Why do I have a free day today? New Years’ Edition

Are you kidding me? Januari 1st is an institutionalized get-over-your-hangover-day. Why are you actually reading this site? You should be in bed with a headache. Courtesy of the people who didn’t drink too much on New Years Eve, there are some traditional events in Europe and the Netherlands.

  • Ski jumping at Garmisch-Partenkirchen: I have to admit that seeing people plummet from a mountain is an entertaining way to start the new year. Just when you started to think you were stupid last night to drink this much you see people doing something even more stupid.
  • New Year’s Concert in Vienna: Also stupid, but frankly too loud to be entertaining. Also, I don’t like Srauss. This years playlist: Franz von Suppé, Johann Strauss, Jr., Josef Strauss, Eduard Strauss, Hans Christian Lumbye, Johann Strauss, sen.
  • New Year’s Dive: At various places in the Netherlands (and across the world I guess) people try to get over their hangover by jumping in the see or lakes. They did this for years and as it gained popularity it attracted commercial interest. Uno, maker of low-quality sausages, started to sponsor the event and advertised it, making it even more popular. Now you can see people dive into the see with a stupid Unox-hat on. Once they are out of the water they can eat a disappointing sausage. No harm done, but not my hangover-curing cup of tea.

Why do I have a free day today? Christmas-edition

What can I say about this holiday? Ages ago people recognized the periodical passing of the seasons. Midwinter was a day to celebrate, as the days were shortest and would be getting longer again. On the other hand midwinter is also the start of the actual winter. A long and cold period during which you can endlessly ponder if your family will survive. After all, the harvest is in and the animals slaughtered (no need to feed them precious food). Most of the meat is preserved for the long winter ahead, but what about the better cuts? Why not eat them to celebrate midwinter?

The Syrians had a feast called “Sol Invictus” which started on December 21st and lasted a few days (three, later five). The Romans adopted the feast, renamed it Saturnalia and celebrated it on December 25th [1]. It included naked dancing and singing.

When Emperor Constantine converted the Roman Empire to Christianity he realized that it would be unpopular to take away this holiday and he decided to co-opt it for Christianity instead. The birth of Jesus, also a sort of new hope for some people, seemed like a good fit.

So what is celebrated?

And more importantly: do I have the day off?


The countdown to Christmas starts four Sundays before Christmas: the advent period. Every Sunday a new candle is lit. This is the meaning of the candles:

  • 1st candle: Start thinking about Christmas dinner.
  • 2nd candle: Start thinking about Christmas presents.
  • 3rd candle: Make a spreadsheet with all the things you’ll need to buy.
  • 4th candle: Run to the shops in panic because you actually sat on the couch the previous three weeks.

I don’t think there is a real religious reason for advent. In the church of my grand parents the period was used to remember the people who died during the year. Some people (I think it is very popular in Germany) give each other an advent calendar, with a small present for every day.

December 24th: Christmas Eve

To make sure that the Christmas days can be used for traveling to family members and eating, there usually is a church service on Christmas Eve [2]. For some reason it is not unusual that people who are usually not very religious attend this service as well. It is a cheesy story about a kid being born with some singing. Is there booze afterwards? I hope so.

December 25th: Christmas Day

The day that the birth of Jesus is celebrated, even though there is only a 1 in 365 chance that this was actually the case.

People who call this the most holy day of the Christian calendar are of course mistaken. Christianity is about Jesus dying for our sins and then walking (floating?) away. In order to die he had to be born first [citation needed] [4], but it is not the most holy day of Christianity.

People who say Christmas is not about food are also wrong: as written earlier, the pagan feasts that preceded Christmas had everything to do with eating, drinking and dancing around naked.

December 26th: Second Christmas Day (or Boxing Day)

Why have one free day when you can have two? I couldn’t find any reason for this day being a holiday. It is convenient if your parents are divorced though. Or if you have a massive hangover from the day before.

For unknown reasons the English call this Boxing Day. Maybe Santa Claus had to clean up the boxes or something [5]. A more plausible explanation is that boxes were filled with stuff for the poor. Nobody really knows.

January 6th: Epiphany

Christmas is a holiday that just keeps giving… especially for the Germans, who have yet another free day (no such luck elsewhere). Epiphany “celebrates the revelation of God the Son as a human being in Jesus Christ” (copy-pasted from Wikipedia — this is too much for me to type).

What exactly happened (or is supposed to have happened) is not entirely clear to me. Wikipedia spends a lot of text on which day it is celebrated and the by which names it is called, but is rather unclear about the event itself. It seems that a star rose and “three wise men from the East” came to visit the newborn Jesus and baptized him. Sometimes it seems as if the emphasis is on the presents, the baptizing or the realization that something was going on.

There is also confusion about what these men (no women) were. Were they kings or wise men? The Economist has a nice article about the different possibilities. In Dutch we call them “Driekoningen” (Three kings). The Dutch Wikipedia page also says that the number three is actually nowhere to be found in the Bible. The number was probably chosen because there were three gifts (gold, incense and myrrh) which means there probably were three kings as well [6].

So… where does this leave us?

Well, probably with a feeling of having eaten too much, a medium to large hangover and possibly some gifts that you may or may not like. Happy Saturnalia!

[1] Wikipedia says this was considered the winter solstice, but winter solstice is on 21st-22nd of December, not the 25th.

[2] Other people say that it was usual to go to church the day before the actual holiday. Yet other people say that the service [3] should take place at midnight, but that is not very popular with parents of young kids.

[3] Catholics called it a mass, Protestants a service.

[4] Was it naive to expect ‘citation needed’ more often in Wikipedia articles about religion?

[5] This would explain why the Dutch don’t call it Boxing Day: they had their gifts with Sinterklaas

[6] I imagine that there was a fourth cheapskate king. His failure to bring a present came to bite him by being erased from history.

Why do I have a free day today? December 5th/6th: St. Nicholas

It is usually not a free day [1], but St. Nicholas Day is widely celebrated in mainland Europe. It also served as inspiration for Santa Claus in the US. The details differ widely per country, but there are three overarching themes:

  • There is a bishop-like figure, St. Nicholas.
  • He usually has helpers.
  • Good kids get presents, naughty kids get punished.

The story is that Bishop Nikolaos of Myra (15 March 270 — 6 December 343) had a reputation for secret gift-giving. Children would leave their shoes out overnight and the day after it would be filled with a small gift. The next 1000-1500 years are a bit sketchy but there was a bit of a gift-giving tradition around December 6th.

In most of Europe it is celebrated one way or the other. In Southern Germany and Austria Sankt Nikolaus is accompanied by Krampus, a beast-like figure. In Switzerland it is called Samichlaus and there are no beasts involved. Wikipedia has a summary of celebrations in different countries.

In the Netherlands

In the Netherlands Sinterklaas (a corruption of Sint Nicolaas, the Dutch version of Saint Nicholas) is celebrated on December 5th, not December 6th. The modern version was introduced in an illustrated children’s book written by a teacher. According to Wikipedia:

The modern tradition of Sinterklaas as a children’s feast was likely confirmed with the illustrated children’s book Sint-Nicolaas en zijn knecht (‘Saint Nicholas and his helper’), written in 1850 by the teacher Jan Schenkman (1806–1863). Some say he introduced the images of Sinterklaas‘ delivering presents by the chimney, riding over the roofs of houses on a grey horse, and arriving from Spain by steamboat, then an exciting modern invention. Perhaps building on the fact that Sint Nicholas historically is the patron saint of the sailors (many churches dedicated to him have been built near harbors), Schenkman could have been inspired by the Spanish customs and ideas about the saint when he portrayed him arriving via the water in his book. Schenkman introduced the song Zie ginds komt de stoomboot (“Look over yonder, the steamboat is arriving”), which is still popular in the Netherlands.
In Schenkman’s version, the medieval figures of the mock devil, which later changed to Oriental or Moorish helpers, was portrayed for the first time as black African and called Zwarte Piet (Black Peter). [2]

Since then a lot has changed. In the 19th century Sinterklaas had a large carrot-and-stick element. Good kids got presents and candy, naughty kids would get “the birching rod” (i.e. corporal punishment). For the worst kids there would be a single ticket to Spain. I guess the last thing was more scary back then than it is today. In the old days kids were actually afraid of Sinterklaas. Nowadays there are more presents and no punishments.

The role of Zwarte Piet also changed. It started out a bit like the Krampus in Germany: a scary figure. Remember that it wasn’t until the 1950’s that mass immigration of non-white people to the Netherlands started. Up until then the few colored people were considered a scary oddity. After the Second World War, and especially after television started to broadcast the arrival of Sinterklaas, the number of Zwarte Pieten increased. They have their own dedicated tasks that they usually screw up (for example, Route-finding Piet is never going to find the right route). Zwarte Piet transformed from a scary oddity to a clown-like figure. I expect Zwarte Piet will transform a bit more in the coming years…


A few weeks before December 5th Sinterklaas arrives from Spain. At night the kids can leave the shoes with a carrot (for the horse of Sinterklaas) near the chimney. The next morning they find some candy in it. [3]

Finally, december 5th is the gift-giving day. Young kids wait impatiently until the presents arrive. Older kids help making the presents, which are usually packaged in a humorous way (“surprises”) and accompanied with a small poem.

Sinterklaas really is the gift-giving day for families (parents + children) in the Netherlands. As the kids leave the house the celebration is discontinued, moved to the weekend before/after December 5th or moved to Christmas.

[1] The title of this post really should be ‘Why wasn’t I free last week?’

[2] I don’t know how it happened, but somehow the Bishop Nikolaos of Myra moved from Turkey to Spain.

[3] My mom sometimes tells that at some point she almost got sick of eating all the carrots.

Human elements

Today Google Research posted an interactive periodic table of elements with statistics about the abundance of different elements in, among others, the earth’s crust, the sea and in literature. One of them, showing the the abundance of elements in humans (Figure 1), looks a bit weird… it says 61% of all atoms in the human body are oxygen, 23% carbon, 10% hydrogen and 3% nitrogen. This can not be correct.

Figure 1: Periodic table of elements with the abundance of atoms in the human body. It is WRONG!

A quick back-of-the-envelope calculation:

  • half of the human body weight is water (2/3 hydrogen and 1/3 oxygen)
  • the other half is proteins (amino acids), lipids (fat), DNA and other stuff. Most of them have a carbon backbone. Intuitively I would say that most carbons have one or two hydrogens attached and only a few have oxygen attached.

In both cases there is much more non-oxygen than oxygen… so where does the oxygen come from?

The Google Research page refers to a Wikipedia page about the composition of the human body [1]. A quick look at the table makes the problem clear: Google used mass percentage instead of atomic percentage (or mole percentage). Every school kid knows that this makes quite a difference. For example, water is H2O. The atomic percentage oxygen is 33%. Because oxygen is 16 times heavier than hydrogen the mass percentage of oxygen in water is 89%.

It is of course nice to prove Google wrong. It is also nice that Wikipedia gives you an answer, but I was wondering how accurate my back-of-the-envelope estimation would have been.

Let’s take a person who weighs 100 kg and contains 53 mass-% water. With a molar mass of 18 g/mole this means there is ~2950 mole of water. This means 2950 mole of oxygen and 5900 mole of hydrogen. [2]

The other 47 mass-% of the human body is more difficult. Totally unscientifically I decided to only consider proteins (actually: amino acids). Even more unscientifically I will only consider the protein backbone, with two carbons, an oxygen, a nitrogen and three hydrogens. This adds up to a molecular weight of 57 g/mole, giving 824 mole of “other stuff”. Using these numbers we can calculate the moles, mass and mole-%. Table 1 summarizes the results and compares them with the data found on Wikipedia.

Element Molar mass Mole Mass (kg) Mole-% Mole-%
(g/mole) (Estimation) (Wikipedia)
C 12 1649 19.8 11.3 12
O 16 3769 60.3 25.8 24
N 14 824 11.5 5.6 1.1
H 1 8362 8.4 57.3 62
Total: 14605 100 100 99.1

Table 1: Abundance of elements, for 100 kg person with 53 mass-% water.

Frankly, the results are freakishly close. The estimation adds up to 100 mole-% because I didn’t consider the rest of the periodic table (which is only 0.9 mole-%). The calculation overestimates the mole-% nitrogen and underestimates the mol-% hydrogen because I neglected the lipids. Lipids (fat) are long chains of carbons with one or two hydrogens attached and hardly any nitrogens.

How many lipids does a person have? Like water, this depends on the person. Wikipedia also has a list with the composition by molecule type. It is difficult to compare the results with the data above because this table assumes 65 mass-% water (Table 2 shows the results of my estimation with 65 mass-% water). In any case, the Wikipedia table says humans have 20 mass-% proteins and 12 mass-% lipids.

Element Molar mass Mole Mass (kg) Mole-%
(g/mole) (Estimation)
C 12 1228 14.7 8.1
O 16 4225 67.6 27.9
N 14 614 8.6 4.1
H 1 9064 9.1 59.9
Total: 15131 100 100

Table 2: Abundance of elements, for 100 kg person with 65 mass-% water.

What did I learn from this?

  • Google is not infallible.
  • My back-of-the-envelope calculation is surprisingly accurate.
  • The mass-% of water in humans obviously differs. Wikipedia is not very consistent in using a particular percentage or indicating what percentage was used.
  • 4 elements make up more than 99 mole-% (96 mass-%) of the human body. That is kind of amazing.
  • The next most abundant elements are calcium and phosphorus, with 0.22 mole-% each (1.4 and 1.1 mass-% respectively). I had expected that humans would contain much more calcium. If not calcium, what are bones made of?

[1] Google Research uses Wikipedia as a source? Seriously?

[2] A mole is shorthand for a large number. If you have 1 mole of bikes and you take them apart, you have 1 mole of steers and 2 moles of wheels.

The off-center close button

Directly after I installed Mac OS X Yosemite on my computer last week I had the impression that the “x” in the close-window button was off-center (Figure 1).

Figure 1. The “x” in the close button appears off-center.

I was not the only one. John Siracusa (of Mac OS X review fame) tweeted:

A reminder for glasses wearers: this is why the “x” looks like it’s not centered in the close widget in Yosemite chromatic aberration.

The index of refraction of materials is wavelength dependent. This is visible when lenses are used because the focal point differs slightly for different wavelengths (1). In photos this results in colors that don’t overlap perfectly. Photos taken with cheap cameras/lenses sometimes show a colored band next to a sharp edge (a building or a head). It looks as if a printer (of the professional sort) had difficulty aligning the different colors correctly (you see this sometimes in newspaper photographs). More expensive lenses have a coating to compensate for this chromatic aberration.

It seems that glasses do suffer from chromatic aberration as well, when you look away from the center. Simple test: look at the close button straight, then turn your head sideways and see how the “x” appears to move, googly eye style. However, when there is a straight line between the close button, the center of your glasses and your eyes, the chromatic aberration distorts the image in all directions equally. This would make the “x” look fuzzier, not shifted. Note also that when you rotate your head (or the screen) 90 degrees, the shift is not visible. There must be something else going on.

I decided to take a photo camera and make a picture of the screen (details (2)). After some experimenting I had a picture with 4 camera pixels for every screen pixel, shown in Figure 2. I added a raster of the screen pixels, a yellow square around the “x” and a blue circle around the button. It is clear that the “x” is shifted in the button by half a pixel. On the left there are 2.5 pixels, on the right 3.5 (3). You can argue about the position of the blue circle. You can move it a bit to the left, giving 2.7 pixels on the left and 3.3 on the right. I don’t think you can argue that it can be 3 pixels on both sides.

Figure 2. Zoomed in. One screen pixel is four camera pixels. The black raster shows the screen pixels, the yellow square shows the outline of the “x” and the blue circle the outline of the button. The circle is half a pixel to the right.

What I think we see is an artifact of the display. A pixel is really three sub-pixels (red, green and blue) positioned next to each other (Figure 3). The positioning of pixels next to each other, horizontally, would explain why we only see this distortion horizontally and not vertically. The three subpixels may also explain why we see 2 2/3 pixels to the left and 3 1/3 pixel to the right (2 and 1 subpixels respectively). On the other hand, I think there is a lot of trickery going on to make screens look good (sub-pixel aliasing and what not), so I am careful with that last statement.

Figure 3. Four types of computer displays. The MacBook probably has the LCD configuration. More information: https://en.wikipedia.org/wiki/Pixel. Source: https://upload.wikimedia.org/wikipedia/commons/4/4d/Pixel_geometry_01_Pengo.jpg.

In conclusion, the off-center “x” is real and probably an artifact of the display or how it is rendered. It is unlikely that it is the result of chromatic aberration.

Update (2014/10/20, 17:34): Figure 4 shows the situation when the circle and square are centered at the same point. The overlap between the circle and button is clearly incorrect.

Figure 4. Zoomed in. I moved the circle to the left. The circle and square are now centered at the same point. It is clear that the circle does not overlap properly with the button.

(1) In the lab I once had a lens with a 150 mm focal length for IR (6000 nm) and a 140 mm focal length for red light (632 nm). This is an extreme case of course.

(2) The camera (Pentax K20D, with Pentax SMC DA* 16-50 mm lens) was placed on a tripod. The screen was perpendicular to the optical axis, the close button was centered. The picture was imported into Lightroom 5, cropped and exported as TIFF, without any compression. I added the raster, square and circle in Affinity Designer. The raster was aligned on the ‘x’. I took a screenshot and cropped that in Affinity Designer. I have a mid-2010 15′ MacBook Pro with high-density screen (1680×1050 pixels).

(3) It depends on your frame of reference. I aligned the raster with the “x”, making the button (circle) look off-center. But it can be the other way around. In any case, the two are shifted relative to each other.