Posts about Science (old posts, page 4)

I am a physicist, so naturally I also have things to share in this area. Here you can find articles about physics, but also about mathematics and statistics. Sometimes I also look at financial matters, these sometimes end up in this category.


Risk Analysis for Risk

In 2011 I was on vacation with friends, we played a lot of Risk. Somehow we ended up having fights of hundreds of armies against each other. Since with every dice rolling you can only eliminate up to three armies, you need a lot of rounds until a battle is settled. While my friends were occupied in a battle of 200 against 150, I used my freshly acquired Python skills to write a program to do the dice rolling, risk-auto-dice.

The program does exactly what the players do until one player runs out of armies:

  • The attacker rolls up to three dice, the defender up to two. The number of dice cannot exceed the number of armies. In the game a player can choose to use less dice, the program uses the maximum amount.

  • The results are ordered descending and paired up. For every pair which is unequal, the person with the lower number loses one unit.

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Three And Five Liters

There is this classic riddle where you are given two containers, one has a capacity of three liters and the other five liters. Your task is to extract exactly four liters. There are no further markings on the containers.

To measure two liters, it is quite straightforward: Fill the five liter container, transfer to the three liter container until the latter is full. Then there will be two liters remaining in the five liter container. To obtain one or four liters takes more steps. I wondered what results are possible with this setup. Can you achieve any amount of liquid in both of the containers?

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Physik in »Mass Effect«

Zur Zeit spiele ich die Mass Effect Trilogie. Im Gegensatz zu anderen Science Fiction Universen stolpere ich häufig über die Physik.

Gute Beispiel für glaubwürdiges Science Fiction sind:

Stargate

Hier kommt die Technologie von den Antikern, die ursprünglich auf der Erde gelebt haben und die Technik hinterlassen haben. Das Stargate kann ein Wurmloch aufbauen und stabilisieren. So wirklich ausgeschlossen ist das nach meinem Verständnis der allgemeinen Relativitätstheorie (ART) nicht.

Die Raumschiffe legen große Distanzen im Hyperraum zurück, in dem unsere vierdimensionale Raumzeit eine Oberfläche ist. In diesem höherdimensionalen Raum gibt es dann Abkürzungen, weil die normale Raumzeit hier gekrümmt ist. Je nach dem, wie das exakt gemacht ist, ist das noch kein Widerspruch zur aktuellen Physik, Stringtheorie hat ja auch mehr Dimensionen.

The Expanse

Dies ist letztlich »nur« mit Ingenieursleistung zu schaffen. Die Arbeit von Ingenieuren schätze ich sehr; ich meine, dass es keine neue Physik für diese Serie braucht. Es existiert einzig ein hocheffizienter Antrieb und ein Serum, das Menschen Beschleunigungen von 40 Erdbeschleunigungen aushalten lässt. Das ist insgesamt sehr plausibel.

In Mass Effect gibt es aber so ein paar Dinge, bei denen ich echt lachen musste.

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Half a Cube

In lattice QCD you have a qubic lattice. It has certain symmetries:

  • Rotation around an axis perpendicular to a face. This goes with 90, 180 and 270 degrees.
  • Rotation around an axis along a face diagonal. This goes with 180 degrees.
  • Rotation around an axis along the volume diagonal. This goes with 120 and 240 degrees.
  • There is also the inversion symmetry.

Taking all of them together you will get 48 elements, the octahedral symmetry group.

The question then was how the symmetries break down when we make a volume diagonal a special direction. In other words: What symmetries does a cube have when it is cut perpendicular to a volume diagonal? We know from group theory that it only has the rotations with 120 degrees left, but can one see that visually?

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