Mathematics Is Physics

In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.Comment: 15 pages, LaTeX. Second prize winner in 2015 FQXi Essay Contest (see http://fqxi.org/community/forum/topic/2364

Voltage from mechanical stress in type-II superconductors: Depinning of the magnetic flux by moving dislocations

Mechanical stress causes motion of defects in solids. We show that in a type-II superconductor a moving dislocation generates a pattern of current that exerts the depinning force on the surrounding vortex lattice. Concentration of dislocations and the mechanical stress needed to produce critical depinning currents are shown to be within practical range. When external magnetic field and transport current are present this effect generates voltage across the superconductor. Thus a superconductor can serve as an electrical sensor of the mechanical stress.Comment: 3 pages, 1 figure

Experimental Studies for the Detection of Protein in Trace Amounts Quarterly Status Report, 1 Mar. - 31 May 1965

Methods for separating inorganic compounds from organic materials in investigation of trace proteins in soil

Polymorphism of the tumor necrosis factor beta gene in systemic lupus erythematosus

We investigated the Nco I restriction fragment length polymorphism (RFLP) of the tumor necrosis factor beta (TNFB) gene in 173 patients with systemic lupus erythematosus (SLE), 192 unrelated healthy controls, and eleven panel families, all of German origin. The phenotype frequency of the TNFB*I allele was significantly increased in patients compared to controls (63.6% vs 47.1%, RR = 1.96, p <0.002). The results of a two-point haplotype statistical analysis between TNFB and HLA alleles show that there is linkage disequilibrium between TNFB*I and HLA-A1, Cw7, B8, DR3, DQ2, and C4A DE. The frequency of TNFB*I was compared in SLE patients and controls in the presence or absence of each of these alleles. TNFB*I is increased in patients over controls only in the presence of the mentioned alleles. Therefore, the whole haplotypeA1, Cw7, B8, TNFB* I, C4A DE, DR3, DQ2 is increased in patients and it cannot be determined which of the genes carried by this haplotype is responsible for the susceptibility to SLE. In addition, two-locus associations were analyzed in 192 unrelated healthy controls for TNFB and class I alleles typed by serology, and for TNFB and class II alleles typed by polymerase chain reaction/oligonucleotide probes. We found positive linkage disequilibrium between TNFB*I and the following alleles: HLA-A24, HLA-B8, DRBI*0301, DRBI*ll04, DRBI*1302, DQAI*0501, DQBI*0201, DQBI*0604, and DPBI*OIO1. TNFB*2 is associated with HLA-B7, DRBI*1501, and DQB I *0602

Phonon-induced relaxation of a two-state system in solids

We study phonon-induced relaxation of quantum states of a particle (e.g., electron or proton) in a rigid double-well potential in a solid. Relaxation rate due to Raman two-phonon processes have been computed. We show that in a two-state limit, symmetry arguments allow one to express these rates in terms of independently measurable parameters. In general, the two-phonon processes dominate relaxation at higher temperature. Due to parity effect in a biased two-state system, their rate can be controlled by the bias.Comment: 5 PR pages, 1 figur

Clusterization, frustration and collectivity in random networks

We consider the random Erd{\H o}s--R\'enyi network with enhanced clusterization and Ising spins $s=\pm 1$ at the network nodes. Mutually linked spins interact with energy $J$. Magnetic properties of the system as dependent on the clustering coefficient $C$ are investigated with the Monte Carlo heat bath algorithm. For $J>0$ the Curie temperature $T_c$ increases from 3.9 to 5.5 when $C$ increases from almost zero to 0.18. These results deviate only slightly from the mean field theory. For $J<0$ the spin-glass phase appears below $T_{SG}$; this temperature decreases with $C$, on the contrary to the mean field calculations. The results are interpreted in terms of social systems.Comment: 10 pages, 6 figures; serious change of result

Letters between Albert A. Faurot and William Kerr\u27s secretary

Letters concerning a position in the modern languages department at Utah Agricultural College