~~:.|:;~~

I might have made this up as well, but I have a very distinct memory of basically suddenly becoming conscious at around being 3 years old. I woke up from a nap and for a couple hours or possibly days, I wasn't sure whether I was dreaming or the world around me was actually real. After a couple of days of waking up in the same environment, I eventually accepted this to be reality. I of course don't remember everything from this point on in my life, but it really felt like the first time I was able to explicitly think about stuff.

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.

I don't like this cover particularly much, but it definitely stays true to the feel of the original.

"Bye bye love" is a pretty funny one by S&G as the lyrics are all about heartache bordering full on depression, but people love to clap along to the upbeat melody.

Dieses Mantra wiederholen Politiker und Ökonomen soooo gerne, und es ist auch technisch korrekt, aber auch völlig sinnfrei.

Zugegeben, ich hab nicht genau erklärt, was ich damit meine. Mir geht es vor allem darum zu betonen, dass ein Staat seine Schulden nicht so wie du und ich irgendwann zurückzahlen muss. Eine (übermäßige) Rückzahlung ist sogar kontraproduktiv, da viele Banken eben genau ihr Geld in dieser Weise anlegen und Zinsen verdienen wollen. So können dann (unter Umständen auch risikoreichere) Kredite an Privatpersonen oder Unternehmen vergeben werden.

Die zukünftige Generation zahlt daher nicht die Schulden zurück, die jetzt aufgenommen werden, das war auch noch nie so.

Letztendlich geht es darum die Wirtschaft am Laufen zu halten, damit Staatsanleihen einfach immer und immer wieder ausgegeben und deren fällige Zinsen (durch Verkauf neuer Staatsanleihen) getilgt werden können. Kann man sich natürlich drüber streiten, ob man das gut findet, aber darauf läufts in unserem jetzigen Wirtschaftssystem hinaus.

Und zu deinem zweiten Punkt: völlig egal wieviele Schulden ein Staat macht ist es natürlich auch wieder nicht, da hast du schon Recht. Aber solange sich die Investition lohnt, macht es aus ökonomischer Sicht keinen Sinn sich von einer selbstauferlegten Schuldenbremse davon abhalten zu lassen. Auch hier kann man natürlich diskutieren, was sich lohnt und was nicht, aber bei ein paar Themen, beispielsweise erneuerbare Energien, ist das aus meiner Sicht relativ unstrittig.

Steuererhöhungen in gewissen Bereichen würden sicherlich auch helfen (Vermögenssteuer, Erbschaftssteuer, Kapitalertragssteuer), schuldenfinanzierte Investitionen heute, z.B. in wichtige Infrastruktur, sorgen aber schon an sich dafür, dass zukünftige Generationen eben nicht für die durch Vernachlässigung entstanden Kosten zahlen müssen. Zusätzlich zahlt der Staat seine Schulden auch nicht mit Steuergeld, sondern mit der Ausgabe von Staatsanleihen. D.h., bei einer schlechten oder zumindest nicht gewinnbringenden Investition zahlen in erster Linie jetziger Halter einer Staatsanleihe, da die Bonität des Ausgabelandes sinkt und damit der beim Kauf festgesetzte Zinssatz nicht mehr der Höhe des eingegangenen Risikos entspricht.

Ein Staat, vor allem die mit eigener Währung, sind in Ihrer Ein- und Ausgabenstrategie absolut nicht mit einem Privathaushalt und nur bedingt mit einem Unternehmen vergleichbar.

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".

You can add the Lakers to that. I guess it's natural for scoring to distribute over the quarters since being behind incentivizes playing your best players for longer and hustle in general. In addition, if you know your opponents are slow starters for example, part of the game plan might be trying to exploit that which would make it a self enforcing feedback loop.

I think the text tries to make the point that it doesn't work not because but despite him being black. The argument Perry and others make in this case is not one in the form of material benefits but rather moral ones. A member of a marginalized group makes it big, which is supposed to inspire others from this group. The point is that this form of trickle down economics works just as badly as the "regular" one, which is hardly at all.