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Section 6 | https://section6.nz | Remote within New Zealand/Australia/Asia Pacific | DevOps / Software Engineers.

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I have an education in physics and economics. My current role is as an energy markets consultant, but in practice I develop internal and external apps using Typescript/React/Material UI. I would like to pursue this line of work in full.

You would like it to have a lot of entropy. It's not about being random in the sense if being up to chance, it's about making the interactions between the electrons so complicated that any passing photon does not get absorbed or does not produce stimulated emission.

When there is enough entropy/complexity/randomness the electrons have no state that they can jump to of a similar range of energy to the frequencies of light that you would like the glass to be transparent to.

Fascinating post. I had always assumed that the 3rd most irrational number would be the third metallic mean given by n = (n+ sqrt(n^2+4))/2, and subsequently the fourth metallic mean etc. The metallic means also pack the disks nicely. I have recently had my interest in them sparked after I came across solution to point vortex equilibria involving them.

Do you know what the metallic means are bounded by? Are they as bad as the silver ratio/(1+sqrt(2))?

These most irrational numbers, (9+sqrt(221))/10, (13+sqrt(1517))/26... how interesting that they are not just the simple generalization of the continued fraction for the golden ratio.

I am not sure what you mean by the probability waves (amplitude?) becomes unresolvable for the condensate, but it is true that the condensate will have a continuous phase with integer windings of 2 pi around vortices etc. The wavefunctions of the atoms overlap below the critical temperature and you get Bose-Einstein condensation for atoms with integer spin.

But those atoms themselves are still made up of electrons, protons and neutrons which have half integer spin, and at even smaller scales of quarks and gluons. If you probe the condensate with high enough frequency without thermalizing it you would be able to resolve those details, but at the macroscopic level of the condensate those details are not resolvable (is that what you were getting at?).

When you cool an atomic cloud below a critical temperature there will be a condensate fraction and non condensate fraction. If you are just looking at the condensate fraction then you can use Bose-Einstein statistics.

At zero temperature with 100% of the atomic cloud as condensate ( in reality we can never get to zero temperature, but we can get pretty damn close), the Gross–Pitaevskii equation ( https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equat... ) is a good model for the dynamics of the condensate. If you want to go above zero temperature and include interaction with the thermal cloud (the non-condensate fraction), then you can use the SPGPE, the stochastic projected Gross–Pitaevskii equation.

I disagree. Many of the rules do not come down to only enforcing individual property rights. An optimal outcome for society and each individual can reached by enforcing them in many scenarios, but not all.

For example, how do you reach an optimal solution for orphans with the enforcement of private property rights? Or what about regulation of the relationship between a doctor and their patients? If the patient is mentally unable to act as a rational agent, there may be a conflict of interest between the doctor and patient without regulation.

What about health and safety standards? How does only focusing on private property rights deal with the vast asymmetry of information out there?