I didn’t see the pattern either and had to look it up. Apparently, you can rewrite 1 + 1/(1+2) + 1/(1+2+3)+… as 2(1 - 1/2 + 1/2 - 1/3 +…+1/n - 1/(n + 1)) = 2(1 - 1/(n + 1))
From there, the limit of 2 is obvious, but I guess you just have to build up intuition with infinite sums to see the reformulation.
The t-distribution approaches the normal distribution with increasing degrees of freedom. It is certainly more relevant in for example hypothesis testing, since t-Tests (variance is estimated from the data) is much more common than z-tests (variance is treated as fixed and coming from a normal distribution).
In all of statistics or probability theory, the normal theory is however way more influential.
Nonetheless, it’s a cool bit of history where modern statistics got its roots. As a lover of both statistics and guinness, i approve!🍻
First of all, I agree that it would be great if a drug/medicinal procedure would cure a certain condition in each and every patient or at least the vast majority of them. Sadly, that is rarely the case, but that by no means is equivalent to say that when this drug or procedure helps, it’s mostly or entirely due to the placebo effect. That’s the whole reason we need randomised controlled trials as their might be a significant difference in treatments that only becomes clearly observable once a certain sample size is reached and possible confounding variables are controlled for (usually by randomisation). The human body and many of diseases are incredibly complex so it’s naive to assume we could forsee each and every possible influence on a drugs efficacy and therefore determine without error how a patient will react to it.
While there is quite a big group of non-responders when it comes to psychotherapy, it is, on average, an effective treatment clearly proven by a vast body of research. There is still much more to find out, but putting it on the same level as not consuming gluten is in no way defensible.
Now to get back to chiropractics, I don’t know too much about it, but I thought it’s mostly short term pressure and pain relief, which however rarely combats the underlying issues. Can still be helpful, of course, as pain relief helps with getting more physical activity, as this is often a culprit for example back problems.
That said, I personally wouldn’t let anyone touch my spine or neck like some chiropractors do. I’d be too scared of irreparable nerve damage.
Not trying to defend the decision, but as far as I know, the reasoning is that if you charge significantly less than you could, it might be because you have other undisclosed agreements with the tenants, like them doing some extra chores for you, repairing the flat or something else. This way, you could avoid a lot of taxes. The sentence also doesn’t seem to be a fine in the narrow sense, but rather a demand of additional taxes. If I’m not mistaken, it’s perfectly legal to charge very little for a flat, but you still have to pay taxes as if you would have rented it out for a regular price.
I think quite some people heard of the concept of different kinds of infinity, but don’t know much about how these are defined. That’s why this meme should be inverted, as thinking the infinities described here are the same size is the intuitive answer when you either know nothing or quite something about the definition whereas knowing just a little bit can easily lead you to the wrong answer.
As the described in the wikipedia article in the top level comment, the thing that matters is whether you can construct a mapping (or more precisely, a bijection) from one set to the other. If so, the sets/infinities are of the same “size”.
While I don’t want to deny that people try to put words into others mouths, I think context is still important. It is possible and even quite typical to send messages beyond the meaning of the actual words used in a statement and simply playing dumb when someone calls you out for doing that is also not a great look.
Think of going to a waffles-convention and just walking around claiming that you, in fact, like pancakes. Of course people are going to assume you’re a troll.
It’s important to think of different perspectives and at least consider if something you meant in a very innocent way might still not sit right with someone else. Certainly not easy to do, mistakes will always happen, but honestly trying makes a huge difference imo.