This opinion piece by Hossenfelder in the NYT makes the claim that "Only Supercomputers Can Do the Math" of modeling the global climate:

https://www.nytimes.com/2019/06/12/opinion/climate-change-supercomputers.html

I recall that Hossenfelder wrote a book called "Lost in Math: How Beauty Leads Physics Astray"

> "Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. "

I don't know if the latter helps explain the former view.

Next week's geophysics fluid dynamics conference presentations illustrates the potential simplicity

> [*Infinite U(1) Symmetry of the Quasi-Linear Approximation*](https://ams.confex.com/ams/22FLUID/meetingapp.cgi/Paper/360248

) :

> "Particle-relabeling symmetry of inviscid fluid equations, equivalent in the case of incompressible fluids to the infinite dimensional group of volume-preserving diffeomorphisms, is broken by the quasi-linear approximation. Instead the equations of motion are invariant under an infinite U(1) symmetry as the phase of each wave may be independently varied, reflecting the absence of wave + wave —> wave interactions. "

> "The infinite U(1) symmetry of linear waves manifests, by Noether’s theorem, as separate conservation of the pseudomomenta for each zonal wavenumber. The pseudomomenta are approximately conserved for quasilinear dynamics due to the separation in time scales between the evolution of the zonal mean and the waves. Whether or not an action principle or a Hamiltonian can be found that generates the quasilinear dynamics remains an open question; if one can be found then it should be possible to find exactly conserved pseudomomenta as the quasilinear system retains the infinite U(1) symmetry. Pseudomomenta are not conserved by the fully nonlinear dynamics"

> ![](https://imagizer.imageshack.com/img924/5267/NLgOou.png)

U(1) corresponds to the unitary group of dimension 1, i.e. complex numbers of norm 1 residing on the unit circle. This is a global symmetry and corresponds to conserved quantities via Noether's theorem.

Not surprising that the solution used in ENSO and QBO is appropriately sin(a f(t) + θ). This appears fairly elegant to me, resulting from the real (observable) part of the complex number.

And also this presentation from the conference:

> [*The Kelvin and Mixed Rossby Gravity Waves on the Spherical Earth*](https://ams.confex.com/ams/22FLUID/meetingapp.cgi/Paper/359154) :

>"While the theory developed by Matsuno for the equatorial \beta-plane allows for exact analytic solutions, the corresponding theory developed by Longuet-Higgins on the sphere can only be solved analytically at some asymptotic limits. In the present work we revisit the Kelvin and MRG waves on the sphere using two complimentary forms of analysis: (i) Special ad hoc analytic solutions that yield accurate approximations for the latitude-dependent amplitudes and dispersion relations of the Kelvin and MRG waves over a wide range of the parameters space. (ii) A Schrodinger formulation that provides a classification for the waves in terms of the mode numbers of the associated Sturm-Liouville problem. "

The ENSO and QBO solution above comes directly from transforming the complete Navier-Stokes through the Laplace's Tidal Equation linearizing simplification into a Sturm-Liouville formulation that could be analytically solved.

They might be getting close, perhaps a year or two they will catch on.

https://www.nytimes.com/2019/06/12/opinion/climate-change-supercomputers.html

I recall that Hossenfelder wrote a book called "Lost in Math: How Beauty Leads Physics Astray"

> "Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. "

I don't know if the latter helps explain the former view.

Next week's geophysics fluid dynamics conference presentations illustrates the potential simplicity

> [*Infinite U(1) Symmetry of the Quasi-Linear Approximation*](https://ams.confex.com/ams/22FLUID/meetingapp.cgi/Paper/360248

) :

> "Particle-relabeling symmetry of inviscid fluid equations, equivalent in the case of incompressible fluids to the infinite dimensional group of volume-preserving diffeomorphisms, is broken by the quasi-linear approximation. Instead the equations of motion are invariant under an infinite U(1) symmetry as the phase of each wave may be independently varied, reflecting the absence of wave + wave —> wave interactions. "

> "The infinite U(1) symmetry of linear waves manifests, by Noether’s theorem, as separate conservation of the pseudomomenta for each zonal wavenumber. The pseudomomenta are approximately conserved for quasilinear dynamics due to the separation in time scales between the evolution of the zonal mean and the waves. Whether or not an action principle or a Hamiltonian can be found that generates the quasilinear dynamics remains an open question; if one can be found then it should be possible to find exactly conserved pseudomomenta as the quasilinear system retains the infinite U(1) symmetry. Pseudomomenta are not conserved by the fully nonlinear dynamics"

> ![](https://imagizer.imageshack.com/img924/5267/NLgOou.png)

U(1) corresponds to the unitary group of dimension 1, i.e. complex numbers of norm 1 residing on the unit circle. This is a global symmetry and corresponds to conserved quantities via Noether's theorem.

Not surprising that the solution used in ENSO and QBO is appropriately sin(a f(t) + θ). This appears fairly elegant to me, resulting from the real (observable) part of the complex number.

And also this presentation from the conference:

> [*The Kelvin and Mixed Rossby Gravity Waves on the Spherical Earth*](https://ams.confex.com/ams/22FLUID/meetingapp.cgi/Paper/359154) :

>"While the theory developed by Matsuno for the equatorial \beta-plane allows for exact analytic solutions, the corresponding theory developed by Longuet-Higgins on the sphere can only be solved analytically at some asymptotic limits. In the present work we revisit the Kelvin and MRG waves on the sphere using two complimentary forms of analysis: (i) Special ad hoc analytic solutions that yield accurate approximations for the latitude-dependent amplitudes and dispersion relations of the Kelvin and MRG waves over a wide range of the parameters space. (ii) A Schrodinger formulation that provides a classification for the waves in terms of the mode numbers of the associated Sturm-Liouville problem. "

The ENSO and QBO solution above comes directly from transforming the complete Navier-Stokes through the Laplace's Tidal Equation linearizing simplification into a Sturm-Liouville formulation that could be analytically solved.

They might be getting close, perhaps a year or two they will catch on.