Science education researchers have found that those lost students “hungered—all of them—for information about how the various methods they were learning had come to be, why physicists and chemists understand nature the way they do, and what were the connections between what they were learning and the larger world.

Might curb the drain a little to international schools. Not clear how this is going to be administered. Back dated, those that have left uk and come back, non contiguous treatments.

The energy curves of certain strongly correlated systems have a kink at √2N. The associated peak for these systems is the Tracy-Widom distribution, which appears in the third derivative of the energy curve — that is, the rate of change of the rate of change of the energy’s rate of change. This makes the Tracy-Widom distribution a “third-order” phase transition.

...Third order is very unusual, my favourite rate of change of rate of change of rate of change is the "snap" of displacement: the rate of change of acceleration. Not sure if related but want it to be.

Witten’s covariant formalism is used to explore the symplectic structure
of various cohomologous Einstein-Cartan Lagrangians. The only novelty offered here is a pedagogical introduction of the geometric formalism that makes frequent contact to the more familiar presentation of Noether's theorems.

https://mcmurmerings.files.wordpress.com/2018/08/quasi-local-energy-pseudo-charge.pdf

The functional derivative of the boundary term from these Lagrangians being the symplectic potential results from performing an ’integration by parts’ in the Variational Principle. The quasi-local Noether charge as a surface Boundary term is used to define distinct energy-momentum pseudo-tensor-valued forms. The respective Noether surface ”charge densities” on the boundary will need to be appropriately fixed in order that distinct solutions from the equations of motion can be determined.

Applying the spinor-valued symplectic formalism the gauge freedom afforded to the contact one form for a Chiral (left-handed) Rarita-Schwinger Lagrangian is revealed. This related the associated Noether symmetries implicitly to the on-shell satisfaction of linearised Einstein’s Vacuum equations and its connection as a Lax Pair to the Twistor equation is made. The charge for a complex half-flat space is derived and on the way a chiral N=1 Lagrangian for supergravity is constructed.

On fixing boundary conditions according of Dirichelet (scalar field) potential type versus Neumann (of first derivative of) potential type applied to Hamiltonian of gravitation.

Specification of the normal derivative is known as applying the Neumann boundary condition, an example of which is in considering the electrostatic potential inside a bound 2-surface S, with a charge σ specified on the boundary.

Quasi local charge definitions of General Relativity differ by boundary terms that mean boundary condition specification can take either Neumann or Dirichelet form

According to the equivalence principle, inertial mass can be distinguished from gravitational mass only non-locally. Being indistinguishable at a point makes for unhappy marriage with principle of general covariance. This is partially resolved by saying physical energy-momentum is quasi-local, rather defined within closed 2-surfaces,S.

The Hamiltonian 3-form associated through the standard Legendre transformation L=Pdq/dt-H for fields for a first order Lagrangian 4- form is obtained by contracting the Lagrangian with a timelike spacetime displacement vector field that specifies the time evolution:
i_N L = £_Nφ ∧ p − H(N),
H is then the generator of “time” evolution. Here a variation by an infinitesimal diffeomorphism is given by the Lie derivative with respect to some vector field, N as £_N ≡ di_N + i_N d (here i_N is the interior product). Consequently, for diffeomorphism invariant systems, we have δ → £_N,

The freedom to have a different boundary term, that in itself both determines the quasi-local energy-momentum while controlling boundary conditions, is not arbitrary and thus (by General "gauge" principles) must have a physical significance. The presence of an additional boundary term while necessarily not changing the dynamical evolution of the system does change the value of its conserved quantities.

The variation of Hamiltonian for electrostatics which includes a boundary term will vanish if we fix (according to Neumann) on the boundary the normal component of the electric field, E i.e. fixing σ, the surface charge density. An alternative Hamiltonian H(ϕ) derived from a cohomologous Lagrangian scalar density differing by a boundary term, will have Hamiltonian variation with different boundary term that will vanish rather if we fix the scalar potential (Dirichlet) field on the boundary.

physics.usask.ca/~hirose/p812/notes/Ch2.pdf

Nicely put and well meaning from someone admittedly who came through the whole charade relatively unscathed and still curious.

"A diversity of experiences and methods among the population is a great way to ensure that more problems can be solved; absolute uniformity is as bad for human society as monoculture is for agriculture. The greatest advances in science and society have come about because of the unique backgrounds and approaches some of the greatest minds in history possessed and utilized. Unless our goal is societal stagnation, we need to encourage creativity and excellence, not only in our students, but in our educators as well."

Musical maths

Let's cannabalize the profits of those educational (examination) boards

Interesting dialogue on how to illicit questions from those you have just confounded.

Why 7 items are all we can handle at one time...

Their modeling confirmed that the three brain regions act like jugglers engaged in a complex game of catch. The prefrontal cortex seems to help construct an internal model of the world, sending so-called “top-down,” or feedback, signals that convey this model to lower-level brain areas. Meanwhile, the superficial frontal eye fields and lateral intraparietal area send raw sensory input to the deeper areas in the prefrontal cortex, in the form of bottom-up or feedforward signals. Differences between the top-down model and the bottom-up sensory information allow the brain to figure out what it’s experiencing, and to tweak its internal models accordingly.