Author Archives: Robbert Bloem

Analysis of my bike commute

Last year I purchased a sports watch to keep track of my bike commute. Recently I got the impression that I’m slowing down. I downloaded the data and analyzed it a bit.

Figure 1: my route to work (most of it). I live in the lower right corner.

My commute is about 9.4 km. I selected data that is between 9.2 and 9.6 km. This accounts for small variations, but it excludes when I go into the city and do some shopping. The problem is not so much the different distance, but the speed. I want to keep it safe and won’t rush. Most of my commute is however on a long bicycling path next to a canal, as shown in the image above. I live in the lower right corner and I work in the upper left corner.

Figure 2: average speed over time, separated for going to work and going home. The gap in december 2017/januari 2018 is because of the Christmas holidays. The gap in February is due to syncing issues. 

The figure above shows the average speed for every day. The two colors show my commute to work (blue) and home (orange). The green and red line are a running average over 5 data points. My average speed has indeed dropped a bit. It used to be about 22.5 km/h, now it is about 21.0 km/h. This is still a very nice average speed for a completely human-powered bike.

At least as interesting is the difference between going to work and going home again, with average speeds of 21.3 km/h and 22.2 km/h respectively. The histogram below shows the difference clearly.

Figure 3: Histogram of the average speed going to work (blue) and going home (orange).

I suspect that the rail bridge plays a role. On my way to work, the downhill section has a sharp U-turn and another inconvenient corner, really slowing me down. On my way home the road after the bridge is more or less straight, so I can continue biking at high speed.

Figure 4: the bridge over the canal.

An obvious suspect is the wind. For individual bike rides this is obviously a factor. For example on March 2nd I had a 31 km/h south-east head wind when I went home, resulting in an average speed of 15.8 km/h. In November the wind was more north-westerly, resulting in a higher average speed going home. The predominant wind direction in the Netherlands is however from the south-west and my route is perpendicular to that.

What can be the reason for the recent slowdown? Part of it is that I am wearing different, longer, gloves that make it impossible to look at my watch. The watch shows different heart rate ranges and I tried to keep an eye on it to maintain a constant heart rate. Because of the gloves I can’t do this anymore.

Figure 5: average heart rate over time, separated for going to work and going home.

In the figure above I plot my average heart rate, and a running average. Aside from the first month or so it is stable between 140 and 150 bpm. Below, I made a plot of the correlation between average speed and average heart rate. For the bulk of the data there is no obvious correlation.

Figure 6: (lack of) correlation between average heart rate and average speed.

Is there an obvious conclusion to this story? Not really, but it was fun to look at the data in more detail.

Van stemmen naar zetels

Met de gemeenteraadsverkiezingen in aantocht komt de aloude vraag weer boven: “hoe wordt het aantal zetels ook alweer berekend?”. Dit is niet simpel afronden en er zijn subtiele verschillen tussen de verschillende soorten verkiezingen en hoeveel zetels er te verdelen zijn.

Voor alle soorten verkiezingen geldt dat het totaal aantal stemmen wordt gedeeld door de hoeveelheid zetels die er te verdelen zijn, dit is de kiesdeler. Vervolgens wordt het aantal stemmen dat elke lijst heeft gehaald gedeeld door de kiesdeler. Dit getal wordt naar beneden afgerond en is het aantal volle zetels dat een lijst krijgt. Omdat er naar beneden wordt afgerond zijn er altijd nog wat zetels over, de restzetels. Er zijn twee systemen om restzetels te verdelen, afhankelijk van het aantal zetels van de raad in kwestie. Bij 19 of meer zetels wordt het systeem van grootste gemiddelden gebruikt, anders het systeem van grootste overschotten.

De twee systemen worden hieronder verder uitgelegd. Uit gewoonte gebruik ik een punt als decimaalteken, niet een komma. 1.999 is dus bijna 2, niet bijna 2000. Ik zal proberen zoveel mogelijk te voorkomen dat hier verwarring over kan ontstaan.

Grootste gemiddelden

Als er 19 of meer zetels te verdelen zijn (zoals in het Europees Parlement, Eerste en Tweede Kamer, Provinciale Staten en de meeste Gemeenteraden) dan worden restzetels verdeeld met het systeem van grootste gemiddelden. Na het verdelen van de volle zetels (z) heeft elke partij een aantal stemmen per zetel (S/Z). Dan wordt voor elke partij wordt uitgerekend hoeveel stemmen per zetel ze zouden hebben als 1 extra zetel zouden krijgen (S/(Z+1)). Het aantal toegekende zetels plus de extra zetel is het aantal virtuele zetels. De partij met het hoogste gemiddelde krijgt de extra zetel. Als er meer restzetels te verdelen zijn dan wordt het aantal stemmen per zetel opnieuw uitgerekend, inclusief de eerder toegewezen restzetel(s).

Partij Stemmen Zetels s/z s/(z+1) Zetels % stemmen % zetels
A 101 9 11.22 10.1 10 84.2% 90.9%
B 19 1 19.00 9.5 1 15.8% 9.1%

Tabel 1: Rekenvoorbeeld van grootste gemiddelden

Tabel 1 geeft een rekenvoorbeeld. Partij A heeft 101 stemmen, partij B 19. Er zijn 11 zetels te verdelen. De kiesdeler is 120/11 = 10.91. Partij A komt in aanmerking voor 9 volle zetels, partij B voor 1 volle zetel. Het aantal stemmen per zetel (S/Z) voor partij B is veel hoger dan voor partij A. Voor de verdeling van de restzetel wordt echter gekeken naar het gemiddelde met een extra zetel, S/(Z+1). Dit is voor partij A hoger dan voor partij B en deze krijgt dan ook de restzetel toegewezen.

partij s z s/z s/(z+1) z s/(z+1) z s/(z+1) z s/(z+1) z s/(z+1) z s/(z+1) z s/(z+1) z s/(z+1) z r %s %z
VVD 2238351 31 72205 69948 32 67829 32 67829 32 67829 32 67829 33 65834 33 65834 33 65834 33 2 21.29 22.0
PvdA-GL 1559299 22 70877 67796 22 67796 22 67796 22 67796 22 67796 22 67796 23 64971 23 64971 23 1 14.83 15.3
PVV 1372941 19 72260 68647 19 68647 20 65378 20 65378 20 65378 20 65378 20 65378 20 65378 20 1 13.06 13.3
SP 955633 13 73510 68260 13 68260 13 68260 13 68260 14 63709 14 63709 14 63709 14 63709 14 1 9.09 9.3
CDA 1301796 18 72322 68516 18 68516 18 68516 19 65090 19 65090 19 65090 19 65090 19 65090 19 1 12.38 12.7
D66 1285819 18 71434 67675 18 67675 18 67675 18 67675 18 67675 18 67675 18 67675 19 64291 19 1 12.23 12.7
CU-SGP 575221 8 71903 63913 8 63913 8 63913 8 63913 8 63913 8 63913 8 63913 8 63913 8 0 5.47 5.3
PvdD 335214 4 83804 67043 4 67043 4 67043 4 67043 4 67043 4 67043 4 67043 4 67043 5 1 3.19 3.3
50+ 327131 4 81783 65426 4 65426 4 65426 4 65426 4 65426 4 65426 4 65426 4 65426 4 0 3.11 2.7
Denk 216147 3 72049 54037 3 54037 3 54037 3 54037 3 54037 3 54037 3 54037 3 54037 3 0 2.06 2.0
FvD 187162 2 93581 62387 2 62387 2 62387 2 62387 2 62387 2 62387 2 62387 2 62387 2 0 1.78 1.3

Tabel 2: De uitslagen van de Tweede Kamerverkiezingen 2017. Er zijn twee lijstverbindingen, tussen PvdA en GroenLinks en tussen ChristenUnie en SGP. De kiesdeler was 70107. Partijen die de kiesdeler niet haalden zijn weggelaten. 

Tabel 2 laat de situatie voor de Tweede Kamerverkiezingen 2017 zien. Het is een grote brij van cijfers omdat er meerdere rondes nodig waren voor het verdelen van restzetels. Aan de rechterzijde is de extra kolom R opgenomen, dit is het aantal restzetels dat een partij heeft gekregen.

Grootste overschotten

Als er minder dan 19 zetels te verdelen zijn (zoals bij sommige gemeenteraden) dan worden restzetels verdeeld door het systeem van grootste overschotten. Dit systeem wordt ook gebruikt voor de verdeling van zetels binnen lijstverbindingen (later meer daarover). Eerst wordt bepaald hoeveel volle zetels elke lijst krijgt. Vervolgens wordt het aantal zetels maal de kiesdeler afgetrokken van het aantal stemmen, dit zijn de overschotten. De partijen met de grootste overschotten krijgen de restzetels. Partijen moeten minimaal 75% van de kiesdeler hebben gehaald om in aanmerking te komen voor zo’n restzetel. Elke partij kan op deze manier 1 zetel toegewezen krijgen. Mochten er meer restzetels te vergeven zijn dan wordt daarvoor het systeem van grootste gemiddelden gebruikt. Dit kan gebeuren als er veel partijen zijn die de net niet genoeg stemmen halen voor een (rest)zetel.

Partij Stemmen Zetels Overschot Volgorde Zetels % stemmen % zetels
A 101 9 2.8 2 9 84.2% 81.8%
B 19 1 8.1 1 2 15.8% 18.2%

Tabel 3: Rekenvoorbeeld van grootste overschotten

Ook hier een voorbeeld. De uitgangssituatie in Tabel 3 is hetzelfde als in Tabel 1, maar nu wordt het grootste overschot gebruikt om de restzetel te verdelen. Deze is duidelijk hoger voor partij B, die nu de restzetel krijgt.

“Grootste gemiddelden” is nadeling voor partijen met weinig zetels

Het is duidelijk dat de twee rekenmethoden leiden tot verschillende resultaten. In de voorbeelden hierboven krijgt partij A 84% van de stemmen. Met “grootste gemiddelden” krijgen zij 91% van de zetels, met “grootste overschotten” 82% van de zetels. Dit is natuurlijk een voorbeeld met slechts 2 partijen. Bij de Tweede Kamerverkiezingen 2017 verschillen de percentages stemmen en zetels met minder dan 1%. Toch is het systeem van grootste gemiddelden voordelig voor grotere partijen. De 6 grootste lijsten hebben elk een restzetel gekregen (de VVD zelfs 2). Van de 5 kleinste lijsten heeft alleen de PvdD een restzetel gekregen.

De reden is dat gekeken wordt naar wat het aantal stemmen per zetels is als er een extra zetel wordt toegekend. Bij partijen met veel zetels is de relatieve toename van de extra zetel kleiner en daardoor is de daling van het aantal stemmen per zetel ook kleiner. Hieronder probeer ik dit te illusteren. Let’s get technical!

In plaats van over een concreet aantal stemmen (S) te praten gebruik ik het aantal kiesdelers dat een lijst haalt. Je kan het vermenigvuldigen met het aantal stemmen per kiesdeler om tot het aantal stemmen te komen. Omdat het aantal stemmen er toch wat natuurlijker uit ziet heb ik het wel in de figuren gezet, in italic, voor een kiesdeler van 1000.

In Figuur 1 staat de verdeling van het volle aantal zetels. Dit is duidelijk trapsgewijs: zowel een partij met 1x de kiesdeler of 1.9x de kiesdeler haalt slechts 1 zetel.

Figuur 1: De verdeling van volle zetels

In Figuur 2 staat het aantal kiesdelers per volle zetel. Dat getal is altijd gelijk aan of groter dan 1. De zaagtand komt doordat het aantal kiesdelers per volle zetel daalt als er een extra virtuele zetel wordt toegekend. Bij 1.99x de kiesdeler wordt 1 zetel toegekend. Het aantal kiesdelers per zetel is dan 1.99. Bij 2.00x kiesdeler worden 2 zetels toegekend. Daardoor daalt het aantal kiesdelers per zetel weer naar 1.00. Bij 2.99 keer de kiesdeler is het aantal kiesdelers per zetel 1.495 (2.99 kiesdelers/2 zetels). Bij 3.00x kiesdelers daalt het weer naar 1. Bij 9.99x kiesdeler is het aantal kiesdelers per zetel 1.11 (9.99 kiesdelers/9 zetels). Het is duidelijk dat het aantal kiesdelers per volle zetel heel sterk fluctueert voor lijsten met weinig kiesdelers (stemmen) en veel minder voor lijsten met veel kiesdelers.

Figuur 2: Het aantal kiesdelers per volle zetel

Om de restzetels toe te kennen worden er extra zetels toegekend. De echte zetels plus extra zetels heten virtuele zetels. Hiermee wordt het aantal kiesdelers per virtuele zetel uitgerekend. Figuur 3 laat dit zien voor 1, 2, 3 en 4 extra zetels.

Figuur 3: Het aantal kiesdelers per virtuele zetel. De verticale lijnen zijn het aantal kiesdelers die partijen C en D hebben gehaald, in het voorbeeld in de tekst. De grijze horizontale lijn is het aantal kiesdelers per virtuele zetels voor partij C met 1 extra zetel.

De restzetels worden één voor één toegekend. Eerst wordt bij elke partij 1 extra zetel opgeteld en het aantal kiesdelers per virtuele zetels berekend, dit is de blauwe lijn. Laten we als voorbeeld partijen C en D nemen. Partij C heeft 1.3x kiesdeler en heeft dus 2 virtuele zetels (1 echte en 1 extra) en komt op 0.65 kiesdelers/virtuele zetels (dit staat aangegeven met een horizontale grijze lijn in Figuur 3). Partij D met 6.1x de kiesdeler heeft (6+1=) 7 virtuele zetels en heeft heeft 0.87 kiesdelers per virtuele zetel (waar de vertical grijze lijn van D de blauwe lijn kruist). D heeft dus een hoger gemiddelde dan C (het is boven de horizontale grijze lijn) en de eerste restzetel wordt dus aan partij D worden toegekend.

Voor een tweede restzetel wordt voor partij D het aantal kiesdelers per virtuele zetel opnieuw berekend, nu voor (7+1=) 8 virtuele zetels (de oranje lijn). Voor partij C veranderd er niets en kijken we dus nog steeds naar de blauwe lijn. Partij D heeft in dit geval 0.76 kiesdelers per virtuele zetel, weer meer dan partij C. De tweede restzetel wordt dus ook aan partij D toegekend.

Voor een derde restzetel kunnen we deze exercitie herhalen. Partij D heeft met 3 extra zetels 0.68 kiesdelers per virtuele zetel (groene lijn) en de derde restzetel zal dus ook naar partij D gaan. Pas bij een vierde restzetel daalt het aantal kiesdelers per virtuele zetel voor partij D tot 0.61 (rode lijn) en zou de zetel dus aan partij C worden toegekend.

Uit Figuur 3 en het voorbeeld hierboven blijkt wel dat kleine partijen een nadeel hebben bij het verdelen van restzetels. Het is eigenlijk alleen mogelijk als ze bijna een extra zetel hadden gehaald. Hoe meer zetels een partij haalt, hoe minder het gemiddelde daalt als er extra zetels worden toegekend. Figuur 4 laat hetzelfde zien als Figuur 3, maar dan voor een groter aantal kiesdelers.

Figuur 4: Het aantal kiesdelers per virtuele zetel

In Figuren 3 en 4 gaan het over het aantal keer de kiesdeler en daar zit een maximum aan: het aantal zetels. Als er 19 zetels zijn dan kan een partij maximaal 19 keer de kiesdeler aan stemmen halen (als ze alle stemmen halen, in welk geval restzetels geen issue meer zijn). In de Tweede Kamer zijn er maximaal 150 kiesdelers te halen. Partijen kunnen dus 30, 40 of zelfs 50 keer de kiesdeler halen. Gemeenteraden hebben tussen de 9 en 45 zetels, afhankelijk van hoe groot de gemeente is. De sterke fluctuaties zijn de reden dat voor kleinere gemeenteraden (minder dan 19 zetels) een ander systeem wordt gebruikt. Toch zullen ook in grotere gemeenteraden de partijen relatief klein zijn.

Voor de volledigheid het systeem met grootste overschotten. Figuur 5 laat zien hoe de overschotten fluctueren voor het aantal kiesdelers. De toewijzing van restzetels is dus onafhankelijk van het aan kiesdelers dat behaald is.

Figuur 5: Overschot aan kiesdelers


Met een lijstverbinding konden twee of meer partijen hun lijsten samenvoegen en profiteren van het voordeel van het hebben van meer kiesdelers (stemmen), zoals hierboven besproken. De CU en SGP deden dit vaak, net als de PvdA, GroenLinks en SP (soms met z’n tweeën, soms met z’n drieën). Binnen een lijstverbinding worden de zetels dan verdeeld met een lijstkiesdeler en het systeem van grootste overschotten voor restzetels. Een belangrijke voorwaarde was dat partijen in een lijstverbinding individueel in ieder geval één zetel zouden moeten hebben gehaald. In 2017 zijn lijstverbindingen afgeschaft.

Verschillen tussen verkiezingen

Bij de Tweede Kamer en Europese verkiezingen komen alleen partijen die de kiesdrempel hebben gehaald in aanmerking voor restzetels. Bij verkiezingen voor gemeenteraden met minder dan 19 zetels komen alleen partijen die 75% of meer dan de kiesdeler hebben gehaald in aanmerking voor restzetels.

Why do I have a free day today? Easter edition

In my ongoing effort to explain to people who are not used to continental-European and/or religious holidays, I’m going to explain the Easter holidays. I’m not a Christian so there may be some inaccuracies (unintentional or not) in the story. If you are easily offended, you may want to read something else.

The story starts 2000 or so years ago in Jeruzalem. The Romans had occupied Judea and their policy was clear: if you are with us, we treat you badly, and when you are against us, we kill you. This policy lives on at United Airlines. The prefect of the region at the time was Pontius Pilot who probably had a side-job at that airline.

The people of Judea were not entirely happy. One of the beliefs of Judaism is that at some point a Messiah will come and save peoples souls, or something. People longed for some relief and left and right people showed up saying they were the Messiah. In many cases they were harmless fouls, but some managed to get quite a following. One of the latter category was a carpenter who went by the name of Jesus Christ. Jesus was not so much of a problem while he was making tables and chairs in some stupid village away from the masses, but then he decided to go to Jeruzalem.

The problem of rabble-rousers with a following is that you can’t easily kill them. The Romans would need at least some “evidence” to convict him for something. Luckily (for the Romans), one of Jesus’ disciples, a guy named Judas, came forward and in exchange for 30 silver coins he betrayed Jezus. Jezus was arrested for claiming to be a king and therefore questioning the Roman occupation. Then the story becomes a bit unclear. The Bible sort of suggests that Pontius P. was reluctant to sentence Jezus because it would cause unrest. He decided to ask the people to choose who should be sentenced: Jesus Barabbas (a murderer) or Jesus Christ (a loud-mouth). The people (read: the Jews) chose Christ. (While checking references I found that, confusingly, the first name of Barabbas was also Jesus).

This part of the story is quite controversial. After Jesus’ death the movement continued to grow and spread to Rome. At first the Christians were persecuted and thrown before lions. Later the Emperor Constantine was converted to Christianity. Until then Christianity was a religion without much of a structure. State support inevitably added bureaucracy and the need to agree on the stories. The result of this was the Bible. The Bible was not meant as an accurate telling of history, but as a political document that suited the rulers of the time. There were no women present (other than some prostitutes, probably) so they were conveniently reduced to a place were they couldn’t share in power (the kitchen). The Romans also had to decide who killed Jesus: the Romans or… somebody else? Spoiler alert: the Romans didn’t blame themselves. Blaming the death of Jesus on the Jews resulted in rampant anti-semitism in the last centuries and is still visible today.

In any case, Jesus was convicted and sentenced to death. Because European pharma companies were opposed to using their medicines for execution, it was done by crucifixion (which is actually a terrible way to die). They were also out of trucks or donkeys or whatever and Jesus had to carry his own cross through the streets to the place of execution. There he was nailed to it and died while singing always look on the bright side of life. After Jesus died he was buried in some cave. It is a bit weird to call this burying because that would imply he is underneath something (presumable some sand), but this is not the weirdest part of this story. A few days later some people went to the cave, opened it… and it turned out to be empty! First question: why would they go to the cave? Second question: why would they open it? Third question: where did Jesus go? Did they enter the right cave into their GPS? Did somebody pull a prank? No, Jesus must have resurrected. And with that Christianity was born.

The interesting thing is that everybody thinks Christmas is the most important Christian holiday, but it isn’t. Without the resurrection-bit Jesus would be just another Messiah who died prematurely. Christmas is a prequel added later on. Like the Star Wars prequels it has a lousy story and bad special effects. The importance of the crucifixion lives on in the cross that Christians wear. It makes you wonder, if Jesus had been poisoned, would everybody wear an Erlenmeyer?

How is this “celebrated” nowadays? The Table below gives some names for the various days (see also this blog post). In churches Easter is part of Holy Week. Palm Sunday (the week before Easter) is the day Jesus walked into Jeruzalem. People apparently waved with palm leaves, possibly for religious reasons, possibly just because it was hot. On Wednesday Jesus was betrayed by Judas. On Thursday he had his last supper (although he didn’t know that yet). Wikipedia doesn’t say when Jesus was arrested, but on Friday he is tried and executed. That is some quick justice. The day is called Good Friday, but the reason for that is not entirely clear to me. In some places this is commemorated by carrying crosses through the streets. In the Netherlands there are performances of the John/Matthew Passion by Bach. I thought Good Friday was a standard day off, but that turns out not to be the case, as I found out halfway the day. On Black Saturday all the shops have massive discounts (or am I confusing it with something else?). It is also the day Jesus was buried in a cave. On Easter Sunday Jesus resurrected. In the Netherlands (and in some other European countries) we have Second Easter day. This is to recover from eating too many Easter eggs and to do some furniture shopping. This is always a day off.

Of course, this all could be bullshit. In the same way that Christmas is really the old pagan festival to celebrate the shortest day of the year (off by a few days because the Christians were too busy persecuting astronomers), Easter is really the pagan celebration that winter is over.

There are no references to Easter eggs in the Bible. The eggs are the result of Lent. Lent is a fasting period that starts 40 days before Easter (which is preceded by Carnival (also not in the Bible)). People are not allowed to eat eggs during Lent, but chickens still lay eggs. At the end of Lent there is a massive amount of eggs that have to be eaten.

The Easter bunny, which may be a rabbit or a hare, was said to bring the eggs to children, but only if they behaved good. People also thought that rabbits/hares could reproduce without losing their virginity (which makes you wonder where the saying “they breed like rabbits” comes from), which makes an association to the Virgin Mary (the virgin part, not the breeding part).

There are two more holidays associated with Easter. The first is Ascension day, forty days after Easter. The disciples find zombie-Jezus who promptly decides to leave them again and go to heaven. Ascension day is always a Thursday and always a free day. Many people take the Friday off as well. Ten days later on Pentecost (or Whitsun) the Holy Spirit descends back to earth. This is always on a Sunday. To recover from this shocking event the Monday is a day off as well.

iPhone 6S review

When a colleague upgraded his iPhone a few years ago I was a bit of a killjoy. I told him that after 5 minutes of excitement it would dawn on him that it is just another phone. He reminded me of this when I showed him my new iPhone 6S, which replaced my iPhone 5. He was right now, and I was right then.

My first iPhone was the 3G, just after it arrived in Europe (and after I arrived in Switzerland). It was totally amazing — a computer in my pocket. After two years I upgraded to an iPhone 4. A big improvement, it was much faster and had a Retina screen. The iPhone 5 had a bigger screen while the phone didn’t get much larger — it was even much thinner and lighter.

For financial reasons (I didn’t have a job) I decided not the buy the 6 even before it was announced. I frowned on some of the decisions Apple made: keeping the same battery life while making it thinner, a larger screen, rearranged buttons and, worst of all, a camera lens that sticks out. Wasn’t that what we made fun of with Android phones?

Although it was easy not to buy the 6, it would be more difficult with the 6S. The 5 started to get old and too slow (for my taste). It sometimes wouldn’t recognize touches on the lower part of the screen — the part that you use to answer a phone call. It didn’t support the new content blockers in iOS 9. And I had a job so I could afford one. Despite my doubts I decided to buy the 64 GB Space Grey 6S. Here are some impressions after using it for a month or so.


The purchasing experience was both good and bad. I first ordered the via the online store so that it would be delivered. Unfortunately, this was with UPS. In the Netherlands most delivery companies offer the option to pick up a package at a pickup point (a store, supermarket or post office). For the three major ones there are pickup points within one kilometer of my home. UPS is not one of them. Do they seriously expect me to stay at home to accept the package? I have a job! That is why I could afford the phone in the first place! In the end I decided to cancel the online order and to pick one up in the store here in The Hague. I made an appointment, I walked in, paid and left. Done and done.

Setting up the phone

I had made an encrypted backup of the 5 in iTunes (locally, not in iCloud) so setting up the 6S was not too much of a hassle. It annoys me when Apple asks for the Apple ID password during setup. I store my passwords in 1Password and it is an annoyance to enter the long password by hand. Then you get the login for iCloud, the App Store etc. I mostly skipped them and used 1Password to enter them later.

Touch ID

Touch ID is the most brilliant addition to the iPhone since the introduction of the iPhone. Finger on the home button and voila, you’re in. My main complaint is that I still have to enter a passcode on my non-Touch ID iPad, like an animal.

Touch ID much on the 6S is much faster than on the 6. Some people mentioned they were used to glancing at the notifications while pressing the home button, but that this was not possible anymore. I definitely understand this. I turn almost all notification off (except for things where people try to reach me) and when there are notifications, I’m too late to see which app needs its settings changed.


First the positives: the phone feels like a quality product that is nice to hold. The weight is nicely balanced. After the 3G, 4 and 5 this is what I expect and Apple delivers. I’m not entirely happy though.

I don’t really care about the larger screen. The 5 had a taller screen (without making the phone much bigger) making space for the menu bars at the top and bottom of the screen. The screen of the 6 is just… bigger. I haven’t seen any apps that make good use of the space. There isn’t a 5th app in the dock. Tweetbot doesn’t have six tabs instead of five. When I want to read a book I still prefer my iPad. I’m writing this on my iPad, because the iPhone is still too cramped. It may be better on the 6S Plus, but I’m not going to walk with an aircraft carrier in my pocket. The downsides of the larger screen are obvious. Even with my large hands I can’t reach the top of the phone anymore. More than before I need to use the phone two-handed, or run the risk of it falling out of my hands. I hope Apple at some point releases a smaller phone again.

It is difficult for me to compare the battery life of the new iPhone. The old one was 3 years old. I also work in a lab with very bad cell phone and no wifi reception. Because phones try to connect to the network by increasing the power, this really drains the battery of any phone. I still recharge my phone at work, but with the 6S it is not as essential as with the 3-year-old 5.

The place of the on/off button on the new phone is still confusing me, especially after using my iPad. The on/off button is not on the top anymore, but is now on the place were the volume buttons of the iPad are. I now try to turn my iPad on by clicking the volume button… This might be something I can get used to. Worse is the problem that whenever I press a button on one side, I usually also inadvertently press a button on the other side. It looks nice and symmetric, but damn it is irritating.

The worst thing about the new iPhone is the camera lens that sticks out like a sore thumb. A friend wrote on Twitter:

Someone should be shot over this iPhone camera lens protrusion. Obvious + useful fix: taper the phone. Would also allow for extra battery.
— Philip

I wouldn’t go as far as saying “shot”, I would use a more general “killed”, but the point stands. I usually put my phone on the table, but the 6S doesn’t lie flat and it scratches the table. Before the iPhone I used to put my phone on top of my wallet to prevent wobbling and I notice I get back to that habit. Back to the flip phone days… yay?


I guess the camera is better — except for that awful lens. Even though the phone is larger, they couldn’t make some space for the type-of-photo-selector-thing. Until now I mostly used the camera to document which cables go to which connectors in the lab. The point of Live Photos escapes me because I don’t have kids/pets/other-things-that-move-a-bit-in-a-potentially-funny-way. It was remarkably unclear how to watch them on the phone (it turns out to be a 3D Touch). On my computer I now have .MOV files in my Pictures folder.

Force 3D Touch

Talking about 3D Touch, it may be an interesting addition to the way we interact with the phone but it is hard to discover, both if it is possible and what is possible. It is a pity that Force Touch sounds like sexual harassment because it is a much better description than 3D Touch. You really have to press it a bit. The phone gives a very satisfying vibration when you do this.

I hope it doesn’t end up like all the other obscure-but-useful shortcuts on iOS. There is a whole Morse code of useful things you can do with the home button, but I never remember them.


The iPhone 6S is a fine phone but, as expected, I’m not enthusiastic. The phone feels good in your hand… until you reach the camera lens at the top of the phone. Touch ID is brilliant but turning the volume up usually turns the screen off, or the other way around. I don’t care about the larger screen. Some of the features (Live Photos and 3D Touch) need some getting used to.

I seriously considered buying an 5S instead of a 6S, but it is a bit too expensive for such an old phone (509 vs 749 euro for the 16GB 5S and 6S models, respectively). Like the 5, the 6S should last me for the next three years. With the 5S I expect to replace it next year already. On the other hand, if the iPhone 7 next year has a smaller screen and no lens sticking out, then there is a big chance that one of my family members is going to be very happy with a hand-me-down iPhone 6S.

Don’t mistake my lack of enthusiasm for disappointment. The bar is very high for me to get excited. I was excited about the iPhone 3G and for the 5K iMac that Apple released last year. With the 6S I wanted a faster phone and I got a faster phone. If only they could get rid of this bloody camera lens.

The gold alloy of the Apple Watch

Update: this is a nice story, but somebody pointed out that the glass of the Sport Watch is of a different material. This is not taken into account in the calculation, which must be wrong.

Last week Apple revealed more details of the new Apple Watch. There has been an ongoing discussion about the materials used, especially regarding the gold model. Is it the new light weight gold that Apple patented? How much gold is used in the case? And what is the cost of the gold?

Apple has released information about the weight of the watches (without bands) (nicely summarized by Rob Griffiths). Using the available data a reasonable estimation of the density of the gold alloy can be made, making a comparison with traditional gold alloys possible.

With this Numbers spreadsheet you can play around with the numbers yourself.


The density of the rose gold alloy is calculated to be between 12.5 and 13.0 g/cc. This is lower than the typical density of rose gold alloy, 15.1 g/cc. The calculation assumes the volume of the metal parts of the different models to be the same. If the actual volume of the gold case is smaller, the density would be higher. To explain the difference between the calculated and typical density the volume has to be smaller by 15 %. It is unlikely that Apple wouldn’t take advantage of this reduction for the aluminium and steel watches as well. It is more likely that Apple reduced the volume by a smaller percentage, in combination with a less dense alloy, using the technique described in the Apple patent.

Gold alloys

An alloy is a mix of a metal with other metals/materials. Alloys are designed to have better properties than the constituent materials: stronger, more resistant (against rust), more beautiful, cheaper, lighter (less dense) etc. In this post we are interested in the last property: density.

Most gold we encounter is in an alloy because pure gold is rather soft. By adding silver and copper it is made stronger. The karat is used to indicate the purity of gold. 24 karat is 99.9 mass-% pure gold. 18 karat gold (used in the Apple Watch) contains between 75 and 79 m% gold (I’ll use 75 m% in this post). The remaining 25 m% is other material.

The density of alloys can be approximated using the densities and mass fractions of the original materials, as explained by Dr. Drang.

[A]ssume a conventional 18k gold alloy with 75% gold (19.3 g/cc), 15% silver (10.5 g/cc), and 10% copper (8.96 g/cc) by weight. The alloy will have a density of […] 15.6 g/cc

Different gold alloys have different densities. According to Wikipedia 18K rose gold (one of the two golds used by Apple) contains 75% gold, 22.25% copper and 2.75% silver. This has a density of 15.1 g/cc, 0.5 g/cc lower than the earlier example.

The patent application of Apple goes a step takes this to the extreme:

Now assume an 18k gold with 75 % gold and 25 % boron carbide by weight (that’s one of the ceramics mentioned in Apple’s patent). Boron carbide has a density of 2.52 g/cc, so a gold/boron carbide metal matrix composite would have a density of about […] 7.24 g/cc.

The idea is that the gold content (karat) is measured in mass-percentage, but that you have to fill a volume. Most of the volume is filled with boron carbide, which doesn’t weight very much. 25 m% boron carbide is an extreme example: 7.24 g/cc is less than stainless steel (8.0 g/cc) or copper (9.0 g/cc).

An interesting but inconclusive bit of information is the Jony Ive video from Apple. Ive says that “precise adjustments in the amount of silver, copper and palladium in the alloy result in very specific hues of yellow and rose gold”. Are these the only materials in the alloy, or are these the four materials responsible for the hues?

How do we know if Apple used a fancy alloy? Table 1 shows the densities for different gold alloys. The data for pink, rose and red gold are from Wikipedia. For the traditional gold, copper and maybe-something-else alloy the density is at least 15.0 g/cc (red gold). If the density of the gold alloy used by Apple is below that, they must have done something special.

Another thing we can learn from Table 1 is that to obtain rose gold a fairly high amount of copper is needed. The rose gold color is also very sensitive to the amount of copper, a 2 m% difference changes the color significantly. Therefore, it is not possible to add significant amounts of boron carbide, certainly not 25 m%. The lower part of the table shows possible alloys with 2 to 5 m% boron carbide. The choice for the silver and palladium content is arbitrary, I chose a low value because both silver and palladium are denser than copper.

The data in Table 1 gives us an idea of what we are looking for. If the density is around 15 g/cc it is unlikely that a fancy alloy was used. However, if a fancy alloy was used we shouldn’t expect to obtain a ridiculous density of 7.24 g/cc, but something in the range of 11-14 g/cc or so. In this post I will calculate the density and discuss how accurate the calculation is.

Gold (m%) Silver (m%) Copper (m%) Palladium (m%) Boron carbide (m%) Density (g/cc)
Pink gold 75 5 20 0 0 15.16
Rose gold 75 2.75 22.25 0 0 15.08
Red gold 75 0 25 0 0 14.98
Possible alloys 75 0.5 22 0.5 2 13.84
75 0.5 21 0.5 3 13.32
75 0.5 20 0.5 4 12.83
75 0.5 19 0.5 5 12.38
Density (g/cc) 19.3 10.5 8.96 12.02 2.52

Table 1: Densities for different alloys. The data for pink, rose and red gold is from Wikipedia, the “possible alloys” are speculation.


The calculation is based on the assumption that the weight different between the different models (aluminium, steel, gold) is only due to the different density of the metal. The weight of everything that is not metal (internals like electronics etc) is the same for the models. The volume of the metal (the case, crown etc) is also the same for all models. Of course, the weight of the non-metal internals and the volume of the metal case are different for the two watch sizes.

Using the weight difference between the aluminium and steel models we can, using the density of the materials, calculate the weight of the internals and the volume of the case. Using the weight of the gold watches we can then calculate the density of the gold.

Material properties

To do the calculation we need to know the densities of the materials. The Apple website writes that 316L stainless steel is used for the steel watches, this has a density of 8.0 g/cc.

For the aluminium case it is more difficult. Greg Koenig writes how the Apple Watch is made. Regarding the aluminium alloy he writes:

‘With the Watch, Apple has upgraded from 6000 series alloy compositions (using magnesium and silicon) to a custom 7000 series alloy that relies on zinc. The closest commercial equivalents would be the 6061 aluminum alloy (the world’s most common manufacturing material) and 7075 aluminum – the comparison between the two tracks very precisely with Jony Ive’s language about having “custom designed a new alloy that it 60% stronger, but just as light.”’

The densities of these materials are 2.81 g/cc for 7075A and 2.7 g/cc for 6061 aluminium. I think 2.7 g/cc is a reasonable choice.


To calculate the volume of the case, the weight m is divided by the density p:
V(case) = m(case) / p
We don’t know the weight of the case, but we know:
m(total) = m(case) + m(internals)
Apple has given m(total) and we assumed m(internals) was the same for cases of the same size. We get:
(m(total aluminium) – m(internals)) / p(aluminium) = (m(total steel) – m(internals)) / p(steel)
We can solve this for m(internals): 17.4 and 19.8 g for the 38 and 42 mm watches respectively. Presumably the larger watch has a larger battery.

This means the weight of the gold cases is 36.6 g and 47.2 g for the 38 and 42 mm sizes respectively. Using a gold price according Wolfram Alpha of 37.23 USD/g, this means the 18 karat gold cases cost about 1050 and 1350 USD.

The volume of the cases are 2.8 and 3.8 cc respectively. Given the weight of the gold cases and these volumes, the density of rose gold is between 12.5-13.0 g/cc, for yellow gold it is between 13.0-13.3 g/cc.


In this section I will discuss how accurate the result is. Since I only have a reference density for rose gold, I will only use that in the discussion below, unless otherwise noted.

Different gold alloy densities for the two watch sizes

Because Apple rounded the watch weights to grams the gold alloy density differs slightly between the two watch sizes. We can get a feeling of the error by looking at the extremes: the cases where the weight difference between the aluminium and steel watch are the largest and where it is the lowest. This is shown in Table 2. A similar problem exists for the weight of the gold watches, although the effect of this is smaller, as shown in Table 3. A density between 12.5 and 13.0 g/cc seems realistic.

Model m(total aluminium) (g) m(total steel) (g) Gold density (g/cc)
38 mm 25 40 13.0
24.5 40.5 12.5
25.5 39.5 13.5
42 mm 30 50 12.5
29.5 50.5 12.2
30.5 49.5 12.9

Table 2: Variation in gold density because of rounding errors in watch weight.

Model m(total rose gold) (g) Gold density (g/cc)
38 mm 54 13.0
53.5 12.8
54.5 13.1
42 mm 67 12.5
66.5 12.4
67.5 12.6

Table 3: Variation in gold density because of rounding errors in watch weight of the rose gold models.

The volume for the case is the same for all models

The central assumption in my calculation is that the volume of the cases is exactly the same. This is however incorrect for the gold case. At the end of Greg Koenigs article you can clearly see that the inside of the aluminium and gold cases are not the same. The video for the steel watch shows that the case is very similar to the aluminium one. Table 4 shows that differences in case volume have a significant effect on the gold alloy density. This makes the question whether the volume of the gold is larger or smaller relevant.

Gold density for case volumes
Model 85% 90% 95% 100% 105% 110%
38 mm 15.2 14.4 13.6 13.0 12.3 11.8
42 mm 14.7 13.9 13.2 12.5 11.9 11.4

Table 4: Variation in gold density because of differences in case volume. For example: if the case volume is reduced to 85 % of the aluminium/steel case, the rose gold density would be 15.2 g/cc instead of 13.0 g/cc for the 38 mm watch.

Apple may have added more material to make the watch stiffer. This would increase the volume of the case and decrease the calculated density of the gold alloy. Most of the material seems to be in the sides of the case, not the underside. This would mean that the volume increase is relatively small.

On the other hand, it makes sense to reduce the volume of the gold case. Gold is a dense (and expensive) material and removing some of it makes the watch lighter (and cheaper). The question is why Apple wouldn’t try to achieve the same volume reduction for the other watches. It may have to do with the complexity/cost of the production, but it is also less relevant for less dense materials. Table 5 shows how a change in case volume would affect the weight of the total watch. For the 38 mm aluminium watch a 15 % reduction in case volume would result in a 1.1 g lighter watch (4.4 %), the 42 mm steel watch would be 4.5 g lighter (9.0 %).

Watch weight for case volumes
M(internals) (g) M(case) (g) 85% 90% 95% 100% 105% 110%
Aluminium 38 mm 17.4 7.6 23.9 24.2 24.6 25.0 25.4 25.8
42 mm 19.8 10.2 28.5 29.0 29.5 30.0 30.5 31.0
Steel 38 mm 17.4 22.6 36.6 37.7 38.9 40.0 41.1 42.3
42 mm 19.8 30.2 45.5 47.0 48.5 50.0 51.5 53.0

Table 5: The weight of the aluminium and steel watches for a variation of case volumes. For example: if the case can be reduced by 15 %, the total weight of the watch (m(internals) + 0.85 x m(case)) would be 23.9 g instead of 25 grams.

One unknown is the crown. The aluminium crown seems to be from solid aluminium. The crowns of the steel and gold watches have a colored… thingy on the side. It is unclear what is on the inside. I don’t know how this affects the weight.

Density of aluminium

A third unknown is the actual density of the aluminium. I used 2.7 g/cc. Table 6 shows how the gold alloy density varies aluminium density. Given the other errors I think it is negligible.

Model Aluminium density (g/cc) Gold density (g/cc)
38 mm 2.7 12.95
2.6 13.04
2.8 12.85
42 mm 2.7 12.51
2.6 12.59
2.8 12.42

Table 6: Variation in gold density because of differences in aluminium density.


The calculations show that there is a difference between the weight of the internals of the 38 and 42 mm watches: 17.4 and 19.8 g respectively. The gold cases weigh 36.6 and 47.2 g, at the current gold price this means about 1050 and 1350 USD of pure gold is used. The density of the rose gold alloy is calculated to be between 12.5 and 13.0 g/cc. The calculated density is significantly lower than the 15.1 g/cc of typical rose gold.

The main uncertainty in the density calculation is the volume of the gold case. You can equally argue that Apple made the volume smaller (to reduce the weight) or larger (for extra stiffening). To explain the obtained values using the volume alone, Apple would have to make the gold case volume 15 % smaller than for the steel and aluminium models. Because aluminium and steel are less dense than gold a small decrease in volume is not as important, but if they could have shaved of 15 % of the case of the 38 mm aluminium model, it would be 1.1 g lighter (4.4 %). The 42 mm steel case would be 4.5 g lighter (9.0 %). It is unlikely that Apple would not take advantage of such a possibility to reduce the weight.

Alternatively, Apple could have used something like boron carbide in the alloy. To reach a density between 12.5 and 13.0 g/cc about 4 m% boron carbide is needed (Table 1). This would mean the copper content has to be low, making the gold more pink than rose.

The most likely explanation is that Apple used a combination of volume reduction for the gold case and a fancy gold alloy.