sethoflagos

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?

Sounds like the one I scanned through on Jstor recently, and yes of course, what you say is unarguably so. Your own point regarding natural gastric alcohol production suggests that the concept of 'total abstinence' is illusory. We all consume alcohol to a certain extent. Gauging the effects of one extra milligram here or there would be challenging in the extreme.

There have been a multitude of studies on mortality vs alcohol consumption. High on the search-engine listings is Alcohol Consumption and All-Cause Mortality: A Systematic Review The balance of the evidence is perhaps surprisingly in favour of limited consumption of alcohol being a healthier choice over total abstinence. The argument isn't proven, but it suggests your fears are indeed difficult to justify.

Your input combination was one of the 1,300 other possible solutions also given on my spreadsheet. There is no unique 'correct' solution. If D is volume, and d is specific volume, then yes. If any of the various q values share a common factor, there will likely be multiple solutions. This is readily apparent in the coins problem as the common factors are of a similar order of magnitude to q. The problem does not go away even with irrational numbers. Express in terms of specific volume rather than density and the form is identical to your stated rule of mixtures.

Pretty much it. Main point is kids understand stairs so there's a clear physical and intuitive link to each operation that you can leverage. Give boys half a chance to compete at who can take stairs two or three at a time and they'll be doing it at playtime too.