Helge Rebhan
272 followers -
per aspera ad astra .. or below
per aspera ad astra .. or below

272 followers
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Gute Zusammenfassung der aus dem Ruder laufenden Dieseldiskussion:
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Gehen euch diese Warnmeldungen von Apple oder Google auch so auf den Geist? Diesen Rechner verwende ich nun schon fast 3 Jahre und noch immer gibt es "unbekannte" Anmeldungen. Wenn das die Sicherheitskonzepte der aktuellen Hipster-Generation seien soll dann Gute Nacht....

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Das kurze Porträt über diesen Mann sagt mehr aus als alle (pseudo)intellektuellen Journalisten–Analysen der letzten 2 Jahre:
#spd #migration
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Very nice animations.
A pleasing diversion for your weekend: In 1735, Leonhard Euler proved that 1 + 1/4 + 1/9 + 1/16 + ... = π²/6. You can show this through various algebraic means, but when π is involved, it's often a sign that you can think of it in some geometric way involving circles. That's exactly what this video does, using lighthouses around the shore of an infinite lake. It uses two key insights.

First, if (like me) you have three spatial dimensions, then the brightness of a light decreases as the inverse square of your distance from it. There's a simple geometric reason why: imagine a light in empty space, surrounded by a spherical screen. All of the light ends up touching that screen. If you double the radius of the screen, the exact same amount of light reaches it, but the surface area of the screen has quadrupled. More generally, if you multiply the radius of the screen by x, the total amount of light stays the same, but the surface area increases proportionally to x². That means that the amount of light per unit area of the screen must decrease, proportional to 1/x², so that the total stays the same. And if your "sensor screen" -- say, the retina of your eye -- stays the same size, then as it moves away from the center, the total amount of light it receives goes down by 1/x² as well.

Why does this depend on us having three dimensions? Because if you have three spatial dimensions, you need a two-dimensional surface to surround a light, and so its area scales as x². If we lived on a plane, you would instead surround the light by a circle, whose circumference scales as x, and we would have an inverse-linear law; if we lived in four spatial dimensions, you would need a 3-sphere, and you would get a 1/x³ law instead. This is a very important fact in modern physics, where lots of things happen in higher- or lower-dimensional spaces, not least because this doesn't just apply to light: it applies to any force that gets "radiated" from a point, which is anything from light, to electric fields, to gravity.

But in this problem, we aren't using any of the physics, or thinking about other dimensions: we just use the fact that the brightness of lights scales as 1/x² to let us think about this infinite sum, which we can now think of as the total brightness you would see from an infinite series of identical lights, 1, 2, 3, 4, and so on units away from you on a line.

The second trick is to figure out how we can rearrange those lights, keeping the total brightness constant, into something else which is easier to think about. And that's where the video shows some clever geometry, using the Pythagorean Theorem: a way to replace one light with two lights whose total brightness is the same. They apply this idea to a single lighthouse on the opposite shore of a circular lake, and show it's the same as two lighthouses, equally angularly spaced on the shore of a lake twice as large. That, in turn, is the same as four lighthouses on the shore of a lake four times as large, and so on, and so forth... until you end up with lighthouses evenly spaced along an infinitely large lake. And since an infinitely large circle, viewed from along its edge, looks like a line, you end up with a pattern that looks very much like the infinite line of lighthouses that describe the sum. That means that we can replace those infinite lighthouses with just the single light on the opposite shore of the original lake -- and so compute its brightness.

Go watch the video, if you have some time; it's a fun way to get some mathematical intuition, all the while imagining how a small lake can be a lot like an infinite one.
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Danke #Amazon für diese kostenlose Lieferung von soviel Luft! Damit habt ihr einen neuen Rekord in dümmlicher Logistik und Resourcenverschwendung aufgestellt.
PS: Die Alustangen sind die Ware...
#fail #mogelpackung
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Unglaubliche Geschichte über #hatespeech im Netz. Offenbar brauchen wir doch ein #NetzDG und bessere Strafverfolgung.
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Quantum physics explained in one picture ;-)