The importance of understanding toilets and politics

tl;dr: Understand things before you have an opinion

In today’s world, there is much discussion about fake news, about political movements becoming more extreme and about a divided society. Unfortunately, I rarely hear anyone discuss why our society is diverging and what can be done to prevent this. So please bear with me while I introduce a psychological issue which is a promising tool for cooling off and understanding the origin of heated political disagreements.


Picture a flush toilet and ask yourself: how well do you understand how this toilet works? Maybe rate it from 1-7? Are you above the average, which would presumably go for a 3 or 4? Now please stop reading and explain to yourself how that toilet you (hopefully) use every day works! Go through every step before reading on.

Did you explain where the water comes from, why there is water down there in the first place, how the toilet knows how much water to flush, how it refills the correct amount,…? Do you still think you understand it as well as you assessed a few seconds ago?

You may be under the illusion of explanatory depth, termed and examined by Leonid Rozenblit and Frank Keil in 2002, in short, IOED. People feel they understand complex phenomena with far greater precision, coherence and depth than they really do.

One of the most important reasons for IOED is the confusion of higher and lower levels of analysis. Most complex systems are hierarchical in terms of explanations of their natures. In explaining a cell phone, one might describe the components such as a camera, buttons, loudspeakers and apps. If then asked what a camera is, you might start explaining flashes, apertures, lenses etc. The illusion of explanatory depth occurs when we gain a surface layer understanding and then stop asking any questions!

Another reason for IOED is the rarity of production: we rarely give explanations and therefore have little information on past successes and failures which would help us classify our knowledge. In contrast, we often tell narratives of events or retrieve facts; hence it is often easy to assess our average level of knowledge in these cases by inspection of past performance.


In case I you are still reading (thanks, I guess), you may be starting to wonder why I am boring you with toilets. To be fair, you will (almost) never need to know how these things work, this is simply the division of cognitive labor and ultimately how our society can function on a high level.

But of course, the IOED extends well beyond toilets, to how we think about scientific fields, mental illnesses, economic markets, politics and virtually anything we are capable of (mis)understanding. Not understanding how toilets work is one thing, not understanding the history of Jerusalem and all the involved parties and still having a strong opinion on how this should be handled – that is a very different thing. Today, the IOED is profoundly pervasive, given our access to infinite information which we consume in large quantities – however, most do this in a superficial manner. Most of us consume knowledge widely, but not deeply!

Fortunately, understanding the IOED allows us to combat political extremism. In 2013, Philip Fernbach and colleagues demonstrated that the IOED underlies people’s policy positions on issues like single-payer health care, a national flat tax, and a cap-and-trade system for carbon emissions. As in Rozenbilt and Keil’s studies, Fernbach first asked people to rate how well they understood these issues, and then asked them to explain how each issue works and subsequently re-rate their understanding of each issue. In addition, participants rated the extremism of their attitudes on these issues both before and after offering an explanation. Both self-reported understanding of the issue and attitude extremity dropped significantly after explaining the issue – people who strongly supported or opposed an issue became more moderate. These studies suggest that IOED awareness is a powerful tool for cooling off heated political disagreements.


In a time where income inequality, urban-rural separation and strong political polarization have fractured us over social and economic issues, recognizing our own (at best) modest understanding of these issues is a first step to bridging these divisions.

The next time you are having an intense debate about Trump’s politics, unconditional basic income or your educational system, take a step back and contemplate on whether you are in a position of real understanding or rather throwing superficial arguments at one another.

And as always, stay curious!


For deeper insights on this topic, I can highly recommend Dr. Fernbach’s book, “The Knowledge Illusion: Why We Never Think Alone“, Keil and Rozenblit’s original paper: “The misunderstood limits of folk science: an illusion of explanatory depth” and, of course, the Wikipedia page on flush toilets!


When the Sir Isaac Newton explained the colours of the rainbow with refraction the poet John Keats was horrified. Keats complained (through poetry of course) that a mathematical explanation robbed these marvels of nature of their magic.

Whether you, dear reader, agree with Keats’ view or not, it is time to deep dive into the mathematical explanation, requiring just basic geometry of lines and circles. As we will see, the explanation is just as elegant as the rainbows themselves.
When sunlight enters a droplet from any angle some light is reflected and some is refracted into the raindrop. We most commonly encounter refraction when we look at a straw in a glass, it seems distorted and cut off. How much light is refracted is determined by the refraction index Latex formula which is simply Latex formula; the speed of light in vacuum divided by the speed of light in the new medium which makes n a number between one and (usually) two.
Due to this underlying mechanism, the angle of the light beam changes according to Snell’s law Latex formula , where Latex formula is the geometry1refractive index of the first medium (air, Latex formula = 1) and Latex formula is the incidental angle. The secondary angle is a bit smaller because the refractive index of water is around 1,34.  From here some of the sunlight reflects off the back side of the raindrop and then leaves the raindrop through the “bottom” where the light is refracted again, same as when it entered the raindrop.

Now, depending on where the light enters the raindrop it will exit the raindrop at different angles. We can calculate the total deflection D by adding up all grey angles Latex formula. We then calculate the derivative for the incidental angle to find the minimum. This minimum angle has the most intense light and creates what we can see as a rainbow. Remember that we are plotting the total deflection, the angle between the sunlight and you looking up will be 180°-D. This ends up to be around 42° and does not depend on the size of the water droplet.

observerSupposedly Descartes (mostly known for his philosophy) figured all this out graphically, but he did not understand why the rainbow showed different colors. He didn’t know that every medium has a different refractive index for each color which is a wavelength in the electro-magnetic spectrum, Blue’s refractive index is around 1,342 while red’s is around 1,331 resulting in different deflection angles.

There are so many further interesting facts to point out but I will try to keep the list short:

26273684822_26a9df07f0_zIn theory there are many more orders of the rainbow, each one reflects light once more inside of the rain trop. The second order rainbow which has its colors reversed is the only one you can frequently see with bare eyes and is located about 10° above the first order rainbow.

Rainbows seen from the ground can only occur in the morning or the evening due to the 42°-degree angle between you and the sun. If the sun is higher than 42° -degrees, the rainbow will be below the horizon (unless you are up high and looking down). Seen from an airplane, rainbows are full circles directly opposite of the sun!

seawaterrainbowLast but not least, seawater has a higher refractive index than rain water, so the radius of the seabow is a bit smaller, making for some crazy photos!



So next time you see one of these colorful arcs appear in the sky, try to remember the elegant math behind what you’re seeing!

And as always, stay curious!


You may have encountered rolling-shutter-effect (RSE) when taking photos of a fast moving object, like propellers or a car on the highway. Propellers and cars get distorted or straight lines bend; so what’s going on here?

RSE, photo credit:
RSE, photo credit:

Most smartphone and digital cameras use so called Complementary Metal-Oxide-Semiconductor (CMOS) sensors while many other reflex cameras use CCD pixels (charge-coupled device). I won’t go into any detail on the physical difference between these because in order to understand our RSE we need to look at the light exposure.

photo credit:

With a CCD camera light exposure is what you would expect it to be: shine light on all pixels for x amount of time, then save that and move on. This is called global exposure. However, with the cheaper CMOS pixels the camera scans in horizontal line, usually from top to bottom. If any object in your frame is moving (or if you are) pixels will be exposed at different times thus objects will appear at different places in one snapshot.

photo credit:

Depending on how fast your object is moving in comparison to your cameras screening different patterns will appear

Try this with your smart phone the next time you’re on the highway (not as the driver) and try to figure out how your camera scans; left to right or top to bottom?

And as always, stay curious!

Polar lights

Polar lights are one of my favorite phenomena. They are colorful, hard to catch and still not fully understood! But let’s dive into the science behind them!

If this is too much physics for you, skip to the tl;dr a the bottom of the page for some practical takeaways.

We need to start out somewhere very hot, the sun. Here convections of charged particles (plasma) in the outer parts of the sun cause strong magnetic fields. Sometimes these fields move outwards creating rings that act like rubber bands. These will snap now and then, blowing out great amounts of plasma. These events are called solar flares, or when they are big: coronal mass ejections. The frequency of such events is linked to the suns 11-year cycle as the suns inverts its whole magnetic alignment though the intensity of each cycle varies.Sunspot_Numbers
We may even head into another Maunder-minimum which would be unfortunate for the science community and everyone who wants to see some aurora. The next peak in sun activity is set for 2023.

As you probably have guessed, these solar flares are part of the so called solar wind which ultimately causes the polar lights. This constant stream of mostly electrons, protons and some nuclei such as helium moves towards earth at speeds between 400 and 700 km/s (250 to 430 mps). Now a complicated process of deflecting, magnetic recombination, particle acceleration and other crazy stuff starts. The whole process hasn’t been understood fully and many effects (or theories) have been shown to play a role but how they all interact with each other is mostly unknown! I will try to map out the clearest elements of this complicated process.

Earth’s Magnetosphere

Coming from the sun we encounter the bow shock about 12.000 km (7500 miles) away from earth. Most low energy particles are diverted by the earths outer most magnetic fields and move around to the magnetotail. Some particles move into the polar cusp, creating the so called day-light aurora which we can obviously not see with our eyes. Other particles will move into one of the two Van Allen radiation belts. These belts hold great amounts of plasma and act as a reservoir for the aroura but are also constantly washed away and then refilled by stronger solar flares.

Fields_in_magnetic_bottlesThese belts as well as the plasma moving into earth’s atmosphere act in as an first approximation like magnetic bottle. These “bottles” are two magnetic mirrors placed together to create a trap for charged particles. In case of earth’s field, the poles act as the mirrors. When an electron moves in a helical (corkscrew) path along the magnetic field he will eventually approach a pole. Here the magnetic fields become denser and thus creating a backwards force on the particles due to the Lorenz force.

Aurora_australis_ringNow there are several conflicting but also non-conflicting theories about why particles on the night side are being accelerate towards the poles which I won’t go into in detail. Fact is that sometimes particles have enough energy to come spiraling as close as 80km (50 miles). This creates a so called auroral zone as seen in this image of the south pole from one of NASA’s satellites. This auroral zone will move towards the equator as long as the particles have enough energy, they will then move to the pole again. So once you’ve experienced some strong polar lights moving southward (if you’re on the north hemisphere), then wait for them to come back!

Typical green curtains

Generally, we can differ between discrete, often shaped like curtains, and diffuse aurora. The most iconic and frequently seen aurora are green curtains at 100-150km (60-90 miles) due to fairly high concentrated oxygen emitting light at a wavelength of 557.7 nm. These curtains have a sharp cut of at 100km due to a fast concentration drop of oxygen. Slightly below the curtains one may spot some blue due to Nitrogen molecules being the dominant light source. These two colors are considered discrete aurora due to concentration drops or electrons with more or less discrete energy distributions. The most common diffuse aurora is the red emission of oxygen at high levels of altitude. These can be hard to spot by eye because of the dominant green curtains, but can often been seen on the horizon or in pictures due to the cameras better sensitivity (in comparison to our eyes) to red.

Most of these spectral lines are “forbidden”. This is a misleading term; one should rather call them highly improbable, due the selection rules of quantum mechanics. “Normal” emissions function on a nanosecond timescale. The red emission of oxygen however is very slow (107s) therefore this color will only occur in very high altitudes (>150km) where the probability of colliding with another atom is low enough. Otherwise if an excited atom collides, it will transfer energy and will not emit any red light anymore. Of course now and then other colors will appear often due to an overlap of green and blue or red and green etc.

I hope you have enjoyed this little deep dive into the aurora. It is definitely a very active and interesting field of science, be curious and check it out on your own!

Too long, didn’t read:

The next peak of sun activity should be in 2023, so that’s definitely a year to plan some polar vacation. The process of particles like electrons moving from the sun down to our atmosphere is not fully understood. There are indicators for polar lights that you can look up online every night. If you happen to experience strong polar lights moving towards the equator don’t leave! They are probably going to come back to the poles in the next hours.

Ion thrusters

This technology sounds and looks like it is more fiction than it is science and “Ion engines” are common in the Star Wars universe on TIE-fighters (Twin Ion Engine), but are they real?

Short answer: Yes!
Long answer: Yeeeeeeeeeeees!

The first time ion propulsion has been mentioned is as early as 1906. From then it took a long path to the 1970’s to actually employ this technology as was done on American and on Soviet satellites. Deep Space 1 was NASA’s first interplanetary mission using ion thrusters in 1998.

So if this technology is real, then why aren’t we seeing anything of this when we watch rocket launches now and then?

To get a rocket off the ground and away from earth’s gravity it needs thrust which is the formal term for the force pushing you up. If a spacecraft has an effective thrust of 10 Newton it could accelerate an object with a mass of 1 kg into outer space (considering the gravitational constant g=10 m/s²). Ion thrusters simply have a very low thrust; we’re talking about a maximum of 250 mN! This could carry a rocket weighing about 25 grams. Or in other terms: It would take more than a day to accelerate your car to highway speed with an ion thruster, not taking any resistances into account (of course!).

photo credit:

Before I get into why we even use this propulsion even though it is so weak, I want to take you through a simple explanation of how ion thrusters work. Generally, we can differentiate between electrostatic and electromagnetic thrusters, the former using the Coulomb force and the later using the Lorenz force as the main acceleration mechanism. There are, of course, several different variations but I will only explain one of the most common: The gridded electrostatic ion thruster.
As seen in the diagram, gas is vented into the ion chamber where it is ionized (kick out an electron) by fast electrons coming from the hot cathode on the left. Magnetic coils help hold the ions and electrons in place, as well as help ionize the gas. The ions then move to the positive grid on the right and are then accelerated to about 1 keV and shoot out of the chamber. A second cathode emits electrons into the ion beam in order to compensate for the positive charge leaving the spacecraft and stop the ions from being attracted back to the thruster.

For most thrusters, Xenon is used as a propellant gas. What you are looking for is an easy to ionize and heavy atom because the thrust is proportional to the mass of the accelerated ions. Xenon is also a noble gas and therefore doesn’t erode any parts of the thruster. However, Xenon is globally in short supply and expensive.

Now that we have a crude understanding, we can see how these thrusters are different from conventional rocket propellant. The biggest difference is the effective speed at which particles leave the spacecraft. For conventional rockets, e.g. the Space shuttle, the escaped velocity is around 4.400 m/s (16.000 km/h; 10.000 mph). For our standard ion thruster, the ions are accelerated to about 30.000 m/s! In space exploration the specific impulse of a propellant is very important, that is the total impulse delivered per unit of propellant consumed. If you accelerate your particles to high velocities, every little bit of mass you eject will have a relatively big impact in comparison to lower escape velocities. So ion thrusters have about ten times the specific impulse of conventional rockets which is really important because that simply means you need less propellant. Thus the overall mass of the spacecraft is smaller, reducing the amount of propellant again. This goes on until the spacecraft has no mass at all… just kidding.

Space Shuttle Atlantis; photo credit:

There are two reasons conventional rockets don’t just use higher escape velocities as well. Firstly, conventional rockets are like big heat machines and a thing called Carnot’s law limits their exhaust velocity; secondly, the energy you need to accelerate stuff goes with the velocity squared and conventional rockets have limited energy reserves, ion thrusters though basically have unlimited electrical energy from their solar panels!

So in the end, ion thrusters are much more efficient, lighter and precise, but lack the ability to create strong thrust and can only be operated in outer space. A conventional rockets brings a spacecraft to outer space and then the ion thrusters take it from there in a well … slow manner.

This definitely isn’t the only promising technology out there but it is the most practical at the time and has been and will be a crucial part of many space mission.

And as always, stay curious!