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.

# Simple Captcha with Deep Neural Network

The other day I had to fill in a captcha on some website. Most sites today use Google's reCAPTCHA. It shows little image tiles and asks you to classify them. They use this to train a neutral network to classify situations for autonomous driving. Writing a program to solve this captcha would require obscene amounts of data to train a neutral network. And if that would already exist, autonomous cars would be here already.

The captcha on that website, however, was of the old and simple kind:

It is just six numbers (and always six numbers), the concentric circles and some pepper noise. These kind of captchas are outdated because one can solve them with machine learning. And as I am currently working through “Deep Learning with Python” by François Chollet and was looking for a practise project, this captcha came as inspiration at just the right moment.

# Physics in Star Trek: Enterprise

I've always enjoyed the science fiction genre, and there are many books shows available. Especially I like works where the physics are credible. The Enceladus series by Brandon Q. Morris is such a work. Also The Expanse show seems pretty great in that regard.

Recently I have watched Star Trek: Enterprise and loved the plots, the characters and their development, the recurring arch enemies and the general uplifting spirit. But from the physics side I needed to chuckle quite often. Some people just take the science to be fictitious and don't bother; but I prefer credible science fiction and complain a lot.

First off: Why does always something explode on the bridge when they get hit? On a navy warship the bridge is exposed, that could happen as well. But they have a CIC which is a bunker inside the ship. Enterprise does not have a window on the bridge, so why is it located at the edge of the hull? In The Expanse, the MCRN Donnager seems to have a combined bridge and CIC well protected in the ship. In the fight nothing explodes in the CIC. And even the railgun hit is unspectacular, as it should.

# 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.

# 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?

# 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.

# 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?

# Referendum and Overlap

I have seen a few referendums in the past:

• The Turkish presidential system referendum with 51.41% for the new system. Source
• The Brexit with 51.89% for leaving the EU. Source
• The Irish abortion referendum with 68% for allowing it. Source
• The Swiss "Billag" vote for publicly financed broadcasting with 71.6% for keeping the current system. Source
• The annexion referendum on the Crimea with 95.5% to join Russia. Source.

The first two ones are awfully close to a tie, and that makes it problematic. When the result of a "Yes or No" referendum end that close to 50%, I would argue that the referendum asks the wrong question.

# Gewinnschwelle bei VL

Manche Arbeitgeber zahlen Vermögenswirksame Leistungen (VL), welche in einen Aktienfond eingezahlt werden können. Dazu schließt man einen entsprechenden Vertrag mit einer Depotbank und bittet den Arbeitgeber, die Leistungen an diese zu überweisen. Dieser Vertrag kostet, bei ebase beispielsweise 12 EUR/Jahr. Das Geld muss dort 7 Jahre ruhen und kann vorher nicht ausgezahlt werden.

Als Doktorand kann ich 3,33 EUR/Monat bekommen (Quelle), natürlich nur während der Promotion, also angenommen drei Jahre. Lohnt sich das denn?

# Vergleich der VBL Modelle

Im öffentlichen Dienst erhält man eventuell eine Zusatzrente durch die VBL. Der Arbeitgeber (AG) zahlt dort einen Beitrag zusätzlich zum Einkommen ein. Es gibt zwei Modelle, VBLklassik und VBLextra.

Das Folgende sind meine persönlichen Überlegungen und können natürlich Fehler enthalten. Daher ist es ratsam, sich selbst direkt bei der VBL zu informieren.

Der wichtigste Unterschied der Modelle ist die Wartezeit. So erhält man aus der VBLklassik erst dann Zahlungen, wenn man 60 Monate eingezahlt hat. Die Wartezeit wurde ab 2018 reduziert, diese ist nur noch 36 Monate. Allerdings gilt das nur für Beitragsmonate, die in 2018 oder später liegen. Somit müssen in der Übergangsphase entweder 60 Monate zusammenkommen oder die Beschäftigung bis Dezember 2020 laufen.

# Vergleich von Unfallversicherungen anhand der Gliedertaxe

Ich habe nach einer Unfallversicherung mit monatlicher Rentenzahlung geschaut. Natürlich gibt es hier diverse Versicherungsunternehmer, die ein derartiges Produkt anbieten. Jeder Versicherer bietet wieder unterschiedliche Tarife an, die dann unterschiedlich viel abdecken. So ist in einer Versicherung ein Schaden durch Insektenstich abgedeckt, in der anderen nicht. Dafür zahlt die eine Kosten für die Nutzung einer Dekompressionskammer nach einem Tauchunfall nicht. Es ist also schwer, die Tarife hier zu vergleichen, weil man es für den Einzelfall schlecht quantisieren kann.

# Der statistisch signifikante Einzelfall

Gerade noch einen schönen Artikel zum Thema Fahrradhelm gelesen. Dort wurde gesagt, dass ein Helm viel nützt.

Der erste Kommentar war von jemandem, der anscheinend noch keinen Unfall hatte. Er meinte, dass man keinen Helm braucht, wenn man umsichtig fährt. Jemand anderes meinte, dass bei einem Unfall sich jemand am Bauch verletzt hat, da hätte ein Helm ja nichts gebracht.

Beim Thema Rauchen kommt immer wieder einer an, der einen kettenrauchenden Großvater hat, der über 90 ist. Somit kann Rauchen ja nicht pauschal tödlich sein.

# Is Cashback Worth It?

For one insurance contract I have the option to pay 6 or 12 months in advance and get a cashback for that. For 6 months it is 2%, for 12 months it is 4%. The general assumption for this article is that the rate is cheap enough that I can afford to pay a whole year in advance, that I have 11 monthly rates available.

At first it is obvious that one should take the cashback because that is a cost saving of 4%. However, I could just invest the spare money and pay the rates with my monthly salary. Perhaps that would give a better result?

# Knowledge Management

In my master thesis, I have to learn a lot of new things and keep track of them. With a thesis like this there is the danger of insufficient documentation along the way. When it comes to actually writing the thesis, one might not remember what one spend the last year on in sufficient detail to write a hundred pages.

This I try to prevent by constantly organizing my knowledge along the way. The cornerstone is a mind map:

# Visualizing Cellular Automatons

Visualizations can be really great. They can quickly demonstrate a concept which we can understand much faster than trying to grasp it from words. The majority of people probably thinks visually at lot of the time. This is not the case for all problems or people, of course, as this quote from Lagrange shows:

The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure.

Preface to Mécanique Analytique. (Source)

In physics, there are a lot of things that one can visualize in experimental physics. In theoretical physics, one visualizes different things (e.g. Feynman diagrams). Numerical simulations very often lend themselves to visualizations. The class of systems I want to introduce here are systems that are defined on a square grid. Representing the whole state of the system in a single picture allows to create movies from that. Let me demonstrate with some examples and then source code.

All the matter around is is made up from atoms. The atoms are really small, about $10^{-8} \, \mathrm{cm}$. That is $0.000\,000\,01 \, \mathrm{cm}$. Each atom consists of a nucleus and electrons. The movement of the electrons around the nucleus is described by quantum mechanics. The image I drew below is not very accurate; the accurate thing is really hard to draw. The atomic nucleus is just a ten-thousandths of the size of the whole atom; the atom is mostly empty! Inside the nucleus, there are protons and neutrons, those are called nucleons. Each of the protons and neutrons consist of three quarks. The quarks are bound together by the strong force which is mediated by gluons.