Murray Gell-Mann on Complexity (2)

i) Introduction

ii) Additional Information

iii) Simplicity and Complexity

iv) Complexity ≠ (Strong) Emergence

v) The Autonomy of Higher Levels

vi) Higher-level Laws

[The short biographical introduction which opens this piece is a copy-and-paste from Part (1) – 'Murray Gell-Mann on Reductionism'.]

Murray Gell-Mann died on the 24^th of May, 2019.

In 1964 Gell-Mann postulated the existence of quarks. (The name was coined by Gell-Mann himself and it's a reference to the novel Finnegans Wake, by James Joyce.) Quarks, antiquarks and gluons were seen to be the underlying elementary elements of neutrons and protons (as well as other hadrons). Gell-Mann was then awarded a Nobel Prize in Physics in 1969 for his contributions and discoveries in the classification of elementary particles at the nuclear level.

More relevantly to this piece. In 1984 Gell-Mann was one of several co-founders of the Santa Fe Institute - a research institute in New Mexico. Its job is to study complex systems and advance the cause of interdisciplinary studies of complexity theory.

Gell-Mann wrote a popular science book about physics and complexity science, The Quark and the Jaguar: Adventures in the Simple and the Complex, in 1994. Many of the quotes in this piece come from that book.

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The following words of Lee Smolin (an American theoretical physicist) sum up both Murray Gell-Mann's work and the man himself. (At least as they are relevant to this piece.) Firstly he explains Gell-Mann's work:

“[P]hysics needs a new direction, and the direction should have something to do with the study of complex systems rather than with the kind of physics [Murray Gell-Mann] did most of his life.”

Then Smolin continues with a few words on Gell-Mann himself:

“The fact that after spending a life focused on studying the most elementary things in nature Murray can turn around and say that now what's important is the study of complex systems is a great inspiration, and also a great tribute to him.”

Of course all the above is hardly a philosophical or scientific acount of the need to move from the “elementary” to the “complex”. However, it does hint at the importance of gaining a broader picture of nature (or the universe). And that's what both Smolin himself and Gell-Mann realised. (In Smolin's own case, he moved from theoretical physics to adding cosmology and philosophy to his repertoire.)

Despite that, surely it can't be said that “what's important is the study of complex systems”. That's simply to reverse the “reductionist hierarchy”. Complex systems are simply part of the picture: not the most important part of the picture. Indeed it seems a little naïve to reverse that previous ostensible hierarchy with a new one. 

(Lee Smolin's take on Gell-Mann isn't surprising when one bears in mind the fact that he advances the philosophical position called relationalism.)

Murray Gell-Mann himself did appear to offer us a middle-way between (strong) reductionism and the complete autonomy of the individual (“special”) sciences.

Gell-Mann believed that it's all about what he called the staircases” between the sciences. As Gell-Mann put it (in the specific case of the relation between the levels of psychology and biology):

“Many people believe, as I do that when staircases are constructed between psychology and biology; the best strategy is to work from the top down as well as from the bottom up.”

What's more:

“Where work does proceed on both biology and psychology and on building staircases from both ends, the emphasis at the biological end is on the brain (as well as die test of the nervous system, the endocrine system, etc), while at the psychological end the emphasis is on the mind—that is, the phenomenological manifestations of what the brain and related organs are doing. Each staircase is a brain-mind bridge.”

Interestingly enough, a man who has often been accused of “reductionism” (the American biologist and naturalist E.O Wilson) expressed a similar view in the following:

“Major science always deals with reduction and resynthesis of complex systems, across two or three levels of complexity at a step. For example, from quantum physics to the principles of atomic physics, thence reagent chemistry, macromolecular chemistry, molecular biology, and so on – comprising, in general, complexity and reduction, and reduction to resynthesis of complexity, in repeated sweeps.”

So instead of Gell-Mann's simplicity and complexity, in this case we have the “reduction” and “resynthesis” of complex systems in “repeated sweeps”.

In addition, the philosopher Patricia Churchland (who classes herself as a “reductionist”) also advances a position which is similar to Gell-Mann's. In her case, she confronts the neuroscience-versus-psychology debate. And, in so doing, she mollifies psychologists about that scareword “reductionism” by saying that the

“reductionist research strategy does not mean that there is something disreputable, unscientific or otherwise unsavoury about high-level descriptions or capacities per se”.

The words above can be summed up in this way:

i) Simply because a scientist (or philosopher) says that x can be reduced to y (not necessarily without remainder),

ii) that certainly doesn't also mean that this scientist (or philosopher) also believes that x is (to use Churchland's words) “disreputable, unscientific or otherwise unsavoury”.

Then Patricia Churchland goes on to say something that may surprise some philosophers. She argues that reductionism can exist side-by-side with what she calls “high-level descriptions or capacities”. This too perfectly expresses Gell-Mann's own position (as we'll see).

To return to E.O. Wilson, he was also well aware that the “very word 'reductionism'” has a “sterile and invasive ring, like a scalpel or catheter”. He went on to say that the

“[c]ritics of science sometimes portray reductionism as an obsessional disorder, declining towards a terminal stage one writer recently dubbed 'reductive megalomania'”.

Additional Information

A seemingly extreme reductionist position is actually put by Gell-Mann himself (in relation to the domain of biochemistry). He writes:

“The proponents of this view are saying in effect that going from the fundamental laws to the laws of biochemistry involves almost no new information, and thus contributes very little effective complexity.”

Here the case for complete reduction is expressed in terms of information content. Or, as Gell-Mann puts it, “going from the fundamental laws to the laws of biochemistry involves almost no new information”. Nonetheless, here we also have “complexity” alongside possible reduction. That is,

“a computer might have to do a great deal of calculating to derive the near-uniqueness of biochemistry as a theoretical proposition from die fundamental laws of physics”.

That biochemical complexity is compounded by the important fact that it “also depends in an important way on history”. (Gell-Mann mentions “additional information” and “history” many times.) For example:

“The laws of biology do depend on the laws of physics and chemistry, but they also depend on a vast amount of additional information about how those accidents turned out.”

However, that seems like the problem of complete knowledge, rather than an argument against reduction... Unless, of course, a lack of complete knowledge rules out reduction. But that would still mean that a reduction is possible... “in principle”. After all, that additional information may be entirely peripheral or irrelevant. (This is in the sense that if an investigating officer were to ask about the killing of a person, telling him about the colour of the neon signs above the dead body wouldn't help.)

So “accidents” and “additional information” have always been known or accepted by physicists – even by “reductionists”. It's just that they factored out their relevance. Were they right to do so? (Lee Smolin – with his “physics in a box” - and the philosopher Nancy Cartwright question all of this.) How would any physicist or scientist have ever denied that they were factoring out additional or extraneous information? Of course they knew that such information existed. The problem is that taking on board everything in every experimental (or scientific) situation is impossible – and even complexity theorists and “holists” must accept this. (That's unless they hold the position of Absolute Idealism like F.D. Bradley's; or one of extreme holism.)

Simplicity and Complexity

Gell-Mann gave two interesting examples of the opposite of complexity. Firstly, he wrote:

“[In] the environment in question is the center of the sun, at a temperature of tens of millions of degrees, there is almost total randomness, nearly maximal algorithmic information content, and no room for effective complexity or great depth—nothing like life can exist.”

It's interesting that Gell-Mann lumps simplicity and “randomness” together at “the center of the sun”. By “nearly maximal algorithmic informational content” I take Gell-Mann to mean that in order to fully account for this “information content”, that content would simply need to be replicated in its entirety. Gell-Mann himself puts this case elsewhere. He talks about a “bit strings” and says that “it can shown mathematically that most bit strings of a given length are incompressible”. In more detail:

“In other words, the shortest program that will produce one of those strings (and then have the computer stop) is one that says PRINT followed by the string itself.... It is called a 'random' string precisely because it contains no regularity that will permit it to be compressed.”

In any case, Gell-Mann then jumps to the other extreme:

“Nor can there be such a thing as life if the environment is a perfect crystal at a temperature of absolute zero, with almost no algorithmic information content and again no room for much effective complexity or great depth.”

Here again randomness or lack of “algorithmic information” rules out complexity.

Complexity ≠ (Strong) Emergence

What stops the reduction of the whole of chemistry (for example) to physics can be summed up with one single word: complexity. This is how Gell-Mann puts it:

“In practice, even with the aid of the largest and fastest computers available today, only the simplest chemical problems are amenable to actual calculation from basic physical theory. The number of such amenable problems is growing, but most situations in chemistry are still described using concepts and formulae at the level of chemistry rather than that of physics.”

These concessions don't rule out reduction per se. That is, there's no strong emergence being hinted at here. All that's being admitted to is that some chemical phenomena are so complex that it would be impossible to get all the information required to reduce a given chemical x to a physical y. That's not say that the chemical x doesn't reduce to the physical y. It's simply to say that the reduction hasn't been done... Indeed perhaps it can't be done. But even here there's still no strong emergence. The only thing that's accepted is complexity.

And because of that complexity, Gell-Mann goes on to say that

“[i]n general, scientists are accustomed to developing theories that describe observational results in a particular field without deriving them from die theories of a more fundamental field”.

The very fact that observation is being stressed (elsewhere Gell-Mann also uses the word “phenomenological”) shows that the micro level is being automatically ruled out (as it were). It's also odd (bearing in mind traditional biases in physics - right up to the birth of quantum mechanics) that observation is being stressed at all.

In any case, here again reduction hasn't been rejected in principle, and that's because

“[s]uch a derivation, though possible in principle when the additional special information is supplied, is at any given time difficult or impossible in practice for most cases”

So reduction is trumped by complexity and/or by the contingencies of scientific “practice”.

Gell-Mann then gives us a specific example of complexity trumping (strong) reduction. He writes:

“[C]hemists are concerned with different kinds of chemical bonds between atoms (including the bond between the two hydrogen atoms in a hydrogen molecule). In the course of their experience, they have developed numerous practical ideas about chemical bonds that enable them to predict the behavior of chemical reactions.”

Despite all that, physicists and “theoretical chemists” are still hanging around on the sidelines. That is, “theoretical chemists endeavor to derive those ideas, as much as they can, from approximations to QED”. However,

“[i]n all but the simplest cases they are only partially successful, but they don't doubt that in principle, given sufficiently powerful took for calculation, they could succeed with high accuracy”.

Gell-Mann goes into more detail in the following:

“In very simple cases, an approximation to QED is used to predict directly the results at the chemical level. In most cases, however, lam are developed at the upper level (chemistry) to explain and predict phenomena at that level, and attempts are then made to derive those laws, as much as possible, from the lower level (QED). Science is pursued at both levels and in addition efforts are made to construct staircases (or bridges) between them.”

Here again complexity trumps (full/strong) reduction.

It's also worth stressing “causal” dependency here, rather than reduction. That is, one can stress causal dependency without demanding any kind of complete reduction.

That is, x can physically entail y (x can be a set of conditions, properties, etc.); and yet y will still not be entirely accounted for by x.

The Autonomy of Higher Levels?

Gell-Mann also puts the case for what E.O Wilson has called “concilience” (which doesn't rule out either reduction or reductionism) in the following words:

“One lesson to be learned from all this is that, while the various sciences do occupy different levels, they form part of a single connected structure. The unity of that structure is cemented by the relations among the parts. A science at a given level encompasses the laws of a less fundamental science at a level above.”

If we have “a single connected structure”, then it's difficult to see how we can also have autonomy when its comes to the special sciences or to higher-level descriptions/laws. (Isn't this why the philosopher Jerry Fodor advanced what he called “strong autononomy”?)

There also seems to be a commitment to at least some kind of reductionism here. How else can we interpret the following words? -

“[A] science at a given level encompasses the laws of a less fundamental science at a level above.”

Though it depends on how we interpret the words “reductionism” and “encompasses”. Nonetheless, Gell-Mann's words can be seen to be in favour of specific reductions; though not in favour of the philosophical standpoint of reductionism itself.

And then complexity does indeed raise its head:

“But the latter [e.g. chemistry], being more special, requires further information in addition to the laws of the former.”

Here we need to know what the words “further information” mean because, clearly, that further information may not block (or rule out) reduction or even reductionism itself.

Yet despite Gell-Mann's acceptance of the autonomy of different scientific disciplines, it may seem strange that he should also argue (of psychology) that it is “not yet sufficiently scientific”. What's more, he argues that his

“preference would be to take [them] up in order to participate in the form of making them more scientific”.

The words above can be read in two ways:

i) The “special sciences” aren't autonomous.

ii) In order to make the special sciences autonomous, we would need to “make them more scientific”.

Of course I'll now need to explain why I'm using the word “autonomy” here.

I do so because, for example, the theoretical physicist Sean Carroll often stresses the autonomy of the special sciences and higher-level descriptions. (The philosopher Jerry Fodor also stressed what he called “strong autonomy”.) Indeed Carroll's advances the “autonomy” of what he calls "emergent theories". (This is a vital part of his “poetic naturalism”.) Carroll writes:

“The emergent theory is autonomous... it works by itself, without reference to other theories...”

Elsewhere, Carroll says that with strong emergence “all stories are autonomous, even incompatible”. Yet, in other places, Carroll also stresses emergent theories and their compatibility with fundamental theories. Indeed Carroll hints at a lack of complete autonomy when he says that “we might learn a little bit about higher levels by studying lower ones”.

Carroll also emphasises the “mapping” of a fundamental theory onto an emergent theory in a process called “course-graining”. So how can we have mapping as well as autonomy?

In a seminar, Carroll also used the word “consistence” in reference to the fit between emergent and more basic theories. How can that consistency - between two very different autonomous theories - be established? Carroll also assumes compatibility (clearly related to consistency) between emergent theories and more fundamental (basic) theories. In addition, Carroll says that (some) emergent theories are accurate... Who says so? Does Carroll simply assume an accuracy that's tacitly and essentially guaranteed by a more fundamental (or basic) theory - thus limiting the emergent theory's supposed autonomy?

In opposition to Sean Carroll, it seems that Gell-Mann didn't believe in this (complete) autonomy. That's because he believed in both a “bottom-up method of building staircases between disciplines” and a “top-down approach” as well. Yet if the higher-level disciplines were autonomous, then why would they require either a “top-down” or a “bottom-up” method? Surely they could stand on their own feet. Indeed the fact that Gell-Mann even raises the question of both bottom-up and top-down approaches (or methods) means that he did indeed have a “bias in what invites the charge of 'reductionist'”. In other words, because Gell-Mann didn't believe in the (complete) autonomy of the special sciences, he could be classed as a “reductionist” - as he says himself. A non-reductionist, on the other hand, would say that the special sciences are autonomous and don't need to account for themselves (at least not via lower-level disciplines).

Higher-level Laws

Despite Gell-Mann's “reductionist” inclinations, he still believed that there are new scientific laws at higher levels. He wrote:

“At each level there are laws to be discovered, important in their own right. The enterprise of science involves investigating those laws at all levels, while also working, from the top down and from the bottom up, to build staircases between them.”

And what Gell-Mann said of chemistry, he also said of biology. That is,

“like chemistry, biology is very much worth studying on its own terms and at its own level, even as the work of staircase construction goes on. “

Gell-Mann also cited psychology and even the social sciences and history. In full, he wrote:

“[I]t's essential to study biology at its own level, and likewise psychology, the social sciences, history, and so forth, because at each level you identify appropriate laws that apply at that level.”

However, Gell-Mann did qualify all this by basically saying that higher-level laws are dependent on lower-level laws - “plus a lot of additional information”! However, that dependency doesn't in and of itself mean that completely new laws don't exist at higher levels. Nonetheless, all that additional information may not be lawlike – at least not as yet.

Gell-Mann continues by talking about “staircases” again. However, at a prima facie level, none of his talk about staircases rules out reduction; or, more specifically, it doesn't rule out the reduction of higher-level laws to lower-level laws. So it may be a little surprising that Gell-Mann finishes off by saying that

“[a]ll of these ideas belong to what I call the doctrine of 'emergence'”.

Here all that can be said is that Gell-Mann is stressing weak (rather than strong) emergence. And, according to the philosopher Mark A. Bedau, “the notion of weak emergence is metaphysically benign”. Strong emergence, on the other hand, certainly is not.

Murray Gell-Mann on Reductionism (1)

[To follow: 'Murray Gell-Mann on Complexity'.]

[I also used the following short biographical introduction for my essay ‘Murray Gell-Mann on Complexity’.]

The physicist Murray Gell-Mann was born in 1929 and died in 2019.

In 1964 Gell-Mann postulated the existence of quarks. (The name was coined by Gell-Mann himself and it’s a reference to the novel Finnegans Wake, by James Joyce.) Quarks, antiquarks and gluons were seen to be the underlying elementary elements of neutrons and protons (as well as other hadrons). Gell-Mann was then awarded a Nobel Prize in Physics in 1969 for his contributions and discoveries in the classification of elementary particles at the level of the nucleus.

More relevantly to this piece. In 1984 Gell-Mann was one of several co-founders of the Santa Fe Institute — a research institute in New Mexico. Its job is to study complex systems and advance the cause of interdisciplinary studies of complexity theory.

Gell-Mann wrote a popular science book about physics and complexity science, The Quark and the Jaguar: Adventures in the Simple and the Complex, in 1994. Many of the quotes in this essay come from that book.

Reductionism

Reduction in science has been vitally important. It has sustained and advanced science since the 19th century — if not long before that.

The question is whether or not science is all about reduction. In simple terms. If reductionists (let’s not take that as a scare-word) say that science is “all about reduction”, then there’s a problem. If reductionists don’t say that, then there isn’t problem.

Many individual scientific reductions may be largely correct. Still (as we’ll see Murray Gell-Mann argue later), reduction itself could never be the whole story. (Even that can be deemed a generalisation!) First of all:

1) It depends on what exactly is being reduced.

2) It depends on what is being said about what’s being reduced.

3) It also depends on what a given phenomenon is being reduced to.

In the end, the reductionist’s claim may not be as monumental and all-encompassing as one first imagines. Indeed it’s often people’s gut reactions to some kinds of reductionism (rather than the claims of reductionists themselves) which overstretch things

That said, most people are happy with some — or even many — reductions in science. This is primarily the case because such reductions don’t seem to have any direct impact on people or society; either philosophically, morally/religiously or politically.

Murray Gell-Mann himself focuses in on this debate (in this case) not by talking about reductionism; but by stressing the interplay between “simplicity” and “complexity”. He wrote:

“It is important, in my opinion, for the name to connect with both simplicity and complexity. What is most exciting about our work is that it illuminates the chain of connections between, on the one hand, the simple underlying laws that govern the behavior of all matter in the universe and, on the other hand, the complex fabric that we see around us, exhibiting diversity, individuality, and evolution. The interplay between simplicity and complexity is the heart of our subject.”

Yet it’s hard to say if Gell-Mann endorses or castigates reductionism in the words above because — again — it entirely depends on how people define that word.

For a start, have many — or any — reductionists ever actually claimed that literally everything can be said and explained at the reduced level?

No; usually reductionists have simply said that most things can be reduced to another level. And that’s not the same thing.

In any case, reductions have been vitally important in many sciences (as already stated) and they’ve come up with many important results. Nonetheless, it doesn’t follow from this that all forms of reduction have no room for what’s often called “higher-level descriptions”. The philosopher Patricia Churchland (1943-), for example, says that

“research techniques reveal structural organisation at many strata: the biochemical level; then the level of the membrane, the single cell, and the circuit; and perhaps yet other levels, such as brain subsystems, brain systems, brain maps, and the whole central nervous system”.

Gell-Mann on Reduction & Reductionism

Where there’s reduction, there’s also that which is classed as “fundamental”. In other words, any given phenomenon (whatever it may be) can be reduced to its fundamental components (whatever they may be). Nonetheless, the word “fundamental” seems to be much more philosophical in timbre than merely saying that the physics explains (or even entails) some higher-level phenomena. It’s almost as if the word “fundamental” is normative, rather than descriptive.

Murray Gell-Mann himself gives an explicit characterisation of the word “fundamental” as it’s used in physics. He writes:

“I suggest that science A is more fundamental than science B when

1. The laws of science A encompass in principle the phenomena and the laws of science B.

2. The laws of science A are more general than those of science B (that is, those of science B are valid under more special conditions than are those of science A).”

The problem with the quote above are the two words “in principle”. They make all the difference. (They’re also used a few times in this piece; as well as by Gell-Mann himself.) In basic terms:

What we can know “in principle” = what we can know if we had complete (or total) access to all the information/data/evidence/etc.

That is:

i) B can fully accounted for (or explained) by A if A contains all the information/data/ evidence/etc. about B.

ii) If not, then there can be no complete or total account.

We can tackle the notion of such fundamentality in relation to what Gell-Mann said about quantum electrodynamics (QED).

Gell-Mann tell us that “QED meets the two criteria for being considered more fundamental than chemistry”. What’s more, the “laws of chemistry can in principle be derived from QED”. Thus:

i) If QED is “more fundamental than chemistry”,

ii) then it may follow that chemistry can be reduced to QED.

Gell-Mann goes further and says that

“of course the basic laws of physics are fundamental in the sense that all the other laws are built on them”.

However, he then qualifies this by saying

“that doesn’t mean you can derive all the other laws from the laws of physics, because you have to add in all the special features of the world that come from history and that underlie the other sciences”.

So, in a strong sense, reduction could be possible in the same sense that Laplace’s demon could predict the future state of the world from what he knows about the world today… at least in principle.

Then Gell-Mann qualifies the status of physics and chemistry (or at least parts thereof). Thus:

“Physics and chemistry stem from the fundamental laws, although even there, in the complicated branches of physics and chemistry, the formulation of the appropriate questions involves a great deal of special additional information about particular conditions that don’t obtain everywhere in the universe.”

Here again:

B stemming from the fundamental laws of A doesn’t mean that B is identical to A or vice versa.

Nor does it mean:

A tells us everything we need to know about B.

It simply means:

A underpins (or physically entails) B.

But the reality of A, and even its entailment of B, doesn’t mean that we only need A and can therefore reduce B entirely to A.

Additionally, even if A underpins — or entails — B, that doesn’t mean that B can’t have features, qualities or even laws which are (somewhat) independent of A. Or, as Gell-Mann put it, we need to factor in

“a great deal of special additional information about particular conditions that don’t obtain everywhere in the universe”.

All that gives B an important and relevant independence from A.

(We’ll see later than Gell-Mann’s words above can be applied to condensed matter physics.)

Good Reductionism

Gell-Mann himself explains what reductionism is. He writes:

“The process of explaining the higher level in terms of the lower is often called ‘reduction’.”

Of course if those words are taken literally, then there’s no explicit commitment to reduction — let alone to reductionism. (This is a little unfair because one can’t use the word to be defined in the definition itself.) After all,

i) If we’re “explaining the higher level in terms of the lower level”,

ii) then that doesn’t itself mean that the higher level is being reduced to the lower level.

And it certainly doesn’t imply a commitment to (hard) reductionism. That is, what’s being stated isn’t that the higher level can be reduced to lower level without remainder. Indeed, because of the word “explaining”, we can say that this is a partly epistemic enterprise, rather than a purely scientific or ontological one.

To put this as simply as possible:

Does scientific explanation necessary entail reduction?

Gell-Mann then goes on to tell us why reduction is a thoroughly scientific phenomenon:

“I know of no serious scientist who believes that there are special chemical forces that do not arise from underlying physical forces. Although some chemists might not like to put it this way, the upshot is that chemistry is in principle derivable from elementary particle physics.”

In fact we can go so far as to say that if some “special chemical forces” occurred which weren’t dependent on “underlying physical forces”, then we wouldn’t really be justified in calling them chemical forces at all. The fact that chemistry is derived from, dependent upon, or entailed by physics is built into the discipline of chemistry itself. Thus if anything chemical (as it were) runs free of the physics, then we can question its status as chemistry in the first place.

Now here comes a confession that most (or even all) physicists and chemists must admit to:

“In that sense, we are all reductionists, at least as far as chemistry and physics are concerned.”

Indeed it would be hard to see how things would work in science (or at least in physics) if reductions weren’t employed. Speaking Platonically, reduction seems to be the very essence of physics (if not also of some other sciences).

Elsewhere Gell-Mann again admits to being a reductionist. (In this case, in relation to the status of the “mental”.) He wrote:

“Here again, it must be a rare contemporary scientist who believes that there exist special ‘mental forces’ that are not biological, and ultimately physicochemical, in nature. Again, virtually all of us are, in this sense, reductionists.”

Gell-Mann was also well aware that he’d used the scare-word “reductionist”. So he continued:

“Yet in connection with such subjects as psychology (and sometimes biology), one hears the word ‘reductionist’ hurled as an epithet, even among scientists. (For example, the California Institute of Technology, where I have been a professor for almost forty years, is often derided as reductionist; in fact I may have used the term myself in deploring what l regard as certain shortcomings of our Institute.)”

Thus a scientist can fully accept the autonomy of all (or most) scientific disciplines and yet still be a reductionist. (There’s certainly no contradiction here.) Gell-Mann (sort of) puts this position when he says that

“human psychology — while no doubt derivable in principle from neurophysiology, the endocrinology of neurotransmitters, and so forth) — is also worth studying at its own level”.

In that simple case, reduction simply doesn’t serve much of a purpose. It could be done (at least “in principle”). However, that wouldn’t necessarily get us very far.

Bad Reductionism

Gell-Mann explicitly put the bad-reductionist position of his own faculty (i.e., the California Institute of Technology) at that time. He wrote:

“If a subject is considered too descriptive and phenomenological, not yet having reached the stage where mechanisms can be studied, our faculty regards it as insufficiently ‘scientific’.”

Gell-Mann’s way of distinguishing the non-scientific is very interesting and very particular. Firstly, he sees Real Science as being primarily about “mechanisms”. (That isn’t giving us much to go on.) As for non-science, it is “phenomenological”. Now that can be a reference to the “what it is like” aspects of the mind or brain (e.g., consciousness or subjectivity) or it could refer to the phenomenological accounts of literally any scientific study. (Such as an account of scientists’ “subjective” interactions with particle accelerators!)

Then Gell-Mann himself cites a specific case of bad reductionism:

“At Caltech, it is mostly the brain that is studied. The mind is neglected, and in some circles even the word is suspect (a friend of mine calls it the M-word). Yet very important psychological research was carried our some years ago at Caltech, particularly the celebrated work of the psychobiologist Roger Sperry and his associates on the mental correlates of the left and right hemispheres of die human brain.”

And elsewhere, Gell-Mann writes:

“In that sense, the founding of the Santa Fe Institute is part of a rebellion against the excesses of reductionism.”

Gell-Mann even hints at the possibility that some contemporary reductionists might have excluded Charles Darwin from their faculties! He wrote that

“[i]f Caltech had existed with those same proclivities in Darwin’s time, would it have invited him to join the faculty?”.

Gell-Mann then went on to explain his reasons for his original question:

“After all, [Darwin] formulated his theory of evolution without many clues to the underlying processes. His writings indicate that if pressed to explain the mechanism of variation, he would probably have opted for something like the incorrect Lamarckian idea.”

So, with reference to the earlier quote from Gell-Mann (in which he said that certain disciplines have “not yet reached the stage where mechanisms can be studied”), can we say that Darwin himself wasn’t concerned with mechanisms? Does that also mean that Darwin’s approach was (as Gell-Mann put it) “phenomenological” and purely “descriptive”? Yet Darwin’s approach was indeed very theoretical. In addition, even though Darwin hadn’t the science to explain the underlying mechanisms, that didn’t mean that he was entirely unconcerned with mechanisms.

Paul Dirac’s Classic Example of Reduction

In one respect Paul Dirac (1902–1984) put the quintessential (scientific) reductionist position when he stated that his relativistic quantum-mechanical equation for the electron (of 1928) “explained most of physics and the whole of chemistry”. So here we have a kind of meta-reduction in that the whole of physics is being reduced to a yet more fundamental physics.

Of course the interpretation of what Dirac said is entirely dependent on what the word “explained” means. In one sense, what Dirac said was simply a statement of the facts. (Or, at the least, the facts as he saw them.) That is, he presciently realised that

“[a] great many of the phenomena of chemistry are governed largely by the behavior of the electrons as they interact with the nuclei and with one another through electromagnetic effects”.

In that limited sense, then, Dirac was right. However, if we take Dirac to have meant that literally everything about chemistry could by “explained” by his equation (or by physics generally), then he certainly would have been wrong. So it all depends on both what Dirac claimed and what can be deduced from what he claimed. (What’s true of Dirac is also true of other “reductionists”.)

Gell-Mann agreed with Dirac’s grand claim. He wrote:

“QED [quantum electrodynamics] does explain, in principle, a huge amount of chemistry. It is rigorously applicable to those problems in which the heavy nuclei can be approximated as fixed point particles carrying an electric charge.”

Indeed Gell-Mann went further than this. He continued:

“In principle, a theoretical physicist using QED can calculate the behavior of any chemical system in which the detailed internal structure of atomic nuclei is not important.”

Gell-Mann was justifying and explaining some of the (as it were) science of reduction(ism) above. He cited why it is, precisely, that physics can explain “the behaviour of any chemical system”. So this isn’t normative or methodological reductionism: it’s descriptive.

Nonetheless, and surprising as it may seem (to the layperson at least), even condensed matter physics is problematic from the standpoint of reductionism and reduction (as well as emergence). Indeed one definition of the words “condensed matter physics” gives the game away. It states that this field of physics “deals with the macroscopic and microscopic physical properties of matter”. Thus the very fact that macroscopic physical properties are part of the story shows us that condensed matter physics can’t all be about the reduction of macroscopic properties (or “higher levels”) to microscopic properties (or “lower levels”).

As for Gell-Mann, he told us that condensed matter physics “is concerned with systems such as crystals, glasses, and liquids, or superconductors and semiconductors”. More relevantly, condensed matter physics is a

“very special subject, applicable only under the conditions (such as low enough temperature) that permit the existence of the structures that it studies”.

In addition:

“Only when those conditions are specified is condensed matter physics derivable, even in principle, from elementary particle physics.”

Thus, if I’m reading Gell-Mann correctly, condensed matter physics is simply not reducible to “elementary particle physics”.

And since we’re on the subject of condensed matter physics, we must also raise the controversial issue of emergence.

In the case of condensed matter physics again, it can be said that “complex assemblies of particles behave in ways dramatically different from their individual constituents”. One specific example of this is that a range of phenomena related to high-temperature superconductivity are poorly understood; yet the physics of electrons, etc. is understood very well.

Gell-Mann then seemed to strike a middle-way between strong and weak emergence in the following quote. Here’s the hint at strong emergence:

“[I]t’s essential to study biology at its own level, and likewise psychology, the social sciences, history, and so forth, because at each level you identify appropriate laws that apply at that level.”

Then Gell-Mann also hinted at weak emergence:

“Even though in principle those laws can be derived from the level below plus a lot of additional information, the reasonable strategy is to build staircases between levels both from the bottom up (with explanation in terms of mechanisms) and from the top down (with the discovery of important empirical laws). All of these ideas belong to what I call the doctrine of ‘emergence’.”

In conclusion, Gell-Mann wrote:

“Here, much more than in the case of nuclear physics, condensed matter physics, or chemistry, one can see a huge difference between the kind of reduction to the fundamental laws of physics that is possible in principle and the trivial kind that the word ‘reduction’ might call up in the mind of a naive reader. The science of biology is very much more complex than fundamental physics because so many of the regularities of terrestrial biology arise from chance events as well as from the fundamental laws.”

This leads onto Gell-Mann’s interest in complexity; which is the subject of my essay ‘Murray Gell-Mann on Complexity’.

[I can be found on Twitter here.]