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Ooh, good point.
Ooh, good point.
Armchair geopolitics explanation: it’s a culture/societal difference between a thousand year old monarchy and a federalist state that lost 2 world wars on their own land. Not to mention the federalist state had a “communist” power structure in control of about half of their lands for half a century while the other half birthed a regional free trade juggernaut. Meanwhile, the monarchy has a landed elite class/aristocracy that persists to this day.
What I’m getting at is that the wealth in the UK could be much more heavily tied up in individual fortunes and estates than the wealth in Germany. That kind of wealth seems easier to “protect” by offshoring (and/or the UK has evolved to prefer/rely on it).
In contrast, I expect the wealth in Germany to be more tied up in corporations, stocks, etc. This in turn would lend itself to corporate forms of tax evasion that can happen domestically.
From 1/√3 to 1/√4 is less of a decrease than from 1/3 to 1/4, just as from 1/3 to 1/4 is less of a decrease than from 1/(3²) to 1/(4²).
The curve here is not mapping 1/4 -> 1/√4, but rather 4 -> 1/√4 (and 3 -> 1/√3, and so on).
So, for starters, any exponentiation “greater than 1” is a valid candidate, in the sense that 1/(n^2), 1/(n^3), etc will all give a finite sum over infinite values of n.
From that, inverting the exponentiation “rule” gives us the “simple” examples you are looking for: 1/√n, 1/√(√n), etc.
Knowing that √n = n^(1/2)
, and so that 1/√n can be written as 1/(n^(1/2)), might help make these examples more obvious.
If I remember my series analysis math classes correctly: technically, summing a decreasing trend up to infinity will give you a finite value if and only if the trend decreases faster than the function/curve x -> 1/x
.
Disclaimer: not a physicist, and I never went beyond the equivalent to a BA in physics in my formal education (after that I “fell” into comp sci, which funnily enough I find was a great pepper for wrapping my head around quantum mechanics).
So space and time per se might be continuous, but the energy levels of the various fields that inhabit spacetime are not.
And since, to the best of our current understanding, everything “inside” the universe is made up of those different fields, including our eyes and any instrument we might use to measure, there is a limit below which we just can’t “see” more detail - be it in terms of size, mass, energy, spin, electrical potential, etc.
This limit varies depending on the physical quantity you are considering, and are collectively called Planck units.
Note that this is a hand wavy explanation I’m giving that attempts to give you a feeling for what the implications of quantum mechanics are like. The wikipédia article I linked in the previous paragraph gives a more precise definition, notably that the Planck “scale” for a physical quantity (mass, length, charge, etc) is the scale at which you cannot reasonably ignore the effects of quantum gravity. Sadly (for the purpose of providing you with a good explanation) we still don’t know exactly how to take quantum gravity into account. So the Planck scale is effectively the “minimum size limit” beyond which you kinda have to throw your existing understanding of physics out of the window.
This is why I began this comment with “space and time might be continuous per se”; we just don’t conclusively know yet what “really” goes on as you keep on considering smaller and smaller subdivisions.
For what it’s worth: I self-host gitea, and it gives me the possibility to import not only repos but also issues, projects, etc from GitHub, gitlab, bit bucket, and a handful of others.
I don’t know if Utterances can work with gitea’s API. If it does, then in theory you should be able to migrate to gitea from GitHub for this use case.
Top right are the Botez sisters, if I’m not mistaken.
An important part of that process that needs mentioning is that when the mothers are convinced by Nestle to feed their babies formula instead of their breast milk, their bodies will stop producing the milk before the baby is weaned from it.
So Nestle literally endangers babies’ lives just to sell more baby formula.