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Philip Anderson (1923–2020)

Anderson argued that the laws of physics at each level of complexity are genuinely new — not derivable from the level below, even in principle. “More Is Different” (1972), a two-page paper in Science, is the founding statement of modern emergence: “The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.” The claim is not that higher-level phenomena violate lower-level laws, but that they cannot be predicted from them — that at each scale of organisation, new regularities, new symmetries, and new organising principles appear. Anderson’s technical work in condensed-matter physics — Anderson localisation, the theory of symmetry breaking, the Anderson model of magnetic impurities — provided the concrete cases from which the philosophical claim was drawn. He was also a co-founder of the Santa Fe Institute, where the emergence programme extended beyond physics into biology, economics, and the social sciences.

Life

Born 13 December 1923 in Indianapolis, Indiana. His father Harry was a professor of plant pathology at the University of Illinois. Undergraduate at Harvard (BS, 1943). Graduate work interrupted by wartime service at the Naval Research Laboratory (1943–45), working on antenna design. PhD at Harvard (1949), under John Van Vleck, with a thesis on spectral-line broadening.

Joined Bell Telephone Laboratories (1949), where he spent the core of his career (1949–84). Bell Labs in this period was the world’s leading industrial research laboratory — the transistor, information theory, the laser, the cosmic microwave background, and Unix all emerged from it. Anderson’s condensed-matter work was done in this environment: a setting where fundamental physics and practical engineering coexisted, and where the question of how macroscopic phenomena relate to microscopic laws was not merely academic.

Visiting professor at Cambridge (1961–62, 1967–75). Professor of physics at Princeton (1975–2006). Nobel Prize in Physics (1977, shared with Nevill Mott and Van Vleck) for “fundamental theoretical investigations of the electronic structure of magnetic and disordered systems.” Co-founder of the Santa Fe Institute (1984), alongside Murray Gell-Mann and Kenneth Arrow. National Medal of Science (1982). Died 29 March 2020 in Princeton, New Jersey.

More Is Different

“More Is Different: Broken Symmetries and the Nature of the Hierarchical Structure of Science” (Science, 1972) is Anderson’s most influential paper outside condensed-matter physics. The argument:

Reductionism is true: the laws of physics at one level are consistent with the laws at the level below, and in principle derivable from them. But the ability to derive does not imply the ability to reconstruct. At each level of complexity — particles, atoms, molecules, cells, organisms, ecosystems, societies — new phenomena appear that are not obvious from the laws of the level below. The laws of chemistry are not derivable from the laws of particle physics in any practical sense; the laws of biology are not derivable from chemistry; the laws of economics are not derivable from biology. Each level has its own regularities, its own organising principles, and its own scientific discipline.

The concrete mechanism is symmetry breaking. The fundamental equations of physics are highly symmetric — they treat all directions in space equally, all moments in time equally. But the solutions of those equations are not symmetric: a crystal breaks the spatial symmetry of the underlying interactions; a magnet breaks the rotational symmetry; a superconductor breaks a gauge symmetry. The new properties (rigidity, magnetism, superconductivity) are emergent — they exist only in the solution, not in the equation. The equations permit them; they do not require them. And the emergent properties are as real as the fundamental ones: they support their own laws, their own conservation principles, their own experimental signatures.

Anderson’s target was the reductionist hierarchy in which particle physics sits at the top and everything else is “applied” — a hierarchy he saw embedded in the funding structures and status systems of physics. “The arrogance of the particle physicist and his intensive research may be behind us,” he wrote. The claim is not anti-reductionist in the sense of denying that atoms obey quantum mechanics; it is anti-hierarchical in the sense of denying that knowing quantum mechanics tells you what atoms will do when they are many.

Condensed-matter physics

Anderson’s technical work provided the cases for the philosophical claim.

Anderson localisation (1958). In a disordered material — a crystal with random impurities, for example — quantum-mechanical wave functions do not propagate freely; they become localised. A wave that would extend throughout a perfect crystal is trapped in a finite region by the disorder. The result is that disordered materials can be insulators even when their ordered counterparts would be conductors. Anderson localisation is a quantum interference effect: it arises from the constructive and destructive interference of waves scattered by random impurities, and it cannot be understood classically. The phenomenon has been observed in electrons, light, sound, and cold atoms.

Symmetry breaking and the Anderson-Higgs mechanism. Anderson (1962) showed that in a superconductor, the gauge symmetry of electromagnetism is “broken” — the photon acquires an effective mass, which is why magnetic fields are expelled from superconductors (the Meissner effect). The mechanism was extended to particle physics by Peter Higgs, François Englert, and Robert Brout, producing the Higgs mechanism — the process by which elementary particles acquire mass. Anderson’s paper predated the particle-physics application; the condensed-matter origin of the idea illustrates his point about emergence: a fundamental mechanism of the standard model of particle physics was first understood in a condensed-matter context.

Where Anderson stops

“More Is Different” is a philosophical argument supported by physical examples, but it leaves the concept of emergence imprecise. Anderson shows that new laws appear at each level; he does not provide a general criterion for when a system is complex enough for new laws to emerge, or a theory of what determines which new laws appear. The examples (symmetry breaking, localisation) are specific and well-understood; the general principle is stated but not formalised. Whether emergence can be given a precise definition — and whether it is a single phenomenon or a family of loosely related phenomena — is debated in the philosophy of science. Jaegwon Kim and others have argued that the philosophical notion of emergence is either trivially true (complex systems have properties that are hard to predict) or incoherently strong (complex systems have properties that are not even in principle derivable from their constituents). Anderson’s version sits between these: he claims not that emergence violates reductionism but that the reduction, even when possible in principle, is uninformative in practice. Whether “uninformative in practice” is a deep structural claim or a practical observation about computational limits is the open question.

The Santa Fe Institute programme — extending emergence from physics to biology, economics, and the social sciences — was ambitious, and Anderson was cautious about it. He supported the institution but expressed skepticism about whether the mathematical tools of physics (scaling laws, phase transitions, renormalisation) could be applied to social and biological systems with the same rigour. The tension between the physicist’s confidence that universal principles exist and the social scientist’s insistence that their systems are not like condensed matter has been a recurring theme at SFI. Anderson’s own position was closer to the cautious end: emergence is real, but the form it takes varies by domain, and the assumption that one set of tools fits all is itself a form of the reductionism he criticised.

Anderson’s anti-hierarchical stance — that condensed-matter physics is not “applied” particle physics but a discipline with its own fundamental questions — was politically effective (it influenced science funding and departmental organisation) but philosophically underspecified. The claim that each level has “its own laws” requires an account of what a law is and what it means for a law to be “its own” — questions that Anderson gestured at but left to philosophers. Nancy Cartwright’s The Dappled World (1999) develops a related but distinct position; whether Anderson’s emergence and Cartwright’s disunity of science are the same claim under different descriptions is debated.

Key works

See also: Gell-Mann · Boltzmann · Kauffman