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More is different: Broken symmetry and the nature of the hierarchical structure of science

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More is dierent
More is dierent: Broken symmetry
and the nature of the hierarchical
structure of science
P.W. Anderson (with an introduction by Jerey A. Goldstein)
Reduction, construction, and emergence in P. W.
Anderson’s “More is dierent”
The central task of theoretical physics in our time is no longer to write down the
ultimate equations but rather to catalogue and understand emergent behavior in its
many guises…
—Laughlin and Pines (2000)
P. W. Anderson’s classic paper was selected for republishing in this issue for sev-
eral reasons. First, because it presages several of the major constructs underly-
ing the contemporary study of complex systems. Second, that the central focus
of the paper is on what later became known as “emergence”, one of the dominant
themes of our classic papers. Third, because Anderson was one of the founders of
the Santa Fe Institute in the mid-eighties where his earlier formulation of ideas like
spin glasses, complex optimization, simulated annealing, evolution on rugged land-
scapes, collective excitations, and spontaneous symmetry breaking were taken up
Classic Paper Section
Anderson, P.W. (1972) “More is dierent: Broken symmetry and the nature of the hi-
erarchical structure of science,” Science, ISSN 0036-8075, 177(4047): 393-396. Repro-
duced by kind permission.
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Anderson & Goldstein
by researchers coming from diverse disciplines (see the very informative interview of
Anderson conducted by Alexei Kojevnikov, 1999, 2000; and Anderson’s webpage at
Princeton University where as an
nonagenarian, he is
still active as a professor
emeritus, Anderson, nd).
Although Anderson’s ideas on emergence had long been a rich source of inspira-
tion for me, the more I read in preparing this introduction, the more startled I became
by the vast breadth, depth, and prescience of his work. The era of neo-emergentism
which we are passing through now—Emergence: Complexity & Organization being
an emblem of the kind of themes explored in contemporary work into complex sys-
tems—has been marked by a movement away from the more speculative character of
proto- and mid-phase emergentism; a shift largely made possible by innovative tools
of empirical research and experimental design, as well an impressive array of sophis-
ticated mathematical and computational perspectives. Anderson’s paper “More is dif-
ferent” can be viewed as a primer of what a large part of the study of complex systems
would later include.
That his early work extends out beyond partisan issues in solid state physics can
be appreciated by considering the fact that Anderson’s championing of the notion of
spontaneous-symmetry breaking (SBB), although in this paper as a general “mecha-
nism” for the processes of emergence, had originally been oered by Anderson to
Peter Higgs and other progenitors of the now notorious Higgs Particle as an explana-
tion for mechanism by which the Higgs particle acquires mass. In fact, many physicists
have urged that the name of this momentous discovery at CERN be changed to the
Anderson-Higgs” mechanism, an appellation that can already be found in many inu-
ential papers in the eld (see Moat, 2014). Although the idea of SBB has the advan-
tage of being a way of accounting for processes of emergence in a theoretical realm
all-too-often neglecting the whole issue of process (see Goldstein, 2013b, 2014), it is
not an idea coming without a certain measure of obscurity and even ambiguity as to
what it ultimately amounts to explanatorily, a topic I will say more about below.
It is worthwhile to recognize that Anderson’s paper was written within the context
of an ongoing, and at the time vituperative debate, between particle physicists, on
the one hand, with their highly eective Standard Model of the so-called fundamental
forces (such as weak, strong, electro-magnetic on up to their nal unied “theory of
everything”) and mostly negative attitude towards emergence in the past, and sol-
id state or condensed matter physics, on the other hand, whose investigations into
phenomena such as phase transitions, superconductivity, ferromagnetism and so on
required the introduction of constructs and methods pertaining to higher scale dy-
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More is dierent
namics, organizing principles, and emergent collectivities. Two of the chief antago-
nists in this conceptual battle have been the Nobel Laureate particle physicist Steven
Weinberg known for his work on the unication of the electro-magnetic and the weak
forces and Anderson who of course is another Nobel Prize winning physicist (on this
dispute see Silberstein, 2009). This clash shows itself in this classic paper through An-
derson’s attack on strident reductionism, of which Weinberg has long been a vigorous
proponent, along with Victor Weiskopf whose reductionist stance involving extensive
and intensive explanatory strategies Anderson takes on in his paper.
Later, Anderson (2001) looked back and saw those early times as when he had
become fed up with the denigration he believed the particle physicists were aiming
at solid state and other physicists. He pointed out that most physicists were conduct-
ing research in what he considered a harder eld than particle physicists; a “frontier
between the mysterious and the understood: the frontier of complexity…where the
watchword is not reductionism but emergence.” Of course I don’t know the inside
story, but the more I have read about this acrimony the more I see how much ordinary
old ego has been involved in these so-called theoretical debates in physics. Perhaps
there is a touch of envy on both sides, for example, the SSB notion that Anderson
put forward very early had a big inuence in Weinberg’s later work. And then there’s
the rancorous story of how Anderson opposed Weinberg’s plea for the building of a
super-duper collider in Texas before the Large Hadron Collider was built at CERN, with
Anderson’s side winning-out of course.
In his classic paper, Anderson did not then, nor does he now, completely renounce
reductionism as such as if he were calling for an embrace of some kind of “holism”. In-
stead his criticism is of the totalizing type which he describes through his notion of the
constructionist hypothesis”: “The ability to reduce everything to simple fundamental
laws does not imply the ability to start from those laws and reconstruct the universe”.
Strident reductionists should give fealty to the contructionist hypothesis since they
hold that what the reductionist approach discovers about the foundational dynamics,
formulated as foundational equations (e.g., through the formats of canonical Lagrang-
ians and Hamiltonians), are what’s ultimately causing the system under scrutiny to be
and act as it does. From such a perspective, if you know the foundational equations
you certainly should be able to reconstruct the whole thing from the foundation up.
For Anderson, though, the constructionist hypothesis does not and cannot live up
to its promise since the reduction on which it is based had not included the equally
fundamental fact that “entirely new properties” arise at each new level of complex-
ity and scale (scale here is not simply a synonym for level of resolution). It is these
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Anderson & Goldstein
entirely new properties”, which later would be termed “emergent properties”, which
require the introduction of a new formulation, the order parameter, which is the metric
of the new order expressed in the emergent properties. The notion of an order pa-
rameter went back to the great Russian physicists Lev Landau and Vitaly Ginzburg in
their “phenomenological” models of such emergent phenomena as superconductivity.
Later, Hermann Haken, and to a lesser extent Ilya Prigogine, took up the mantle of or-
der parameter in the Synergetics approach and the Far-from-equilibrium approach to
understanding collective or coherent phenomena (dissipative or partly ordered struc-
tures as one of the prototypes of emergence). The very fact of needing a new variable
like an order parameter to formulate these collective phenomena shows that there
was something seriously lacking in a strictly reductionist strategy.
By the way, it seems that Anderson was not particularly fond of the work of
Prigogine, a sentiment that he was not bashful to frequently and publicly announce.
According to Anderson (cited in Hartman, 2000), although Prigogine’s dissipative
structures did indeed consist of new patterns, Anderson held such patterns to be
only temporary modications that did not possess enough permanence to account
for enduring emergent phenomena. Furthermore, Anderson doubted that in the far-
from-equilibrium conditions within which dissipative structures arise, there was a well-
dened function behaving as an order parameter. One can surmise, however, that be-
sides genuine scientic disagreement, one might see not a little ego involved here as
well: they both received Nobel Prizes in 1977 with Anderson in physics and Prigogine
in chemistry; some have held that it was not uncommon for Prigogine to strut his
ideas around as solving deep issues in quantum mechanics, cosmology, and meta-
physics without a great deal of experimental support for their generality; and Ander-
son was well-known as a curmudgeon whose blunt hammer could land on subjects
about which he did not know that much.
Superconductivity and spontaneous symmetry-breaking
Anderson’s push for emergence and allied concepts for explaining collective
phenomena has had a deep and lasting eect in many elds where complexity
constructs have been applicable. Usually, this application of emergence also
includes the theoretical framework of spontaneous symmetry breaking as how emer-
gence comes about. In the BCS theory of superconductivity of 1957 which led to the
award of a Nobel Prize to its three theorists—John Bardeen, Leon Cooper, and Robert
Schrieer—one does nd a micro-level theory on the emergence of the radically novel
feature of resistance-free electrical current in a metal taken to a very low temperature,
an unexpected micro-level pairing of electrons (called Cooper Pairing). However, the
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More is dierent
Cooper Pairing eect on the micro-level is only a doorway to the generation of a mac-
ro-level collection action, a macro-level “quantum wave”, a surprising collectivity that
seems to go against what the foundational equations would suggest since electrons
are supposed to repel and not attract each other because they have the same charge.
This puzzle was eventually solved after thirty years of intense investigations by
some of the world’s most eminent physicists and chemists who already knew most
of the foundational equations that would be operative, and one of the keys to this
solution would be SBB. Taking a complicated and convoluted story and boiling it
down intentionally to a simplistic model: rst, the metal has to have a unique consti-
tution whereby at normal temps it is not a good conductor of electricity. This neces-
sity means that the mechanism at work in superconductivity cannot be explained as
an extension of an already existing metallic property. Second, very low temperatures
are required, eventually realized as a necessary way that the expected thermal noise
in the system could be diminished to the extent that allowed something unique to
take place. Then, once this noise was low enough, electrons could pair up against ex-
pectations through the intermediary actions of phonons, quasi-particles or “collective
excitations” composed of vibrations of the atoms on the metallic lattice structure. As
the thermal noise decreased, the electrons could be attracted to the phonons which
played the role as kind of marriage brokers which then passed the attraction on to
another electron. Of course, there is a lot more going on here concerning the role of
the phonons and the forming of layers of electrical ow and the emptying out of the
magnetic eld and so forth. What is important for appreciating the role of SBB is that
the collective “quantum wave” of the electron pairs became a kind of order parameter
representing a breaking of the original gauge symmetry, a feat accomplished by the
low temperature.
In two quite illuminating but dicult papers on the SBB in emergent supercon-
ductivity, the philosopher of science Margaret Morrison (2006, 2012) has called at-
tention to how it is indeed tempting to interpret the Cooper-pairing scenario as an
example of an eective reductive explanation. Yet, Morrison goes on to demonstrate
how a close scrutiny of the foundational equations with their accompanying gauge
symmetry simply cannot predict the ensuing emergent novelty. One reason has to do
with the property of universality, which refers to how a replacement with a completely
dierent metal with its dierent micro-level, i.e., foundational, composition can yield
the same phenomena of superconductivity (for more on universality and this view of
emergence, see Batterman, 2005).
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Anderson & Goldstein
According to Morrison, it is because Cooper pairs only manifest at the critical low
temperature required, their presence demonstrates that the system has undergone a
phase transition which calls into play a novel order parameter (and I might add, not
just more criticalizations of any control parameters) measuring the amplitude of this
emergent macro-level collective quantum wave. She argues that it is possible to de-
rive the exact, emergent properties of the superconductive phenomena by empirical
measure of the ostensive phenomena and not through appeal to the foundational
Lagrangian and its symmetry.
It is a general principle in physics that systems seek to be in the most stable state.
A simple example is the instability of a pencil balanced on its end. A very slight move-
ment of a table underneath will perturb this instability so the pencil falls down and as-
sumes the much more stable condition of lying horizontally on the table. It would take
an appreciably much stronger jolt to get the horizontally lying pencil to move and
maybe fall o the table. In a superconducting metal, at low temperatures the Cooper
pairing and collective electron ow is an unstable energy condition. The symmetry of
the original equations is still being conformed with, but it is now in an unstable state.
A more stable state is for the macro-scope wave function of the collective electrons
to form. It has been said that the context of the appearance of this emergent phe-
nomena at the low temperature “solves” its governing equations by assuming a more
stable dynamics. The stability of the asymmetric emergent phenomena in the system’s
new context trumps the unstable but symmetric equations it is supposed to follow. As
stated by the prominent quantum eld theorist and historian of physics, Silvan Schwe-
ber (cited in Mainwood, 115) that Anderson’s main message with his use of SBB:
... it is not enough to know the ‘fundamental’ laws at a given level. It is the solutions to
equations, not the equations themselves, that provide a mathematical description of the
physical phenomena. ‘Emergence’ refers to properties of the solutions in particular, the
properties that are not readily apparent from the equations.
The micro-level explanation utilizing foundational equations with their original
symmetry is not wrong—rather the symmetry is “hidden” behind the appearances of
the observed non-symmetrical but stable condition. Thus, at higher temps, the stable
states show the symmetry of the Hamiltonian, e.g., with no regular spatial arrange-
ments (special spatial arrangements break the symmetry—compare a circle with a
circle in which a pod is forming aimed in some preferred direction). To be sure, the
construct of SBB has not struck only a few eminent physicists as somehow shy in the
sense of its peculiar ability to ad hoc explain via the dierence between equations and
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More is dierent
their solutions and an appeal to hidden and revealed symmetries. We’ll come back to
this seemingly explanatory legerdemain later in this introduction.
A helpful discussion for what is going on in the case of this bi-fold explanatory
strategy, contrasting equation and solution, can be found in a very accessible paper
(Laughlin & Pines, 2000) authored by Robert Laughlin, another Nobel Laureate and
David Pines, Anderson’s eminent nonagenarian colleague and Santa Fe Institute pio-
neer (see references for the webpage of the Institute for Complex Adaptive Matter
founded by Pines). They distinguish between knowing the rules operative in the actual,
manifested domain of the emergent phenomena (calling such collectivities “protector-
ates” because of their independence from micro-level uctuations) and knowing the
rules of the foundational equations. A close examination of the emergent protector-
ates reveals they are governed by emergent rules which cannot be determined by the
foundational equations. Rather, one needs experiment, measurement, and how exper-
iment and measurement reveals the emergent context and its new asymmetric rules.
Furthermore, according to Laughlin and Pines, the emergent protectorates require
“higher organizing principles” which are not discernible at the level of the founda-
tional equations and are consequently typically downplayed by reductionist scientists:
The fact that the essential role played by higher organizing principles in determining
emergent behavior continues to be disavowed by so many physical scientists is a
poignant comment on the nature of modern science. To solid-state physicists and
chemists, who are schooled in quantum mechanics and deal with it every day in the
context of unpredictable electronic phenomena such as organogels, Kondo insulators,
or cuprate (high temperature) superconductivity, the existence of these principles is so
obvious that it is a cliché not discussed in polite company. However, to other kinds of
scientist the idea is considered dangerous and ludicrous, for it is fundamentally at odds
with the reductionist beliefs central to much of physics. But the safety that comes from
acknowledging only the facts one likes is fundamentally incompatible with science…
(Laughlin & Pines, 2000: 30).
Finally, concerning the unpredictability of higher-level emergent collective phe-
nomena from foundational equations, Gu et al. (2008) oer a very sophisticated up-
dating of Anderson’s early work (using the Ising model formulations of collective phe-
nomena) within the context of ndings from mathematical logic and computational
complexity theory concerning undecidability in formal systems (in a previous paper,
Goldstein, 2014, I tried to show a related way of linking undecidability, uncomput-
ability, and the emergent gap). The Gu et al. paper demonstrated how in the eld
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of solid state physics, systems manifesting emergent collectivity that is observable
macroscopically, the dening properties or behaviors cannot be deduced from rst
principles …[so that] from knowledge of the lattice Hamiltonian … any macroscopic
law that governs these quantities must be logically independent of the fundamental
interactions” (on a closely related connection of physics with undecidabilty see Moore,
The process of emergence, SBB, and the need for
contextual exploration
Recently (Goldstein, 2013a, 2013b, 2014), I have called attention to what I see
as a troubling lack of inquiry into how emergence works, i.e., the mechanisms,
processes, and operations possessing the requisite potency for generating
emergent phenomena with their unique and radical properties. This trend can be no-
ticed not only in critiques of the idea where it might be expected because emergence
itself is denied, but also somewhat surprisingly in strong endorsements of the idea.
For instance, in o-handed remarks about emergence happening on a higher level
out of interactions on a lower level, not much of interest at all is given. Such a de-
ciency can damage the credibility of the idea which I think has happened in the case
of the questionable and strikingly lightweight co-optations of the idea by the particle
physics and cosmology community.
Anderson though does oer a “mechanism” or process by which emergents
emerge, namely, spontaneous symmetry-breaking as described above in the emer-
gence of superconductivity. To better appreciate what SSB can oer to an understand-
ing of the processes of emergence, it needs to be distinguished from other types of
symmetry-breaking. One type, sometimes called “explicit” symmetry breaking (see,
Anderson, 1984) involves adding a symmetry-breaking a term that is added to the
fundamental equations, e.g., a term representing an operation that leads to a particu-
lar spatial direction thereby breaking an initial state when no special spatial direction
is chosen. Related is the kind of symmetry breaking associated with bifurcation in a
dynamical system occurring when a bifurcation parameter reaches a certain threshold,
e.g., a bifurcation parameter which leads to a criticalization so that symmetry breaks
in the so-called “one hump” (quadratic) maps studied by May and Feigenbaum and
which inspired so many aspiring complexity bus in the nineteen eighties. It has not
been uncommon for approaches to emergence to include the arising of new attrac-
tors at bifurcation thresholds.
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However, the SBB that Anderson is known for and that he talks about in this clas-
sic case is a stranger beast. Above we came across such descriptors as “hidden” and
“apparent”, equation versus solution, gauge symmetry versus actual ostensive man-
ifestations of emergent phenomena, stable versus unstable, and others. Of course,
there is nothing particularly misleading by such ways of interpreting SBB and thereby
how emergence works. But what have we really added to our store of understanding
through these metaphors? The problem is not that we are resorting to metaphors,
since all explanations at some point employ metaphors, a “nucleus” is a metaphor,
electric current” is a metaphor, “string” is a metaphor. Instead, the problem is more
like that something has occurred and yet one cannot quite get a conceptual grasp,
and what is oered instead is something as vague and non-forthcoming as “hide and
seek.” In an important sense the supposed symmetry of the foundational symmetries
have to break since the apparent symmetry was nothing more than supercial any-
way: “a way for nature to say, ‘your theory of symmetry is wrong in the rst place’” and
this is related to kind of epistemological ltering (this way of putting it is thanks to
Kurt Richardson, Managing Editor of E:CO and complexity-oriented physicist himself).
I’ve had the sense of a kind of conceptual sham being perpetrated, but not inten-
tional, rather out of ignorance and failure to see that at some point the mathematical
predictability has to be seen as not the essential fundamental nature of nature.
I propose thinking about the dierence between symmetry and the ensuing bro-
ken symmetry as like the shift in “aspect seeing” of the famous “duckrabbit” draw-
ing appealed by Wittgenstein in The Philosophical Investigations. From one perspec-
tive, the drawing appears as a duck’s bill with the duck’s eye facing to the left, while
from the other perspective, the drawing shifts to the duck’s bill now having been
transposed to a rabbit’s long ears and the rabbit’s eye (the same eye but direction
switched) facing to the right. Does this mean it is all totally arbitrary as to which as-
pect one is seeing? I suggest no, since the sequence of the aspect-seeing manifests
the temporal unfolding of the phase direction from symmetry to symmetry breaking.
One starts, say, with the duck and assumes there is the same duck mirrored looking
in the opposite direction. But then the aspect shifts and one sees the rabbit thereby
realizing there is another perspective, but to see this perspective demands one breaks
the symmetry of the presumed mirror image of the duck. In a sense, this new aspect
can only be discerned through the recognition of the entirely new properties which is
occasioned by experiment, measurement, and the subsequent new context. I believe
Anderson would go along with this since he remarks in this classic paper that at some
point even symmetry breaking needed to be overtaken by considerations of increas-
ing complexity, since it is complexity involved with entirely new properties that is re-
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vealed as we ascend the hierarchy of the special sciences. Each of these new sciences
are investigating new levels with their own new foundational stories which underlay
that “basically new types of behavior can result.
Much of this, in my opinion, has to do with the explanatory gap that nearly all
accounts of emergence claim for emergence. This is the gap of predictability, deduct-
ibility, computability. In terms of SBB this is the gap of the symmetry-breaking, this is
the gap of not able to go from the foundation to the emergent outcome. As I have
pointed out in Goldstein (2014). In fact, upon rst coming across it, it can evoke a
sense of trickery or sham, that it is postulated to have occurred and yet one cannot
quite see how. This sentiment is related to how SBB talks about a hidden symmetry
associated with the foundational formulation. At high temperatures, the stable state
is the one with the foundational equations symmetries. The strange thing is that the
foundational equations, and the symmetries associated with them, remain even with
the transition occurring at the very low temperature. At that point, however, for the
system to remain stable (which seems to be the stronger pull) these symmetries break,
but breaking doesn’t mean they are deleted.
The self-transcending construction hypothesis
Anderson, not content to leave his paper with just the negative message of de-
crying reductionist science, also emphasizes that “at some point we have to
stop talking about decreasing symmetry and start calling it increasing com-
plication.. with increasing complication at each stage, we go on up the hierarchy of
sciences”. Today, of course are more likely to use the term “complexity” for what he
meant by “complication”. Furthermore, he shifts the concept of fundamental from re-
ferring only to one fundamental set of laws at the level of the tiniest micro-scopic to
the recognition that each level has its own set of foundational dynamics, behaviors
and thereby laws of the new dynamics at that new level.
I propose following this sentiment by relooking at his constructionist hypothesis
by means of inverting it and adding to what we normally take as constructions, crucial
aspects of the entirely new properties discovered at each new level. In previous work,
I have termed these emergent generating constructions “self-transcending construc-
tions”, the qualication of “self-transcending” indicating the unique nature of this kind
of construction: they must be capable of producing the requisite emergent novelty at
each new level. For example, superconductivity, as an actual real world phenomena,
results from self-transcending constructional processes. In this perspective, the sym-
metry breaking of course remains, but the emphasis instead is on how the founda-
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More is dierent
tional equations are combined with the numerous other factors in the facilitation of
the radical new properties of the ultra-cold metal to the outcome of an STC. Most im-
portant is that observation, context, and measurement are coupled with whatever can
be gleaned from foundational questions. Insight into what will need to be included in
the formulation of the self-transcending construction will require, in each instance of
experiment that discovers “new laws, concepts, and generalizations”, “inspiration and
If emergence eludes explanation via strict reductionism, then the specic ways
such systems elude reduction makes up the crucial factors that must be added to how
the self-transcending constructional process works. This is a call to envision construc-
tional processes that somehow or other manage to incorporate what reduction on its
downward trajectory to the foundation has left out, that is, the entirely new proper-
ties at each level of scale or complexity. This very dierent type of construction would
need to be able to, de facto, contain those operations, processes, and constraints able
to construct emergent phenomena with their radically novel properties. Emergence is
quite dierent than ordinary change and the ordinary novelty that results from ordi-
nary change. That is why its construction needs to be radically dierent than ordinary
change processes.
Since processes of constructions are all about the building-up of structure, pat-
tern, organization, ordering, self-transcending construction consist of what possesses
the potency for the building-up of novel structure, pattern, organization, ordering. This
implies that processes with this potency must have a capacity for continually taking
extant structure and subjecting it to operations which transform this structure to now
have “entirely new properties.” This seems a tall-order and, as I have tried to indicate
in past work, our imaginations have not been shaped to easily accept its possibility.
That is why in previous papers I have oered examples from mathematics that spe-
cically demonstrate in which kinds of operations that self-transcending constructions
consist. That was meant to pry open the imagination and not that the self-transcend-
ing constructions at work in the instances of emergence all around us must conform
to such obscure mathematics. Instead, it is a call to attend to what Laughlin and Pines
say in the opening quote to this paper, that it is time to shift our attention away from
the foundational equations and focus on observation and context.
In fact, the challenge facing the conceptualization of a self-transcending construc-
tion contains something akin to a paradox (as I’ve said before, a “irtation with para-
dox” and not an embrace): what is being constructed via operations on substrates at
their own level must at the same time transcend the level of these substrates since
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Anderson & Goldstein
the emergent phenomena as “protectorates” being constructed are independent of
the lower more micro-scopic level. These emergent protectorates possess what can
be taken as the opposite characteristic to that found, e.g., in chaotic attractors with
their sensitivity to initial conditions: emergent protectorates must be in an important
sense insensitive to initial or micro-level conditions or they would be capable of en-
during. One response to this challenge is that even though emergent phenomena are
built out of lower level substrates, Ganeri (2011) has pointed out the key operation of
transformation, i.e., the substrates or part are so transformed that the resulting emer-
gent is constituted by what are eectively radically novel parts no longer tethered as
before to their roots on the original level. The independence of emergent protector-
ates doesn’t happen by magic or creation ex nihilo but by the action of self-transcend-
ing constructional operations on phenomena below.
By the way, certain readers might nd the working out of similar ideas but in a
very dierent mathematical framework, that of category theory (Ehresmann & Van -
bremeersch, 2007). There emergence can be likened to the mathematical object of a
category” on which four prototypes of construction are operated: absorption, elimi-
nation, binding, and classication (or association). The self-transcending construction
leading to the emergent phenomena of the category is understood as a “complexi-
cation” whose formation has been the result of so much intermingling, the substrates
of the formation “cannot be untangled”, Chapter 4 especially).
The anti-reductionist stance described by Anderson in this classic paper as well
as his later work is obviously not some uninformed and poorly thought-out gib-
berish condemning science that unfortunately one nds too much of these days,
even among those who should denitely know better. Rather it an attempt, on the
part of a celebrated Nobel Laureate and coming-out of his seven decades of research
and theorizing, to lay-out serious limitations in the thought-numbing variety of strict
reductionism. Furthermore, the position taken in support of the idea of emergence
and its application in the sciences did not emanate from any preconceived scientic
or philosophical commitment to the idea—Anderson has intimated in interviews that
he had not even known of the word “emergence” before he wrote this classic (which is
why one cannot nd the word used in the paper). It was only later after his paper be-
came more well-known that complexity/emergentist accolytes contacted him, inviting
him to conferences and to contribute papers that he felt himself drawn to a complex-
ity perspective. It was only a dozen years later that the Santa Fe Institute was founded
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More is dierent
for complexity oriented research and theorizing and Anderson was one of its chief
intellectual architects.
One can read about Anderson’s own work as well as the history of the SFI in many
places. Here, I would like to very strongly recommend one of his recent works, More
and Dierent: Notes from a Thoughtful Curmudgeon (Anderson, 2011) a fun and en-
lightening read replete with popular writings, essays, anecdotes, book reviews, and
so on covering an incredible and prolic career and life. Anderson was never one to
be bashful in expressing his viewpoints, a curmudgeon not afraid to call out when
the Emperor is truly not wearing any clothes. Without even knowing it, without even
having to struggle with dicult technical ideas, after reading this book I felt that an
enormous amount of information was mysteriously transmitted to my brain. I think it
had to do with the book being a peek into the thinking of a truly great thinker.
Anderson, P.W. (1984). Basic Notions of Condensed Matter Physics, ISBN 9780201328301.
Anderson, P.W. (1995). “Physics: The opening up to complexity,” Proceedings of the National
Academy of Sciences, ISSN 1091-6490, 92: 6653-6654.
Anderson, P.W. (2001). “More is dierent: One more time,” in N.-P. Ong and R. Bhatt (eds.),
More is Dierent: Fifty Years of Condensed Matter Physics, ISBN 9780691088662, pp. 1-8.
Anderson, P.W. (2001). “Science: A ‘dappled world’ or a ‘seamless web’?” Studies in the History
and Philosophy of Modern Physics, ISSN 1355-2198, 32(3): 487-494.
Anderson, P.W. (2011). More and Dierent: Notes from a Thoughtful Curmudgeon, ISBN
Anderson, P.W. (n.d.). Anderson’s personal webpage at Princeton University.
Batterman, R.W. (2005). The Devil in the Details: Asymptotic Reasoning in Explanation,
Reduction, and Emergence, ISBN 9780195314885.
Ehresmann, A.C. and Vanbremeersch, J.P. (2007). Memory Evolutive Systems: Hierarchy,
Emergence, Cognition, ISBN 9780444522443.
Ganeri, J. (2011). “Emergentisms, ancient and modern,Mind, ISSN 0026-4423, 120 (479): 671-
Goldstein, J. (2013a). “Re-imagining emergence, Part 2,Emergence: Complexity &
Organization, ISSN 1521-3250, 15(3): 121-138.
Goldstein, J. (2013b). “Re-imagining emergence: Part 1,Emergence: Complexity &
Organization, ISSN 1521-3250, 15(2): 78-104.
Goldstein, J. (2014). “Reimagining emergence, Part 3: Uncomputability, transformation, and
self-transcending constructions,Emergence: Complexity & Organization, ISSN 1521-
3250, 16(2): 116-176.
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Hartman, H. (2000). “Symmetry breaking and the origins of life,” in Y. Bar-Yam (ed.), Unifying
Themes in Complex Systems: Proceedings of the International Conference on Complex
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Kojevnikov, A. (1999, 2000). “Interview with Dr. Philip Anderson. Oral history transcript
(conducted at the Princeton Physics Department Building, March 30, 1999, May 30, 1999,
November 23, 1999, and, June 29, 2000).
Laughlin, R. and Pines, D. (2000). “The theory of everything,” Proceedings of the National
Academy of Sciences, ISSN 1091-6490, 97 (1): 28-31.
Mainwood, P. (2006). Is More Dierent? Emergent Properties in Physics, Doctoral Dissertation,
University of Oxford, Oxford, England,
Moat, J. (2014). Cracking the Particle Code of the Universe, ISBN 9780199915521.
Moore, C. (1990). “Unpredictability and undecidability in dynamical systems,Physical Review
Letters, ISSN 0031-9007, 64(20): 2354”2357.
Morrison, M. (2006). “Emergence, reduction, and theoretical principles: Rethinking
fundamentalism,Philosophy of Science, ISSN 0031-8248, 73: 876”887.
Morrison, M. (2012). “Emergent physics and micro-ontology,Philosophy of Science, ISSN
0031-8248, 79: 141-166.
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reduction battles between particle physics and condensed matter theory,” Conference:
Integrated History and Philosophy of Science, South Bend, Indiana: University of Notre
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... To explore chimera states in a system of generalized KS oscillators in two-population networks, we introduce a suitable coupling matrix in this section, which corresponds to the phaselag parameter α in equation (1). Moreover, the BF instability point is obtained for this coupling matrix. ...
... For simplicity, we assume that the first population is incoherent and the second population is synchronized, i.e. |ψ 1 (t)| < 1 and |ψ 2 (t)| = 1. Also, we use the following notations to denote components of each order parameter vector: ψ 1 ...
... Here, m (1) ...
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Chimera dynamics, an intriguing phenomenon of coupled oscillators, is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto-Sakaguchi (KS) phase oscillators. In recent developments, the system has been extended to the so-called generalized Kuramoto model, wherein an oscillator is situated on the surface of an $M$-dimensional unit sphere, rather than being confined to a unit circle. In this paper, we exploit the model introduced in [New. J. Phys. \textbf{16}, 023016 (2014)] where the macroscopic dynamics of the system was studied using the extended Watanabe-Strogatz transformation both for real and complex spaces. Considering two-population networks of the generalized KS oscillators in 2D complex spaces, we demonstrate the existence of chimera states and elucidate different motions of the order parameter vectors depending on the strength of intra-population coupling. Similar to the KS model on the unit circle, stationary and breathing chimeras are observed for comparatively strong intra-population coupling. Here, the breathing chimera changes their motion upon decreasing intra-population coupling strength via a global bifurcation involving the completely incoherent state. Beyond that, the system exhibits periodic alternation of the two order parameters with weaker coupling strength. Moreover, we observe that the chimera state transitions into a componentwise aperiodic dynamics when the coupling strength weakens even further. The aperiodic chimera dynamics emerges due to the breaking of conserved quantities that are preserved in the stationary, breathing and alternating chimera states. We provide a detailed explanation of this scenario in both the thermodynamic limit and for finite-sized ensembles. Furthermore, we note that an ensemble in 4D real spaces demonstrates similar behavior.
... 1. Form and function in biology are related by a multi-scale [119] hierarchical structure, forming an integrated whole [89,164] with structure/function relations occurring at all emergent scales [31,139], involving variables relevant to that level [5]. 2. Metabolism involves a). ...
... • Broken symmetries. More complex emergence is based in broken symmetries, as pointed out by Anderson [5]. This is key inter alia to biological emergence through the immense complexity of macromolecular shape [111,112], and to technological emergence through the structure of transistors [67]. ...
... • Through these effects, new properties occur at every emergent level that were not present at lower levels. They are characterised by effective theories at each level [64,139] in terms of emergent variables appropriate to that level [5]. • Multiple realisability takes place whereby higher level functions or adaptations can be realised by many different configurations at lower levels [21,82,110]. ...
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This paper discusses complexity theory, that is, the many theories that have been proposed for emergence of complexity from the underlying physics. Our aim is to identify which aspects have turned out to be the more fundamental ones as regards the emergence of biology, engineering, and digital computing, as opposed to those that are in fact more peripheral in these contexts. In the cases we consider, complexity arises via adaptive modular hierarchical structures that are open systems involving broken symmetries. Each emergent level is causally effective because of the meshing together of upwards and downwards causation that takes place consistently with the underlying physics. Various physical constraints limit the outcomes that can be achieved. The underlying issue concerns the origin of consciousness and agency given the basis of life in physics, which is structured starting from symmetries and variational principles with no trace of agency. A possible solution is to admit that consciousness is an irreducible emergent property of matter.
... Schelling's model, like Hopfield's, illustrates a very important phenomenon, which has in a way become the major trophy of statistical physics: totally unexpected behaviour can appear when we observe groups of interacting individuals. This is what Phil Anderson emphasised in his famous 1972 article entitled "More is Different" [13]: collective behaviour cannot be understood as a simple superimposition of individual behaviour. 9 In particular, even when individual behaviour evolves continuously, collective behaviour can be discontinuous. ...
... The phase transition paradigm therefore makes it possible to account for such discontinuities, for catastrophic effects without commensurable causes, and for endogenous instabilities rather than those due to exogenous events. 13 These instabilities are often the direct consequence of a certain form of optimality, and this seems to me to be an important lesson: the search for an optimum often leads to a complex system becoming fragile. 14 These are the avenues I intend to follow in the sessions to come and also during the lecture that will close my lectures, which is entitled 'More is Different', in homage to Anderson's article (see Appendix). ...
... I hope that these lectures will provide an opportunity to strengthen these links, to give rise to innovative research projects -since this is the title of the chair I have been given this year -and to invent new models, 13 whatever their nature -phenomenological, metaphorical, foundational -as long as they enable us to better understand emerging social phenomena, if only to try to prevent certain disasters of the past from happening again, or to better manage those that will undoubtedly happen again. ...
This is the English version of my inaugural lecture at Coll\`ege de France in 2021, available at I reflect on the difficulty of multi-disciplinary research, which often hinges of unexpected epistemological and methodological differences, for example about the scientific status of models. What is the purpose of a model? What are we ultimately trying to establish: rigorous theorems or ad-hoc calculation recipes; absolute truth, or heuristic representations of the world? I argue that the main contribution of statistical physics to social and economic sciences is to make us realise that unexpected behaviour can emerge at the aggregate level, that isolated individuals would never experience. Crises, panics, opinion reversals, the spread of rumours or beliefs, fashion effects and the zeitgeist, but also the existence of money, lasting institutions, social norms and stable societies, must be understood in terms of collective belief and/or trust, self-sustained by interactions, or on the contrary, the rapid collapse of this belief or trust. The Appendix contains my opening remarks to the workshop ``More is Different'', as a tribute to Phil Anderson.
... As a famous saying goes, "more is different" 46,47 ; this saying describes a well-established observation whereby new phenomena may emerge when the physical scale of interest changes. As a result, multiscale modelling was developed to reduce computational costs while still delivering reasonable accuracy and even finding new physics hidden in the higher dimensions. ...
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Most molecular generative models based on artificial intelligence for de novo drug design are ligand-centric and do not consider the detailed three-dimensional geometries of protein binding pockets. Pocket-aware three-dimensional molecular generation is challenging due to the need to impose physical equivariance and to evaluate protein–ligand interactions when incrementally growing partially built molecules. Inspired by multiscale modelling in condensed matter and statistical physics, we present a three-dimensional molecular generative model conditioned on protein pockets, termed ResGen, for designing organic molecules inside of a given target. ResGen is built on the principle of parallel multiscale modelling, which can capture higher-level interaction and achieve higher computational efficiency (about eight-times faster than the previous best art). The generation process is formulated as a hierarchical autoregression, that is, a global autoregression for learning protein–ligand interactions and atomic component autoregression for learning each atom’s topology and geometry distributions. We demonstrate that ResGen has a higher success rate than existing state-of-the-art approaches in generating novel molecules that can bind to unseen targets more tightly than the original ligands. Moreover, retrospective computational experiments on de novo drug design in real-world scenarios show that ResGen successfully generates drug-like molecules with lower binding energy and higher diversity than state-of-the-art approaches.
... They defined an emergent ability as an ability to solve a task which is absent in smaller models, but present in LLMs. The works of Wei et al. (2022b) and Srivastava et al. (2023), published approximately concurrently, base their definition of emergent abilities on the more general definition of emergence in physics: "Emergence is when quantitative changes in a system result in qualitative changes in behaviour" (Anderson, 1972). As such, emergent abilities in LLMs are characterised by the fact that they typically do not present themselves in smaller models, which makes their emergence unpredictable. ...
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Large language models have exhibited emergent abilities, demonstrating exceptional performance across diverse tasks for which they were not explicitly trained, including those that require complex reasoning abilities. The emergence of such abilities carries profound implications for the future direction of research in NLP, especially as the deployment of such models becomes more prevalent. However, one key challenge is that the evaluation of these abilities is often confounded by competencies that arise in models through alternative prompting techniques, such as in-context learning and instruction following, which also emerge as the models are scaled up. In this study, we provide the first comprehensive examination of these emergent abilities while accounting for various potentially biasing factors that can influence the evaluation of models. We conduct rigorous tests on a set of 18 models, encompassing a parameter range from 60 million to 175 billion parameters, across a comprehensive set of 22 tasks. Through an extensive series of over 1,000 experiments, we provide compelling evidence that emergent abilities can primarily be ascribed to in-context learning. We find no evidence for the emergence of reasoning abilities, thus providing valuable insights into the underlying mechanisms driving the observed abilities and thus alleviating safety concerns regarding their use.
... It should be noted that due attention has been paid to the problems of complexity in the last half century. There are known fundamental works in this direction by P. Anderson [1], M. Gell-Mann [24], I. Prigogine [48], G. Parisi [45]. ...
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The process of plastic deformation of steel DC04 is considered a complex, non-linear, irreversible, and self-organized process. An analysis of the irreversibility of the stress-strain time series makes it possible to identify characteristic areas of (quasi-)elastic, plastic deformation, and necking. The last two sections are the most informative. The region of inelastic deformation is characterized by collective self-organized processes of dislocation structures transformation, turning into pore formation and, ultimately, the formation of microcracks and a general crack as the cause of sample failure. Measures for the quantitative assessment of the irreversibility of the deformation process are proposed. Such measures as multiscale asymmetry, Poincaré, network-, and permutation-based measures are found to be especially informative measures, which can be used not only to classify the stages of plastic deformation but also can be applied as a precursor of the material irreversible destruction process.
... Leon Trotsky's theory of U&CD re-emerged from niche political debates and found itself at the forefront of a vigorous set of debates and novel perspectives within IR nearly three decades ago, thanks principally to the pioneering efforts of Justin Rosenberg (1994;1996;2006;2016). At the heart of U&CD lies the basic idea that 'more is different' (Anderson, 1972;quoted in Oatley, 2019: 3). Because multiple societies interact with one another in a systematic (rather than sporadic or random) fashion under capitalism, the development of each unit and of the system as a whole changes over time in complex, open-ended and irreducible ways. ...
U&CD scholarship has made vital conceptual and analytical contributions to international relations and international historical sociology scholarship during recent decades. However, so far, it has mainly focused on the longue durée of capitalist transitions rather than contemporary analyses of the dynamics, crises and policy shifts within the global political economy. A small body of literature has recently begun to apply a U&CD conceptual toolkit towards just such ends. In this special issue, we showcase a range of original thought and empirical work which advances the U&CD perspective within the growing and critically oriented field of global political economy. Transcending the pitfalls of orthodox liberal and realist approaches, U&CD draws a direct link between ruptures, contradictions and crises in the global economy and its ongoing division into a multiplicity of nominally sovereign territorial political units. Focusing on a breadth of divisions and antagonisms across lines of class, race, gender and nationality, the articles contained herein point to the immense potential for creative applications of U&CD to play a role in GPE scholarship as it emerges from the grip of the stifling orthodoxies of international political economy.
... Nevertheless, there are critical voices regarding the designation of AI-driven systems as "black boxes" and the associated demand for explanations and transparency (see Bryson 2019; in a normative sense: Robbins 2019). The demand for transparency is dismissed by arguing that an explanation of "how" a decision is reached is not helpful to a user, since the explanation of how the algorithmic decision is reached is difficult to understand anyway (Anderson 1972). It is necessary, but also sufficient, for those who program and use AI software to keep detailed records of how it works. ...
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Algorithmic recommendations and rankings have become a key feature of the user experience offered by digital platforms. Recommender systems determine which information and options are prominently presented to users. While there is abundant technical literature on recommender systems, the topic has only recently attracted the attention of the European legislator. This chapter scrutinizes the emerging European regulatory framework for algorithmic rankings and recommendations in the platform economy with a specific focus on online retail platforms. Surveying the new rules for rankings and recommender systems in consumer contract law, unfair commercial practices law, and platform regulation, it identifies shortcomings and inconsistencies and highlights the need for coherence between the different regulatory regimes. The Digital Services Act could change the regulatory trajectory by introducing (albeit hesitantly and incompletely) a new regulatory model that shifts the focus from algorithmic transparency to algorithmic choice. More importantly, a choice-based approach to recommender governance and a market for third-party recommender systems (“RecommenderTech”) could also be facilitated by the new interoperability requirements introduced by the Digital Markets Act.
... Nevertheless, there are critical voices regarding the designation of AI-driven systems as "black boxes" and the associated demand for explanations and transparency (see Bryson 2019; in a normative sense: Robbins 2019). The demand for transparency is dismissed by arguing that an explanation of "how" a decision is reached is not helpful to a user, since the explanation of how the algorithmic decision is reached is difficult to understand anyway (Anderson 1972). It is necessary, but also sufficient, for those who program and use AI software to keep detailed records of how it works. ...
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Recommender systems that support us in our everyday lives are becoming more precise and accurate in terms of the appropriateness of recommendations to users’ needs – with the result that the user often follows these recommendations. This is mainly due to the filtering methods and various algorithms used. In our paper, we will look specifically at the recommender systems on gaming platforms. These consist of different components: a shopping component, a streaming component and a social media component. The recommender systems of these components, when considered individually, have certain characteristics in terms of the machine learning and filtering methods used, which are mixed by combining them on one platform. As a result, it is unclear which of the information collected about the user at any time is lost and disappears into obscurity, and what information is used to generate recommendations. The frequently discussed “black box” problem exacerbates at this point and becomes a “black hole.” With the interests of platform users, platform operators, and software developers in mind, we examine the legal provisions that have been established to address this opaqueness: transparency obligations. Derived from the Digital Services Act and the Artificial Intelligence Act, we present various legally valid solutions to address the “black hole” problem and also lead them to practical suggestions for implementation.
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This paper considers how a classification of causal effects as comprising efficient, formal, material, and final causation can provide a useful understanding of how emergence takes place in biology and technology, with formal, material, and final causation all including cases of downward causation; they each occur in both synchronic and diachronic forms. Taken together, they underlie why all emergent levels in the hierarchy of emergence have causal powers (which is Noble’s principle of biological relativity) and so why causal closure only occurs when the upwards and downwards interactions between all emergent levels are taken into account, contra to claims that some underlying physics level is by itself causality complete. A key feature is that stochasticity at the molecular level plays an important role in enabling agency to emerge, underlying the possibility of final causation occurring in these contexts.
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This paper concludes a three part series by reimagining processes of emergence along the lines of a formal "blueprint" for the "logic" of these processes, a topic surprisingly neglected even within the camp of those advocating some form of emergence. This formalism is presented according to the following conceptual strategy. First, the explanatory gap of emergence, the presence of which is one of the main defining characteristics of emergent phenomena, is interpreted in terms of uncomputability, an idea introduced in complexity science in order to supplement the more traditional features of unpredictability, nondeducibility, and irreducibility. Uncomputability is traced back to a method devised by Georg Cantor in a very different context. I label Cantor's formalism a type of "self-transcending construction" (STC), a phrase coined by an early commentator on Cantor's work. Next, I examine how Cantor's STC was appropriated, respectively, in the work of Gödel and Turing on undecidability and uncomputability. Next, I comment on how self-transcending constructions derive a large measure of their potency via a kind of "firtation" with paradox in a manner similar to what Gödel and Turing had done. Finally, I offer some suggestions on how the formalism of an STC can shed light on the nature of macro-level emergent wholes or integrations. This formalism is termed a "self-transcending construction" a term derived from the anti-diagonalization method devised by George Cantor in 1891 and then utilized in the limitative theorems of Godel and Turing.
Conference Paper
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Philip Anderson was educated at University High School in Urbana, Illinois, at Harvard (BS 1943, PhD 1949), and further educated at Bell Laboratories, where his career (1949-1984) coincided with the greatest period of that remarkable institution. Starting in 1967, he shared his time with Cambridge University (until 1975) and then with Princeton, where he continued full time as Joseph Henry Professor until 1997. As an emeritus he remains active in research, and at press time he was involved in several scientific controversies about high profile subjects, in which his point of view, though unpopular at the moment, is likely to prevail eventually. His colleagues have made him one of the two physicists most often cited in the scientific literature, for several decades. His work is characterized by mathematical simplicity combined with conceptual depth, and by profound respect for experimental findings. He has explored areas outside his main discipline, the quantum theory of condensed matter (for which he won the 1977 Nobel Prize), on several occasions: his paper on what is now called the “Anderson-Higgs mechanism” was a main source for Peter Higgs' elucidation of the boson; a crucial insight led to work on the dynamics of neutron stars (pulsars); and his concept of the spin glass led far afield, to developments in practical computer algorithms and neural nets, and eventually to his involvement in the early years of the Santa Fe Institute and his co-leadership with Kenneth Arrow of two influential workshops on economics at that institution. His writing career started with a much-quoted article in Science titled “More is Different” in 1971; he was an occasional columnist for Physics Today in the 1980s and 1990s. He was more recently a reviewer of science and science-related books for the Times (London) Higher Education Supplement as well as an occasional contributor to Science, Nature, and other journals. © 2011 by world Scientific Publishing Co. Pte. Ltd. All right reserved.
This book focuses on a form of reasoning in science that I call “asymptotic reasoning.” At base, this type of reasoning involves methods that eliminate details and, in some sense, precision. Asymptotic reasoning has received systematic treatment in physics and applied mathematics, but virtually no attention has been paid to it by philosophers of science. I argue that once one understands the role played by asymptotic reasoning in explanatory arguments of scientists, our philosophical conceptions of explanation, reduction, and emergence require significant modification.
Jaegwon Kim has argued (Kim 2006a) that the two key issues for emergentism are to give a positive characterization of the emergence relation and to explain the possibility of downward causation. This paper proposes an account of emergence which provides new answers to these two key issues. It is argued that an appropriate emergence relation is characterized by a notion of ‘transformation’, and that the real key issue for emergentism is located elsewhere than the places Kim identifies. The paper builds on Victor Caston’s important work on ancient philosophy of mind (Caston 1997, 2001), but appeals to sources he has not considered.