Michael Freedman
At a disarmament conference of 1932 Einstein described our technological vs. social maturity as a razor blade in the hand of a three-year-old. Ninety years has led to little gains in our social maturity and vast expansions of technological risk. I admire those who are bold enough and creative enough to rethink our social arrangements from the ground up. Our current situation demands new ideas: equitable and robust social arrangements, and, crucially, avenues to approach them. For the power of vested things will delay and resist. History, by its own ineluctable lights, has brought us to our present impasse: nuclear threat, climate threat, and income divergence, all made cruelly ironic by the increasingly tight, acrimonious, and polarizing networks of communication which bind us together, friend and foe. Together apart.
I have learned, from Glen Weyl, the quadratic – or “radical” (read: square root) approach to equity. The idea can be traced back to Lionel Penrose’s 1946 paper [P] on voting systems, In which quadratic voting was proposed as the unique mechanism giving equal influence to citizens of polities of unequal size. Now the cornucopia quadratic proposals cover, finance of public goods, polling, and the establishment of social preferences generally [PW]. The “square” in these mechanisms is strongly reminiscent of the norm square of the Born rule for extracting probabilities in quantum mechanics, as explored in a recent essay [FFW]. In this blog I’d like to suggest also looking to physics for inspiration on achieving robustness of social mechanisms. Notably, all mechanisms of digressive proportionality, quadratic proposals included, are vulnerable to collusion and may not be stable as model assumptions are relaxed.
This brings us to the title: In what domain has human endeavor outmatched our complement, the vast inhuman universe? How does a painting of flowers stack up against a flower? Or Alex Honnold’s ascent of Free Rider compare to El Cap itself? Unclear. But when it comes to cold we are the masters. The universe can produce high temperatures and energies dwarfing our efforts at the LHC, but there is no known natural refrigerator. It is quite possible that the coldest place in the universe is in Pasadena (if not at Caltech, some other terrestrial lab.) Surprisingly, the vapor pressure of He3 in He4 exceeds that of He3 in the vacuum, enabling the dilution refrigerator and opening millikelvin temperatures to experimental study. Even in deep space the background radiation sets a lower temperature limit of 2.8 Kelvin; colder temperatures, as far as we know, are our unique creation.
What have we learned from low temperature physics? Famously, superconductors – but this is hundred-year-old news, more recently topological phases of matter [NSSFD]. Such phases inherently manipulate quantum information and, incidentally, are at the heart of Microsoft’s quantum computing program. But from another point of view, they are physical manifestation of cryptography. Topological states, by definition, are protected from the action of local (plane text) operators. Their stability, robustness, derives from the fact that only string (cyphertext) operators can act. Most of what we know of topological states comes from the fractional quantum Hall effect in cryogenic labs or from mathematical considerations. Although topological states are too delicate to survive outside dilution refrigerators, the fact they exist at all is a cryptographic miracle.
For me, it was a revelation that cryptographic protection is fundamental to the stability of these fragile states of matter. Cryptography is not just for spies and password protection. It confers protection to fragile systems. Intuitively, the reason is that codes have redundancy that permits reconstruction of information in the presence of (a limited amount of) error, thermal error in the case of topological phases, loss or alteration of bits in more usual settings.
By analogy, cryptographic approaches, even those suggested by quantum physics, may add robustness to social mechanisms. Here, by cryptography, I am thinking more broadly than user identification and secure communication, I’m thinking of its power to stabilize system response functions as manifest in cryogenic condensed matter systems. Quadratic (radical) thinking has begun to address questions of equity, but vulnerabilities remain. Topological physics teaches us that: cryptography = robustness. Perhaps some fusion of quadratic and crypto can yield the equity of the former and the robustness of the latter. Quantum physics may yet inspire social application.
References:
[P] L. Penrose, The Elementary Statistics of Majority Voting, Journal of the Royal Statistical Society (109) (1946)
[PW] E. Posner, G. Weyl, Radical Markets: Uprooting Capitalism and Democracy, ISBN 9780691177502 (2018)
[FFW] M. Fabinger, M. Freedman, G. Weyl, Prospecting a Possible Quadratic Wormhole Between Quantum Mechanics and Plurality
[NSSFD] C .Nayak, S. Simons, A. Stern, M. Freedman, S. Das Sarma, Non-Abelian Anyons and Topological Quantum Computation, Rev. Mod. Phys. 80, 1083 (2008)