sethoflagos

I'm sure I'm missing something only a little opaque here... ...but at least I've discovered how to select 'hidden' on Android

Consider case b) being physically realised by flow through a perfectly insulated porous plug. The pore resistance of the plug is sufficiently high for kinetic energy terms to be very small. For an ideal gas, the operating equation is d(PV) = VdP + PdV = nRdT The VdP term represents a differential loss of internal energy converted to kinetic acceleration of the flow through the plug. The PdV term represents a differential increase of internal energy due to heating from the frictional resistance opposing that acceleration. For low flow rates these two terms become equal in magnitude, opposite in sign. Hence dT = 0 I've attached a copy of my backpocket cribsheet for this sort of system. 'Isothermal' generally implies heat exchange between the system and surroundings. This case is an adiabatic one that just happens to maintain a constant temperature. The process is far from reversible due to the large increase in total entropy. Porous Plug.pdf

Consider the extensions: N (mod 2) in [1] (2 - 1) = 1 element (1/2 of population) N (mod 2*3) in [1, 5] (2 - 1)*(3 - 1) = 2 elements (1/3 of population) N (mod 2*3*5) in [1, 7, 11, 13, 17, 19, 23, 29] (2 - 1)*(3 - 1)*(5 - 1) = 8 elements (4/15 of population) N (mod 2*3*5*7) in [1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209] (2 - 1)*(3 - 1)*(5 - 1)*(7 - 1) = 48 elements (8/35 of population) ie we have successive screenings via Aristotle's sieve so they're neither definite primes nor non-primes. For want of a better term, I labelled them 'potential primes' back in the days when I dreamt of being able to solve the prime pairs conjecture.

Curious possibility:

In the UK, arguably, the 2008 global banking crisis led to the fall of the Labour government in the following general election, just as the Covid crisis precipitated (in a similarly toxic campaign to the US) a landslide victory back to the left this year. Actual policies seem pretty irrelevant. It seems quite depressingly random.

Possibly. Or maybe post-covid inflation, a large section of society felt that they had more money in their pockets under the previous administration.

One major difference between the far right in Europe and the US is that the religious fundamentalists have far less influence in the former, so gender and reproduction issues gain less traction than racism and immigration. The hidden agenda is the same - economic deregulation and erosion of workers' rights.

Indeed. Neither factor can be divisible by 3.

Power is failing, so no time to check

The thought that struck me in this presentation was the distinction between theoretical research that is observation driven and that which is not. Clearly, the twin pillars of GR and QM arose out of trying to resolve observed phenomena that did not agree with the prevailing concensus theory of the time (eg photoelectric effect, orbit of Mercury etc) Today, attempts to resolve the Hubble tension perhaps falls into the same category. It seems that Sabine's issues are more associated with the the various "What If?"-type explorations that have little to no observational justification. Such as "What if the universe isn't flat" in advance of any clear observational evidence that it isn't. Similarly, what observed failing of GR is the quest to quantise gravity actually trying to address? There's no denying that such questions are interesting to speculate on. In much the same way as "What if ancient Egyptians were educated by aliens?"

There are a lot of teeth in a pretty smile 😁

Fair point, but we're talking digestive enzymes plus neurotoxins. When I looked there's over 7000 described species of assassin flies. I think it's one of them. 😀

Compare and contrast: x + 1/x = 51/2

My impression of equations of that type are dominated by: x - 1/x = 1

Force of habit. I ALWAYS do the check longhand just to be sure. (Chem Eng thing)

Sometimes, you are simply in awe of the brutality of the design. Just now on the balcony of my apartment in Abuja, Nigeria. The lit strip is ~3cm wide. I'm told that the bite is 'best avoided'.

... what else could you be looking for?

Why do I remember this more clearly than my twenties and thirties? Scary.

We learnt factorisation first as I remember. Then cancellation of common factors.

The main issue the YT clip addressed were the multitude of locations, not just web but science papers too, where the 60 kmile figure was produced with no authentic source quoted. The 'correct' figure was of secondary interest; the main issue was traceability. They obviously put a lot of work into both research and presentation.

My first wild stab in the dark would be their shared initial value and symmetry about zero. = common end point?

I'm sure I missed most of the subtlety of @studiot's point, but if as he seems to be saying, (-1)*(-1) only has a value of +1 by convention, then reading it backwards, -1 is simply a label for the 'other' root of +1, isn't it?. This instantly reminded me of my picture of +/-i being axiomatic labels for the roots of -1. As someone who habitually conceptualises ideas in geometrical terms, the paralellism is certainly apparent when the two relationships are expressed as rotations of a unit vector in the complex plane: two rotations of 0 or pi radians restore the unit vector; two rotations of +/-i*pi/2 give the negative unit vector. ... or to preserve the state of the unit vector under zero rotations. NB this is far from the OP objective: just trying to better explain what seems to have been seen as a daft idea.

So does -1 stand to 1 as i does to -1, no more no less?