motl, even comes close to saying all this (in his review of The Problem With Physics) about Smolin himself. He writes:

“Because these statements [of Smolin] are of mathematical nature, we are sure that Lee is wrong even in the absence of any experiments.”

Thus if some string theorists believe that Smolin is an (mathematical) “outsider”, then you can be sure that they think the same about everyone else on the outside. As Smolin puts it:

“The views of outsiders must be disregarded because outsiders are not skilled enough in the tools of the trade to evaluate evidence and pass , of judgment.” (287)

This insider-outsider situation is also, of course, the case with philosophers; as well as with all other specialists (or professionals). And in both the case of string theorists and philosophers (perhaps also panpsychists), there's much justification for this insider-outsider mismatch.

Despite that, string theorists still find themselves in an extremely neat and convenient position. That position is expressed by William Poundstone in his book, Labyrinths of Reason. (Poundstone puts the quandary into the mouth of Sherlock Holmes.) Thus:

“'I subscribe to several esoteric journals to ease the tedium of the apiarist's life. I was reading in one of them that William Shanks, a mathematician of our fair island, has recently computed pi to 707 decimal places. It took him twenty years. His result filled a whole page with quite senseless, random numbers. Should anyone doubt Mr. Shank's result, he would have to budget an equal amount of time and duplicate his work. In that case also, verifying the answer would be precisely as difficult as coming up with the answer in the first place – the very antithesis of an obvious solution.'....”

Sherlock Holmes, of course, was a layperson when it comes to higher mathematics. However, even within mathematics and mathematical physics, some such professionals are essentially laypersons when it comes to the domain of string theory. Indeed, if we split string theory up into its many sections, then some string theorists will be (almost) laypersons when it comes to the work of other string theorists.

Of course what's been said is also partly true of all physics. That is, the entirety of physics includes mathematics which laypersons won't understand. Nonetheless, such areas of physics don't – one can argue – suffer from the same problems which string theory faces (i.e., the problems discussed in this piece).

Having said all the above, and also having read The Problem With Physics, I'm still not entirely sure what Lee Smolin's final stance on string theory actually is. Obviously it's true that he has very big problems with it. (E.g., the fact that it offers no predictions; has no experimental input; has no precise mathematical formula which is systematic and works for all string theories; has an unhealthy academic hegemony; etc.) Though, despite that, Smolin also seems to argue that string theory may well still be true/correct/accurate. He definitely does say – in accordance with his Feyerbendian theoretical pluralism (see later) – that string theory has both a value and an important role to play in physics. Indeed he spends much time making precisely that point.

Smolin also stresses his string-theory credentials. For example, he writes:

“.... there have been periods when I avidly believed in string theory and devoted myself to solving its key problems. While I didn't solve them, I wrote eighteen papers in the subject...”

More relevantly to this piece, Smolin says:

“Nor am I for anything except science, or against anything except that which threatens science.”

That quote gets to the heart of the matter. Smolin believes that string theory is, in many ways, unscientific; or, at the least, non-scientific (see later). This is where philosophy comes in. That is, in order to claim that x is non-scientific, one has to advance philosophical arguments in order to justify that claim.

To sum up Smolin's positions on string theory, it can be said that his two main (scientific) claims are the following:

i) String theory makes no testable predictions.

ii) String theory has no accepted or systematic mathematical formulation. (This claim is far less relevant to this piece.)

Thus it's of course ironic that in the review of The Trouble With Physics mentioned earlier, Luboš Motl also turns on Smolin's claim that string theory is non-scientific by saying that "the concentration of irrational statements and anti-scientific sentiments has exceeded my expectations”.

Despite Motl's hyperbolic statement, and as previously said, Smolin also says that string theory may still be at least partly true/correct/accurate without thereby also abiding by (all of?) science's rules... That's if science has any rules! I make this point because there's an entire chapter (called 'What is science?') in Smolin's book which is devoted to Paul Feyerabend . This American/Austrian “anarchist philosopher” rejected the very existence of a “scientific method”. He also argued that it would be counterproductive for science even if it the scientific method did exist. And Smolin seems to at least partly endorse Feyerabend's position. This, at least prima facie, seems to work against Smolin's strong position on string theory's non-scientific nature. Indeed, when speaking against string theory, he does so by saying that it goes against the scientific method. (Incidentally, Motl too says that Smolin is both "anti-scientific" and "against the scientific method".) For example, this is Smolin on Fotini Markopoulou's results on quantum gravity. He writes:

“... it shows promise of leading to unique predictions, which will either be in agreement with experiment or not. Most important, this obviates the need to revise the scientific method.... Science done the old-fashioned way is moving ahead.”

Of course it may simply be the case that Smolin accepts Feyerabend's theoretical pluralism (or theoretical “anarchism”) and rejects his positions on the scientific method itself.

Unscientific or Non-scientific?

The relevant - and obvious - point here is that panpsychism is a philosophical theory; whereas string theory is part of science. Nonetheless, some of the philosophical (i.e., not scientific) problems which both face are very similar.

In any case, panpsychist philosophers don't claim that panpsychism is a science or even that it's scientific.

Indeed philosophy itself isn't a science. And that must mean that panpsychism isn't a science.

However, many panpsychists (as do various “analytic metaphysicians”) claim that panpsychism must still be beholden to science. Alternatively, they say that it shouldn't (directly) contradict anything in science. (David Chalmers, for example, classes himself as a “naturalist” - actually, he calls his position “naturalistic dualism”!) Indeed because panpsychism deals with “intrinsic natures”, then - almost by definition - it can be said that it can't contradict anything in physics.

All this parallels – at least to some extent - the Wittgensteinian claim that science and religion don't contradict each other because they're dealing with different phenomena. (Alternatively, Wittgensteinians claim that science and religion sometimes deal with the same phenomena; though in different ways.) Thus science and religion are – in the language of Steven Jay Gould - “non-overlapping magisteriama”. (There will be more on the overlapping-worlds idea later.) This may also mean that panpsychism and physics are non-overlapping worlds. And, if that's the case, then how they they contradict one another?

The other point which has to be made is that the scientific criticisms of panpsychism can also be applied to many other philosophical theories. Indeed the entirety of metaphysics can be said - and has been said - to be suspect from a scientific point of view (at least according to some scientists). Thus panpsychism's relationship with science is far from being unique.

Yet philosophy can indeed be unscientific rather than simply non-scientific. So is panpsychism unscientific or non-scientific? What about string theory? Is it – at least partly - unscientific or is it non-scientific?

A simple - and perhaps naive - example of this problem relates to the question as to what is and what isn't observable. If what can be observed – or can be in observed “in principle” (as it's often put) – is ignored or rejected, then that would be an unscientific position to take. However, even within science many things are unobservable (e.g., quarks, protons, the iron core at the center of the earth, distant galaxies, fields and forces, etc.). Some things are even unobservable in principle (e.g., the past, numbers, laws, universals, perhaps other minds, etc.). That clearly has relevance to both string theory and panpsychism.

Indeed in terms of most/all of the claims of metaphysics (even those claims about things which are observable): they're still primarily about things which aren't observable.

Perhaps a quote from the English philosopher C.D. Broad will help here. (As found in his paper, 'Philosophy', in Inquiry I.) Thus:

“We must distinguish between being non-scientific and being un-scientific. What I have admitted is that philosophy is a subject which is almost certainly of its very nature non-scientific. We must not jump from this purely negative statement to the conclusion that it has the positive defect of being unscientific. The latter term can be properly used only when a subject, which is capable of scientific treatment, is treated in a way which ignores or conflicts with the principles of scientific method.” 

Very controversially, it must be said here that Broad might well have had telekinesis, mind-reading and even backwards causation in mind when he wrote the above. That alone shows us how problematic the distinction between x being unscientific and x being non-scientific is. That is, that distinction may simply allow too much even when it comes to what's non-scientific: never mind what's unscientific.

In any case, if we forget telekinesis and mind-reading, it's feasible that both string theory and panpsychism can be non-scientific without also being unscientific. However, there's an obvious difference. As stated, string theory is a science and panpsychism isn't. Thus if string theory is either non-scientific or unscientific, then that's a problem. Panpsychism, on the other hand, is only problematic if it's unscientific. Thus if we say that panpsychism is non-scientific (to quote Broad again), “[w]e must not jump from this purely negative statement to the conclusion that it has the positive defect of being unscientific”. The same can't also be said of string theory.

The last statement from Broad is very helpful in this context. Let me re-quote it:

“The latter term ['unscientific'] can be properly used only when a subject, which is capable of scientific treatment, is treated in a way which ignores or conflicts with the principles of scientific method.” 

That means that if panpsychism deals with a subject “which is capable of scientific treatment” (and which “is [also] treated in a way which ignores or conflicts with the principles of scientific method”), then we may have a philosophical problem. (We certainly do if we're naturalists.) The point here is that panpsychists will simply claim that panpsychism – or at least most/all of the claims from panpsychists – have nothing whatsoever to do “with the principles of scientific method”. Philosophers may again claim – in the Wittgensteinian sense - that panpsychism and science are non-overlapping worlds. That claim, however, may be both too convenient and simply false. After all, take the following:

i) If physics states that there are no “intrinsic natures” (certainly if it claims that micro-entities don't have “phenomenal properties”),

ii) then panpsychism does indeed “conflict with the principles” of physics.

The problem is, however, that some/many panpsychists claim that physics simply “ignores” intrinsic natures. That is, it has no position on them. As the philosopher Philip Goff puts it:

“This [panpsychist] argument presses us to the conclusion that there must be more to physical entities than what they do: physical things must also have an ‘intrinsic nature’...”

And elsewhere he says:

“... given that physics is restricted to telling us only about the behaviour of physical entities – electrons, quarks and indeed spacetime itself – it leaves us completely in the dark about their intrinsic nature. Physics tells us what matter does, but not what it is.”

Some physicists, on the other hand, will simply claim that intrinsic natures don't exist. Thus we can conclude by saying that physics as a whole – as stated - doesn't have a universal or systematic position on intrinsic natures (or on “micro-minds”).

This also means that if science/physics has no problem with panpsychism (or even accepts the fruitfulness of research into it), then that would also fit in well with Smolin's Feyerabendian theoretical pluralism.

So what about string theory and the non-scientific/unscientific bifurcation?

We can say that because of the current state of play, many of the claims and theories of string theory aren't (to use Broad's words again) “capable of scientific treatment”. (Though not only for reasons of the experimental limitations brought about by deficiencies of contemporary technology.) Nonetheless, that doesn't necessarily also mean that string theory also “conflicts with the principles of science”. Of course it can now be said that if string theory's claims aren't capable of scientific treatment, then how can they also be scientific? Though this, of course, would also render very many 19th and 20th century theories (in physics) and statements (from physicists) non-scientific. That is, many claims and theories were made before the evidence or experiments were in. Does that mean that such claims or theories were non-scientific or even unscientific? If the experiments and evidence came to be available, then surely we can't say that such claims and theories were unscientific. Thus they were non-scientific, rather than unscientific. Indeed perhaps they weren't even non-scientific: they might have simply been (as it were) protoscientific.

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*) See my 'The Scientific Problem with String Theory (With Lee Smolin): Maths and Reality (2)' and
'The Problem with String Theory & Panpsychism: the Aesthetics of Theory-Choice (3)'... To follow: 'Predictions and Experiments'.