The Problem with String Theory & Panpsychism: the Aesthetics of Theory-Choice (3)

Much is made (by both laypersons and scientists) of the fact that many mathematicians and physicists stress the “beauty” and “elegance” of their theories. Philosophical panpsychists do the same. Indeed the aesthetic values of both string theory and panpsychism may even be their major appeal.

So perhaps there's an over-indulgence in (or over-reliance on) aesthetics in both panpsychism and string theory.

String Theory

Lee Smolin (in his book, The Trouble With Physics) quotes string theorists talking about the beauty of the theory (or theories) in the following:

“... 'How can you not see the beauty of the theory? How could a theory do all this and not be true?' say the string theorists.”

Smolin is at his most explicit when he also tells us that “string theorists are passionate about is that the theory is beautiful or 'elegant'”. However, he says that

“[t]his is something of an aesthetic judgment that people may disagree about, so I'm not sure how it should be evaluated”.

More importantly, Smolin concludes:

“In any case, [aesthetics] has no role in an objective assessment of the accomplishments of the theory.... lots of beautiful theories have turned out to have nothing to do with nature.”

Perhaps Smolin is going too far here. Surely it's the case that aesthetics has some role to play when it comes to theory-choice. And who's to say that whether a theory is elegant or not – at least in some sense - isn't itself an “objective” issue? Whether something is simpler than another theory is surely an objective fact. It's whether or not such simplicity can also be tied to elegance and beauty that's the issue here. (See later section.)

Despite that, Smolin does quote a string theorist (ironically enough), Leonard Susskind, arguing that simplicity and elegance aren't everything. (In this instance, Susskind talks about “anthropic theory”; though this is tied in with string theory – at least for Susskind.) Smolin quotes Susskind thus:

“… '… in an anthropic theory simplicity and elegance are not considerations. The only criteria for choosing a vacuum is utility...'.”

So with some – or all - theories, “utility” may – at some point - override “simplicity and elegance”. Isn't that also true of string theory? It can't be, surely. As yet, it can't be said that string theory has any utility, either in terms of technology or in terms of predictions or experiments. (Perhaps the anthropic theory may run somewhat free of string theory, at least according to Leonard Susskind.)

Panpsychism

In terms of panpsychism, the philosopher Philip Goff stresses “scientific values” when he talks about panpsychism. (He says that “panpsychism is a scientific research programme in its own right”.) He also tells us that panpsychism is “parsimonious” and “extremely elegant”. In his piece, 'The Case For Panpsychism', he writes:

“Panpsychism offers the hope of an extremely elegant and unified picture of the world. In contrast to substance dualism (the view that the universe consists of two kinds of substance, matter and mind), panpsychism does not involve minds popping into existence as certain forms of complex life emerge, or else a soul descending from an immaterial realm at the moment of conception.”

It's usually theories in physics and mathematics – not philosophy – which are seen to be “elegant”, “unified” and “parsimonious”. Perhaps that doesn't really matter. Perhaps philosophy too should adhere to these aesthetic values. Nonetheless, panpsychist philosophers are doing something that's very different to that which physicists and mathematicians do. There may indeed be similarities here and there; though, on the whole, surely the dissimilarities are more striking.

The Final Unification

Both string theory and panpsychism offer us so much. Primarily, they offer us unification. And these package deals also offer us their unifications in ways which are very neat and (as it's often put) “elegant”.

In any case, after so many failures in physics and the philosophy of mind, surely it's time to come up with a solution (or a theory) which offers us unification. Both panpsychism and string theory offer us such a solution.

String Theory

So what does string theory offer us? According to Lee Smolin:

“[String theory] purports to correctly describe the big and the small – both gravity and the elementary particles...... it proposes that all the elementary particles arise from the vibrations of a single entity - a string – that obeys simple and beautiful laws. It claims to be the one theory that unifies all the particles and all the forces in nature.”

As evolutionary psychologists and cognitive scientists have told us, human beings have an innate need for both simplicity and explanation – sometimes (or even oftentimes) at the expense of truth. Thus, in the case of string theory, we may have a juxtaposition of the psychological need for simplicity and explanation along with highly-complicated and arcane mathematics.

Perhaps that highly-complicated maths is but a means to secure us simplicity and explanation. That is, the work done towards simplicity and explanation is very complex and difficult; though the result – a theory which is both simple and highly explanatory – evidently isn't. After all, in terms of the omnipresent Theory of Everything, for example, the science journalist and author, Dan Falk, suggests that

“the ideas at the heart of the theory may turn out to be extremely simple – so simple, in fact, that the essence of the theory can be written on a T-shirt”.

(This wouldn't be that unlike the Hitchhiker's Guide to the Galaxy theory that the "answer to the Ultimate Question of Life, the Universe, and Everything" is the number 42.)

Lee Smolin also tackles the issue of the aesthetics of physics within the specific context of scientific unification. And, of course, string theory is a great unifier. Smolin writes:

“There are good lessons here for would-be unifiers. One is that mathematical beauty can be misleading.”

What's more, he concludes by saying that “simple observations made from the data are often more important”.

It's fairly hard to make sense of the word “misleading” here except to say that the statement “beauty is truth” may not be a truth itself. Or at least it may not always be applicable to every mathematical or physical theory.

The other point Smolin stresses is that maths should never run free of reality. Or, in this case, from “observations made from the data”. Of course theories (or at least hypotheses or speculations) often come before observations and data. However, they must still – at least at some point - be justified or legitimised by observation and data: or by reality.

Panpsychism

In terms of panpsychism, it too is a unifying philosophical theory. For a start, it's generally regarded as a kind of monism. That is, it unites the seemingly physical with the seemingly non-physical. That means that it can hardly fail to be unifying. (The philosopher Philip Goff also says that “the nature of macroscopic things is continuous with the nature of microscopic things”.) More technically, if all entities (even the elements of fields and forces), are (to use Goff's term) “little subjects” (or little minds), then that must mean that there's no huge jump from these entities to human consciousness (or human minds). It's minds all the way down. What can be simpler than that? What can be more unified than that?

Philip Goff writes:

“Yet scientific support for a theory comes not merely from the fact that it explains the evidence, but from the fact that it is the best explanation of the evidence, where a theory is ‘better’ to the extent that it is more simple, elegant and parsimonious than its rivals.”

Not accepting this position - according to Goff - “adds complexity, discontinuity and mystery”. This makes panpsychist monism seem very need and tidy. Or, as Goff often puts it, it makes panpsychist monism “elegant” and “parsimonious”. But does neatness, elegance and parsimony make this theory true? Not really. Aesthetic criteria may contribute to our reasons for accepting it, though such things surely don't – in and of themselves - make a theory true, accurate or valid.

Yet anything can explain anything else if the links are suitably tangential. It's whether or not we should believe (or accept) that particular explanation which matters. Many religions, after all, explain many – sometimes all - things. It's true that Philip Goff may say that these positions don't hold much philosophical or scientific water; yet exactly the same is said about panpsychism. Indeed panpsychism (according to Goff) is classed as “crazy”.

So frustration about the nature of consciousness, the mind-body-problem, etc. shouldn't entirely motivate us to accept the elegant and parsimonious theory of panpsychism. There has to be more to it than aesthetics.

This is partly why Raymond Tallis (in his piece 'Against Panpsychism') correctly smells the “ontology of the gaps” (which is a variant of the “God of the gaps”) when it comes to panpsychism.

The panpsychist idea is that no theory has satisfactorily explained consciousness. Thus:

i) No theory has explained consciousness.

ii) Panpsychism explains consciousness.

Iii) Therefore we should accept panpsychism. (Or, at the least, do research on its behalf.)

The same is true of string theory. Thus:

i) No theory has satisfactorily offered us a grand unification of physics and cosmology.

ii) String theory does.

iii) Therefore we should accept string theory. (Or, at the least, do research on its behalf.)

Thus, after so many failures, surely it's time to come up with a solution. Are string theory and panpsychism such solutions?

Beautiful Theories and Reality

There's one strong aspect of this debate the needs to be stated here: the connection between theory and reality. Put simply, a "beautiful theory" (however it's defined) may have no connection at all to reality.

Smolin offers a powerful example of the disjunction of a beautiful theory and reality: the aether theory. Smolin asks:

“Could there have been a more beautiful unification than the aether theory? Not only were light, electricity, and magnetism unified, their unification was unified with matter.”

Then Smolin also offers us an earlier example of such a disjunction. Thus:

“There are many examples of theories based on beautiful mathematics that never had any successes and were never believed, Kepler's first theory of the planetary orbits being the signal example.”

Aesthetically, one may ask a very simple question here:

Why is unification beautiful in and of itself?

That will depend on what one takes beauty to be. You can of course stipulate a link between an x which unifies and x thereby being beautiful. However, what is the aesthetics of such a link?

Is it that unification is also simplification? Thus perhaps we can tie unification to simplicity. After all,

If x is unified both within itself and to other things, then x is also simple.

That simply moves the problem on:

What is the aesthetics of the link between simplicity and beauty?

Thus according to the definitions commented upon above, the panpsychist theory must also be beautiful. That means, again, that we've a tight link between unification and simplicity; and both unification and simplicity tie together to make theory x beautiful.

*) See my 'The Scientific Problem with Panpsychism & String Theory (With Lee Smolin) (1)' and 'The Scientific Problem with String Theory (With Lee Smolin): Maths and Reality (2)'. To follow: 'Predictions and Experiments'.

Daniel Dennett's Elimination of Qualia

“[Others] note that my 'avoidance of the standard philosophical terminology for discussing such matters' often creates problems for me; philosophers have a hard time figuring out what I am saying and what I am denying. My refusal to play ball with my colleagues is deliberate, of course, since I view the standard philosophical terminology as worse than useless—a major obstacle to progress since it consists of so many errors.” - Daniel Dennett (in 'The Message is: There is No Medium', 1993).

I'm going to start with an ad hominem and say that the real reason why Daniel Dennett is against qualia (or believes that the word qualia is “a philosopher's invention”) is because they're unscientific; not because he thinks that they don't exist (or aren't real).

Qualia are indeed unscientific. In fact many believers in qualia will happily admit that. They may also say: Qualia are indeed unscientific... and...?

It can be seen that Dennett's scientific attitude (as only partly exemplified by his position on qualia) was there from the very beginning of his professional career.

Dennett was taught by Gilbert Ryle and the former adopted the latter's position in defining first-person experiences in third-person (or behaviourist) terms.

What are Qualia?

Take Dennett's oft-quoted list of what he believes other people take qualia to be:

(1) ineffable

(2) intrinsic

(3) private

(4) directly or immediately apprehensible in consciousness.

What a terribly unscientific list we have there! Indeed, even if we were talking about something else (say, numbers), that list would still make that something else problematic from a scientific perspective.

The list above reminds me of David Hume's problem (as quoted by Kant in his Prolegomena to Any Future Metaphysics) with monotheistic definitions of the word God which only include “ontological predicates” (such as “eternity, omnipresence, omnipotence”); none of which are in concreto (i.e., about God-as-a-substance). And qualia too, just like God, are given no “conditions of identity” (to use Quine's phrase): only conditions of attribution (as it were).

Let's give the members of Dennett's list of qualia attributes a quick scientific telling off.

(1) Ineffable. Nothing should be/is ineffable in science. At least not ineffable in principle (as the believers in qualia supposedly believe). If x is ineffable – especially ineffable in principle – then, almost by definition, it's unscientific.

(2) Intrinsic. The word 'intrinsic' isn't often explained or defined; at least not in relation to qualia. But the thought is that if qualia have intrinsic features, then they must also be scientifically irreducible. That is, there are qualities which are intrinsic to qualia and to nothing else. Thus even if there were an attempted reduction of qualia or of a single quale (which some philosophers believe is possible), it would still leave out what makes a “subjective experience what it is” (as Thomas Nagel put it).

(3) Private. The whole of the behaviourist movement (in philosophy and science) had a problem with privacy (as did Wittgenstein). In order to make both psychology and the philosophy of mind scientific, they had to get rid of everything that is private – at least when it came to the mind.

(4) Directly or immediately apprehensible in consciousness. This commits more than one sin. Until that last couple of decades, conciousness was verboten in science and even with many philosophers. And we also have the very Cartesian sounding “immediately apprehensible”. Why would scientists care about that which is immediately apprehensible? Indeed many scinetists wouldn't even accept it as a meaningful notion.

Wittgenstein

Dennett often lets Wittgenstein put his scientific position for him; which is strange really because Wittgenstein isn't usually cited to back-up what are often called “scientistic” positions.

Wittgenstein mentioned his box; which is taken to be the mind. Dennett puts qualia in Wittgenstein's box; instead of Wittgenstein's very own little beetle. (Wittgenstein doesn't mention qualia.) Dennett quotes Wittgenstein when the latter writes:

“The thing in the box has no place in the language-games at all; not even as a something; for the box might even be empty. - No, one can 'divide through' by the thing in the box; it cancels out, whatever it is.”

This can be said to be part of Wittgenstein's behaviourist phase; though, no doubt, many of his acolytes would deny that.

The “language-game” Dennett has in mind is science. However, for Wittgenstein's own argument, it didn't need to be science he had in mind. (In fact he didn't have science in mind.) His argument or position works regardless because it's really an argument against the possibility of a “private language”.

From a scientific position, the mind can indeed be seen as a black box –hence behaviourism and the reluctance to deal with consciousness.

When it comes to qualia the situation is worse because even though beliefs, desires, etc. can be connected to behaviour, the case of qualia isn't quite so clear-cut. After all, qualia may have no behavioural outputs; or, on some accounts, no “functional properties”. To some philosophers qualia may indeed have a functional role. However, the route from qualia to behaviour is so hazy or circuitous that, yes, qualia may as well be erased from the picture entirely. That would be the scientific thing to do.

Wittgenstein's problem with the possible beetle in the box was as strong as Dennett's problem with qualia. Dennett quotes Wittgenstein again saying that the beetle in the box (or qualia) is “something about which nothing can be said”. Dennett's concludes that the word qualia is a “philosopher's term which fosters nothing but confusion, and refers in the end to no properties or features at all”.

Dennett's Red Balls

Dennett displays his scientific credentials in a rather conventional manner when he deals with colour.

He believes that colour is a scientific property after all. This scientific story, of course, has nothing to do with qualia or “inner experiences”. Basically, Dennett deems colour to be a “relational property”. In his paper, 'Quining Qualia', he writes:

“All but the last of these [redness] are clearly relational or extrinsic properties of the ball. Its redness, however, is an intrinsic property. Except that this is not so. Ever since Boyle and Locke we have known better. Redness – public redness – is a quintessentially relational property.”

Dennett seems to be making a pretty obvious mistake here. He's conflating the effects of a quale (or of a “colour experience”) with the quale itself. Indeed Dennett explicitly says that he's only concerned with “public redness”, not private redness.

What makes the redness of the ball public is its “relational or extrinsic” properties. Thus, in consequence, private redness must be a private property and, therefore, unscientific.

Indeed Dennett is so keen on the public properties of a ball (as opposed to the private ones) that he even champions non-material (or relational) properties.

For example, one relational property cited by Dennett is the ball's “belonging to Tom”. Now that's not a very scientific property.... surely?. Dennett's ball also has the relational property of being “made from rubber from India”. (It's the “from India” clause that's relational here; not the “being made of rubber”.) In fact Dennett goes one step further and includes the bizarre (though accurate) relational property of “having spent the last week in the closet”. (So why didn't Dennett also include the relational property of not being a banana or being thrown 187 times?)

Above and beyond that: red balls aren't a fit subject for science in any case. Red balls aren't natural kinds. Cricket balls aren't natural kinds. Indeed generic balls aren't even natural kinds. Sure, not being natural kinds doesn't automatically make them unscientific; though it does stop them from being, well, scientific.

What is Bitterness?

In the same paragraph as the colour example, Dennett also gives us a scientific account of what he wants from - what used to be called - “secondary properties”. This time he deals with taste instead of colour.

What is it for for an x to be bitter? According to Dennett, it's “to produce a certain effect in the members of the class of normal observers”. Bitterness, then, is also a relational property.

It's not quite clear what “certain effect” Dennett is referring to here. Whatever it is, it must be objective (or intersubjective). Presumably it's objective because it will be behaviourally expressed by “the class of normal observers”.

Do we learn anything about bitterness by such uniform behavioural responses – even if they're examples of uniform “overt behaviour” (such a vocalised statements)? No; we learn about how persons react to bitterness. Uniform reactions to bitterness aren't themselves bitterness. (They are, well, uniform reactions to bitterness.) This is almost equivalent to saying that the throwing a ball is the same as the smashing of a window. That is, the throwing of a ball resulted in the smashing of a window; just as the tasting of something bitter leads to a “certain effect in the members of the class of normal observers”. Basically, Dennett is fusing (or conflating) cause and effect.

In addition to that, it's possible that a seemingly bitter piece of food can have a uniform “certain effect” even if it tastes differently to each person tested. Or, alternatively, something that tastes the same can have different certain effects in the class of normal observers.

These standard philosophical possibilities will of course be rejected by Dennett because they're unscientific. He would probably tell us that we have no way of knowing if these possibilities are actualities. And if that's the case, then such possibilities are merely idle from a scientific – if not a philosophical – point of view. Again, qualia differences don't make a difference. Behavioural differences do make a difference.

Alvin I. Goldman expresses Dennett's scientific position on these possibilities when he says that Dennett's

“claim is that there is no way to distinguish between these competing stories either 'from the inside' (by the observer himself) or 'from the outside', and he appears to conclude that there are no genuine facts concerning the putative phenomena experience [or differences] at all”.

This reiterates Dennett's Wittgensteinian point that there are no facts about the private. And, of course, this is something that has been repeatedly debated in Frank Jackson's What Mary Knew scenario.

Considering Dennett's scientific leanings, it's perhaps not a surprise that he believes that Mary “knew everything about colour”. Dennett believes this because Mary's complete understanding of neuroscience, physics, etc. couldn't fail to supply her with complete knowledge. (Including experiential knowledge?) However, Dennett is wise enough to realise that the full knowledge so often posited for Mary would almost be miraculous in real terms. In fact Mary would need to be (virtually?) omniscient to have it. Thus, by definition, of course Mary would know what red looks like if she were omniscient.

Despite all that, here again one can accept that qualia have no factual status (just as they have no scientific status) at the very same time as accepting that they exist or are real.

It's here, I suppose, that Dennett could ask me the following question:

If qualia have neither scientific nor factual status, then exactly what kind of status do they have?

Well, at a prima facie level, I don't have an immediate answer to that.

Peacocke's Pseudo-analysis of Experience?

Intersubjectivity (or, as it is sometimes called, objectivity) has always been primary in science. And, lo and behold, Dennett says that “no intersubjective comparison of qualia is possible, even with perfect technology”.

That's true; and there are a handful of philosophical arguments which demonstrate that. And since it's taken that qualia don't exist (or may as well not exist) as far as science is concerned, then by definition no intersubjective comparison of qualia is possible and neither would one be accepted.

Thus Dennett would automatically rule out Christopher Peacocke's analysis of an experience. Peacocke writes:

“Our perceptual experience is always of a more determinate character than our observational concepts which we might use in characterising it.”

Surely this wouldn't as much as make sense to Dennett. It's an analysis of something that's entirely private and indemonstrable.

Perhaps Dennett would now ask:

How do we know it's “more determinate”? How do we know it goes beyond our “observational concepts”?

According to Dennett's logic, could an individual even offer an analysis of one of his own experiences? Some would say: Why not? Though surely Dennett would say: No he couldn't. Or, at the very least, Dennett may say:

Analyse away if you wish. However, it serves no scientific - or any other - purpose.

In that, perhaps he's (partly) right.

Indeed even Christopher Peacocke himself says that “the nonrepresentational properties of another's experience would be unknowable”. And surely we can now offer the Wittgensteinian and Dennettian point that they would also be unknowable to the subject analysing (?) his own experience. In fact isn't it the case that the former leads to the latter? That is, because they are unknowable to third persons then, in effect, they must also be unknowable to the subject undergoing the experience. That is the obvious conclusion to this (late) Wittgensteinian logic.

Conclusion

Considering Dennett's 'scientism' as regards qualia, you'd think that if scientists accept qualia (at least as described by philosophers), then he'd accept them too. After all, philosophical naturalists believe that what science (not individual scientists!) says goes, goes.

Erwin Schrödinger (1887–1961), for example, once wrote the following:

“The sensation of colour cannot be accounted for by the physicist's objective picture of light-waves. Could the physiologist account for it, if he had fuller knowledge than he has of the processes in the retina and the nervous processes set up by them in the optical nerve bundles and in the brain? I do not think so.”

Schrödinger mustn't have believed that even a scientifically omniscient Mary would know what red looks like. Of course it would be moronic to now conclude:

If Erwin Schrödinger believed that qualia exist, then qualia must exist.

Indeed it can even be argued that what Schrödinger says above isn't really a commitment to qualia in the way some philosophers of mind (as well as laypersons) are committed to qualia.

And of course not all scientists accept qualia. Indeed I suspect that the majority of scientists haven't even given the subject of qualia serious thought.

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.

*********************

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'.